Market Microstructure: Intermediaries and the Theory of the Firm

Market microstructure: intermediaries and the theory of the firm

This book presents a theory of the firm based on its economic role as an intermediary between customers and suppliers. Professor Spulber demonstrates how the intermediation theory of the firm explains firm formation by showing why firms arise in a market equilibrium with costly transactions. In addition, the theory helps explain how markets work by showing how firms select market-clearing prices. Models of intermediation and market microstructure from microeconomics and finance shed considerable light on the formation and market-making activities of firms. The intermediation theory of the firm is compared with existing economic theories of the firm, including neoclassical, industrial-organization, transaction-cost, and principal-agent models. Daniel F. Spulber is the Thomas G. Ayers Professor of Energy Resource Management and Professor of Management Strategy at the J. L. Kellogg Graduate School of Management, Northwestern University, where he has taught since 1990. He has also taught at Brown University, the University of Southern California, and the California Institute of Technology. Professor Spulber is the author of The Market Makers (McGrawHill/Business Week Books, 1998) and Regulation and Markets (MIT Press, 1989) and coauthor with J. Gregory Sidak of Deregulatory Takings and the Regulatory Contract (Cambridge University Press, 1997) and Protecting Competition from the Postal Monopoly (AEI Press, 1996). He is founding editor of the Journal of Economics & Management Strategy, published by MIT Press, and is the recipient of eight U.S. National Science Foundation grants for economic research.

Market microstructure: intermediaries and the theory of the firm Daniel F. Spulber

CAMBRIDGE UNIVERSITY PRESS

PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE

The Pitt Building, Trumpington Street, Cambridge, United Kingdom CAMBRIDGE UNIVERSITY PRESS The Edinburgh Building, Cambridge CB2 2RU, UK http://www.cup.cam.ac.uk 40 West 20th Street, New York, NY 10011-4211, USA http://www.cup.org 10 Stamford Road, Oakleigh, Melbourne 3166, Australia © Daniel F. Spulber 1999 This book is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 1999 Typeset in Times Roman ll/13pt. in L£TEX2 £ [TB] A catalog record for this book is available from the British Library Library of Congress Cataloging in Publication Data Spulber, Daniel F. Market microstructure: intermediaries and the theory of the firm / Daniel F. Spulber. p. cm. Includes bibliographical references. ISBN 0-521-65025-9 (hardcover). - ISBN 0-521-65978-7 (pbk.) 1. Industrial organization (Economic theory) 2. Securities. 3. Stock exchanges. 4. Microeconomics. I. Title. HD2326.S72 1998 98-34680 CIP ISBN 0 52165025 9 ISBN 0 52165978 7

hardback paperback

Transferred to digital printing 2004

Contents

Preface and acknowledgments page ix Introduction xiii The intermediation theory of the firm xiii Market microstructure xvii Intermediated exchange versus matching and searching xix Alleviating adverse selection xxii Mitigating moral hazard and opportunism xxv Delegation to intermediaries xxvii Outline of the book xxix Part I: Market microstructure and the intermediation theory of the firm 1 Market microstructure and intermediation 1.1 Who decides? 1.2 The circular flow of economic activity 1.3 Comparison with other economic theories of the firm 1.4 Intermediation in the U.S. economy 1.5 Conclusion 2 Price setting and intermediation by firms 2.1 Price setting by intermediaries 2.2 Allocation under uncertainty and over time 2.3 Price adjustment by intermediaries 2.4 Inventories and market clearing by intermediaries 2.5 Conclusion Part II: Competition and market equilibrium 3 Competition between intermediaries 3.1 Bertrand competition for inputs with homogeneous products 3.2 Bertrand price competition with differentiated products and purchases 3.3 Bertrand competition with switching costs

3 4 7 13 21 26 27 28 34 40 48 57 61 64 68 71

vi

Contents

3.4 Bertrand competition when costs differ 3.5 Conclusion

74 79

Intermediation and general equilibrium 4.1 The neoclassical theory of the firm 4.2 Transaction costs and Walrasian equilibrium 4.3 Monopoly intermediation in general equilibrium 4.4 Monopolistic competition 4.5 Conclusion Appendix

81 83 94 96 104 106 108

III:: Intermediation versus decentralized trade Matching and intermediation by firms 5.1 Intermediation versus a matching market 5.2 Costly intermediation 5.3 Intermediation with random matching 5.4 Intermediation and matching with production 5.5 Conclusion

117 118 126 130 134 137

Search and intermediation by firms 6.1 The market model 6.2 Market equilibrium 6.3 Comparison with Walrasian equilibrium and with monopoly 6.4 Market equilibrium with continual entry of consumers and suppliers 6.5 Conclusion Appendix

159 162 164

Part IV: Intermediation under asymmetric information 7 Adverse selection in product markets 7.1 Intermediated trade 7.2 Intermediated trade with production 7.3 Market clearing by intermediaries 7.4 Product quality and guaranties by experts 7.5 Conclusion Appendix

171 173 179 182 193 197 198

8 Adverse selection in financial markets 8.1 Insiders, liquidity traders, and specialists 8.2 Competition between specialists 8.3 Informed intermediaries 8.4 Credit rationing by financial intermediaries 8.5 Conclusion

140 144 150 154

203 205 211 215 219 224

Contents

Part V: Intermediation and transaction-cost theory 9 Transaction costs and the contractual theory of the firm 9.1 Transaction costs versus management costs 9.2 Transaction costs, uncertainty, and bounded rationality 9.3 Transaction costs and opportunism 9.4 Transaction costs and ownership 9.5 Conclusion

vii

229 232 236 245 251 254

10 Transaction costs and the intermediation theory of the firm 256 10.1 Transaction costs and market microstructure 259 10.2 Intermediation and vertical integration 266 10.3 Intermediation and opportunism 276 10.4 Intermediation and ownership 281 10.5 Conclusion 285 Part VI: Intermediation and agency theory 11 Agency and the organizational-incentive theory of the firm 11.1 Vertical integration and the boundaries of the firm 11.2 Coordination of agents by the firm 11.3 Delegation of authority by owners to managers 11.4 Delegation of authority by managers to employees 11.5 Conclusion

289 291 299 306 314 317

12 Agency and the intermediation theory of the 12.1 What is an agent? 12.2 Delegated bargaining 12.3 Delegated competition 12.4 Delegated monitoring 12.5 Conclusion

319 321 329 332 335 342

firm

Conclusion The intermediation theory of the firm Market microstructure and intermediation Management implications Public policy implications

344 345 348 350 351

References Index

353 369

Preface and acknowledgments

Two fundamental and closely related questions raised by microeconomics are "Why are there firms?" and "How do markets work?" In this book, I set out an intermediation theory of the firm that addresses these two important questions. The intermediation theory of the firm provides explanations for the formation of firms by showing how firms arise in a market equilibrium. In addition, the theory helps explain how markets work by showing how firms select market-clearing prices. Models of intermediation and market microstructure from microeconomics and finance shed considerable light on the formation and market-making activities of firms. The analysis of firms begins with the observation that firms act as intermediaries between their customers and their suppliers. Without firms, consumers acting as buyers and sellers would engage in direct exchange, searching for each other and bargaining over the terms of trade. The intermediation theory of the firm can then be summarized: Firms are formed when the gains from intermediated exchange exceed the gainsfrom direct exchange. Intermediated exchange can have advantages over direct exchange for many reasons, which are set forth in this book. These include lowering the costs of transacting through centralization of exchange, reducing costs of searching and bargaining, reducing moral hazard and opportunism, alleviating the effects of adverse selection, allowing buyers and sellers to make credible commitments, and reducing the costs of monitoring performance through delegation. Resources are allocated through decentralized processes of direct exchange, through centralized exchange managed by intermediaries, or through some combination of the two. The institutions of exchange are referred to as market microstructure. The analysis suggests an intermediation theory of markets that explains how markets work. With intermediated exchange, firms select prices, clear markets, allocate resources, and coordinate transactions. Thus firms establish and operate markets. IX

x

Preface and acknowledgments

I confine my analysis to economic issues pertaining to the economic theory of the firm and market mechanisms. The book does not cover a number of related topics. I do not consider the vast and rapidly growing literature on empirical analysis of financial markets. See Campbell, Lo, and MacKinlay (1997) for an outstanding integrative survey of the econometrics of financial markets. I do not consider research on the sensitivity of market outcomes to changes in the rules for price setting, matching orders, time priority, market versus limit orders, size precedence, trade class (specialist, market maker, or dealer quotes), and so on. Some of these issues are specific to financial markets in which market performance can depend significantly on small variations in trading rules.1 Financial studies of market microstructure raise important theoretical and empirical questions about how prices are adjusted and communicated and how changes in demand and supply are reflected in the allocation of goods and services over time. I also do not address theoretical issues bearing on the detailed theory of financial institutions. For excellent treatments of the theory of financial market microstructure and financial institutions see O'Hara (1995) and Frankel, Galli, and Giovannini (1996). I consider only briefly issues pertaining to the theory and institutions of banking; see the excellent recent text of Freixas and Rochet (1997) on the microeconomics of banking. I draw on the following previously published papers. Spulber, Daniel R, 1996, "Market Making by Price-Setting Firms," Review of Economic Studies 63, 559-80. Spulber, Daniel P., 1996, "Market Microstructure and Intermediation," Journal of Economic Perspectives 10, 135-52. Spulber, Daniel R, 1995, "Bertrand Competition when Rivals' Costs are Unknown," Journal of Industrial Economics 43, 1-12. Spulber, Daniel R, 1994, "Economic Analysis and Management Strategy: A Survey Continued," Journal of Economics & Management Strategy 3, 355—406. Spulber, Daniel R, 1992, "Economic Analysis and Management Strategy: A Survey," Journal of Economics & Management Strategy 1, 535-74. Spulber, Daniel R, 1993, "Monopoly Pricing," Journal of Economic Theory 59,222-34. Spulber, Daniel R, 1993, "Monopoly Pricing of Capacity Usage Under Asymmetric Information," Journal of Industrial Economics 41, 1-17.

The present work is the product of two decades of teaching economics to students of economics, law, and business. I thank my many students whose stimulating questions helped me to reevaluate neoclassical economics and especially my business students, whose concerns required addressing the economic theory of the firm. 1

See Domowitz (1992,1993) for taxonomies of automated trade execution systems that consider these and other aspects of market microstructure.

Preface and acknowledgments

xi

I particularly thank Dean Donald P. Jacobs of the J. L. Kellogg Graduate School of Management for his great encouragement and generous support for my research. I also thank Academic Dean Dipak Jain for his extraordinary understanding and consideration for my work. I thank my editor at Cambridge University Press, Scott Parris, for his great interest and belief in the value of the project and his expert guidance in bringing it to fruition. I also express my gratitude to my wife Susan and to my children Rachelle, Aaron, and Benjamin for their wonderful enthusiasm and delightful company. The book is dedicated to my children for future reference.

Introduction

The intermediation theory of the firm provides an explanation for why firms exist. Firms are formed when intermediated exchange provides greater gains from trade than direct exchange between consumers and suppliers. The theory also helps to explain how markets work. Markets reach equilibrium through strategic pricing and contracting by intermediaries. Under some circumstances, intermediaries may have advantages over direct exchange in a number of activities: 1. 2. 3. 4. 5. 6.

Reducing transaction costs. Pooling and diversifying risk. Lowering costs of matching and searching. Alleviating adverse selection. Mitigating moral hazard and opportunism. Supporting commitment through delegation.

In this introductory chapter, I illustrate the intermediation theory of the firm with a series of basic examples. Later chapters present a more complete analysis of the models that underlie these examples. Some advantages derive from coordination economies: the firm is recognized as a central place of exchange, thus reducing costs of search. Other advantages derive from economies of scale and scope in subtle ways. For example, because an intermediary can handle a higher volume of transactions than individual buyers and sellers, the intermediary is able to reduce risk through pooling and diversification. Other advantages stem from longevity and economic incentives to build a reputation. In particular, intermediaries who are able to make credible commitments bring advantages over contracts between buyers and sellers that are subject to renegotiation.

The intermediation theory of the firm In this section, I illustrate the intermediation theory of the firm by means of a simple example. The example is consistent with a pure exchange economy but applies to production economies as well.

xiv

Introduction

Consider a simple economy with one consumer and one supplier (who may be another consumer). The supplier has one unit of a good available for purchase by the consumer. The supplier has an opportunity cost C of supplying the good. The consumer has a willingness to pay V for a unit of the good. I use the term direct exchange to refer to the consumer's purchase of a unit of a good from the supplier. The consumer and the supplier meet and bargain over the terms of exchange. I start with a simplistic notion of transaction costs as a lump sum. Later on, I will be much more specific about the nature of transaction costs. Suppose that the consumer and the supplier encounter total transaction costs equal to T. Assume for now that there are positive net gains from trade: V - C - T > 0. The process of decentralized exchange can involve noncooperative bargaining processes such as first-and-final offers and exchanging alternating price offers. Assume for simplicity that the consumer and the supplier evenly divide the net gains from trade:

(V -C - T)/2. All the results in this chapter generalize easily to uneven splits in gains from trade.1 Suppose that an intermediary can purchase the good from the supplier at some price w and resell it to the consumer at some price p. Assume that the intermediary can commit to price offers. With intermediated exchange, suppose that the intermediary bears all the transaction costs, which equal K. The intermediary competes with direct exchange. Suppose for now that the consumer and the supplier have the same willingness to pay and the same opportunity cost in intermediated exchange and in direct exchange. Then it is apparent that intermediated trade will occur if and only if intermediation lowers transaction costs: K < T. This is the main building block of the intermediation theory of the firm. In general, the introduction of intermediaries can change the equilibrium levels of gains from trade and even the transaction costs of direct exchange, as later examples will demonstrate. The entry of an intermediary can be illustrated by means of a basic noncooperative game. The consumer and the supplier must choose individually whether to trade directly or through an intermediary. If the 1

An even division of the net gains from trade corresponds to the Nash bargaining solution.

Introduction

xv

buyer and the seller decide to trade directly, they can make side payments to each other before negotiating the terms of trade. The sequence of events is as follows. Period 1. The intermediary makes a binding offer of an ask price p and a bid price w. Period 2. After observing p and w, the consumer and the supplier decide whether to try to trade directly with the other agent or to accept the intermediary's offer. If they do not agree to transact with each other, they both transact with the intermediary. Period 3. If the consumer and the supplier both choose to transact with the intermediary, trade takes place at p and w. If the consumer and the supplier both choose to transact with each other, they negotiate over the allocation of gains from trade. The game among intermediaries, consumers, and suppliers assumes that intermediaries are able to make binding commitments to prices. Individual consumers and suppliers are able to commit to trade with each other, but they are not able to make price commitments. The ability of the intermediary to make price commitments reflects the idea that the intermediary wishes to uphold a reputation for trading at posted prices. An intermediary trades a larger volume of goods than individual buyers and sellers. Moreover, an intermediary is in the market for more periods of time than individual buyers and sellers. Firms often are said to be bearers of reputation that outlasts the individuals who comprise the firm at any particular time. The volume of trades and the longevity of the intermediary create returns to building a reputation. Consider first the case of a monopoly intermediary. The monopoly ask price pM and bid price wM leave the buyer and the seller indifferent between transacting with the intermediary and direct exchange: V - pM = (V - C - T)/2 = wM

-C.

The monopolist's markup exactly equals the transaction cost of direct exchange, pM — wM = 7\ so the monopolist's profit equals pM -wM

-K

= T -

K.

Thus the monopoly intermediary is economically viable if and only if K < T. Consider the case of Bertrand price competition between intermediaries. Competition drives the profits of the intermediaries to zero so that the markup just equals their transaction costs:

pc - wc = K.

xvi

Introduction

The consumer and the supplier who deal with competitive intermediaries obtain total gains from trade equal to V — C — K. Suppose that these gains are split evenly by the competitive prices:

V - pc = (V - C - K)/2 = wc - C. Consumers and suppliers will be attracted by the prices pc and wc if and only if transaction costs of intermediated exchange do not exceed those under direct exchange. As in the monopoly case, the competitive intermediaries are economically viable if and only if K < T. Transaction costs under intermediated and direct exchange can arise because of many different factors. Suppose for example that intermediated exchange occurs immediately while direct exchange requires a delay for search and bargaining. After the delay, gains from trade V — C are realized and divided evenly between the consumer and the supplier. If the consumer and the supplier discount future benefits at rate 8, then the present value of returns from direct exchange equal S (V — C)/2. This is equivalent to assuming that the transaction costs of direct exchange are T = (1 - S)(V - C). An intermediary is viable if and only if K < (1 — S)(V — C). The intermediary is more likely to be viable if the discount factor is low, the consumer's willingness to pay is high, and the supplier's opportunity cost is low. Because there are time costs of search and bargaining, higher gains from trade increase the chance that an intermediary will be economically viable. The process of search can be imperfect so that the consumer and the supplier meet only with some probability /J. Suppose that the intermediary has a well-known address. Then the transaction costs of direct exchange are T = (1 - P)(V - C). If the matching process is inefficient so that ft is small, intermediated exchange will have an advantage over direct exchange. These examples introduce the intermediation theory of the firm. The existence of firms can be justified even in a pure-exchange economy, since the comparison between modes of exchange does not depend on production of goods. Firms arise as a means of economizing on transaction costs, not by internalizing transactions but by carrying them out more efficiently. I now turn to other ways in which intermediated exchange can lower transaction costs.

Introduction

xvii

Market microstructure Neoclassical economics leaves open the question of how markets attain equilibrium prices. In contrast, intermediation theory identifies price setting by firms as the mechanism by which the economy attains marketclearing prices. I address these issues in Chapters 1-4, which look at market microstructure in a number of settings including monopoly, oligopoly, Bertrand competition with entry, and general equilibrium. Firms select prices to balance their purchases and sales. They select ask prices to earn revenues and ration consumer demand. They select bid prices to stimulate suppliers and keep down purchase costs of inventories. Buy and sell prices are adjusted to equate marginal revenues and marginal cost subject to sales not exceeding purchases and inventories. Market microstructure theory requires that some firms have a measure of local market power, that is, there must be some price makers in the economy. In balancing their purchases and sales over time, firms allocate resources and clear markets. Intermediaries provide other important market-making services as well. They hold inventories of goods on hand and stand ready to sell to customers. They further have cash on hand and stand ready to buy from suppliers. This avoids the problem of the coincidence of wants, in which a buyer and a seller need to want to transact with each other at the same time. This function is familiar in securities markets, in which financial intermediaries provide liquidity by standing ready to buy and sell stocks. In retail and wholesale markets, intermediaries provide similar immediacy services by standing ready to buy and sell commodities. The cost of carrying inventories serves to create a bid-ask spread. The dynamic path of prices responds to the intermediary's inventory level and associated risks. The inventories of firms help to clear markets, smooth the patterns of demand and supply fluctuations, and reduce the risks of exchange. Quantity rationing of buyers and sellers is complementary to the firm's price-setting activities. As market makers, firms allocate goods and services across buyers and adjust purchases from suppliers to reduce the costs of carrying inventories while providing availability to customers. In securities markets, intermediaries like stock specialists smooth the pattern of exchange, creating market liquidity by holding inventories.2 Demsetz (1968) investigates the effects of trading volume on transaction 2

Baumol (1965) examines market makers and stability in the stock market. Stoll (1985) surveys alternative views of financial market making, examining the market maker as auctioneer, price stabilizer, information processor, and supplier of immediacy. He observes that only the latter two roles are based on maximizing behavior by the market maker.

xviii

Introduction

costs at the New York Stock Exchange and observes that "the ask-bid spread is the markup that is paid for predictable immediacy of exchange in organized markets; in other markets it is the inventory markup of retailer and wholesaler." Specialists on the New York Stock Exchange are compensated for managing orders and for assuming risk by standing ready to carry out trades on their own account. In an early model of market structure due to Garman (1976), buy and sell orders arrive randomly.3 The rates at which orders arrive can be interpreted as stationary demand and supply functions that depend on the ask and bid prices. A risk-neutral dealer with market power maximizes expected profit per unit of time, subject to the restriction that the stock inventory does not drift upward or downward, which means that the market clears at each date.4 Ho and Stoll (1980,1981) and Stoll (1978b) assume that the securities dealer is risk averse. The bid-ask spread reflects the elasticity of demand and supply and the dealer's degree of risk aversion. In addition, the bid-ask spread tends to increase the longer the dealer's planning horizon. Adding more periods provides the dealer with more opportunities for price adjustment, but increases the dealer's risk, thus requiring greater compensation and widening the bid-ask spread. Firms in product markets provide analogous market-making services. Clower and Leijonhufvud (1975) observe that intermediaries provide availability of products. They note that since consumers and firms face fixed transaction costs, they produce or sell at discrete time intervals, which can create problems of the double coincidence of timing. Intermediaries hold inventories to provide immediacy or availability to buyers and sellers. This happens both when retailers and wholesalers purchase goods from suppliers and hold the inventories needed to serve buyers and when manufacturers keep inventories of parts on hand and create product inventories. Just-in-time inventory management is a means of providing immediacy while lowering inventory costs. By holding inventories, firms acting as intermediaries reduce the risk of market transactions when demand fluctuates randomly. Retail and wholesale intermediaries diversify by purchasing and reselling a variety of products, thus pooling supplier risk; see Lim (1981). Spulber (1985) shows that manufacturers and wholesalers enter into financial 3

4

On the determinants of the bid-ask spread, the interested reader might begin with West and Tinic (1971), Tinic (1972), Benston and Hagerman (1974), Logue (1975), Stoll (1978a, 1978b), Ho and Stoll (1980, 1981), and Cohen et al. (1981). Since profits and inventories of the stock follow random walks, the intermediary with finite inventories will almost certainly go bankrupt at some point. However, Garman (1976) avoids this issue by considering the case in which the intermediary has infinite inventories of both cash and stock.

Introduction

xix

risk-sharing arrangements with retailers and pool inventories in central warehouses to smooth out differences in demand across stores. Large retail chains achieve important advantages through diversification of demand risk across individual stores. Intermediaries have an advantage over direct exchange between buyers and sellers because the increased volume of transactions reduces the variance of sales and of purchases. In direct exchange, buyers and sellers face the possibility of being rationed because of demand and supply side shocks. By standard law of large numbers arguments, the variance of expected purchases and sales falls with scale. Moreover, by serving multiple markets or by handling a broader range of products, intermediaries reduce risk through diversification.

Intermediated exchange versus matching and searching Market intermediaries coordinate the actions of buyers and sellers. Firms carry out transactions, operating the system of payments, inventory control, and record keeping that is essential for markets to function. In addition, firms provide a central place of exchange, thus reducing the search costs of buyers and sellers. Chapters 5 and 6 compare the costs of intermediation with those of direct exchange in markets with matching of buyers and sellers or costly search. Marketers - including retailers, wholesalers, used-car dealers, and energy dealers - purchase and resell goods. Brokers - including travel agents, real estate agents, insurance agents, and stockbrokers-provide coordination services without buying and selling goods.5 These intermediaries improve the welfare of consumers and suppliers by reducing or eliminating the uncertainty associated with making a satisfactory match. Intermediaries also add to the number of potential trading partners, thereby increasing the likelihood of encountering a trading partner and reducing search costs. Intermediaries must compete with decentralized exchange, in which consumers and suppliers seek each other out and negotiate prices directly.6 Sometimes both forms of exchange exist side by side. For example, an organized used-car market operated by automobile dealers coexists with a decentralized market in which buyers and sellers meet informally, often 5

6

In Yinger (1981), real estate brokers set housing prices, fix commissions, and invest in search for buyers and sellers of houses. His model explains the value of shared listings such as the Multiple Listings Service. See Rubinstein and Wolinsky (1987), Bhattacharya and Hagerty (1987), Yavas (1992), Yanelle (1989), and Gehrig (1993).

xx

Introduction

through newspaper advertising. What are the advantages of transacting with an intermediary? Consider first the matching market. Consumers have diverse levels of willingness to pay and suppliers have different opportunity costs. If consumers and suppliers are matched randomly, in a highly decentralized fashion, the terms of the exchange become uncertain and the risk of not completing a trade rises. After all, when consumers and suppliers bargain directly, the buyer has an incentive to understate willingness to pay and the seller to overstate opportunity costs. Asymmetric information about willingness to pay and opportunity costs causes efficiency distortions in the amount traded or even results in the breakdown of trade. An intermediary can eliminate this uncertainty by posting bid and ask prices and thus offer an advantage over a decentralized matching market. Buyers and sellers can choose between using intermediaries to trade at a known price and the risky option of the decentralized market. Gehrig (1993) models this choice and shows the profitability of intermediation. Suppose that each consumer purchases at most one unit of the good and suppliers sell at most one unit. Then the market demand and supply functions represent the distribution of buyer willingness-to-pay levels and supplier opportunity costs, respectively. The intermediary chooses a profit-maximizing bid-ask spread, given the value to buyers and sellers of the matching-market option. At the market equilibrium, consumers with a willingness to pay above a critical level (greater than the ask price) purchase from the intermediary. Suppliers with opportunity costs below a critical level (less than the bid price) sell to the intermediary. Consumers and suppliers with values between these two critical levels enter the matching market. The advantage of intermediated exchange can be illustrated by means of a simple example. Suppose that the consumer's willingness to pay can take one of two values with equal probability, VL and VH> Assume that VL < VH- Denote the expected value of the consumer's willingness to pay by Also suppose that the supplier's opportunity cost can take one of two values with equal probability, CL and c#. Assume that CL Denote the expected value of the supplier's opportunity cost by

c = (l/2)cL + (l/2)cH. Before entering the matching market, the consumer and the supplier do not know the type of their trading partner. Assume that after a consumer and a supplier decide to trade, they learn each other's type. At

Introduction

xxi

that point, trade occurs if and only if they have gains from trade. The consumer and the supplier split the gains from trade evenly. A high-willingness-to-pay consumer can trade with both types of suppliers: t># > c # . A low-opportunity-cost supplier can trade with both types of consumers: vi> CL- The market outcome will depend on whether a high-opportunity-cost supplier can trade with a lowwillingness-to-pay consumer, that is, VL may be greater than or less thanc#. Suppose first that VL > c#, so that all types will trade in the directexchange market. Then, since they are uninformed about the type of their trading partner, the expected gains from trade of a type / consumer and a type j supplier from the direct-exchange market are, respectively, (vt - c)/2,

i = 1, 2,

(v - CJ)/2,

j = 1, 2.

It is easy to demonstrate that there are no prices at which a monopoly intermediary is profitable, (even with zero transaction cost K). For example, suppose that the intermediary chooses the highest ask price and the lowest bid price that will attract the high-willingness-to-pay consumer and the low-opportunity-cost supplier. These prices are PM = VH ~ (vH - c)/2,

wM = cL + (v -

cL)/2,

It follows that pM -wM = (cH - vL)/2 < 0. Now suppose that vi < CH, SO that a high-opportunity-cost supplier cannot trade with a low-willingness-to-pay consumer. The expected gains from trade for a high-willingness-to-pay consumer and a low-opportunity-cost supplier do not change. However, because a lowwillingness-to-pay consumer has only one other potential trading partner, the low-willingness-to-pay consumer expects gains from trade in the direct exchange market equal to (VL — CL)/A. A high-opportunity-cost supplier expects gains from trade equal to (VH — CH)/4. The intermediary offers prices pM and wM and is profitable if (CH — VL)/2 > K. The prices attract the high-willingness-to-pay consumer and a low-opportunity-cost supplier. The low-willingness-to-pay consumer and the high-opportunity-cost-supplier are inactive since they do not gain from direct exchange with each other. Thus, when there is a chance of trade breaking down under direct exchange, vL < CH, an intermediary will enter the market and a separating market equilibrium will result. When consumers search for a product, they face costs of travel and costs of learning about prices and comparing product features. When suppliers search for a willing buyer, they incur costs of travel and

xxii

Introduction

of communicating information about their products. As noted earlier, intermediaries reduce transaction costs by centralizing exchange. However, in a world with multiple intermediaries, consumers and suppliers continue to incur search costs from visiting multiple intermediaries. Spulber (1996a) models a search market with many intermediaries. Consumers and suppliers discount future net benefits, so that the time spent searching is costly. As before, consumers have diverse willingness to pay levels, and suppliers have different opportunity costs. Moreover, firms that intermediate have different transaction costs. Firms set both bid and ask prices. Consumers search across firms to obtain a lower ask price, and suppliers search across firms to obtain a higher bid price. As a result of heterogeneity and costly search, the market equilibrium is a distribution of bid prices and a distribution of ask prices. The equilibrium depends on the discount rate of consumers and suppliers, for which a higher rate of discount lowers the number of active consumers and suppliers and raises the number of active firms. The intuition behind this result is that a higher discount rate increases the cost of time-consuming search for consumers and suppliers. This allows firms to raise ask prices and lower bid prices since consumers and suppliers are willing to pay a premium to avoid further search, thus raising the returns to intermediation by firms. The number of intermediary firms that are active in equilibrium increases. The discount rate determines the costs of search. As the discount rate falls to zero, the costs of search are eliminated, which shows the relationship between the size of the bid-ask spread and transaction costs. In such a model, the Walrasian equilibrium is the limiting case of an intermediated market as transaction costs diminish. The supply-and-demand model can thus be viewed as an ideal case that is consistent with an underlying market with search costs and price-setting firms.

Alleviating adverse selection Chapters 7 and 8 examine models in which intermediaries address problems of adverse selection. In Chapter 7,1 consider allocation by intermediaries under asymmetric information about buyer willingness-to-pay levels and seller opportunity costs and certification of product quality. In Chapter 8,1 turn to adverse selection problems in financial markets, including pricing by informed and uninformed market makers and credit rationing by financial intermediaries. Brokered exchange differs from trade between a buyer and seller in a subtle way. In direct trade, the buyer's payment must equal the seller's receipt, which constrains the possibilities for bargaining. A

Introduction

xxiii

broker introduces many other possibilities for bargaining since the broker can effectively tax or subsidize the transaction. By taxing the transaction, a broker can capture some of the gains from trade by improving the chance that trade takes place.7 The broker designs a trading rule that elicits offers from the buyer and the seller and earns a return by creating a spread between the buyer payments and the seller receipts. In many markets buyers and sellers are asymmetrically informed. Sellers often do not know customer characteristics that underlie market demand. Buyers frequently do not know the quality, durability, or safety of products they seek to purchase. Intermediaries help to fill this gap by collecting and supplying information to their customers and suppliers, often bundled with products and other services. Retailers can test products and describe their characteristics to their customers. Wholesalers report on market demand and customer requirements to their suppliers. Consolidating transactions through intermediaries can yield returns to scale in producing and distributing this information. Intermediaries can capture gains from trade that would be lost because of information asymmetries. Not only do intermediaries have advantages in gathering and reporting information, they can guarantee that the information they provide is accurate, backing up the guarantee with reputation and binding contracts. Product characteristics frequently are difficult for consumers to observe. Consumers are uncertain about the efficacy of Pharmaceuticals, the durability of appliances, or the quality of automobiles. If consumers are less informed than suppliers about product quality, the market can fail to exist as bad suppliers drive out good. In Akerlof's (1970) well-known market-for-lemons model, low-quality used cars drive out high-quality used cars, since consumers are willing to pay only an average price for cars of unknown quality, and only sellers of low-quality cars can trade at that price. The market for lemons fails to realize potential gains from trade. Customers would be willing to pay for a good car if they could observe its quality. An intermediary can capture some of these foregone returns by certifying the quality of the product. Biglaiser (1993) shows that introducing a monopoly intermediary into a market with adverse selection enhances efficiency. The intermediary has a greater incentive to invest in monitoring quality than does an individual buyer, since the intermediary buys more goods. Thus intermediaries are better able to distinguish higher-quality suppliers from those with lower quality. 7

See Myerson and Satterthwaite (1983), Spulber (1989b), and Mookherjee and Reichelstein (1992).

xxiv

Introduction

In addition, the intermediary's incentive to report accurately the quality of goods stems from the returns to building a good reputation. These returns can be greater for intermediaries since they carry out more transactions than individual suppliers. Buyers and sellers decide whether to transact directly with each other or to buy and sell through the intermediary. In equilibrium, all high-quality goods are sold through the intermediary and most low-quality goods are sold directly to buyers. As a result of this separation, the lemons problem is alleviated at the intermediated market equilibrium. A retail or wholesale intermediary can offer many different products for sale, and consumers can rely on the reputation of the intermediary without having to investigate the many product suppliers. In particular, intermediaries can serve as guarantors of the product quality of their suppliers through warranties and contract terms. A manufacturer's brand name often conveys information to customers who then do not need to know the quality of components purchased by the manufacturer. Since intermediaries handle the products of two or more suppliers, their incentives to sell a lower-quality good differ from those of individual suppliers. The intermediary that sells a low-quality product suffers a loss of reputation and thus loses customers for all other products. Intermediation lowers the threshold prices that are required for sustaining high-quality production. To illustrate the basic problem, consider an example with a single consumer and supplier. The supplier's product can be of high or low quality. Supplying a product of quality j entails an opportunity cost of CJ, j = L, //, where the opportunity cost increases with quality: CL Assume that gains from trade are always positive: CL < VL and cH < VHLet k be the probability that the good is of high quality. Assume that the lemons condition holds: v =5 (1 - k)vL + kvH < cH. Thus the consumer's willingness to pay based on expected quality of the good is less than the supplier's opportunity cost of providing the high-quality good. Suppose for example that consumers cannot distinguish in equilibrium between high-quality and low-quality goods, so that the high-quality sellers have an incentive to leave the market. The consumer and the supplier split the gains from trade: (VL — ci)/2. A supplier with a lowquality good will agree to trade, so that trade occurs with probability (1 - k).

Introduction

xxv

Suppose that an intermediary can observe product quality at cost K and then credibly certify its quality to the consumer. The intermediary will offer WH = CH to the high-quality seller. The intermediary will select the price for the low-quality seller WL such that the supplier is indifferent between selling to the intermediary and direct exchange:

wL-cL

= (vL - cL)/2.

The intermediary will select an ask price pu = VH for the high-quality good. The intermediary will offer the consumer a price for the lowquality good PL such that the consumer is indifferent between purchasing the low-quality good and the expected net benefit from direct exchange: VL - PL = (1 - k)(vL -

cL)/2.

The intermediary must invest in the testing technology K before observing the quality of the good. Thus the intermediary's expected profit is

n = (1 - k)(pL - wL) + k(pH -wH)-K = (1 - k)k(vL - cL)/2 + k(vH - cH) ~ K. The intermediary will find entry profitable if there are sufficient gains from trade from both types of goods. Note that the intermediary earns returns certifying the low-quality good by eliminating uncertainty for the consumer. Suppose that VH — CH > K. Then there is a critical value k* that lies strictly between zero and one such that the intermediary is profitable if and only if the proportion of high-quality goods is greater than the critical value. In financial markets, the market maker must deal with informed and uninformed traders. The informed traders may have better information than the intermediary about the value of the asset. Thus the informed traders may know that the value of the asset is above the ask price or below the bid price. In this case, trading with informed traders results in losses for the intermediary. Uninformed traders trade for liquidity and purchase at the ask price or sell at the bid price, depending on their estimates of the asset value of liquidity requirements. The intermediary sets bid and ask prices to recover losses from trades with informed agents through trades with uninformed agents (Copeland and Galai, 1983; Glosten and Milgrom, 1985).

Mitigating moral hazard and opportunism As I have emphasized, firms form if they can lower transaction costs relative to direct exchange. This means improving the performance of

xxvi

Introduction

markets, not necessarily bringing transactions within the firm. In Chapters 9 and 10,1 review the contractual theory of the firm and consider the transaction-cost aspects of the intermediation theory of the firm. Ronald Coase (1937) drew economists' attention to the importance of transaction costs in determining the boundaries of the firm, as firms substitute internal production for costly markets. Intermediation theory presents a different but complementary approach by emphasizing that firms create the least-cost market institutions, substituting marketmaking services when these are less costly than decentralized exchange. Market contracts can be inefficient because of the costs of writing and enforcing contingent agreements. Buyers and sellers can have difficulty making binding commitments. Oliver Williamson (1975, 1985) emphasizes the substitution of organizational management for market contracts that are subject to opportunism. Firms vertically integrate to control transaction-specific assets that require irreversible investment. Grossman and Hart (1986) and Hart and Moore (1990) apply a property rights approach in which firms seek to own assets whose services are complementary to transaction-specific investment. Binding contracts provide a way of mitigating opportunism that does not rely on organizational expansion. Firms acting as intermediaries between buyers and sellers can provide a means of making credible commitments. Intermediaries earn returns from making credible commitments to prices that would not be feasible in direct exchange. To illustrate how this works, consider a simple example. A consumer purchases a unit of a good from a supplier. The supplier has opportunity cost C. Suppose that the consumer can undertake a relationship-specific investment A that enhances the consumer's willingness to pay for the good. Without the investment, the consumer has willingness to pay VL for the supplier's good, and with the investment, the consumer has willingness to pay VH- Suppose that investment is worthwhile if the consumer captures all the returns, but investment costs are greater than half the returns: VH - vL > A > (vH -

vL)/2.

Assume that in direct exchange the consumer and the supplier cannot commit to a price before the consumer's investment decision. After the consumer decides whether or not to invest A, the consumer and the supplier bargain over the division of the gains from trade. Surplus is evenly divided. If the consumer does not make investment A, then both the consumer and the supplier receive (VL — C)/2. If the consumer invests, then the consumer and the supplier each receive (VH — C)/2. This leads to the classic underinvestment result. The consumer will not

Introduction

xxvii

find it worthwhile to make the relationship-specific investment since the buyer must split the returns to investment with the supplier: (vH ~ C)/2 -A<(vL-

C)/2.

Investment is not desirable for the consumer since half of the net return is less than the cost of investment. Suppose that an intermediary can commit credibly to posted ask and bid prices p and w. Equivalently, suppose that the intermediary can achieve binding agreements at fixed prices with both the consumer and the supplier. If the consumer were to purchase the good at price p, the consumer will always make the relationship-specific investment since incremental benefits exceed the cost of investment. Then the intermediary can choose prices such that the consumer and the supplier are indifferent between trade with the intermediary (given transaction specific investment) and direct exchange (without specific investment): vH-A-p

= (vL-

C)/2 =

w-C.

Therefore the intermediary's markup exactly equals the consumer's net return to investment: p — w = VH — VL — A . The foregone net return is the transaction cost of direct exchange. The intermediary is profitable if the net return exceeds the intermediary's transaction cost, VH — VL — A > K. Thus binding commitments with a third party are means of alleviating opportunism in bilateral contracts. In Chapter 10,1 also show that commitment by intermediaries can reduce the efficiency effects of different ownership arrangements for productive assets. This implies that when binding contracts with intermediaries are feasible, the need for firms to own productive assets is correspondingly reduced.

Delegation to intermediaries In Chapter 11,1 review organizational-incentive theories of the firm that identify critical principal-agent incentives within organizations. Firms extend their boundaries when organizations can mitigate adverse selection or moral hazard problems that arise in market contracts. In Chapter 12,1 emphasize that agents often are market intermediaries. This suggests a modification of traditional principal-agent models and helps explain the interplay between agency and intermediation in the theory of the firm.

xxviii

Introduction

The role of the firm as a monitor of its own personnel is well known. For example, Alchian and Demsetz (1972) emphasized the role of the firm as a specialist who monitors team production efforts, designs incentives, and receives the residual rewards: in their words (p. 793), "the firm serves as a highly specialized surrogate market," since the firm collects and implicitly sells information to employees by organizing their production activities. The intermediation theory of the firm, in contrast, views employees as agents who carry out delegated contracting for the firm. Employees act as the firm's purchasing and sales agents. Principals retain agents as intermediaries in part because of their ability to make commitments in third-party relationships by making credible agreements with their agents. Thus agents are a means of influencing the outcome of bargaining by committing to pay a maximum price. Moreover, strategic delegation is a means of influencing the outcome of competition. The firm's owners affect the competition equilibrium through incentives for managers. In addition, the firm itself is a monitor of its suppliers and distributors, making sure that suppliers deliver high-quality parts on time or requiring distributors to improve customer service. Monitoring the efforts of trading partners is costly, leading to moral hazard problems. It can be costly for consumers to observe whether service providers, from auto mechanics to attorneys, are working in their interests. Intermediaries can earn returns through delegated monitoring by supervising suppliers for their customers. In building a house, a consumer hires a contractor who subcontracts with electricians, plumbers, masons, and carpenters. The contractor takes on the transaction costs of locating skilled tradespeople, writing contracts, and monitoring their performance. The contractor gains skills at these tasks, thus lowering the costs of supervision. Specialized intermediaries thus reduce the problem of moral hazard in markets. Financial intermediation can provide economic advantages over direct lending since lenders delegate monitoring of borrowers to intermediaries who diversify risks. In other words, monitoring costs create an opportunity for intermediaries in which intermediaries incur debt from lenders and in return make loans to borrowers. The structure of the debt contracts results in more effective monitoring than would occur without intermediaries. In Douglas Diamond's (1984) model, for example, deadweight bankruptcy penalties are imposed on the borrower because of the unobservability of investment returns. The intermediary has a cost advantage in collecting information about borrowers since lenders would duplicate their efforts if they were individually to monitor borrowers. Also, the

Introduction

xxix

intermediary avoids the free-rider problem, which occurs if all lenders fail to monitor since they rely on the efforts of other lenders. Lenders still incur costs of delegation since they must monitor the intermediary. However, the intermediary maintains a net-cost advantage over direct monitoring because the returns to centralized monitoring of borrowers exceed the cost of delegation to the intermediary. The delegated monitor has a cost advantage because the financial intermediary reduces risk by pooling payments from multiple borrowers.

Outline of the book The book is organized as follows. Part I introduces the concepts of market microstructure and the intermediation theory of the firm. Chapter 1 considers market microstructure and intermediation in the economy. The chapter also compares the intermediation theory of the firm with the main economic theories of the firm-neoclassical, industrial organization, contractual, and organizational incentive. Chapter 2 presents the basic model of market microstructure and sets out the monopoly market-making model. Part II extends the basic monopoly model of market microstructure. Chapter 3 presents a set of models of competition between intermediaries. Chapter 4 examines market microstructure in a generalequilibrium setting and compares the outcome with the Walrasian market equilibrium. Part III compares intermediation with decentralized trade. Chapter 5 examines competition between intermediaries and decentralized markets with direct exchange. Consumers and suppliers can enter into markets that require search or some matching process followed by bargaining or they can transact through intermediaries. If intermediaries are economically viable in equilibrium, then the model explains the formation of firms. Chapter 6 illustrates intermediation by presenting a model of markets in which prices are set by firms. Consumers search across firms for the lowest ask price and suppliers search across firms for the lowest bid price. Search is time consuming and therefore costly, since all agents discount future returns. This emphasizes that operating markets is costly. By posting prices, firms operate the market mechanism. The model features three types of heterogeneity. Consumers differ in terms of their willingness to pay, suppliers in terms of production cost, and firms in terms of transaction costs. The model departs from the law of one price in two significant ways. In equilibrium, there is a distribution of prices across firms as a consequence of the heterogeneity of market agents and the costs of search. In addition, each firm offers a positive bid-ask spread, with a

xxx

Introduction

markup over search costs that reflects the local market power of firms as the result of costly search. This markup provides a return to the firm's market-making activities. It is shown that as the time costs of search fall, market equilibrium approaches the idealized competitive equilibrium. As the time costs of search increase, the market tends toward a monopoly outcome. Part IV examines intermediation under asymmetric information. Chapter 7 examines models of allocation by intermediaries and guaranties of product quality by expert intermediaries. Buyers have private information about their willingness to pay, and sellers have private information about their opportunity cost. Intermediaries design mechanisms to allocate goods and clear markets under asymmetric information. I consider both small-numbers bargaining and markets with many buyers and sellers. Chapter 8 examines the economic role of financial intermediaries in models of adverse selection. I consider pricing of financial assets by specialists, pricing by informed intermediaries, and credit rationing by financial intermediaries. Part V compares the intermediation theory of the firm with the transaction cost or contractual theory of the firm. In Chapter 9,1 review the contractual theory of the firm, including the Coasian analysis of transaction costs, the Knightian consideration of uncertainty and bounded rationality in the organization of firms, Oliver Williamson's analysis of opportunism, and the property rights approach to the firm of Oliver Hart and others. In Chapter 10, I suggest that, in contrast to organizational solutions to transaction costs, firms acting as intermediaries can lower transaction costs by providing alternative institutions of exchange in the market place. Part VI compares the intermediation theory of thefirmwith the agency or organizational-incentive theory of the firm. In Chapter 11,1 review the organizational-incentive theory of the firm, stressing the agencybased analysis of vertical integration, coordination of multiple agents within the firm, delegation of authority by owners to managers, and delegation of authority by managers to employees. Then, in Chapter 12, I consider principal-agent relationships in which agents represent the principals' interests in interaction with third parties, that is, relationships in which agents are intermediaries. I present some models of delegated authority in which agents carry out bargaining, competition, contracting, and monitoring. The final chapter concludes the discussion.

Parti Market microstructure and the intermediation theory of the firm

1

Market microstructure and intermediation

Firms create and manage markets by acting as intermediaries between buyers and sellers. An intermediary is an economic agent who purchases from suppliers for resale to buyers or who helps buyers and sellers meet and transact. Intermediaries seek out suppliers, find and encourage buyers, select buy and sell prices, define the terms of transactions, manage the payments and record keeping for transactions, and hold inventories to provide liquidity or availability of goods and services. This book is concerned with the economic role of firms and the functioning of markets in general. In finance, the study of intermediation and the institutions of exchange is called market microstructure.1 I apply the term market microstructure generically to refer to the operation of markets for all types of goods and services. I show that there are basic similarities between a broad range of intermediation models in economics and finance. Throughout the book, the main results are derived within a common framework, with similar notation and related economic reasoning. Just as producing goods and services consumes resources, so does the establishment and operation of markets to allocate those goods and services. Companies incur costs in adjusting prices and communicating price information to buyers and sellers. The types of information imperfections that are present determine the intermediation activities of firms. When there is demand and supply randomness, intermediaries provide liquidity or immediacy by standing ready to buy and sell. Given uncertainty about the willingness to pay or opportunity costs of trading partners, intermediaries coordinate transactions by matchmaking and brokering activities. When the characteristics of buyers or sellers are unobservable, intermediaries generate market information and provide 1

I do not address finance theory and financial institutions specifically. I focus on general economic applications involving such issues as uncertainty, adverse selection, and moral hazard. Moreover, I do not address issues covered in the literature on market microstructure that deal with the details of double auction markets, including discrete units for price quotes, margin requirements, frequency of order clearing, and so on.

4

Market microstructure and the intermediation theory of the firm

guaranties for product quality to address adverse selection. When the actions of buyers or sellers are costly to observe, intermediaries provide monitoring and contracting services. The main function of market intermediaries is to figure out ways of clearing the market, that is, pricing to match purchases to sales. This crucial price-setting activity provides an explanation for a main puzzle of neoclassical economics: how are market-equilibrium prices attained? The market institutions that provide intermediation have not been given the attention that they deserve. In this chapter, I consider some of the elements of market microstructure. I begin by emphasizing the important economic role played by firms as intermediaries. I then integrate the notion of firms as market makers in the traditional circular flow of economic activity. Next, I compare the intermediation theory of the firm with other economic theories of the firm. Finally, I highlight the importance of market microstructure: it seems likely that the value added by specialized intermediaries represents approximately a quarter of the U.S. economy!

1.1

Who decides?

Paul Samuelson (1980, p. 16), in an often-quoted summary of economic analysis, asserted that any society must solve three classical economic problems: what goods to produce and in what quantities, how to produce them, and for whom particular goods are produced. In economic models, these three problems are solved through markets that coordinate the actions of individual consumers and firms. In the neoclassical framework, for example, the market is a description of an exogenous mechanism for selecting prices that equalize aggregate supply and demand. Individual consumers, taking prices as given, choose their most preferred bundle of goods subject to their budget constraint. Firms, also taking prices as given, choose a bundle of inputs and outputs that maximizes profit, given their production technology. Economists thus offer a standard representation of the market that is at variance with what is observed in most market economies. In practice, the problems of what to produce, how to produce, and for whom are solved directly by the actions of individual firms, through their production, technology, and marketing decisions. Firms perform the activities associated with the market mechanism, most importantly, they select prices and coordinate exchange. Moreover, firms establish organizations, interact strategically with customers, suppliers and competitors, and negotiate the legal and political constraints of the society in which they operate. Economic analysis, by overemphasizing an idealized view

Market microstructure and intermediation

5

of the market mechanism, has downplayed the important role played by the firm. Joseph E. Stiglitz (1993) observes that in addition to the three questions - what, how, and for whom? - one should add a fourth: "How should these decisions be made, and who should make them?" His central point is that economic analysis must address the incentives to acquire and process information. He states, In the economy of Joan Robinson, or Arrow and Debreu, decision makers and the structure of decision making play no role. Robinson described the job of the manager of a firm as simply looking up in the book of blueprints the appropriate page corresponding to current (and future) factor prices. Were life so simple! Of course, if life were so simple, being a manager would be a truly boring job, worthy of the disdain cast by the traditional British academic. Further, the lack of concern of Lange, Lerner, and Taylor for managerial incentives would be of little moment: managers could essentially be replaced by automata. Stiglitz further decries the neoclassical market model: The view of economics encapsulated in the Arrow-Debreu framework (and reflected in contemporaneously written textbooks, such as Samuelson's) is what I call "engineering economics," intending no slur on the engineering profession. Economics consisted of solving maximization problems. Stiglitz concludes that "the failure of market socialism serves as much as a refutation of the Arrow-Debreu model of market economy as it does of the market-socialist ideal." It is apparently a good time to review the underpinnings of economic theory. In my view, the solution to the quandary of "who decides?" is the firm. By shifting the locus of economic decision making to the firm, a realization of the role of its managers as decision makers and strategists inevitably follows. Firms address what goods and services to produce and in what quantity. The variety of goods that a firm supplies is one determinant of the scope of the firm. The characteristics of the goods that the firm supplies include the physical characteristics of goods as well as their location and the date that the goods are made available. The properties of the goods also include the brand name, advertising, and contract terms. Also, the firm must decide on the quantity of goods to supply, which determines the scale of the firm.

6

Market microstructure and the intermediation theory of the firm

Second, the firm's managers determine how to produce the goods and provide the services. Here the decision is much more complicated than the choice of productive technology, although such a choice is often significant. The firm's organization is a hierarchy of positions filled by individual decision makers. The managers must decide how best to structure the organization to achieve the firm's objectives. The actions of managers include the design of incentives, lines of authority, communication channels, and organizational rules. The managers must decide what accounting conventions to follow and what measures of performance to emphasize. The managers determine the method of financing (debt and equity), the skill levels of personnel who will be employed, and the types of capital equipment and other productive inputs that will be needed. The firm decides on whether to make or buy specific inputs, depending on whether it can achieve economies of sequence2 from vertical integration. Finally, the question for whom to produce becomes the more general question for individual firms of what markets to enter, both as a seller and a buyer. Entering a market as a seller consists of identifying customers and entering into transactions with them. The firm defines its product markets in a wide variety of ways based on the characteristics of its intended customers and the types of goods and services that the firm wishes to provide. The important characteristics of consumers can include tastes, risk aversion, rate of time preference, income, location, age, occupation, knowledge, and other factors that affect consumer demand for specific goods and services. Customers are identified through market research, marketing channels (wholesale and distribution), and customer self-selection in response to marketing efforts. The firm addresses specific market segments through advertising, sales expenditures, distribution channels, pricing policies, contract terms, and product design. Deciding on what goods and services to produce and how to produce them depends fundamentally on the customers for whom the goods and services are intended. Similarly, as a buyer, thefirmcan enter a range of markets. The firm enters into capital markets to obtain funds for investment, labor markets to hire personnel, and other factor markets to purchase technology, equipment, manufactured inputs, services, land, and raw materials. Here also, the firm defines its input markets in terms of the characteristics of the suppliers of the types of inputs that the firm demands. 2

Economies of sequence are formally defined in Spulber (1989b). Economies of sequence refer to economies achieved by the vertical integration of steps in a production sequence.

Market microstructure and intermediation

7

Models of the firm can address any subset of these questions and many others besides. However, these three types of questions can provide useful benchmarks to evaluate the applicability of economic models to the many problems that firms attempt to solve. The answers to the three questions that I have just outlined determine the range of the firm's activities and thus define the attributes of the firm: its scope, scale, organization, and market actions. There are many determinants of the firm's attributes, including the characteristics of the firm's customers and suppliers, relative prices; the capabilities, knowledge and preferences of the firm's managers; the degree of competition; and the regulatory, legal, and political environment of the firm.3 Acting as intermediaries, firms answer the three classical questions by making decisions about the mix of products they will purchase from suppliers, the types of suppliers that they will contract with, and the allocation of goods and services to be offered to their customers. The distinction between merchants and manufacturers need not be clear-cut. In combination with managing transactions, intermediaries often transform products to add value: transporting, storing, repackaging, assembling, preparing for final use, and adding information and guaranties. Conversely, manufacturers carry out many market-making activities, intermediating between sellers of raw materials or product components and buyers of manufactured goods.

1.2

The circular flow of economic activity

Firms create and operate markets: setting prices, carrying out transactions, producing and distributing information, and forming and monitoring contracts. When the role of firms as intermediaries is understood, it is possible to take a unified view of diverse theories of the firm. The intermediation theory of the firm suggests that some markets are guided by the visible hand of firms, as observed by Alfred D. Chandler (1977), while in others firms are guided by the invisible hand of the market, as emphasized by Adam Smith. In his classic response to the mercantilist opponents of free trade, Adam Smith, in The Wealth of Nations (1776), emphasized the virtues of the market competition that guides the entrepreneur so that "[b]y pursuing his own interest he frequently promotes that of the society more effectually than when he really intends to promote it."4 Entrepreneurs, seeking to maximize their profits by producing goods and services, act 3 4

Of course, alternative models of the firm will emphasize different characteristics of the firm, depending on the questions the researcher seeks to address. Adam Smith, The Wealth of Nations (New York: The Modern Library, 1937), p. 423.

8

Market microstructure and the intermediation theory of the firm

for the benefit of society as if guided by the external forces of the market. This story has been embellished through over two centuries of economic analysis to such an extent that the activities of individual firms are downplayed and the market is taken to be an explicit coordination mechanism. The market, or the mythical Walrasian auctioneer, establishes prices that equilibrate supply and demand, steering the production activities of price-taking firms and directing the choices of price-taking consumers. The market is said to adjust prices upward or downward in response to shortages or gluts and to summarize information about rapidly changing buying and selling behavior. In neoclassical economics, market prices are the outcome of seller competition and buyer bidding; yet, what is missing is an explicit mechanism for translating those bids into market prices. To be useful, the economic model of the market mechanism must satisfy two criteria. First, it must specify the actions taken by market participants, so that the equilibrium is chosen endogenously. Second, the market model should correspond to those of the observed characteristics of actual price-setting institutions. In particular, it should recognize the importance of firms in setting prices and clearing markets. Intermediation models potentially satisfy these criteria. In these models, the firm sets prices and carries out other market-making activities. These price activities correspond in a realistic way to the complex pricing decisions of retailers, wholesalers, manufacturers, and financial intermediaries. The firm carries out a variety of intermediation activities as outlined in the Introduction, including market making, reducing transaction costs, producing and distributing information, and delegated monitoring. As a market maker, the firm creates and operates markets. First and foremost, the firm is a price setter, establishing prices based on the willingness to pay of its customers and the price responsiveness of suppliers. It is essential to recognize the significant administrative effort involved in price setting. For example, a typical supermarket chain sets prices on well over 50,000 to 70,000 items. Moreover, these prices often vary regionally or across stores and are changed weekly or sometimes more frequently in response to competition, supply fluctuations, changes in demand, or inventory considerations. Price setting by firms provides a valuable service that should be viewed as a central economic activity rather than as an exogenous phenomenon. Thus, in addition to producing goods and services, firms generate transactions that yield economic rents. Price setting by firms implies a different market equilibrium than the auctioneer model. In particular, the law of one price need not hold, since companies choose a positive bid-ask spread, earning profits from the

Market microstructure and intermediation

9

markup of selling prices over their buying prices. In a simple monopolymonopsony framework, where the firm has market power on both the demand and supply sides of the market, the bid-ask spread will straddle the Walrasian price and output will fall below the standard supply and demand equilibrium level. Competition will narrow the bid-ask spread. With costly search and heterogeneous consumers, suppliers, and intermediaries, there will be nondegenerate distributions of bid-ask spreads across firms. Moreover, the spreads will depend on the costs of search to customers and suppliers. Firms coordinate transactions in a variety of ways. By centralizing exchange, they reduce the costs of search to their suppliers and customers, providing an address to which buyers and sellers may direct their communication. Retailers, wholesalers, and other distributors substantially reduce the number of contracts needed to link their many trading partners. Similarly, manufacturers coordinate networks of parts suppliers and output distributors. Firms stand ready to purchase from their various suppliers and hold inventory for the convenience of their customers. Thus firms are market makers, providing immediacy in a manner that is analogous to specialists on organized exchanges for financial assets. Firms perform a variety of other tasks often attributed to an unspecified market mechanism. They allocate goods and services across locations and over time through marketing and sales activities, purchasing decisions, and inventory adjustment. Firms engage in quantity rationing of their customers through priority service contracts, order delays, and unintentional stockouts. These supplement price adjustment as a means of balancing supply and demand in markets. By coordinating exchange, firms reduce transaction costs for their customers and suppliers. Transaction costs include direct costs incurred in carrying out purchases and sales, as well as the time and the inconvenience of search. It is often noted that money, in addition to being a unit of account and a store of value, avoids the double coincidence of wants, which hampers a barter economy. Yet the problem remains; a buyer must locate a supplier that wants to sell what the customer wants to purchase at the desired time and place. Firms address this problem by standing ready to buy and sell and by marketing and purchasing efforts. By dealing through an intermediary rather than entering a decentralized matching market, buyers and sellers reduce the risk that they will fail to find a compatible trading partner. The prices posted by the intermediary avoid the repeated bargaining of decentralized exchange, which entails the possibility that negotiations will break down. The effectiveness of competitive markets as a mechanism for processing vast amounts of information has often been noted. Usually economists point

10

Market microstructure and the intermediation theory of the firm

to the information content of prices and the advantages of decentralized decision making. As Stiglitz observes, however, "prices do more - and less - than is envisaged in the traditional paradigm." They do more in that quality may be signaled by price and quality can depend on the price paid (Stiglitz, 1987b). Prices do far less in that companies and their customers and suppliers communicate in many complex ways in addition to price signals, including negotiation of contract terms. What should be stressed is that individual firms incur the costs and earn the returns from producing and supplying information. Firms, acting as intermediaries, gather information about the patterns of consumer demand and the characteristics of suppliers. This information is used for pricing, product design, and production decisions. Companies inform their customers about product quality and availability through their product selection, catalogs, sales personnel, and advertising. Retailers, wholesalers, and manufacturers pass along market-demand information to their suppliers. Advances in computers and telecommunications and the development of computer networks have spurred the use of electronic data interchange and Internet communication between companies as a means of increasing the speed and the accuracy of transactions and lowering costs. A simple modification of the circular flow diagram represents the economic function of intermediaries (see Figure 1.1). Figure 1.1 recognizes three types of agents in the economy: consumers, market-taking firms, and market-making firms. Market-taking firms take price signals and market institutions as givens. In contrast, market-making firms are intermediaries that create and operate markets. Market makers include not only price-making firms but also other market institutions such as organized exchanges for securities, options, futures, and other financial assets. They coordinate transactions between consumers, between markettaking firms, between consumers and market-taking firms, and between other intermediaries. The consumers send expenditures to market-taking firms in return for goods demanded and receive incomes from intermediaries in return for inputs supplied. Similarly, market-taking firms receive revenues from intermediaries in return for goods supplied and make factor payments to intermediaries in return for goods received. How do prices adjust to clear markets? In the perfectly competitive market model, of course, firms simply react to prices. But in practice, many companies have at least some power over prices because of a variety of factors such as product differentiation, transportation costs, consumer switching costs, transaction costs, barriers to entry, and incomplete information about prices. However, setting prices can be a costly activity. Companies need to gather demand or supply information and monitor competitors' prices.

Market microstructure and intermediation

11

REVENUES AND INTERMEDIATION RENTS

GOODS AND SERVICES

GOODS AND SERVICES

MARKET MAKERS

CONSUMERS FACTORS OF PRODUCTION

MARKET TAKERS FACTORS OF PRODUCTION

FACTOR PAYMENTS AND INTERMEDIATION/ RENTS

Figure 1.1. The circular flow of economic activity with market intermediaries.

They need to perform computations to determine the profit-maximizing prices. They need to communicate prices to their customers and suppliers. In many industries, companies may incur menu costs in changing prices by printing new catalogs or issuing price lists. Price rigidities are observed in a wide range of industries (Carlton, 1986), which also suggests that changing prices is costly (Barro, 1972). When companies act as intermediaries, they not only arbitrage between buyers and sellers, but they also coordinate their transactions through price signals. The traditional supply and demand model can be applied to understanding the market-clearing actions of intermediaries. Consider a retail or wholesale intermediary that has market power in both its customer and supplier markets. For example, the firm could be the primary purchaser and reseller of a differentiated product. Thus the intermediary has some power to set both bid and ask prices for its product and to make profits from the markup between the two.

12

Market microstructure and the intermediation theory of the firm P/W

P*

p

V

s (w)

W

w*

D(p)

0*

QW

Q

Figure 1.2. The bid-ask spread and the supply-and-demand model.

Figure 1.2 illustrates the situation of an intermediary with this kind of market power. The demand curve represents the residual demand of the firm's customers. The supply curve represents the residual amount that the company's suppliers are willing to provide at various factor prices. The firm chooses its profit-maximizing buy and sell prices given its best estimate of these supply and demand functions. There is a bid price w that is offered to sellers, and an ask price p that is proposed to buyers. The sellers' supply function is S(w) and the buyer's demand is D(p). The profit-maximizing firm sets prices to equate its marginal revenue to its marginal factor cost. The profit-maximizing bid and ask prices are w* and /?*, and Q* is the amount traded. The intermediary's profit is the rectangle in Figure 1.2 whose area equals (p* — w*)Q*. In equilibrium, the firm chooses the buy and sell prices to clear the market: Q* = D(p*) = S(w*). The sell and buy prices straddle the Walrasian price pw, and output is below the Walrasian output Qw. The bid-ask spread depends on the elasticity of supply and demand, the company's transaction costs, and the alternatives available to buyers and sellers. How do prices adjust to clear markets? In markets in which there are intermediaries with market power, the simple framework depicted in Figure 1.2 provides an answer. The firm will adjust both its buy and sell prices in response to changes in supply or demand. Suppose for example that the firm observes a rise in demand that shifts the demand curve to the right. The firm generally increases the sell price to ration demand and increases the buy price to encourage supply. Thus the intermediary adjusts prices so that the market clears at a higher output.

Market microstructure and intermediation

Q

13

x

Figure 1.3. Inventory holding by a market intermediary.

Intermediaries provide immediacy by holding inventories and cash. Price-setting intermediaries will adjust prices to maintain inventories. For example, the intermediary might choose to reduce inventories either by increasing the ask price above the level shown in Figure 1.2, thus reducing consumer demand, or by raising the bid price shown in the figure, thus bringing forth additional supplies. In this way, the bid and ask prices will vary depending on inventory levels observed after demand and supply are realized. Figure 1.3 shows the price spread with purchases X exceeding sales Q. Amihud and Mendelson (1980) consider a specialist who adjusts prices based on inventory levels to maximize average profit per unit of time.

1.3

Comparison with other economic theories of the firm

Economic analysis offers an impressive selection of models of the firm that provide both rigorous analytical modeling and penetrating insights.

14

Market microstructure and the intermediation theory of the firm

The principal economic theories of thefirmhave struggled with the difficulty of addressing both decision making by firms and market allocation within the same framework. Economic theories of the firm are largely a matter of perspective they depend on whether the firm and its markets are viewed from far away or nearby. From a very distant perspective, one observes the economy as a whole. At this level of aggregation, there are a large number of individual firms, each of relatively small significance compared with the size of the economy. Moving closer, it is possible to distinguish industries, within which firms play a larger role. Closer still, one observes the transactions of a firm with one or two trading partners. Finally, viewed from nearby, the organizational structure of an individual firm looms large in comparison with the external market forces. Based on this range of economic perspectives, I classify economic theories of the firm into four categories, depending of their level of aggregation: (1) neoclassical, (2) industrial organization, (3) contractual (or transaction cost), and (4) organizational incentive (or principal-agent). The level of aggregation in economic models creates significant qualitative differences in the four types of theories of the firm. Neoclassical market models aggregate across the entire economy. By assuming price-taking behavior, neoclassical analysis effectively considers that thefirmis small in size relative to the economy as a whole, which contains an extremely large number offirms.The industrial-organization theory of the firm focuses on the industry and recognizes the market power of individual firms. Contractual theories of the firm examine the firm's relationships with individual trading partners, taking transactions as the unit of analysis. Finally, organizational-incentive theories of the firm examine hierarchical relationships within an individual firm. These four types of theories of the firm and the corresponding levels of aggregation are listed in Table 1.1. Notwithstanding their fundamental contributions, these economic theories of the firm do not constitute a unified view of the firm. Neoclassical economics stresses the role of the firm as operator of technology. Industrial-organization models emphasize market power and strategic interaction. Contractual theories of thefirmfocus on choosing the boundaries of the firm where market transaction costs exceed the costs of organization. Organizational-incentive theories of the firm stress delegation within hierarchies. The intermediation theory of the firm draws on elements of all four theories. The theory retains the input-output approach of neoclassical theory. Also, the intermediation theory of the firm presumes competitive price setting by firms as in industrial organization. The intermediation

Market microstructure and intermediation

15

Table 1.1. Levels of aggregation in economic theories of the

firm

Theory of the firm

Level of aggregation

Number of firms

Neoclassical Industrial organization Contractual (transaction cost) Organizational Incentive (principal-agent) Intermediation

All firms in the economy The firms in an industry A firm and its trading partner Relationships within the firm N intermediaries (and their / customers and J suppliers)

oo firms N firms Two firms One firm N firms

approach addresses transaction costs and opportunism as in contractual theories of the firm. Finally, the intermediation theory of the firm incorporates principal-agent relationships both within the firm and between the firm and its suppliers and customers. The neoclassical theory of the firm Neoclassical analysis is an impressive achievement that presents a sweeping picture of markets that explains resource allocation, with important contributions to the theory of economic growth, financial markets, and international trade theory. The theory represents the economy as a whole and makes the important point that constraints in one market have complex consequences for equilibria in other markets. I review the neoclassical model of general equilibrium and compare with the intermediation approach in Chapter 4. Neoclassical analysis presents a simplified theory of the firm with a focus on ease of aggregation, and yet individual firms are assumed to have little significance in the determination of economic aggregates. They are described by their production possibilities sets, which underlie their cost functions. Firms take prices as given in choosing how to operate their production processes. The decisions of firms and consumers are aggregated to obtain total demand and supply. The objective of the neoclassical analysis is to characterize marketequilibrium outcomes. Market equilibrium follows the law of one price. There is thus no price discrimination or price dispersion in the model. Moreover, buyers and sellers of a good pay and receive the same price. These prices are freely observable by all market participants, who correctly anticipate the market-equilibrium price in their decisions. There are no market frictions or transaction costs. Consumers and firms are

16

Market microstructure and the intermediation theory of the firm

never rationed since they can purchase or sell all that they want to at the equilibrium price, which clears the market without unemployment, excess capacity, or shortages. An unspecified market mechanism selects the prices that clear all markets. The price-adjustment process is external to the model, so that no economic agents are involved in market institutions. Rather, consumers and firms are restricted to adjustment of their individual demands or supplies. This is an unsatisfactory situation since the market mechanism is the heart of the matter. The model cannot be said to have given a representation of the market mechanism unless the market-clearing process has been modeled and equilibrium prices are determined by the actions of market participants. While not carefully specifying the market model, the neoclassical framework also gives a simplified representation of the firm. All the firm's decisions are the consequence of price-taking behavior at marketclearing prices. It is far from evident that the representation of thefirmby its production possibilities set conveys the relevant aspects of the firm. The organizational aspects of the firm are not distinguished from the technological constraints associated with production and other operations. By focusing on the firm's technology choice and input-output plans, neoclassical theory tends to avoid more complex managerial problems. The intermediation theory of the firm departs from neoclassical theory in several ways. The intermediation theory of the firm does not take equilibrium price setting as an exogenous process, but rather posits price adjustment by firms as the mechanism. Markets are not unobservable clearing mechanisms. Instead, all markets have a microstructure, that is, some specific institutions of exchange and intermediaries who coordinate costly transactions. Rather than being operators of technology and passive price takers, firms are decision makers, choosing competitive strategies and creating innovative transactions. Industrial-organization theories of the firm Industrial-organization models have considerably advanced the theory of the firm and its markets by involving it in the market-allocation mechanism. Strategic pricing models specify explicitly how prices are set and therefore eliminate the Walrasian auctioneer.5 By choosing prices in Bertrand-style competition, firms determine the market-clearing 5

I am referring to models of Bertrand-style price competition. The auctioneer remains in Cournotstyle quantity models, although Cournot-Nash outcomes can occur in models in which firms choose capacity competitively before engaging in price competition.

Market microstructure and intermediation

17

prices. Dynamic competition models provide insights about how prices adjust over time. Additional advances in mechanism design and the theory of optimal auctions address price setting in markets in which prices are set through bidding. Monopoly and oligopoly price-discrimination models examine a wide variety of pricing methods, contracts, and incentive schedules. Thus industrial-organization models have contributed to the modeling of markets since they place the firm at the center of pricing decisions. In industrial-organization models, firms with market power engage in strategic competition with rivals by choosing prices, products, or investment. The recognition of market power contributes increased realism by allowing the study of the many highly concentrated industries. The wide-ranging applications of game theory to entry, signaling, product differentiation, and pricing in static and dynamic models have yielded a deeper understanding of competitive interaction. In this way, industrial organization addresses the role of managers as strategy makers. Managers must select equilibrium strategies. They have beliefs about the characteristics and the potential actions of managers of rival firms. Managers take into consideration the reputation effects of their actions and make inferences about the actions of rivals. This significantly extends the management role beyond input-output choices. It is evident why industrial-organization models are increasingly influencing work in management strategy. Despite these advances, the industrial-organization theory of the firm has not escaped criticism. Rumelt (1984) observes that "by taking the industry as the unit of analysis, industrial organization has largely ignored the theory and evidence of intra-industry differences among firms." He finds that the "dispersion in the characteristic long-term rates of return of firms within industries is five to eight times as large as the variance in returns across industries." The focus on industry-level issues has diverted attention from full consideration of management issues. The integration of organizational issues into a competitive framework continues to present a challenge to industrial organization.6 The intermediation theory of the firm borrows the standard tools of industrial organization. Firms acting as intermediaries generally have market power and select prices. Intermediaries interact strategically as in game-theoretical industrial-organization models. The differences with industrial organization are highly subtle but significant. Industrialorganization models, with notable exceptions, focus on product-market 6

Addressing this question is necessary to achieve a fuller understanding of the manager's dual role as market strategist and organizational coordinator.

18

Market microstructure and the intermediation theory of the firm

competition. Intermediation models integrate competition in factor markets and product markets within the same model. Extending the partialequilibrium approach to encompass these factor-market interactions often yields different market equilibria than those predicted by examination of only the product markets. Industrial organization analyses, particularly in the empirical literature, focus attention on the industry. Consideration of market microstructure suggests paying closer attention to the allocative and pricing activities of individual firms. Contractual theories of the firm Contractual theories of the firm, beginning with those of Ronald Coase (1937), consider the interaction of the firm and its trading partners, whether customer or supplier. The individual transaction is the basic unit of analysis. The firm is a nexus of contracts. Pricing and other contract terms are endogenously determined through negotiation. The costs of using the market include the search for trading partners and contract negotiation. Once formed, there are costs to monitor and enforce contractual performance. Coase emphasizes the centrality of transaction costs in determining the nature of thefirm.He focuses on the make-or-buy decision as an organizing principle. Companies compare the costs of using the market with the organization costs of the activity when choosing what activities to undertake, including engineering, design, parts production, manufacturing, and assembly. For Coase, the market mechanism, which is external to the firm, is supplemented by organizational allocation mechanisms within firms. Transaction-cost theory thus highlights a set of management decisions about how best to organize the firm's labor, production, distribution, and other activities. The manager has a role in organizing production, particularly in choosing between market contracts and organizational expansion. Moreover, the theory implicitly implies that there are organization costs as well; otherwise firms could presumably expand without limit, supplanting costly market allocation. Oliver Williamson (1975, 1985) emphasizes the role of the firm as a solution to opportunism in market contracts. Because of the costs of writing and enforcing complete contingent contracts, agreements are subject to renegotiation. Parties to contracts are subject to holdup when they make irreversible investments in relationship-specific assets. These investments are necessary to enhance the economic value of contractual relationships. However, the threat of opportunism makes economic actors reluctant to make these transaction-specific investments. Faced with this dilemma, organizations are formed to carry out those activities that

Market microstructure and intermediation

19

involve high relationship-specific investments. Activities with high asset specificity are brought within the organization. Similarly, firms have an incentive to own assets that are complementary to activities requiring high levels of specific investment, according to Grossman and Hart (1986) and Hart and Moore (1990). Transaction-cost theory provides an explanation for the boundaries of the firm, but it is less instructive on the nature of markets. What is the source of transaction-cost differences between markets and hierarchies? Markets are much more than the sum of a set of transactions. Moreover, firms are pivotal organizers of exchange, just as they manage internal transactions. By highlighting the costs of using the price system, contractual analysis leads to the realization that the market mechanism can be improved on by activities that lower transaction costs for economic agents. This calls for further inquiry into the nature of the market. The intermediation theory of thefirmbegins from the same premise as that of Coase - market transactions are costly. However, bringing transactions within the firm through vertical integration is only one of many solutions to the costs of operating markets. In addition to organizational structure, the most efficient market microstructure emerges to handle transactions. When direct exchange is costly, intermediaries create and operate market institutions to address problems of risk sharing, adverse selection, moral hazard, and opportunism. The different perspective can lead to different conclusions, as I discuss in Chapter 10. Organizational-incentive theories of the firm Organizational-incentive theories of the firm apply principalagent models and related mechanism design techniques to the study of incentives within the firm. Firms are collections of principal-agent relationships, involving owners, directors, managers, and other employees. The agency analysis yields insights into the optimal design of incentive mechanisms including executive compensation, sales commissions, and rewards for meeting production and cost targets. I review the agency analysis of the firm in Chapter 11 and consider its implications for intermediation theory in Chapter 12. Organizational-incentive theories focus on the costs of delegating authority, monitoring, and rewarding performance within hierarchies. The concepts of moral hazard and adverse selection are applied to study the delegation of authority from owners to managers and from managers to a variety of personnel, including sales, accounting, and production workers. The agency theory of the firm addresses classic management issues by presenting the manager as an agent of owners, as a principal

20

Market microstructure and the intermediation theory of the firm

delegating authority to subordinates in the organization, and as a monitor of employee performance. The agency theory of the firm also addresses the problem of coordinating the activities of multiple agents within the firm. Group incentives address problems of moral hazard and adverse selection in teams. As I emphasize in Chapters 11 and 12, traditional agency analysis focuses on agents as producers. Agents are given incentives for devoting effort in moral hazard models or for revelation of information in adverse selection models. In contrast, legal and business applications generally view agents as intermediaries who carry out business transactions with third parties on behalf of the principal. These applications stress the fiduciary or trust relationship between the principal and the agent in thirdparty transactions. The agent is charged with representing the principal's interest in negotiating and monitoring contractual performance. The intermediation theory of the firm recognizes that agents often act as intermediaries. The firm can act as an agent of its customers or suppliers. The firm itself acts in the market place through its employees or through independent agents who carry out market interaction on behalf of the firm. The firm's agents engage in purchasing, sales, financial transactions, and contracts with other firms. Agents have value to principals as a means of making commitments in bargaining. In addition, firms strategically delegate authority to managers as a means of influencing the outcome of competition with other firms. Finally, agents serve as delegated monitors. Financial intermediaries, for example, have advantages as delegated monitors that stem from risk pooling and diversification. Overview Intermediation models suggest a model of the firm as a market maker, coordinating the actions of its customers and suppliers. The extent of aggregation is narrower than that of neoclassical economics, which looks across markets. The extent of aggregation is broader than that of industrial organization because it incorporates both the firm's input and output markets. The focus is substantially broader than contractual theories of the firm since intermediation theory attempts to examine the full set of the transactions carried out by the organization. Intermediation theory addresses organizational issues by noting that the firm delegates intermediation to managers, employees, and suppliers. The intermediation theory of firms and markets provides an answer to the question of who decides. In intermediation theory, the firm's managers are involved in a wide range of decision-making activities: searching for trading partners, selecting prices, managing customer and

Market microstructure and intermediation

21

supplier relationships, and identifying new opportunities for establishing and operating markets. The intermediation model of thefirmdraws on important insights from the principal economic models of the firm: neoclassical, industrial organization, contractual or transaction cost, and organizational incentive. Intermediation models combine many of the significant elements of these models in a consistent manner. Following the fundamental neoclassical framework, firms acting as intermediaries coordinate input purchasing, production and supply decisions, recognizing the connections between prices in input and output markets. As in industrial-organization models, intermediaries act as competing price setters. Following transaction-cost models, firms acting as intermediaries earn returns from reduction of transaction costs, thus lowering the costs of using markets for their customers and suppliers by carrying out market-making activities. Based on organizational-incentive models, firms acting as intermediaries reduce contracting costs by carrying out delegated bargaining and monitoring activities.

1.4

Intermediation in the U.S. economy

Intermediaries, or market-making firms, make a significant contribution to the U.S. economy. The exact amount is difficult to assess, since it requires estimating the contribution of market-making activities to value added in sectors such as manufacturing, agriculture, mining, construction, transportation, or public utilities. But as a rough estimate of shares of the gross domestic product (GDP), one might begin with the idea that intermediation includes retail trade (8.7%), wholesale trade (6.8%), finance and insurance (7.4%), and some business services and other services (2.1%). On this conservative estimate, assuming that marketmaking activities in all other sectors are zero, intermediation activities would still account for approximately one-quarter of the GDP.7 Table 1.2 offers some broad measures of these intermediation-oriented industries. But it may also be useful to specify more closely what these two million firms do and what intermediation activities they carry out. Retailers include supermarkets, discount stores, department stores, general merchandise stores, specialty apparel stores, warehouse clubs, drugstores, convenience stores, and variety stores. Some sell durable goods, some sell nondurables, and some sell both. The retail sector performs a wide variety of intermediation functions, including pricing, 7

An industry's general product by origin or value added equals its gross output (sales or receipts and other operating income plus inventory change) minus its intermediate inputs (consumption of goods and services purchased from other industries or imported); see Yuskavage (1994).

22

Market microstructure and the intermediation theory of the firm

Table 1.2. Intermediation in the U.S. economy Share of GDP Number Value added to GDP 1996* (current U.S. dollars, U.S. billions) (%) of firms** Retail trade Wholesale trade Finance, insurance0 Selected services'* Total

667.9 516.8 562.3 159.5 1,906.5

8.7 6.8 7.4 2.1 25

1,066,358 386,609 404,243 142,095 1,999,305

a

Source: Survey of Current Business, November, 1997, table 3, p. 23. Source: 1992 Census (Retail Trade; Wholesale Trade; Finance, Insurance and Real Estate Industries, Services). The number of firms for finance, insurance includes real estate agents and developers. c Excludes nonfarm housing service and other real estate. d Includes approximately 1/2 of business services (or 1/10 of total services). b

marketing, inventory holding, selection of suppliers, setting bid prices offered to suppliers, quality certification, and management of transactions. Retailers have enhanced their market making activities through EDI and Internet communication with their suppliers, which lowers costs and increases speed in exchanging data on sales, inventory, and marketing as well as expediting billing and invoicing. Retailers are generating improved data through bar coding of merchandise, point-of-sale scanners, and computerized inventory tracking and reordering. This increases information about sales and allows a rapid response to changing market conditions. Wholesalers act as intermediaries for transactions between businesses. Like retailers, they distribute goods, manage inventories, communicate price and product information, certify quality, and provide credit. Wholesalers market to retailers, search for suppliers, and handle interbusiness transactions. In addition, wholesalers increasingly provide value-added services such as packaging, labeling, bar coding, EDI, product lot tracking, inventory controls, and faster delivery.8 Approximately 90% of firms in the wholesale sector, holding 60% of the market, are merchant wholesalers (U.S. Industrial Outlook 1994, p. 38-1).9 Their business is split approximately 50-50 between durable and nondurable goods. The other 40% of the wholesale sector is split 8 9

See the Commerce Department's U.S. Industrial Outlook 1994. While many people can name retailers, the largest wholesalers are less well known. The ten largest wholesalers in 1994 were Supervalu, Fleming, McKesson, Sysco, Alco Standard, Bergen Brunswig, Cardinal Health, Foxmeyer Health, Merisel, and Genuine Parts (Fortune, May 15, 1995).

Market microstructure and intermediation

23

among a number of other intermediation arrangements. The most important of these alternative distribution arrangements include direct manufacturer-retailer transactions (retail chain stores, warehouse clubs, discount stores, and home center stores), mail order, catalog sales, manufacturer-industrial-user transactions, and retail sales to industrial users.10 Wholesalers also include manufacturer's sales branches, and agents, brokers, and commission merchants. Measuring the wholesale trade industry can be difficult. Retail sales to industry are no longer included in the Census Bureau's sales totals for wholesale establishments.11 However, manufacturer's sales branches, and agents, brokers, and commission merchants continue to be included in the GDP figures. It quotes an industry survey for 1992 in which total wholesale was divided as follows: 46% through merchant wholesalers, 7% through agents, brokers, and commission merchants; 24% through alternative channels, and 23% through manufacturer's sales branches. Clearly some of the wholesaler's traditional activities are being carried out by retailers and are reflected in value added of the retail trade. Also, some of the strategic alliances between retailers and manufacturers appear to reflect increased wholesaling responsibilities for manufacturers, which show as a contribution to manufacturing value added. Financial intermediaries perform a wide array of services, including pricing of some financial assets, providing liquidity, risk allocation, allocation of financial assets over time, combining assets to reduce the transaction costs of diversification, supplying information, and managing transactions. Depository institutions intermediate between borrowers and lenders, setting rates of interest for loans and deposits, screening borrowers for credit worthiness, and monitoring their repayment performance. Securities and commodity brokers provide a range of intermediation services, managing complex financial transactions, carrying out trades on the organized exchanges, and supplying investors with information. Insurance companies manage transactions, allocate risk, and intermediate between investors and buyers of insurance contracts. Finally, many business services can be classified as intermediation, including advertising, credit agencies, direct-mail advertising services, personnel supply services, and computer rental and leasing.12 The gross 10 11 12

See U.S. Industrial Outlook (1994, p. 38-2). Ibid. Services make up $1,264 trillion in value added or 19.93 percent of the GDP in 1993. It is difficult to determine the extent to which services represent intermediation activities. For example, because of data limitations, I chose to exclude accounting services, even though some of these services are directed to information gathering by firms for provision of information to the financial markets. I also excluded legal services, even though there are some legal aspects to intermediation, particularly in forming contracts with customers and suppliers.

24

Market microstructure and the intermediation theory of the firm

sales in these particular areas amount to approximately half of business services. This is the basis for the above estimate that intermediation activities contribute approximately half of the value added of business services, or approximately 2.1% of the GDP. Some activities in the retail and wholesale sector may be closer to production than to intermediation. Conversely, intermediation activities are present that can be difficult to discern in aggregate data on the manufacturing, agriculture, mining, construction, transportation, or public utilities sectors. Manufacturers do expend a substantial effort on marketing and sales, purchasing, personnel recruitment, financing, and technology procurement, and surely such activities account for some share of the value added by the manufacturing sector. However, the aggregate manufacturing data are focused on units of output, employees, total costs, inventories, and receipts, and do not separate out the value added by the retail, wholesale, marketing, and sales activities carried out internally by manufacturers. Many of the companies in manufacturing, mining, construction, transportation, and public utilities sectors are vertically integrated. These companies carry out many intermediation functions that are difficult to identify from company data, including pricing, marketing, inventory management, and ordering from suppliers. This shortcoming in the manufacturing data reflects the traditional economic perspective that the firm is a manufacturer and that market-allocation decisions are handled by an exogenous price system. In addition, manufacturers have significant finance and personnel requirements. They devote effort to raising capital on financial markets, communicating with investors and issuing debt and equity. Manufacturers also invest in hiring personnel, learning about the labor market, and managing the employment relationship. Such labor market activities are explicitly recognized contributions to the GDP as part of business services when they are outsourced to temporary-help firms. Similar considerations apply to companies in the mining, construction, transportation, and public utilities sectors. For example, Exxon, which is one of the largest industrial corporations, with well over $100 billion (U.S. billion, 109, here and throughout) in sales, not only carries out mining and refining, but makes a complex set of decisions about purchases, supplies, inventories, and pricing. In construction, a company such as Fluor acts as a general contractor, coordinating a segment of the market for a variety of construction services. Large transportation companies, such as the United Parcel Service, manage a vast transportation market, intermediating between customers mailing packages and transportation suppliers. The trucking company J.B. Hunt Transport,

Market microstructure and intermediation

25

performs intermediation services by coordinating transfers of shipments with rail and shipping companies. Large utilities, such as Commonwealth Edison, operate large-scale wholesale and retail power markets, contracting with suppliers of fuel and residential, commercial, and industrial customers. Thus companies combine manufacturing with merchant activities, operating markets for goods and services and factors of production. Carrying out such transactions is costly, and these costs would not be incurred in the absence of corresponding benefits. With the aggregate data and case-by-case examples such as those given here, it is possible to gather a rather rough idea of the contribution of intermediation activities to value added in these other sectors. One indicator of market-related activities is that one third of the nation's 18 million manufacturing employees are not classified as production workers. These include sales, delivery, advertising, credit, installation and servicing, clerical, executive, purchasing, financing, legal, personnel, factory supervisors (above line-supervisor level), and professional and technical employees.13 Some of these nonproduction employees are engaged in intermediation activities like sales, purchasing, or advertising; others are not. It is not evident how to relate this information to value added by manufacturing, although it is known that the total manufacturing payroll (of $529 billion) is split almost evenly between the wages of nonproduction employees ($263 billion) and the wages of production workers ($266 billion). A second clue is that the proportion of nonproduction employees varies considerably across and within industry groups. While the overall number of nonproduction workers in food and kindred products is 27%, it is very high in those categories of food that have considerable marketing activities. For example, the proportion of employees in nonproduction activities is 62% in bottled and canned soft drinks, 43% in flavoring extracts and syrups, 35% in wet corn milling, and 32% in potato chips and similar snacks. Printing and publishing has 47% of its employees in nonproduction, reflecting marketing, management, and editorial activities. Primary product industries that might be expected to engage in relatively less marketing and purchasing have a lower share of employees not in production: for example, only 16% of employees in lumber and wood products are not production workers. 13

The Census Bureau does not collect data on the relative numbers of these nonproduction employees. This also includes employees engaged in on-site construction. See Bureau of the Census, 1991 Annual Survey of Manufactures, Statistics for Industry Groups and Industries.

26

Market microstructure and the intermediation theory of the firm

Overall, manufacturing, mining, construction, transportation, and public utilities contribute approximately 31.4% of the GDP. I believe that a conservative estimate of intermediation activities in these sectors would be a tenth of their value added. Adding this figure to the explicit intermediation activities already described implies that intermediation contributes approximately 28% of the GDP. The activities of retail, wholesale, and financial intermediaries account for a host of significant economic developments, including the rise of discount superstores (Walmart, K-Mart, Target), the emergence of category killers (Toys-R-Us, Home Depot, Circuit City), upheavals and consolidation in banking, and the growth of discount brokerage. In addition, new forms of intermediation are flourishing, including mail order and electronic commerce on the Internet. Manufacturers are increasingly outsourcing functions, creating supplier and distributor networks and virtual corporations. The preceding discussion makes clear the significance of intermediation in the U.S. economy while showing the diversity of intermediation activities.

1.5

Conclusion

Intermediaries, by selecting prices, making purchase and sales decisions, managing inventories, supplying information, and coordinating transactions, provide the underlying microstructure of most markets. Intermediation provides an explanation for how the market attains an equilibrium, and how the market adjusts to changes in demand and supply. The analysis of market microstructure also has potential implications for macroeconomics. Rigidities in price-setting and inventory-adjustment decisions play a critical role in business cycles. In this book, I present models of pricing and resource allocation that highlight the economic role of firms as intermediaries. These models emphasize the endogenous determination of institutions of exchange and market-equilibrium mechanisms.

Price setting and intermediation by firms

Firms establish and operate markets by carrying out transactions and performing all the functions traditionally ascribed to market mechanisms. As intermediaries, firms engage in market making by setting prices, allocating goods and services, and holding inventories to coordinate transactions. Intermediation provides an endogenous mechanism for price setting that coordinates the activities of buyers and sellers. Firms choose two sets of prices: ask prices for consumers and bid prices for suppliers. The bid-ask spread, familiar from financial markets, provides an alternative perspective on the economic profit of firms. Economic profit reflects the returns to the market-making activities of firms. The model of price setting by firms addresses the central question of microeconomics: how are market-equilibrium prices determined? Firms maximize profits by choosing prices such that their purchases and sales balance and such that their marginal revenues and marginal factor costs are equalized. I consider the case of monopolistic intermediaries in this chapter. I turn to oligopoly in Chapter 3 and monopolistic competition in Chapter 4. The qualitative results obtained for the monopoly case hold in a more general competitive framework. The model of the market-making firm applies generally to most supply and demand problems. I consider two important and familiar settings: allocation under uncertainty and allocation over time. First I set out the basic insurance model with a bid-ask spread in insurance premiums. The insurance firm intermediates between a customer who is purchasing insurance and an investor. Then I consider a simple financial intermediation model in which afirmsets a bid-ask spread in interest rates offered to a borrower and a lender. Firms adjust ask and bid prices to clear markets, responding to demand and supply shocks while providing price signals to consumers and suppliers. Thefirmsbalance supply and demand by resetting prices to ration customers and stimulate suppliers. Menu costs of adjusting prices can lead to imbalances in customer demands and supplier offers. A firm that sets both input and output prices can act differently from a monopolist 27

28

Market microstructure and the intermediation theory of the firm

that is simply adjusting its output price in response to demand shifts. When the firm has adjustment costs for both input and output prices, there can be increased price stickiness. For example, even if there are no costs to adjusting output prices, an adjustment cost for input prices can create output-price stickiness. In addition to changing its prices, thefirmhas several alternative ways to respond to a supply and demand imbalance. It can hold inventories to smooth the pattern of purchases and sales, providing immediacy or liquidity to the market. Alternatively, thefirmcan quantity ration customers or suppliers to bring its purchases and sales into balance. Through these activities, firms allocate goods and services, coordinate the trades of their customers and suppliers, and reduce the risk of supply and demand fluctuations. In this manner, the pricing and related activities of firms serve to clear markets. The chapter is organized as follows. I begin by examining the pricesetting activities of intermediaries in Section 2.1. Then, in Section 2.2, I apply the basic framework to pricing under uncertainty and pricing over time. In Section 2.3,1 turn to the adjustment of prices and consider the effects of demand and supply elasticities and costs of price adjustment. Finally, in Section 2.4, I study the intermediary's pricing decisions over time when the firm holds inventories or rations customers and suppliers.

2.1

Price setting by intermediaries

Price setting is the most important market-making activity carried out by firms. Firms establish both the ask prices for their outputs and the bid prices for their inputs. Firms post prices for their outputs whether they are manufacturers, financial firms, service providers, wholesalers, or retailers. On the input side, firms may post bid prices for labor services or purchase from suppliers. Firms are price takers for inputs in some markets such as financial and commodity markets. In other cases, firms negotiate prices with their suppliers or take supplier offers as given. An economic theory of the firm must incorporate price setting by firms. Price setting in neoclassical economics Price setting in the Walrasian general equilibrium model does not correspond to any existing market. As is taught in most microeconomics courses, the Walrasian market price pw equates upward-sloping

Price setting and intermediation by

firms

29

supply X = S(p) with a downward-sloping demand Q = D(p):

Q* = D(pw) = S(pw). There are several stories that accompany the description of market equilibrium. One story is that the Walrasian price is simply a solution to the supply and demand equations, not meant to describe price adjustment but merely to verify that the model is internally consistent. In this view, the price, just a fixed point of p = P(S(p)), where P(Q) = D~l(Q), is inverse demand. Another story is that the price is set by a Walrasian auctioneer who sends out price signals p, receives notional demand and supply responses D(p) and S(p) from consumers and firms, and then adjusts prices upward or downward depending on whether D(p) is greater or less than S(p). Clearly the auctioneer is not explicit in the model, nor does the auctioneer correspond to economic institutions in most markets. Finally, the equilibrium price is said to be adjusted by firms if they anticipate a shortage or excess in inventories. Firms correctly anticipate the market price pw. Since they have no market power, firms will make no sales if they price above pw. They maximize profit by selling at pw and producing at an output that equates their marginal cost to the market price. However, such price setting by firms is not formally incorporated in the Walrasian model. In contrast, industrial-organization models of the firm emphasize price setting by firms. Firms set prices in Bertrand competition models and monopsony models, and price setting by firms is an important feature in an array of competition models, including those of Edgeworth (1925), Hotelling (1929), Chamberlin (1933), and Friedman (1971, 1977). Cournot models of output setting by firms implicitly assume that market-clearing prices are established as in the Walrasian model, although the Cournot model can be viewed as representing competition between firms that initially choose capacity levels and then compete on price. Firms in industrial-organization models generally are represented by a neoclassical cost function and a set of feasible strategies. Industrialorganization models generally assume that firms take input prices as given to focus on output pricing. While it may be expected that competitive bidding for inputs will yield qualitatively similar results as outputprice competition, jointly setting output and input prices may bring new insights into the role of firms. In particular, just as firms with market power do not act according to competitive supply functions, so firms with monopsony power do not have a demand function. Firms that set

30

Market microstructure and the intermediation theory of the firm

both output and input prices take into account the elasticity of the output demand and input supply that they face. The basic intermediation model Firms set prices to clear the market, bringing together their input purchases and output sales, whether the firm is a merchant or a manufacturer. Thus the firm's input and output prices generally are not set independently but instead reflect the cost of excess inventories or of unsatisfied demand due to insufficient inventories. To address the main issues, consider a basic model of monopoly intermediation, which combines a monopoly that is setting output prices with a monopsony that is setting input prices. The monopoly intermediary chooses a profitmaximizing bid-ask spread. The firm's ask price is p and the bid price is w. Suppose that the supply and demand functions are twice differentiable. The elasticities of demand and supply are positive: r](p) = —pD\p)/D{p) and t-(w) =

wS'(w)/S(w).

Recall that P(q) is the firm's inverse demand function and assume that the firm's revenue function is concave in output:

P"(Q)Q + 2P\Q)<0. Let W(X) = S~l(X) be the inverse supply function and assume that the firm's factor cost function is convex in the input:

W"(X)X + 2W\X) > 0. I consider first the case in which the firm is a merchant, that is, the firm resells the goods that it purchases. For simplicity, assume that the firm incurs no transaction costs and does not transform the good through productive activities. I assume that the firm is constrained to set prices such that it sells no more than it buys: (1)

D(p) < S(w).

This assumes that the firm can purchase to stock and can freely dispose of its excess inventory.1 The firm's profit function is (2)

n(/7, w) = pD(p) - wS(w).

The firm chooses the ask price p and the bid price w to maximize profit 1

An alternative assumption would let the firm purchase to order and constrain the firm to purchase no more than its demand: D(p) > S(w). Another approach should allow the firm to be rationed by the short side of the market with sales equaling the minimum of demand and supply: min{D(p), S(w)}.

Price setting and intermediation by firms

31

subject to the supply-side constraint (1), D(p) < S(w). It can be shown that the firm will always choose ask and bid prices such that the supply constraint is strictly binding. Therefore, at the profit maximum, the firm chooses ask and bid prices (/?*, w*) that clear the market. The first-order conditions for the firm's profit-maximization problem imply the fundamental equation (3) and market-clearing condition (4): (3)

p*-w*

= p*/ri(p*) + w*/Kw*)9

(4)

2* = D(P*) = S(w%

where Q* is the amount traded. The profit-maximizing prices are set such that the bid-ask spread p* — w* is both positive and finite. The finiteness of the spread is significant since it shows that a monopolist earns arbitrage profits but does not increase the spread without bound. The positive spread is important since the intermediary's market-clearing prices depart from the Walrasian law of one price. The monopoly intermediary's arbitrage profits can be written as (5)

n ( / A w*) = <j>* - w*)Q\

that is, profits equal the bid-ask spread times sales. The monopoly intermediary's ask price and bid price are respectively above and below the Walrasian price: (6)

p* > pw > w*.

The monopoly intermediary's output is below the Walrasian input: (7)

0* < Qw.

The intermediary's optimal bid and ask prices are shown in Figure 2.1. The basic analysis can be extended easily to incorporate such exogenous effects as an excise tax. The intermediation diagram makes clear that thefirmhandling the tax does not fully pass it on to its customers nor does it fully reflect the tax in a price reduction to its suppliers. Instead, the ask price rises and the bid price falls as the firm adjusts to the tax, leading the equilibrium quantity that is sold to customers and bought from suppliers to decline as well. Moreover, the change in the spread does not fully reflect the amount of the tax as a consequence of both the elasticity of demand and the elasticity of supply. Garman (1976), who defined the concept of market microstructure, introduces a monopolist intermediary to represent centralized price setting in a dealership market for securities.2 Buy and sell orders arrive randomly 2

On the determinants of the bid-ask spread, see also West and Tinic (1971), Tinic (1972), Benston andHagerman(1974),Logue(1975),Stoll (1978a, 1978b), Ho and Stoll (1980,1981), and Cohen etal. (1981).

32

Market microstructure and the intermediation theory of the firm

p,w

S(w)

p*

/

Pw

D(p)

! Q*

Qw

Q

Figure 2.1. The basic intermediation model.

with stationary Poisson arrival rates of q and x. The order arrival rates can be interpreted as stationary demand and supply functions that depend on the ask and the bid prices q = D(p) and x = S(w). The monopolist maximizes expected profit per unit of time subject to the restriction that the stock inventory does not drift upward or downward, D(p) = S(w). Garman considers the case in which the intermediary has infinite inventories of both cash and stock. Otherwise, since profits and inventories of the good follow random walks, the intermediary with finite inventories will almost certainly go bankrupt by standard gambler's ruin arguments. Garman (1976) shows that the bid-ask spread chosen by the monopolist follows the solution of the static problem, as shown in Figure 2.1. Price setting by a manufacturer Suppose that the firm is a manufacturer rather than a merchant and transforms an input X into output Q by using the concave technology Q = H(X). The firm maximizes profit as given in Eq. (2) subject to the production constraint D(p) = H(S(w)). The firm's bid and ask prices solve (8)

p*Hf(S(w*)) -w* =

w*/t;(w%

Price setting and intermediation by

firms

33

Therefore, as a consequence of the firm's setting input and output prices, the marginal revenue product of the input exceeds the input price: p*H'(S(w*)) > w*. The firm's profit can be written as the sum of two components. Add and subtract the marginal revenue product of the input pH'(S(w)) to obtain (9)

n(/?*, w*) = [p*Hf(S(w*)) - w*]S(w*) +p*[H(S(w))/S(w*)

-

H'(S(w*))]S(w*).

The first bracketed term represents the firm's return due to the difference between the marginal revenue product of the input and the price of the input. This term is positive by the firm's optimization problem. The second bracketed term is the difference between the average and the marginal products of the input, which is positive given the concavity of the production function. Production technology is readily incorporated into the basic diagram by replacing the input supply function with the intermediary's average factor cost function. The monopsony cost function does not depend parametrically on prices because they are set by the intermediary. The cost function is defined by minimizing factor payments subject to the production constraint at each output level. The firm sets input prices to minimize factor costs. Let H be the firm's production function. Then the factor cost function is derived in the following manner: (10)

C(Q) = subject to Q = H(XU X2, •.., Xm) and Xt = S(wt), i = 1,2, . . . , r a .

Let c(Q) = C(Q)/Q represent the average factor cost. Then the firm chooses the profit-maximizing spread between the ask price and average factor cost, p — c. With one input, the average factor cost function is simply where u;* = W(Q*) = S~l(Q*) is the inverse of the supply function, Q* = D(p*) = H(S(w*)). Profit equals the markup over average factor

cost: [p*-c(Q*)]Q*.

The choice of the average factor cost determines the output produced by the firm since it specifies the prices paid to suppliers for inputs, which in turn determine the output through the production function. The graphical representation resembles the supply and demand diagram in

34

Market microstructure and the intermediation theory of the firm

Figure 2.1, with S(w) replaced with c(Q) and w* replaced with c(Q*). This analysis helps to illustrate why businesses often speak of pricing based on setting markups over unit cost.

2.2

Allocation under uncertainty and over time

In this section, I apply the basic intermediation pricing model to allocation under uncertainty and over time. To illustrate how firms allocate risk, I consider a simple example of an insurance firm that acts as an intermediary between two consumers, setting a bid-ask spread in insurance premiums. To show how firms allocate financial assets over time, I consider the case of a firm that intermediates between a borrower and a lender, setting a bid-ask spread in interest rates. Insurance pricing by an intermediary Consider an insurance company that insures one consumer and receives funding from another consumer. The consumer that purchases insurance from the firm faces a risk of loss. The other consumer, who does not face a risk of loss, acts as an investor, essentially by selling insurance to the firm. Each consumer has wealth co and utility function u(co) that is twice differentiable, increasing, and concave. The consumer's Arrow-Pratt index of absolute risk aversion, pA{co) = —uf/(a))/uf(co), does not increase in wealth. The consumer that purchases insurance is subject to a loss of L with probability /?. The consumer purchases coverage that is equal to y < L and pays a premium of py. The consumer's demand for coverage, y = y{p), is chosen to maximize (11)

V(y, p) = Pu(co -L + y-py)

+ {\- P)u(co - py).

The consumer's demand for insurance solves (12)

/3uf(a) -L + y- py)(l - p) - (1 - P)u'{co - py)p = 0.

The consumer that invests in thefirmsupplies coverage equal to x < co in the event of a loss and receives a premium of wx. The consumer's supply of coverage to the firm, x = x(w), is chosen to maximize (13)

U{x, w) = Pu(co -x + wx) + (l-

P)u(co + w x ) .

The consumer's supply of insurance solves (14)

-Pu\(o -x + wx){\ - w) + (1 - P)u\(o + wx)w = 0.

The consumer's supply function x(w) is upward sloping.

Price setting and intermediation by

firms

35

The insurance firm chooses prices p and w to maximize profit:

(15)

n(/?, w) = py(p) — wx(w) + 0(x(w) — y(p)),

subject to the coverage constraint y(p) < x(w).3 The insurance intermediary sets prices that clear the market, so that the coverage supplied to the firm exactly equals the coverage demanded: x(w*) = y(p*) = y*. Let (/?*, w*) be the optimal ask and bid prices for the insurance firm. The equilibrium of the insurance model has a number of interesting properties. The payment to the investor per unit of coverage is greater than the expected coverage supplied and less than the coverage:

0x < w*x < x. The insurance contract is not actuarily fair: p*y > PyThe consumer does not purchase full coverage y(p*) < L. The insurance intermediary chooses an ask price of insurance p* that is strictly greater than the bid price w*. From the consumer's first-order conditions, the marginal rate of substitution for the consumer purchasing insurance and for the consumer supplying insurance will not be equal: -L + y- p*y) _ 1 - 0 p* 1-0 w* u'((o — p*y) 0 1 — p* 0 1 — w* u'(co — x + w*x) u'(co + w*x) The insurance firm earns positive profit equal to the price spread times the level of coverage: U'(G>

n(/A w*) = (p* - w*)y*. In this example, the insurance firm bears no risk. All risk is shared between the consumer and the investor, with the insurance firm playing an intermediary role. The reason for this is that the insurancefirmwill not obtain coverage from the investor in excess of the demand for insurance coverage. Otherwise the marginal cost of increased investment would exceed the marginal revenue from additional sales, thus lowering the firm's profit. 3

The first-order conditions for the firm's profit-maximization problem are as follows:

y(p) + {p-P-

X)y'{p) = 0,

-x{w) + (-w + fi + k)x'(w) = 0, k(x(w) - y{p)) = 0,

A. > 0.

Then, k > 0 since w > fi, x'(w) > 0, and k = w — fi+ x{w)/x'{w).

36

Market microstructure and the intermediation theory of the firm

Pricing loans by an intermediary To illustrate how markets allocate resources over time, consider a firm that intermediates between a borrower and a lender. The borrower and the lender are assumed to have different rates of time preference. Similar results would be obtained if the borrower and the lender have different income patterns over time. Suppose for simplicity that there are only two time periods. Suppose further that the two consumers have additively separable utility functions, (16)

U(c,C) = u(c) + pju(C),

where c is first-period consumption, C is second-period consumption, and & is the discount factor applied to future benefits by consumer j , j = Z), S. Let fiD represent the discount factor of the consumer who demands a loan, and let /3s represent the discount factor of the consumer who supplies savings, where fiD must be less than /3s because of the greater impatience of the borrower compared with that of the lender. Suppose that each consumer earns income equal to 1 in each period. Let s represent the amount of saving, and let b represent the amount of borrowing. Then, if r is the interest rate on savings, the consumer who saves has a budget constraint in the first period given by (17)

c=l-s,

and a budget constraint in the second period of (18)

C= !+

(!+r)s.

Using budget constraints (17) and (18), it follows that the consumer who saves thus chooses s to maximize (19)

Us = w(l - s) + Psu(l + (1 + r)s),

which yields a supply of savings s = S(r) that solves

The borrowing consumer has a budget constraint in the first period given by (21)

c=l+b.

If i is the cost of borrowing, the borrowing consumer's second-period budget constraint is (22)

C = 1 - (1 + i)b.

Price setting and intermediation by firms

1

37

1 + 1/(1 + i)

Figure 2.2. Borrowing and lending with an intermediary.

Given budget constraints (21) and (22), the consumer chooses b to maximize

(23)

UD = u{\ + b) + pDu{\ - (1 + i)b).

The demand for credit b = D(i) solves (24)

The case of saving is shown in Figure 2.2. The budget line is kinked since the firm's ask price of loans i is greater than its bid price for savings r. Suppose that the intermediary discounts future profit with a factor S. The firm's profit then is a function of the ask price for loans and the bid price for savings: (25)

(i, r) = S(r)

-

r)].

The firm chooses prices i and r to maximize profit n(i, r) subject to two restrictions. First, the amount of credit cannot exceed the supply of savings:

(26)

Sir) > D(i).

38

Market microstructure and the intermediation theory of the firm

Second, the repayment to the lender cannot exceed the repayment by the borrower: (27) Assign shadow prices X and y on the first-period and the second-period inequality constraints and maximize profit subject to the two inequality constraints.4 Combining the first-order conditions for interest rates i and r and canceling terms show that the optimal interest rate spread chosen by the firm again satisfies the fundamental equation,

Suppose that the firm earns positive profit in each period, so that constraints (26) and (27) are not binding. Then the firm's bid and ask prices must be chosen such that the market discount factors are bounded by the discount factor of the consumer that borrows from the firm and the discount factor of the consumer that lends to the firm:

PD < —^— < 8 < < /3s. P (1+/*) (1+r*) P The inequalities 1/(1 + i*) < 8 < 1/(1 + r*) follow from the first-order conditions for i and r.5 The inequalities f)D < 1/(1 + i*) and 1/(1 + r*) < fis follow from the optimization problems of the saving and the borrowing consumers since utility is concave.6 It must be the case that the firm's discount factor lies between the borrowing and the saving consumers' discount factors, fiD < 8 < /3s. Consider what happens if the intermediary's discount factor lies outside of this range. If the intermediary's discount factor is large, 8 > fis, the firm will set interest rates so that it earns income in only the second period.7 The firm will set interest rates such that first-period profit is zero, S(r) = £>(/), so that, from the definition of profit,

n(i\ r) = 8{i - r)S(r). If the intermediary's discount factor is small, 8 < fiD, the firm will set 4

The first-order conditions for the intermediary's maximization problem are as follows: - 1 + 8(\ + i) - A. + y(l + i) = -(8 + 1 - 8(1 + r) + A. - y(l + r) = (8 +

5 6

7

y)D(i)/D'{i),

y)S(r)/S'(r),

A. > 0,

k[S(r) - D(i)] = 0,

Y > 0,

y[D(i)(l + i) - S(r)(l + r)] = 0.

Set A, and y equal to zero in the first-order conditions; see footnote 4. Note that for the saving consumer c=\— s < C = l + ( l + r)s, so fiD < 1/(1 + i *) follows from Eq. (20). Note that for the borrowing consumer c = 1 + b > C = 1 - (1+ i)b, so 1/(1 + r*) < 0s follows from Eq. (24). This follows from pD < l/(l+/*)and l / ( l + r * ) < Ps and thefirst-orderconditions in footnote 4.

Price setting and intermediation by

firms

39

interest rates such that it earns income in only the first period. Since second-period profit is zero, the definition of profit implies that

n(i\ r) = S(r) - D(i) = iD(i) - rS(r). At the intermediated outcome, consumer marginal rates of substitution are not equal. For example, when the intermediary earns positive profit in both periods, K'(1

(29)

+ b)

• = (1 + 0 > 1/5;

u'(l-s) Moreover, b = D(i*) > s = S(r*). Compare the monopoly outcome with the Walrasian outcome, which is depicted in Figure 2.3 at point c 1 , C 1 . The contract curve is represented in an Edgeworth box with two units on each axis representing the total income in each period. With consumer two saving and consumer one borrowing, a Walrasian equilibrium rate of interest r equates marginal rates of substitution:

u\\+b) P u\\ - (1 + r)b) l

r

u\\-s) fiV(l + (1 + r)s)'

Moreover, the amount borrowed equals the amount saved. Consumer 2

Consumer 1

1

c1

2

Figure 2.3. The contract curve with exchange between a borrower and a lender.

40

Market microstructure and the intermediation theory of the firm

The preceding applications of the basic intermediation pricing model show its generality and applicability to the study of market allocation in diverse settings. I have considered production models, allocation under uncertainty and allocation overtime. The intermediation model is fundamentally different from the traditional framework because it places the firm at the center of the action, providing an explicit mechanism for price adjustment. The intermediated equilibrium is a market-clearing equilibrium since demand at the equilibrium ask price equals supply at the equilibrium bid price. In Section 2.3,1 consider the question of how intermediaries adjust prices to changes in supply and demand so as to clear the market.

2.3

Price adjustment by intermediaries

How does thefirmrespond to demand shifts? In the traditional monopoly model, a price-setting firm with a rapidly increasing marginal cost curve will respond with smaller output adjustments and greater price adjustments relative to a firm whose marginal cost curve rises more slowly.8 This analysis must be modified for a price-setting intermediary who can also respond to a shift in demand by changing the price offered to suppliers. This will also modify the firm's output price and quantity decisions. The basic diagram showing the firm's bid-ask spread can be used to illustrate the adjustment of prices to fundamental changes in market conditions. Suppose for example that technological change or favorable production conditions shift out the supply function faced by the intermediary; see Figure 2.4. Then, at the initial ask price, Q\ units are sold, but at the initial bid price, a larger amount equal to X units is offered by suppliers. If the firm acting as an intermediary were to purchase the offered supplies, excess inventories would accumulate. The firm is able to reduce its costs without reducing its purchases by lowering the bid price offered to suppliers. However, the bid price will not be lowered until the original equilibrium output is reestablished, since profits are also increased when the ask price is lowered to consumers. Thus the new equilibrium is reached at a lower bid and a lower ask price as well and a higher equilibrium output, 02A similar analysis can be given for a shift in market demand. If demand increases, for example, the amount demanded Q\ exceeds the amount 8

See Gordon (1981) for further discussion and a literature survey.

Price setting and intermediation by

firms

41

p,w Si(w)

Pi

S2(w)

P2

w2 D(p)

Qi

Q2

X

Q

Figure 2.4. Adjustment of bid and ask prices to an increase in supply.

that the intermediary is able to purchase at the equilibrium ask price; see Figure 2.5. The profit-maximizing firm will raise the ask price to reduce demand but not to the full amount that would reduce demand to its initial level. Instead, the firm will also raise the bid price to bring forth more supplies, resulting in a new equilibrium with higher ask and bid prices and a higher equilibrium output, Q2. The price elasticity of the firm's suppliers thus will enter into the firm's output-pricing decision. Conversely, the output-price decision will be affected by shifts in the firm's supply curve, and the elasticity of demand will affect the firm's input-pricing decisions. To illustrate these issues, consider constant elasticity demand and supply curves:

where r] is the elasticity of demand, § is the elasticity of supply, and y is the market demand shock. The firm's ex post profit-maximizing ask price p(y) and bid price w(y) solve the fundamental equation and clear

42

Market microstructure and the intermediation theory of the firm

p,w

S(w)

D2(p)

D,(p)

I

I

Qi

Qi

I Q*1

Q

Figure 2.5. Adjustment of bid and ask prices to an increase in demand.

the market:

p — w = (p/rj) + (tu/f),

P~v(l +y) = w*.

Solving these two equations gives the equilibrium prices p* and w*:

w

J

P*=

L

J

Define ep = (y/p)dp/dy and ew = (y/w)dw/dy as the respon-

siveness of the ask and the bid prices with respect to the shock y, and eq = (y/q)dq/dy as the responsiveness of output with respect to y: y

i

y

$

An increase in either demand elasticity r] or supply elasticity § reduces the responsiveness of both ask and bid prices to demand shocks. Greater demand elasticity lowers the output response while greater supply elasticity raises the output response. Thus a firm facing a relatively more elastic supply function will respond to a demand shock with smaller adjustments of both bid and ask prices and relatively greater output adjustments. This need not indicate that the prices set by a profit-maximizing

Price setting and intermediation by firms

43

intermediary are sticky as a consequence of market power. The values of ep and eq in the intermediation model are identical with those for the Walrasian equilibrium price and quantity, given the demand and supply functions in the example. Inflationary expectations and menu costs ofprice adjustment In the neoclassical economic framework, market prices adjust costlessly, accurately, and instantaneously to economic fluctuations, as the Walrasian auctioneer takes account of all relevant demand and supply information. In contrast, recognizing thatfirmsselect prices to maximize profit and to balance purchases and sales, implies that price adjustment is a costly, and of necessity, an imperfect process. The debate over whether prices are flexible or sticky has significant implications for both microeconomics and macroeconomics. In microeconomics, the phenomenon of price stickiness should not suggest market failure, but instead should be viewed as evidence that price setting is a costly activity for firms. Price stickiness holds a central place in The General Theory of John Maynard Keynes and in the New Keynesian Economics. Price and wage inflexibility poses a fundamental challenge to the neoclassical model of market equilibrium, which implicitly assumes exogenous price adjustment. There is substantial evidence on price inflexibility in many markets.9 There are a host of explanations for price stickiness including the following: (1) It is costly to adjust prices and communicate price changes to customers, (2) long-term contracts cause some prices to be adjusted with less frequency, (3) imperfect competition reduces pricing flexibility relative to Walrasian price adjustment, (4) coordination failures between competing firms reduce the frequency of price adjustment, and (5) information asymmetries affect contracts in a manner that reduces reliance on price rationing of buyers or sellers.10 All these explanations share one feature in common: Firms are responsible for price adjustment. Some aspect of the firm's choice problem, either a cost of adjusting prices or a trade-off with some other action, underlies practically all explanations for pricing inflexibility. The inflexibility of prices forces one to consider the microstructure of markets to explain the price-adjustment mechanism. According to the administered pricing hypothesis of Means (1935, 1972) and others, industry concentration increases price rigidity because 9 10

See, for example, Carlton (1986), Cecchetti (1986), Danziger (1987), Blinder (1991), and Lach and Tsiddon (1992). See Mankiw and Romer (1991).

44

Market microstructure and the intermediation theory of the firm

the market power of firms represents market failure. The emphasis on market share and industry concentration misses the mark.11 Price stickiness is not necessarily a consequence of imperfect competition. Carlton (1986) suggests that such an effect, where it exists, may be due to large firms' having multiple instruments at their disposal for alleviating transaction costs without exclusive reliance on pricing. Blinder (1991) carries out a survey of managers to evaluate the alternative explanations for price stickiness. He finds support for firms that adjust delivery lags or service quality rather than prices and keep prices constant to honor implicit contracts with customers. Managers also report that lack of coordination with competitors delays price adjustment, as does stability of input costs. He finds evidence for the existence of price adjustment costs but his observations give less weight to the effects of these costs. His survey data seem to reject inventories as pricesmoothing devices. He further finds little support for bureaucratic inertia within firms delaying price adjustments, for constancy of marginal costs holding markups constant, or for prices being held constant to serve as indicators of product quality. Price rigidity is central to the new Keynesian Economics. Mankiw and Romer (1991) define the new Keynesian economics by posing two questions: "Does the theory violate the classical dichotomy?" and "Does the theory assume that real market imperfections in the economy are crucial for understanding economic fluctuations?" According to the new Keynesian economics, sticky prices cause nominal fluctuations, such as changes in the money supply to influence output and employment. Moreover, as they note, imperfect competition, imperfect information, and relative price rigidity are keys to explaining sticky prices. Intermediation by firms poses a challenge to the neoclassical market model that is consistent with and indeed extends the new Keynesian economics. Examining market microstructure yields additional insights into the causes and the consequences of price rigidity. Theories that explain the rigidity of output prices set by firms under imperfect competition are enhanced by consideration of market-making intermediaries that choose both output and input prices. The relationship between changes in product and factor prices can be better understood by examining the decisions of firms that select or at least influence their ask and bid prices. Inflation affects the selling, purchasing, and inventory-holding decisions of the intermediary when there are costs of price adjustment. For simplicity suppose that the expected rate of inflation is constant. Then, given costs of price adjustment, the firm's real prices fall continuously 11

See also Burns (1936) and Galbraith (1952). Stigler and Kindahl (1970) presented contrary evidence that prices used in actual transactions, as opposed to posted prices, were more flexible.

Price setting and intermediation by

firms

45

until its nominal prices are adjusted upward. The fall in real prices increases the amount demanded by the firm's customers while simultaneously reducing the amount offered by the firm's suppliers. If prices cannot be continuously adjusted, the firm can either quantity ration its customers and suppliers or use inventories to adjust to the inflationary cycle. Suppose that the firm adjusts its output and input prices synchronously rather than staggering its price adjustment.12 The relationship between the firm's input and output prices over time has important macroeconomic implications. Consider the single-price-adjustment model of Sheshinski and Weiss (1977).13 In their framework, a firm faces a lump-sum real cost of price adjustment fi. The real rate of interest is r. They show that the firm follows a dynamic price-adjustment rule similar to that of inventory adjustment. Under this rule, referred to as an (s, S) pricing policy, the firm sets its nominal price such that its initial real price equals S. As a result of inflation and the fact that the firm's nominal price is held constant, the real price drifts downward continuously. When the real price hits the critical level s, the firm incurs the cost of price adjustment and adjusts the nominal price upward to the desired initial real price 5, and the cycle is repeated. Sheshinski and Weiss show that the (s, S) prices straddle the profit-maximizing price s*. The optimal solution is depicted in Figure 2.6, where Tl(p) is profit as a function of the real price p.u Initially, the firm operates with negative marginal profit and finishes the cycle with positive marginal profit. The difference in real profits at the beginning and the end of the cycle equals the real rate of interest times the real cost of price adjustment. Sheshinski and Weiss demonstrate that an increase in the rate of inflation increases the initial price and decreases the terminal price, thereby increasing the magnitude of each nominal price change. The rate of inflation generally has an ambiguous effect on the frequency of price changes. An increase in the level of price-adjustment costs leads to larger and less frequent price adjustments. An increase in the real rate of interest decreases both the initial and terminal real prices. Derivation of an optimal dynamic two-price policy is relatively complicated. For purposes of illustration, suppose that the intermediary 12

13

14

Sheshinski and Weiss (1992) present conditions under which a two-product monopolist chooses to adjust both prices simultaneously. This type of analysis could be applied to examine the decision of an intermediary as to whether to synchonize or stagger pricing changes. With many small firms and initial price dispersion, the rigidity of price adjustment at the level of individual firms may cancel out in the aggregate; see Caplin and Spulber (1987). However, the aggregate neutrality of money or demand shocks is unlikely to occur in markets with monopolistic competition between intermediaries; see Spulber (1998b). Let g be the rate of inflation. The prices s and S solve U(S) — U(s) = r/S and n'(z)zr/8 dz = 0.

46

Market microstructure and the intermediation theory of the firm

$

Figure 2.6. The optimal (s, S) pricing policy under inflation with priceadjustment costs p.

follows simultaneous 0 , S) pricing policies in both its input and output prices. The firm sets initial real prices (pi, w\) and readjusts its nominal prices when prices fall to the critical levels (po, wo) at the end of their cycle.15 Let D(p) and S(w) represent demand and supply, respectively, as functions of real prices. Let (/?*, w*) represent the profit-maximizing prices in the absence of inflation, that is, the prices satisfy the fundamental equation and clear the market: q* — D(p*) = S(w*). Assume that, as in the single-price case, prices straddle the profit-maximizing price, po wi)> the firm experiences excess supply because q\ < q* < x\\ see Figure 2.7. The firm also experiences excess demand at the end of the cycle because JCO < q* < q\\ see Figure 2.8. The firm can address this imbalance by initially rationing its suppliers toward the start of the cycle and then rationing customers toward the end of the cycle. Alternatively, the firm can accumulate inventories early in the cycle and draw them 15

See Spulber (1998b) for a discussion of simultaneous and staggered price adjustment.

Price setting and intermediation by

firms

47

p,w

Pi

P*

D(p)

qi

q*

«!

q,x

Figure 2.7. The firm has excess supply at the beginning of the cycle. p,w S(w)

P*

Po

D(p)

Xo

q*

qo

Figure 2.8. The firm has excess demand at the end of the cycle.

48

Market microstructure and the intermediation theory of the firm

down later in the cycle, balancing demand and supply over the cycle. Note that when prices are adjusted synchronously, the ratio of the nominal output price to the nominal input price remains constant. For the individual firm, price stickiness due to adjustment costs creates imbalances in its supply and demand and creates cyclical oversupply and excess demand. If rationing of customers and suppliers is feasible, the firm will choose to adjust its prices such that there is excess supply at the time of price adjustment. If the input is labor, the difference between the amount of labor services offered and the amount hired represents involuntary unemployment at the recently increased wages. This excess supply is relieved as real wages fall, until the firm is eventually supply constrained. Interestingly, actual employment by the firm may not vary much over the cycle, even though there is a significant decline in labor services offered, because the initial labor demand is dampened by the demand-side constraint. If the input is a raw material or some intermediate manufactured good, the amount purchased may also remain more stable than the underlying amount offered by suppliers at the real bid price. As inflation continues, the firm will experience supply shortages and excess demand, before readjusting both prices upward. If the firm relies less on rationing and more on inventories as a buffer, price increases will be followed by a buildup in inventories. As the firm's real prices fall, the combination of increased sales and supply reductions will draw down inventories. With inventories, the firm will experience greater fluctuations in both sales and purchases than with demand and supply rationing, although total purchases and sales over the cycle will be much greater. This suggests that less reliance on inventory holding and more reliance on rationing will lower overall output and employment. Thus just-in-time inventory holding and downsizing might be expected to coincide. Reliance on inventories rather than on rationing depends on the costs of holding inventories and the associated costs of adjusting purchases and sales versus the cost and feasibility of rationing. If employment and supply purchases are quasi-fixed and prices are costly to adjust, the firm will depend on inventory buildups and depletion over the cycle rather than on rationing customers and suppliers.

2.4

Inventories and market clearing by intermediaries

How are supply and demand brought into balance? In the traditional Walrasian framework equilibrium, prices appear that not only ration consumers and stimulate suppliers, but that also equate supply and demand. As I emphasized in Section 2.3, the prices set by firms intermediating between buyers and sellers balance purchases and sales and thus

Price setting and intermediation by

firms

49

continue to serve a market-clearing role. However, firms have a number of other market-clearing instruments in their arsenal, most notably by holding inventories and by quantity rationing buyers and sellers. The inventories held by firms serve to smooth the patterns of demand and supply fluctuations and also reduce the risks of exchange. Firms stand ready to buy and sell. Holding inventories allows the firm to make sales and purchases at different times and provides a buffer that allows the firm to better match its sales and purchase flows. Quantity rationing means that the firm controls the level of its purchases and sales directly. Thus thefirmhas policy instruments in addition to price incentives for its customers and suppliers. The firm may choose to avoid adjusting prices because of the menu costs of changing prices or a desire for stable prices based on marketing considerations or competitive concerns. Even if prices are not adjusted, the firm need not ration if it can meet demand through purchases, production, or inventory depletion. However, these output changes also are costly. Thus allocating scarce stocks among its customers provides another way to balance the firm's demand and supply. Similarly, a firm with multiple suppliers can choose to distribute its purchases among the suppliers rather than change its purchase prices or amount purchased. Through inventory holding and quantity rationing, firms perform market-clearing activities generally thought to take place outside the firm. By balancing its purchases and sales over time, the firm supplements the market-clearing function of prices. Economic analysis generally stresses that firms allocate goods and services internally, for example by allocating labor services to various tasks, by allocating capital investment across its divisions, or by allocating products across its retail outlets. While these activities are certainly an essential aspect of the allocation of scarce resources, the firm does much more in terms of allocating goods and services. What I am emphasizing is the firm's actions that bring market demand and supply into balance. Excess inventories and stockouts Intermediaries are likely to face both supply and demand shocks. This uncertainty complicates the firm's pricing problem and increases the difficulty of balancing supply and demand to clear the market. Imbalances in purchases and sales are costly for the firm. Excess inventories entail carrying costs while stockouts mean sales earnings foregone. The basic issues can be illustrated with a simple model with a single buyer and a single seller, each buying or selling a single unit. The seller's cost c is uniformly distributed on the unit interval, so that the supply function S(w) = w denotes the probability that a unit will be

50

Market microstructure and the intermediation theory of the firm

supplied at price w. The buyer's valuation v is uniformly distributed on the unit interval, so that the demand function D(p) = 1 — p denotes the probability that a unit will be supplied at price p. Suppose first that the firm's sales equal the minimum of its supply and demand:

Q =min{x,q}. So the firm's expected sales equal E Q = (1 — p)w. The firm's expected profit is thus FI = pEQ — wS(w): n = p{\ — p)w — w .

The firm sets the ask and bid prices to maximize expected profit: p* = 1/2, w* = 1/8, n* = 1/64. In this example, which corresponds to purchasing to stock, the firm trades off the risk of lost sales, if the supply is not obtained, against the risk of excess inventories, if the buyer does not make a purchase. How does the preceding purchasing-to-stock case compare with purchasing to order? With purchasing to order, thefirmmust solve for the bid price to be offered to the seller given that the consumer has already placed an order at price p. Thus, given that a unit at price p has been ordered, the firm chooses w to maximize expected earnings (p — w)w. Contingent on having received an order at price /?, the offer to the seller thus is w = p/2. The firm chooses the ask price p to maximize expected profit, which equals expected earnings times the likelihood of making a sale: FI = (p — w)w{\ — p).

Substituting for w — p/2 and solving the maximization problem yields the firm's bid and ask prices and expected profit: p* = 2/3,

w* = 1/3,

n* = 1/27.

In this simple example, purchasing to order yields a higher profit since there is no penalty from stock outs as in the purchase-to-stock case. Of course, purchasing to order usually is not feasible if the firm is to provide immediacy. The lower profit for the merchant purchasing to stock is due to the cost of providing immediacy. The efforts of firms, whether retailers, wholesalers, or manufacturers, to reduce inventories by such methods as just-in-time ordering and delivery are intended to lower the carrying cost of inventories while taking advantage of more current market demand information. In contrast to merchants, who purchase goods for resale, brokers do not purchase goods or hold inventories.16 Brokers in such markets as 16

See Hackett (1992) for a comparison of intermediation by merchants and brokers.

Price setting and intermediation by

firms

51

securities, insurance, real estate, travel, and some commodities fix a commission rate but not bid and ask prices. Suppose that the broker brings together the buyer and the seller and earns a commission equal to sp, where s < 1 is a share of the purchase price. After the buyer and the seller meet, the buyer observes the seller's cost and the seller observes the buyer's valuation. If the buyer's valuation is sufficiently greater than the seller's cost, they divide the surplus according to the Nash bargaining solution. Otherwise, no trade occurs. For trade to take place, there must be a price such that the buyer's willingness to pay is greater than or equal to the price, and the price net of the broker's commission is greater than or equal to the seller's cost: v > P,

p(\ -

s)>c.

This implies that trade takes place only if

v > c/{\ - s). Clearly, firms with costs above (1 — s) will not be able to trade. The price that satisfies the Nash bargaining solution maximizes (v — p)

- s) - c\. P =

+

2 2(1 -s)' The expected price is thus

= (1 - s)/4. The profit of the broker thus is n = (1 — s)s/4, so that the profitmaximizing commission rate is s * = 1/2 and the broker's expected profit is n* = 1/16. In this simple example, brokers earn more than merchants, whether merchants order to stock or purchase to order, because the broker shares the gains from trade without the costs of providing immediacy. The broker also benefits from the buyer and seller bargaining, which in this example reveals buyer willingness to pay and seller cost. With greater transaction costs between buyers and sellers, merchants then would have the advantage over brokers. Pricing and inventories I now examine the basic issues of inventory holding by a marketmaking firm by using a two-period model. To illustrate the effects of uncertainty on the pattern of prices and sales, let the firm's demand and supply functions be subject to random shocks y and z, respectively,

52

Market microstructure and the intermediation theory of the firm

which are uniformly distributed on the interval [0, a], with expected values a/2. Suppose that the shocks are additively separable, so that at time period t, sales and purchases are given as follows:

qt = D(pt,yt)= 1 - pt+yt, xt = S(wt,zt) = wt +zt. The firm's inventory ht is observable at the start of the period, while the inventory left at the end of the period is not known until the demand and supply shocks have been observed. The end-of-period inventory obeys the transition equation,

ht+\ =ht+xt

-qt.

I assume that thefirmcannot stock out, which requires that end-of-period inventory cannot be less than zero, ht+\ > 0. Because the stock-out constraint must hold for any realization of demand and supply shocks, it is sufficient that it hold for the highest realization of the demand shock and the lowest realization of the supply shock:

ht +

S(wt,0)-D(pt9a)>0.

Prices are chosen before current demand and supply shocks are observed. Suppose that unit inventory costs c are paid on inventory held at the start of the period, where 0 < c < 1 + a/2. Also, future earnings are discounted by a factor S = 1/(1 + r), where r is the rate of interest. To analyze the effects of inventory holding on the firm's pricing policies, it is useful to consider a two-period setting. The firm chooses prices pt, wt to maximize the present discounted value of expected profit: 2

V = E J2S'^lPtDipt, yt) - wtS(wt, zt)l subject to the inventory-transition constraint and the stock-out constraint. The firm solves its optimization problem by backward induction, beginning with the second-period maximization: V(h2) = max E[p2D(p2, y2) - w2S(w2, z2) - ch2], subject to h2 + S(w2, 0) - D(p2, a) > 0.17 17

Thefirst-ordernecessary conditions for the firm's problem are as follows: £[/>2£>i(P2, yi) + D(P2, y2)] = A2/>i0>2,«), E[w2Si(w2, zi) + S(u;2, Z2)] = ^iS\{w2, 0), X2[h2 + S(w2, 0) - D(p2, a)] = 0, X2 > 0.

Price setting and intermediation by

firms

53

If realized inventories are low, h2 < (l+a)/2, the stock-out constraint is binding, and prices solve p2 - w2 = (1 + a)/2,

h2 + W2-l + P2-aSecond-period prices are thus p\ = (3 + 3a - 2/z2)/4,

w\ = (1 + a - 2/z2)/4,

and the shadow price is X2 = (1 + 2a — 2/z2)/2. If inventories are moderate, (1 + a)/2 < /*2 < (2 + 3a)/4 then no purchases are made, w2 = 0, and the ask price is constrained by available inventories through the stock-out constraint, h2 = D(p2, a):

p2 =

l+a-h2,

and the shadow price is X2 = (2 + 3a — 4h2)/2. Finally, with large inventories, h2 > (2 + 3a)/4, the shadow price is zero, no purchases are made, and the ask price falls to the unconstrained monopoly price:

p5 = (2 + fl)/4. Consider next the firm's first-period pricing problem. For simplicity, suppose that there is no initial inventory, h\ = 0. Then the firm solves max

Pl,W\

subject to S(wu 0) - D(pua) > 0.18 Note the additive separability of the demand and the supply shocks; the equations yield the fundamental markup equation,

where rj\ — —p\ED\/ED

and §1 = w\ES\/ES. The markup equals

p * - u ; * = (l+fl)/2, which is the same as in the second period. If the stock-out constraint is binding, then w\ + p\ = 1 + a, and the firm's prices are p\ = 3(1 + 2a)/A and w\ = (1 + a)/A. These are benchmark prices for a monopolist maximizing single-period profit subject only to a stock-out constraint. If the stock-out constraint is nonbinding because of the value of holding inventories, the firm increases both the ask and the bid prices to raise expected inventories. 18

The first-order conditions for the firm's problem are as follows:

E[wiSi(wuzi) + S(wu zi)] = 8EV'(h2)Si(wuzi) + ^\Si(wu 0), A-i [S(wi, 0) - D(pi, a)] = 0,

A-i > 0.

54

Market microstructure and the intermediation theory of the firm

(l+2t)/2

(2+3a)/4

h2

Figure 2.9. The marginal value of inventory in the second period.

By the envelope theorem, the marginal value of inventories in the second period is the shadow price on the inventory constraint net of the carrying cost of inventories: V\h2) = X*(/i2) - c. Figure 2.9 illustrates the marginal value of inventory. Note that the marginal value is most responsive to changes in inventory for moderate inventory levels since the firm does not make purchases and simply sells its inventory in that range. The second-period ask price is also most responsive to changes in inventory in the moderate range for the same reason, while the bid price is responsive only with low inventories. The ask price is most responsive in the moderate range since there it is the sole instrument for building up or drawing down inventories.19 If the constraint is nonbinding, the marginal value of inventories in the second period affects first-period prices. For the case in which the firm holds inventories at the end of the first period and both buys and sells output in the second period, the expected shadow price is20 EX2 = 1/2 +a19

20

Eh2 = 3/2 + a - wx - px.

Reagan (1982) obtains a different result for a monopolist; she shows that when the firm drives its stock of inventories to zero, in periods of high demand, price becomes more responsive to demand disturbances. The difference with the model presented here is that the firm builds inventories by producing at a constant unit cost, rather than by purchasing as in the present model. A sufficient condition for inventories to be low in the second period is

Price setting and intermediation by firms

55

Therefore the first-period prices are 1 Pi = W,

=

2(1+8) 1

•0

2(1+8)

HI-

Compare the prices for the inventory-holding firm with the Walrasian equilibrium. The expected value of the Walrasian spot price that equates supply and demand, D(pw, y) = S(pw, JC), is Epw = 1/2. The expected market-clearing output is Eq w — (1 + a) 12. The prices set by the inventory-holding intermediary straddle the Walrasian price; w

w < Ep < p* fort = 1,2. In the second period, the lowest ask price is p\ = (2 + a)/A > 1/2. The highest bid price is w\ = (1 + a - 2h2)/4 < 1/2. As a result of the stock-out constraint, the expected sales and purchases are less than the expected Walrasian market-clearing output:

Eq* < Ex* < Eqw. These relationships are illustrated in Figure 2.10. p,w

ES(w,z) p

Ep w =l/2

Eqt

Ex,

Figure 2.10. The bid-ask spread with inventories.

56

Market microstructure and the intermediation theory of the firm

Quantity rationing Firms adjust prices to balance supply and demand. Inventories allow the firm to smooth out its purchasing and sales patterns. Consequently the firm will modify its pricing patterns when it can hold inventories so as to reduce the carrying costs of inventories as well as foregone revenue from stockouts. Another approach to market clearing and inventory cost reduction is quantity rationing. A growing literature on optimal quantity rationing can be applied to discern the role of firms in allocating goods and services. Rationing can be accomplished through state-contingent contracts. For example, with priority pricing, customers bid more for a higher priority, and rationing occurs if realized customer demand exceeds productive capacity.21 Carlton (1991) observes that, with random demand, there are costs to using the price system since a price that is too high will reduce sales and result in excess inventories, while a price that is too low will require rationing customers and foregoing sales. He suggests that many firms use nonprice-rationing methods, and that "firms and organized markets are competitors in production 'allocations'" (p. 257). Carlton observes that rationing the firm's customers essentially allocates products across those customers. He concludes that "one reason for a firm's existence is to facilitate trade among its customers" (p. 258). Thus consideration of rationing demonstrates how the firm is an intermediary between its customers. Suppose that the firm experiences demand shocks and that it is costly to adjust both bid and ask prices. As a result of demand uncertainty, customer demand and supplier offers will generally not be in balance. The firm can respond by building or depleting inventories or by producing or disposing of output. In addition to adjusting prices, production, and inventories, the firm can quantity ration customers or suppliers. Consider the case of excess demand; the case of excess supply is similar. Suppose that the firm has two customers and that at the firm's prices demand exceeds the firm's purchases: where x = S(w) is the firm's level of purchases. The firm must somehow distribute its stock between the two customers. Without changing the price, at least one consumer will be disappointed. Generally there would be gains from further trade between 21

Priority pricing with demand uncertainty is examined by Harris and Raviv (1981) and Spulber (1992a, 1992b, 1993a, 1993b), and with supply uncertainty by Chao and Wilson (1987), Wilson (1989a, 1989b), Viswanathan and Tse (1989), and Spulber (1992a, 1992b).

Price setting and intermediation by

firms

57

customers. Optimal rationing would require replicating the effects of a market-clearing price, p°, that solves Dl(p°) + D2(p°) = x. Simply distribute the optimal outputs to each consumer, q1 = Dl(p°) and q2 = D2(p°). The problem with this approach is that the firm is not likely to know the demand functions of its customers. I consider allocation by intermediaries under asymmetric information in Chapter 7. The firm can anticipate situations of excess demand by assigning priorities to consumers through a system of contingent contracts. Customers with a high marginal willingness to pay for the good will pay to have a higher priority. Priority pricing is considered in Chapter 7 as well. The output could be allocated randomly across the two consumers, or equivalently, on a first-come-first-served basis if the firm's customers arrive at random. This generally is not optimal since consumer marginal benefits will not be equal. Dividing the pie equally between the two customers suffers from the same problems. The firm can ration the two customers proportionally on the basis of past consumption; see Spulber (1992a, 1992b). The firm can respond to demand and supply imbalances through delivery lags (Zarnowitz 1962; Edlefsen 1981; Carlton 1983). Carlton observes that percentage fluctuations of delivery lags are usually much larger than price changes in many industries, including textile mill products, paper and allied products, steel, fabricated metals, nonelectrical machinery, and electrical machinery. Delivery lags make the qualities of the good endogenous, thus lowering demand. Then, by increasing the delivery lag 7\ the firm can clear the market in the short run, without adjusting the price: Delivery lags may also serve to increase the amount offered by suppliers since delayed production can lower costs. Thus, in the short run, the lag can be adjusted to increase supply and reduce demand: Retailers typically give discounts and rain checks for sale items that have stocked out. The firm can address customer and supplier desire for immediacy through the sale or the purchase of substitute products and services.

2.5

Conclusion

Markets clear through the intermediation activities of firms seeking to balance their purchases and sales. Pricing is the primary means of market

58

Market microstructure and the intermediation theory of the firm

clearing. This chapter presents the basic model of pricing by an intermediary. The intermediary sets a bid-ask spread to maximize profit while equating supply and demand. The intermediation pricing model provides an answer to a central question of microeconomics: How does the market attain its equilibrium? Moreover, the basic intermediation framework begins to provide an explanation for the economic purpose of firms beyond possessing technology and producing goods and services. Acting as intermediaries, firms take on tasks traditionally ascribed to an exogenous market mechanism. Instead, firms adjust prices to clear markets, rationing customers and stimulating suppliers. Market-making firms manage transactions for their customers and suppliers, allocating goods and services across customers, across states of the world, and over time. Managing transactions is an important and costly activity. There can be menu costs of adjusting prices in response to supply and demand shocks. This means that the firm's prices may not adjust perfectly to economic contractions and expansions. The macroeconomic implications of price rigidities are well understood. Price adjustment by intermediaries implies that price rigidity can increase when thefirmmust adjust multiple prices (Spulber, 1998b). For example, rigidities in input prices can contribute to the rigidity of output prices, even if the firm's output prices could be costlessly adjusted. The firm has alternative instruments for market clearing. Inventories can smooth the patterns of purchases and sales. In turn, inventory holding alters the firm's pricing strategies. The firm can further alter its supply and demand patterns by adjusting the features of its products and services, through marketing and sales efforts, delivery lags, and the provision of substitute and complementary goods and services. In Chapter 7, I examine contracting under asymmetric information as a means of market clearing.

Part II

Competition and market equilibrium

3

Competition between intermediaries

Industrial organization presents a theory of thefirmbased on two key elements that represent significant differences with the neoclassical firm: market power and competitive strategy. The firm in industrial organization exercises its market power by being a price maker rather than a price taker, selecting prices for its products and services. Moreover, the firm in industrial organization formulates a competitive strategy in anticipation of, or in reaction to, the strategic actions of rival firms. The presence of market power has several important ramifications for the theory of the firm. First, the focus of attention shifts from technology to market demand. The firm continues to act as a producer as in the neoclassical framework. Its production activities are presumed to be efficient and are represented by a cost function. In addition to its cost function, the firm is described in terms of its market demand, which reflects the willingness to pay of the firm's actual and potential customers. Therefore the industrial-organization model represents the firm by its demand and cost functions. The firm with market power is concerned primarily with how to set profit-maximizing prices. As a price setter, the firm provides the mechanism by which markets clear. The firm changes prices to reflect exogenous shifts in demand and to balance sales with production and inventories. The firm in industrial organization does not have a supply function in the neoclassical sense, although the firm may choose to offer a schedule of prices and quantities to prospective buyers. Therefore the firm in industrial organization plays a greatly expanded economic role, replacing the Walrasian auctioneer, by assessing consumer demands and setting prices to clear markets. Thefirmthus operates markets in addition to operating its productive technology. The intermediation theory of the firm draws heavily on industrialorganization models by assuming that the firm has market power in both product and factor markets. The firm has neither a supply function in the output markets nor a demand function in the input markets. 61

62

Competition and market equilibrium

The intermediaryfirmdoes not have a standard neoclassical cost function since it does not take as given some of its factor prices. The intermediary framework adds a new perspective to many traditional industrialorganization models because it examines the relationship between the firm's purchasing and sales strategies. The discussion of price setting and intermediation in Chapter 2 emphasized the firm's market power in output and input markets, without addressing competitive strategy. Yet intermediated markets often are quite competitive, as discussed in Chapter 1. This chapter examines how competition affect the results of the basic intermediation model. The qualitative results of the monopoly-monopsony case generally carry over to monopolistic competition between intermediaries. Firms offer a bidask spread and select prices by equating marginal revenue to marginal expenditure. Industrial organization recognizes that market-clearing prices are established by firms, while emphasizing the central place of pricing as a competitive strategy. The Bertrand model of price competition is the basic building block of industrial organization. Given homogeneous products, constant marginal costs, and full information, the traditional Bertrand price-competition model implies that firms price at marginal cost, earning zero profit. Stahl (1988) presents a two-period intermediation model with homogeneous products that extends the Bertrand model to competition between intermediaries in input markets, followed by price competition in output markets. The intermediation equilibrium results either in monopoly or in a competitive Walrasian equilibrium, depending on how inputs are allocated between the rival firms. The intermediation model has the appealing feature in that Edgeworth-type capacity constraints are derived endogenously as a consequence of bidding for productive inputs. The traditional Bertrand model results in a price war that eliminates monopoly rents. Various analyses of competitive price setting have extended the Bertrand model to see under what conditions the zero-profit outcome no longer holds. These extensions share a common theme: the derivation of downward-sloping residual demand functions. With downward-sloping demand, the firm retains market power, yet is nonetheless sensitive to the extent of competition. Demand is shown to be downward sloping under a variety of conditions, including differentiated products, consumer switching costs, unknown rival costs, and consumer search costs. These extensions of the Bertrand model carry over into intermediation models with Bertrand-type price competition.

Competition between intermediaries

63

Product differentiation is particularly significant as a consequence and a source of market power. Unlike the neoclassical firm, which chooses from a given menu of products on the basis of technological efficiency, thefirmin industrial-organization chooses the characteristics of its products. This has implications that range far beyond the technological aspects of product design. The firm can alter its demand by altering its products. Product differentiation in industrial organization models, beginning with Hotelling (1929), essentially serves to restore downwardsloping demand to the firm. When products of the firm and its rivals are differentiated, firms retain local monopoly power in the product space or at a geographic location. I extend the basic product-differentiation framework to competition between intermediaries by assuming that the firm's purchases are differentiated from those of its competitors. Because intermediaries have different geographic locations, suppliers may incur different transport costs in serving them. Also, intermediaries may purchase products with different specifications or they may impose different administrative requirements on transactions. Therefore, when purchases are differentiated, intermediaries will have monopsony power in input markets. Their purchases will be substitutes for suppliers. Thus, in bidding for inputs, competingfirmswill face upward-sloping supply curves rather than fixed input prices. I next consider the implications of switching costs for intermediation.l If its customers have switching costs, the firm also will face downwardsloping demand. Similarly, if the firm's suppliers have switching costs, the firm will face upward-sloping supply. I present a duopoly intermediation model in which both customers and suppliers have switching costs. I examine the effects of the distribution of switching costs on the market-equilibrium bid-ask spread and output level. As switching costs becomes small, the equilibrium approaches the Walrasian equilibrium. As switching costs become large, the equilibrium approaches the monopoly intermediation solution. The conclusions of the Bertrand model depend in a crucial way on the assumption that firms have full information about their rival's costs. In light of the significant amount of uncertainty that firms typically encounter about the efficiency and the costs of their rivals, the fullinformation assumption seems unrealistic. The possibility thatfirmscannot perfectly observe their rivals' costs is sufficient to yield positive expected profits for all firms and pricing above marginal cost. Asymmetry 1

Customer switching costs are introduced in Klemperer (1987), and Farrell and Shapiro (1988).

64

Competition and market equilibrium

of information about rivals' costs resolves the discontinuity in the effect of the pricing strategy on profit. Sincefirmshave positive expected profits at equilibrium with asymmetric information, firms have an incentive to enter the market and engage in price competition, which resolves the inconsistency in the Bertrand model. This chapter is organized as follows. I begin with Bertrand competition between intermediaries with homogeneous inputs and outputs. Then I consider a basic model of differentiated-product Bertrand competition between intermediaries. Next, I examine competition between intermediaries when both customers and suppliers must incur costs if they wish to switch intermediaries. Finally, I consider price competition between intermediaries that have private information about their own transaction costs.

3.1

Bertrand competition for inputs with homogeneous products

Stahl (1988) examines the effects of winner-take-all competition for inputs. Firms may choose prices sequentially, competing first for supplies and then for customers or competing first for sales and then for supplies. Inputs are homogeneous, as are outputs. In this section, I consider Stahl's model of purchasing to stock. The analysis of purchasing to order is similar. If two firms offer identical prices, then each firm obtains half of the available supplies at that offer price: x = S(w)/2. If the firms offer different prices, the highest-priced firm obtains all the available supplies at that price: x = S(w), and the other firm leaves the market. Because of the equal-sharing and winner-take-all assumptions and the symmetry of the model, it is sufficient to consider the outcome in which both firms offer the same price in the first stage and have the same stocks x. Next, consider the second-stage output-pricing competition with capacity constraints given by input stocks. There are three possible outcomes. If firm one has a lower price than firm two, its sales are qx = min{x, D(pi)}. If the two firms offer the same price, then firm one's sales are qx = min{x, D(Pl)/2). If firm one has a higher price than firm two, then the firm obtains some share of sales given by the residual demand function RD(p\, p2, x): qx = min{x, RD(px, pi, x)}. The residual demand function is sufficiently general to include both

Competition between intermediaries

65

uniform and random rationing (and any convex combination of the two rationing rules).2 Firm one's residual demand RD(p\, /?2, x) is jointly continuous in both prices and decreasing in p\. As the firm's price approaches that of its rival, the firm obtains the excess demand of the rival: lim RD(p\, p2, x) = max{D(/?2) — x, 0}.

PI-+P2

Finally, the residual demand of the high-priced firm is less than or equal to half of market demand at the high price:

RD(pi,p2,x)

D'1

p2>

(2JC).

In the first stage, the high-priced firm purchases all the inputs supplied: x\ = S(w\) if w\ > W2 and x\ = 0 if w\ < wi. If the two firms offer the same price, they each obtain half of the input that is supplied:

x\ = S(w\)/2 if w\ = W2.

If there is not a tie, the winning bidder earns

n*(w) = R*(S(w)) - wS(w), where R*(x) is defined as the maximum revenue that the stock-constrained firm can obtain:

R*(x) =

max{pD(p)\D(p)<x}.

Assume that pD(p) is strictly concave. Define w° as the zero-monopoly-rent bid, which is the highest price such that

n*(w°) = 0. Clearly no firm will bid higher than the zero-monopoly-rent bid, w°. Moreover, if bothfirmswere to bid w°, their profits could not be positive. Yet thefirmshave an incentive to outbid each other up to the bid price, w°. Let pR be the ask price that maximizes sales revenue, that is, Suppose that the sales-revenue-maximizing price is greater than the Walrasian price, pR > p w; see Figure 3.1. Then no (subgame-perfect) Nash 2

Uniform rationing (Levitan and Shubik 1972) is a parallel inward shift of demand: RD(pi,p2,

x) = max{D(Pl) - x, 0}.

Random rationing (Beckman 1965; Allen and Hellwig 1986) is an inward rotation of the demand curve: 2,x)

= (l-

where a = min{x/D{pi), 1}.

a)D(pi),

66

Competition and market equilibrium

p,w

q*

q

q,x

Figure 3.1. The revenue-maximizing price, pR, exceeds the Walrasian price, P W.

equilibrium exists. If pR > pw, it follows that the zero-monopoly-rent bid must exceed the Walrasian equilibrium price: w° > pw. This is because the firm could earn a positive profit by setting its bid price at pw, setting the ask price at pR, and discarding the excess capacity (qw —q R). The equilibrium fails to exist because both firms will bid the zero-monopoly-rent price w°. To make nonnegative profit in the second stage, they must both set their price at the revenue-maximizing level p R. This cannot be a Nash equilibrium, since then they have excess capacity, so that each firm has an incentive to shade its price below that of the competitor. If the revenue-maximizing price is not greater than the Walrasian price, pR
Competition between intermediaries

67

p,w S(w)

Pw PR

D(p) q

q

q,x R

Figure 3.2. The revenue-maximizing price, p , is less than or equal to the Walrasian price, pw'.

Given that the firms each bid w° in the first stage, the unique Nash equilibrium in the second stage also is the Walrasian price. In the second stage x = S(pw)/2, which is strictly less than D(p)/2 for all prices less than the Walrasian price, so that no additional sales are gained by an undercutting strategy. Moreover, by the definition of residual demand, residual revenues are decreasing for all prices above the Walrasian price, so that no additional returns are obtained by raising prices above PW. The Walrasian outcome is due to the product homogeneity assumption combined with the equal-sharing rule for assigning inputs when bid prices are equal. Suppose instead that if bids are equal, one of the two firms is chosen at random (say with probability 1/2). Then, Stahl (1988) shows that the unique equilibrium involves both firms' choosing the zero-monopoly-rent bid u;0 in the first stage, with the randomly chosen winner acting as a monopolist in the second stage. In the case in which pR > pw, the elasticity of demand at the Walrasian price is less than 1. The bid price and the ask price both exceed

68

Competition and market equilibrium

the Walrasian price,

pR>w°>

pw,

and the output sold is less than the amount purchased, which is less than the Walrasian output,

qR < x < qw. In the case in which pR 1. Then the outcome is Walrasian: p = w° = p w and q = x = q w. In either case, Bertrand competition with homogeneous products eliminates all monopoly rents.

3.2

Bertrand price competition with differentiated products and purchases

The Bertrand model of price competition leads to the dramatic conclusion that, with two or more firms, the market price always will equal marginal cost and that firms will earn zero profit. Many have interpreted this result as implying that a market with two identical firms is perfectly competitive or, if costs are similar, approximately competitive. The Bertrand model provides important insights by focusing exclusively on the firm's price-setting role. The highly simplified structure of market demand, production costs, and product characteristics provide an ideal case in which firms have no market power in equilibrium. This conclusion is troubling because in practice firms generally appear to have some power to set prices in the presence of competition. The Bertrand model of competition is subject to a fundamental discontinuity. If two firms offer the same price, they share the market in some manner. However, if one firm slightly undercuts its rival, it captures the entire market. The discontinuity observed in the Bertrand model suggests that the model fails to describe the process of competition and market allocation in some crucial way. Moreover, the behavioral assumptions are open to question. Since firms always earn zero profit in equilibrium, they lack the incentive to enter the market and to engage in vigorous price competition. Thus, while the basic price-competition model provides a mechanism for establishing the market price, the model neglects the complex ways in which firms compete to set prices. Various models of price competition in industrial organization extend the Bertrand-Nash model of competition by introducing more general descriptions of the firm that serve to eliminate the fundamental discontinuity. Differentiating a product from one's competitors is a means of altering the firm's market power. The firm determines the effects on demand of

Competition between intermediaries

69

distinguishing its product from those of its rivals and selects the product characteristic to increase consumer willingness to pay for its products. Therefore product differentiation by firms is the inevitable counterpart to price setting. Markets operate through the price-setting and the productdesign activities of firms. As a counterpart to product differentiation, firms can gain monopsony power with suppliers by offering attractive working relationships and providing differentiated services to suppliers. Manufacturers and large retailers provide suppliers with technical expertise, logistical and accounting support, and information processing. They supply design specifications to parts suppliers. These activities can lower the cost to suppliers of providing service relative to the cost of serving other firms. Industrial-organization models draw a useful (but somewhat artificial) distinction between horizontal and vertical product differentiation. Horizontal product differentiation refers to product characteristics such as color, style, or flavor, for which one cannot argue individual tastes. Vertical differentiation refers to product features, such as quality and durability, for which consumer preferences agree. In practice, firms distinguish their products in many ways, and the two types of product differentiation are not easily distinguished. Moreover, firms generally offer multiple products arranged in several product lines that combine horizontal and vertical differences. If a product has two vertical features on which consumers agree, they will generally disagree on the best combination of these features. The horizontal product-differentiation model was introduced by Hotelling (1929) as a means of restoring market power to the Bertrand model of price competition. Since products differ, firms have captive customers as well as other customers who are more sensitive to price differences. Firms can set different prices while retaining those customers who prefer the types of products they offer. In this way, the Hotelling model eliminates the fundamental discontinuity of the Bertrand model.3 Consider a simple duopoly intermediation model in which firms offer customers differentiated products. Moreover, suppose that the input purchases of the firms are differentiated as well. This can arise if the firms require customized products from suppliers or if the costs of serving the intermediaries differ because of travel costs or transaction costs. For ease of presentation, consider a symmetric model in which each firm 3

The Hotelling model is itself subject to a discontinuity if products are not sufficiently differentiated since then the firm with the lowest price captures the entire captive market by slightly lowering its price. D'Aspremont, Gabszewicz, and Thisse (1979) show that there is no pure strategy equilibrium if firms are located too near to each other.

70

Competition and market equilibrium

faces the following demand and supply functions: qt = Di(pu

P2)

Xi = St(Wu

W2) = Wi -

= l - pi + tpj9 TWj,

where i, j = 1,2,/ / j . The constant t, 0 < t < 1, represents the degree of interaction in the output market, while r, 0 < t < 1, is the degree of interaction in the input market.4 The two firms choose the output and the input prices simultaneously. Let (/?*, p^w*, w2) be a Bertrand-Nash equilibrium. Then firm one chooses prices (/?*, w\) to maximize profit,

n(pi, wu p\, wl) = p\Di(pi, P2) - wiSi(u;i, wl), subject to S\(w\, W2) > D\(p\, p^). Firm two's problem is similar. In equilibrium, each firm equates its marginal revenue to its marginal factor cost, taking the other firm's equilibrium prices as given. The equilibrium prices solve the fundamental equation for the duopoly case and the stock constraint:

The own-price elasticities 77* and £* are defined by

w* The Bertrand-Nash equilibrium prices are represented in Figure 3.3. At symmetric equilibrium, given the linear demand and supply functions, the prices set by the two firms are

1

4 - 30 + T) + 2tr. Thus, the bid-ask spread is positive and both firms earn positive profits. The output of each firm is 4 - 3(f + r) + 2tx 4

Thefirmscompete by choosing prices. The problem cannot be recast as a Cournot quantity-choice game without changing the equilibrium outcome; see Singh and Vives (1984).

Competition between intermediaries

71

S(w,,w2*)

Pi

Figure 3.3. Competitive equilibrium ask and bid prices with differentiated products and purchases.

A higher value of the demand interaction parameter increases the output prices, the input prices, the bid-ask spreads, and the output of each firm. A higher value of the supply interaction parameter, r, increases the output and the input prices and lowers the bid-ask spreads, and the output of each firm.

33

Bertrand competition with switching costs

Paul Klemperer (1995, p. 517) points out that a "switching cost results from a consumer's desire for compatibility between his current purchase and a previous investment." He lists the following types of investment made by customers: (1) need for compatibility with existing equipment, (2) transaction costs of switching suppliers; (3) costs of learning to use new brands; (4) uncertainty about the quality of contested brands; (5) discount coupons and similar devices (such as "frequent flyer" and other "loyalty contracts"), and (6) psychological costs of switching or noneconomic brand loyalty. Klemperer (1995, p. 518) further observes that "[m]any of consumers' costs of switching to new suppliers have parallels in firms' costs of serving new customers." These can include transaction costs from opening new accounts, learning to work with new customers, and uncertainty about the characteristics of the new customers.

72

Competition and market equilibrium

As a consequence of switching costs, therefore, intermediaries may have both loyal customers and loyal suppliers, each of whom have made relationship-specific investments. Thus the current sales and purchases of the intermediary depend on past sales and purchases. In this section, I recast the basic intermediation model by considering a duopoly that competes for customers and suppliers in the presence of switching costs. I show that when the range of switching costs approaches zero, the competitive equilibrium approaches the Walrasian equilibrium. Conversely, when the range of switching costs becomes large, the competitive equilibrium approaches the monopoly intermediary outcome. Let market demand and supply be linear: D(p) = 1 — p and S(w) = w. The intermediaries' production and transaction costs are assumed to be zero to simplify the example further. Market shares have been determined in a previous period. For purposes of illustration, these are taken as given. The model is easily extended to allow the shares to be determined by price competition in the previous period; see Klemperer (1995) for the one-sided output-pricing case. Let o\ and oi be the initial customermarket shares of firms one and two, respectively. Let f i and & be the firms' initial supplier-market share. Note that o\ + 02 = fi + £2 = 1The customers and the suppliers have switching costs that are the same, without loss of generality. Switching costs k are uniformly distributed on the interval [0, K], A consumer of type k will switch purchases from firm two to firm one only if Pi - P\ > k. A supplier of type k will switch sales from firm two to firm one only if W\ — W2 > k.

Suppose that firm one is the lower-priced firm. Firm one sells to (1) its customers with reservation prices greater than or equal to p\, (2) to the rival firm's customers with reservation prices greater than or equal to P2 and switching costs less than or equal to pi — p\, and (3) to the rival firm's customers with reservation prices in the range (p\, pi) and a reservation price less switching cost greater than or equal to p\. Therefore, if firm one is the low-priced firm, p\ < pi, the quantity sold by firm one equals n

P2

n

_

K Firm two thus sells


cr2 1

(1 -

pi).

ni

Competition between intermediaries

73

By similar reasoning, the quantity purchased byfirmone, if w\ > w2, IS w

(w\ - w2)

"?2

I

**'1 —

/ ~F

Firm two purchases -w2) The marginal own-price effects are 9
7— = - o n - ^2 dpi

(I-P2)

K

Cl+C2T +

(P2-P1)

cr2

K

,

C 2 ^ .

Given equal market shares in the previous period (a\ = o2 = 1/2 and f 1 = £2 = 1/2) and symmetric equilibrium in the current period (px = p2 = p* and w\ = w2 = w*), the own-price elasticities of demand are

+ K - p)

w(K + w)

Apply the fundamental equation (/?i — u;i = p\/rj + w\/%) and market-clearing condition (x\ = q\), and solve to obtain the equilibrium prices and output per firm: p* = 3/4 + # - (1/16 +

Compare the competitive equilibrium with switching costs with the Walrasian equilibrium: pw = 1/2, Qw = 1/2. The prices straddle the Walrasian price, W* < pw < p\

and total output is below the Walrasian output. As switching costs go to zero, the bid and ask prices and total output with competition converge to the Walrasian price and output, respectively. Next, compare competitive equilibrium with switching cost with the monopoly intermediary (or fully collusive) case: pM = 3/4, wM = 1/4, and QM = 1/4. As one might expect, competition narrows the price spread,

wM

<w*
74

Competition and market equilibrium

and raises total output,

QM < 2q\ As the range of switching costs becomes large, competitive equilibrium tends to the monopoly outcome: lim p* = pM, K^oo

lim w* = wM, K^-oo

lim 2q* =

QM.

K^-oo

Therefore the conclusions of the monopoly intermediation model are robust to competition when customer switching costs are present. Because intermediation is most likely to be observed in markets with transaction costs, it is reasonable to expect that multiple intermediaries will enter such markets and acquire loyal customers and suppliers as a consequence of relationship-specific investment. The transaction-cost explanation of market intermediation thus is consistent with the presence of switching costs for both customers and suppliers. As intermediaries compete for market shares in customer and supplier markets, they take into account the future benefits from higher current sales and purchases. Prices for output should be lower in the current period and higher in future periods than if there were no switching costs in later periods. Similarly, prices offered to suppliers will fall over time as a consequence of initial competition for suppliers followed later by periods of supplier loyalty. Thus, for example, manufacturers such as auto companies initially reward their suppliers with favorable contract terms, but later may behave in an opportunistic manner by lowering bid prices to take advantage of the supplier's relationshipspecific investment.

3.4

Bertrand competition when costs differ

The Walrasian outcome observed with homogeneous products and purchases no longer occurs if the competing intermediaries have different costs. Asymmetric information about rival intermediaries' transaction costs is sufficient to yield both downward-sloping demand and upwardsloping supply curves. This implies in turn that the profit function of an intermediary is not linear in its bid and ask prices. Price competition under asymmetric information differs from auctions for contracts, such as those described by Holt (1980). Given nonlinearity of the profit function in the firm's price, price-setting strategies will be based on profit multiplied by the likelihood of winning the market, rather than on the net expected revenue per unit. The firm will trade off the effect of price on marginal profit against the effect of price on the likelihood of capturing the market demand. When the profit function of firms is concave in the

Competition between intermediaries

75

firm's price, the firm will exhibit risk aversion in the price, that is, the firm would strictly prefer profit evaluated at the expected price to profit multiplied by the probability of capturing the market. Bertrand competition when costs differ Suppose that there are n intermediaries with a transaction cost, k(,i = 1 , . . . , n, that is incurred per unit of input purchased. Suppose that transaction costs are indexed in increasing order, k\ < k.2 < - • • < kn. Each firm meets all its demand and purchases that are supplied at its posted prices p, w. This creates a winner-take-all competition as in the traditional Bertrand model. Then the firm with the lowest transaction cost k\ wins the input competition and is a monopolist in the output market. To characterize the equilibrium bidding strategies, define the zeromonopoly-rent input bid wo(k), which depends on the firm's transaction cost k. The monopoly profit is

n(w, k) = R*(S(w)) -(k + w)S(w). Thus the zero-monopoly-rent bid w°(k) solves 7t(w°, k) = 0; see Figure 3.4. The winning bid is derived as follows. The zero-monopoly-rent bid of the next-to-lowest-cost firm is wo(k2). The profit-maximizing input price of the lowest-cost firm w*(k\) solves max^ n(w, k). The lowestcostfirmthat wins the input competition sets its bid price at the maximum of the zero-monopoly-rent bid of the next-to-lowest-cost firm and its own profit-maximizing bid: w\ = m2Lx{w°(k2), w*(ki)}. As in the standard Bertrand model, all firms other than firm 1 earn zero profit. The equilibrium market prices and the profit of the winning firm are independent of the number of firms. The profit-maximizing input price w*(k) and the output price p*(k) solve the fundamental equation

and the market-clearing condition D(p*) = S(w*). Bertrand competition when rivals' costs are unknown Suppose now that the technology parameter is the private information of the firm. The firms act as Bayes-Nash players, choosing bid

76

Competition and market equilibrium

(k+w)S(w)

p*D(p*)

-/-^

R*(S(w))

Figure 3.4. The zero-monopoly-rent bid as a function of the transaction cost k.

prices based on the expectations of the other firm's equilibrium strategies, which depend on the value of their cost parameter. The technology parameters k\,..., kn are independent draws from a cumulative distribution function F(k), which is common knowledge. The distribution F(k) is defined on the unit interval with positive, continuous density f(k). Let v(k) represent the hazard rates, x/

\-F{k)

Then bidding for inputs resembles a variable output version of a privatevalues auction in which the lowest bidder wins the market and supplies all the output demanded at the winning price. The winning bidder will be a monopolist in the output market, with profit X\(w, k), as in the full-information case. In contrast to standard auction models, the firms have a nonlinear objective function. The equilibrium strategies are characterized by applying the framework of low-bid auctions with risk-averse bidders (see Maskin and Riley 1984a). The Bertrand-Nash competitive equilibrium of the

Competition between intermediaries

77

bidding process is a vector of bid prices wf,...,wfj. Since firms are otherwise identical, they follow a symmetric bidding strategy wB(k). The probability of winning the bidding is symmetric. The symmetric equilibrium is the unique equilibrium.5 A firm faces two different incentives. The firm wishes to bid close to the offer price of a monopoly intermediary w*(k) so as to maximize profit contingent on winning the market. On the other hand, the firm must raise its bid price to increase the likelihood of obtaining the input by outbidding rival firms. A bid price increase becomes less attractive the higher the firm's technology parameter, k. The firm's equilibrium bid strategy is always strictly greater than that of a monopoly intermediary: wB(k) > w*(k) for all k in [0,1]. The intuition for this result depends on the trade-off between the profit from winning the market and the likelihood of winning. Starting with a bid at w*(k), if the firm slightly increases its bid, it incurs a second-order loss in profit but enjoys a first-order gain in the probability of winning the market. Charging a price below the monopoly intermediary bid cannot be an optimal strategy since both profit and the likelihood of winning would be lowered. In contrast with the full-information case, simply topping the break-even bid of the next-lowest-cost firm is not an equilibrium strategy. The firm must make a bid that is greater than or equal to its own monopoly bid. The firm will not price below its monopoly intermediary bid since doing so lowers profits without increasing the likelihood of winning the market. It is straightforward to show that the firm will bid strictly above its monopoly intermediary bid.6 5 6

The equilibrium can be shown to be unique since the distribution of types F has a bounded support; see Maskin and Riley (1984a, p. 1486). Given the winner-take-all competition for inputs, let H(wi, iu(,-)) represent the probability of winning the market for firm / if that firm follows strategy iu,- and the other firms follow strategies W(i) = (wi,..., u>i-i, Wi+\,..., wn). Bertrand competition requires that a lower bid cannot raise firm f s chances of winning the market, i.e., H\{wi, u>(,-)) > 0. Let E denote the expectation operator over {k\,..., &,_i, fc,-+i,... ,kn). Then the expected profit of firm i if it chooses price wi is n(tU|, ki) = 7t(wt, kt)EH (wt, W(j)). Then it follows that w*(ki) < wt so that ni(u;,-, it,-) > 0. Now suppose that wB(k) = w*(k) for some k. By definition of n , Ui(wB(k)k) = m(wB(k), k)EH (wB(k), w(i)) + 7T(wB(k),k)EHl (wB(k), w(i)). If wBik) = w*(k), then ni(wB(k), k) = 0 and Ui(wB(k), k) = 7t(w*(k), k)EHx(w*{k), w{i)). Given wB(k) > w*(k) for all k, Bertrand competition implies that bidding above w*(k) must raise the likelihood of winning, EH\(w*(k), w^)) > 0. Thus, if wB(k) = w*(k), then Tii(wB(k), k) > 0, which implies that wB(k) does not maximize expected profit. This is a contradiction, so that wB(k) > w*(k).

78

Competition and market equilibrium

The firm will not bid above its zero-monopoly-rent bid, w°(k), which is the highest bid price such that n{w,k) = 0. Thus the firm's bid strategy is between the monopoly bid and the zero-monopoly-rent bid:

w*(k) < wB(k) < w°(k). Since the equilibrium bid exceeds the monopoly intermediary bid, the winning firm's output price should differ from the monopoly intermediary's ask price. There are two possibilities. If the input purchase exceeds the revenue-maximizing output, thefirmwill have excess capacity. As a result of that excess capacity, the firm will choose the revenuemaximizing price and sales (pR, qR). If the input constraint is binding, then the higher market-clearing price will be chosen. The price will be p = D~l(x), where x = S(wB(k)). The marginal profit for these two possibilities is

k) =

-(w + k)S'(w) - S(w) r D(V) 1 \ k\sf()S()

ifqR < S(w) if S(w)
If there is excess capacity, then n\(w, k) < 0. If the input constraint is binding but wB(k) > w*(k), then <0

,

so that 7t\(w, k) < 0 in this case as well. Therefore the winning firm's output price is below the monopoly intermediary's price, but greater than or equal to the revenue-maximizing price: PR < PB(k) < p*{k). When auction techniques are applied, it can be shown that the equilibrium bid strategy wB(k) is strictly decreasing and differentiable in the transaction-cost parameter.7 With the strictly decreasing bid strategy, the probability of winning the auction is the distribution of the minimum order statistic: The expected profit of a type k firm that acts as if it had cost y is Proceeding informally, maximizing n over the report y, with truth telling as the equilibrium strategy, yields the first-order condition 7

See Spulber (1995) and Maskin and Riley (1984a, Theorem 2).

Competition between intermediaries

79

:, A:) = 0. This implies that the equilibrium bid strategy solves the differential equation and boundary condition B

\k) = (n - \)v{k)n{wB{k\ k)/7n(wB(k), k), wB(kl) = w\ n(w\kl) = 0,

w

where kl < 1 is the highest cost parameter for which bidding is profitable. All firms of type k < k1 have positive expected profit. The bid pricing strategy depends on the number offirmsin the market. The equilibrium bid pricing strategy converges to the zero-monopolyrent bid as the number of firms gets large: lim wB(k) = w°(k). Al—>-00

The reason is that the firm's profit n(wB(k), k) converges to zero as the number of firms gets large.8 This limiting case corresponds to the equilibrium of the Bertrand price competition with homogeneous products and random tie breaking considered in Section 3.1.

3.5

Conclusion

Industrial organization has made substantial progress toward a consistent theory of market allocation. Prices are adjusted endogenously by firms, not by an external auctioneer. Market power provides firms with incentives for price adjustments and price competition. Prices depend on the cost of firms and the characteristics of demand. Firms adjust prices and production so that markets clear. Where the industrial-organization model sometimes falls short is through its emphasis on product markets, with the firm's purchases in other markets subsumed in the firm's neoclassical cost function. The firm is usually presumed to be a price taker in its input markets. The stress on products markets, as in the fundamental Bertrand model, ignores the firm's complex activities in capital, labor, and other factor markets. Part of this narrow focus is for tractability of modeling, and one might argue that little is lost since the general principles derived from studying competition in one market would apply to all others. On the other hand, the prices across markets are not independent, as emphasized in general equilibrium theory. The partial-equilibrium restriction may be too 8

To see why, differentiate U(k) = Tl(k, k) and integrate from k to k l, noting that U(kl) = 0,

rkl

Tl(k)= / S(wB(k))G(k)6k. Jk It is easy to show that lim^oo U(k)/G(k) = 0, so that lim^oo n(wB(k), k) — 0. Thus, by continuity of n, lim^oo wB(k) — w°(k).

80

Competition and market equilibrium

confining since it ignores the simultaneous exercise of market power in product and input markets, thus missing the role of the firm as intermediary. The extension of competitive models of price setting to include input markets provides the building blocks for intermediation models. The traditional concern in industrial organization has been over departures from perfect competition, as represented by the Walrasian framework. The standard view is that the exercise of market power is the result of imperfect competition, which causes prices to depart from marginal cost and other efficiency distortions. However, the exercise of market power gives a purpose to firms beyond operating their technology. Consideration of market power and strategic interaction provides a more complete description of the wide range of activities carried out by firms and their central role in market making.

Intermediation and general equilibrium

The neoclassical theory of the firm, by its emphasis on the productionpossibilities set, suggests a number of related explanations for the existence of firms. Firms are mechanisms for the application of productive technology. Their task is to select feasible input-output plans. The firm's input-output plans, including capital, labor, resources, and commodities, are a manifestation of its underlying technology. The productionpossibilities set is something like a vast cookbook; the firm is charged with reading the recipes and combining input and output choices in the right proportions. Choosing these proportions involves selecting production plans that are not only feasible, but also technologically efficient, that is, plans that are on the upper boundary of the productionpossibilities set. These choices are represented by the production function, which subsumes the firm's operational decisions that make the highest feasible output from any given inputs. The firm manages the technology efficiently by choosing the profitmaximizing production plan, given market prices. This requires the firm to understand the productive trade-offs represented by the technology, marginal products of inputs, marginal rates of technical substitution across inputs, and marginal rates of transformation across outputs. As part of the choice of production plans, the neoclassical firm decides whether or not to enter output markets. The entry decision determines the number of firms in the long-run competitive equilibrium and thus establishes long-run aggregate supply. The neoclassical theory firm makes clear that the firm combines inputs to produce outputs, purchasing inputs in factor markets and selling outputs in product markets. In this manner the firm's position as a market intermediary is highlighted. The firm intermediates through its choice of production plans. The firm manages two systems of accounts: a production account that keeps track of physical quantities of inputs and outputs and a profit account that keeps track of costs and revenues. Closely tied to operating the technology, the neoclassical firm can be viewed as a legal convention for the ownership of the technology 81

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through such devices as patents or licenses. The firm also is a repository of technical knowledge about feasible production activities that reflects the knowledge acquired from prior production. The ownership shares held by consumers reflect legal rights to the returns from operating the technology. This aspect of the firm is given little attention because the neoclassical technology is known and therefore not subject to improvement through learning or research and development and not transferable in the market. Thus technology exists only as a constraint on the firm's choices. The key question is whether operating productive technology is a satisfying explanation for the existence of firms. Certainly, any model of the firm must specify the firm's technological choices to some extent. Operating technology is crucial for those firms that are subcontractors charged with a specific productive task. But firms do many other things besides selecting production plans. The production-possibilities representation is problematic since it constitutes only one of these many activities. The neoclassical model of the firm has several important virtues. The model is constructed to allow great ease of aggregation. The model clearly sets out the firm's intermediate position between its input markets and its output markets. These properties of the model of the firm are particularly useful in general-equilibrium analysis. General-equilibrium analysis attempts to describe the market equilibrium for the economy as a whole. It presents a panorama of all economic activities, including production, consumption, distribution of profits, and market clearing. Moreover, general-equilibrium theory provides a welfare analysis of market economies. The analysis of general equilibrium lends itself to rigorous examination of the economy wide effects of taxes and other parametric changes. General equilibrium has the advantage of keeping track of secondary price effects of changes in the economy that would be missed in an analysis of a single market that takes all other prices as fixed, referred to as partial-equilibrium analysis. With all these advantages it is no wonder that the general-equilibrium theory is an important method of analysis in macroeconomics, finance, international trade, and capital theory. General equilibrium also has a number of serious drawbacks. The main objective of general equilibrium is to establish the existence of a market-clearing equilibrium consisting of a price vector and associated production and consumption plans. The existence results, when fixed-point theorems are applied, represent an impressive mathematical advance over previous methods of matching the number of equations to the number of unknowns. Yet it is precisely here that the weak points

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of general equilibrium appear. The demonstration of the existence of a market-clearing price vector in the model does not establish that the market will attain such a price vector. The general-equilibrium framework, while providing much more than a check for consistency of aggregate supply and demand, nonetheless fails to present a market-clearing mechanism. How does the market reach the equilibrium prices? If there were a price-adjustment mechanism, would that mechanism be consistent with the general-equilibrium framework or would it fundamentally alter the economy? If the marketclearing mechanism fundamentally alters the economy, how can the Walrasian equilibrium price vector be expected to remain the marketclearing price? Finally, if the Walrasian equilibrium price is not the economic equilibrium, will the welfare theorems continue to be valid? This chapter is organized as follows. In Section 4.1,1 consider the neoclassical theory of the firm as represented by the production-possibilities set and the production function and derive the firm's profit, cost, and revenue functions. In Section 4.2, I examine transaction costs within the general-equilibrium setting. Then, in Section 4.3,1 present a basic general-equilibrium model with monopoly intermediation. Finally, in Section 4.4, I consider monopolistic competition between intermediaries.

4.1

The neoclassical theory of the firm

The neoclassical theory of the firm consists of three basic elements: (1) technology, (2) profit maximization, and (3) market equilibrium. The description of the firm is based primarily on the production-possibilities set, which gives the technologically feasible net input-output plans available to the firm. The neoclassical firm, taking prices as given, selects the profit-maximizing net input-output plan, which determines the firm's output supply and input demand functions. Market equilibrium consists of market-clearing prices that equate supply and demand for all goods. In the long run, the competitive entry of firms determines industry size and completes the definition of market equilibrium. The neoclassical firm is fully described by its technology as represented by its production-possibilities set. Thefirmis fully informed about the characteristics of its technology and cannot modify its technology. The firm is not so much a black box as it is a transparent mechanical process that converts inputs into outputs. The firm is concerned with the feasibility and the technological efficiency of its production plans. A production plan is feasible if it is contained in the production-possibilities set. A production plan is technologically efficient if it is feasible and if

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outputs are maximized for any given set of inputs. The set of technologically efficient input-output plans is represented by the firm's production function. The production function as a representation of the firm has a long history. The analysis of the marginal productivity of factors of production, for example, dates back to the work of von Thunen on agriculture, which first appeared in 1826 and was to be an important influence on Alfred Marshall.1 The first general statement of the production function is attributed (Stigler 1949, p. 110) to Leon Walras. Walras (1954, p. 386) examines a production function, taking as given "technical progress brought about by science." Walras (1954, pp. 73-74) speaks of two distinct classes of industrial operations: technical (farming, manufacturing, engineering) and the economic organization of industry (the division of labor).2 Production functions traditionally have been based on engineering analyses of the production process. Stigler (1949, pp. 109-110), for example, observes that "Production functions are descriptive of techniques or systems of organization of productive services, and they are therefore taken from such disciplines as engineering and industrial chemistry: to the economic theorist they are the data of analysis." Dorfman, Samuelson, and Solow (1958, p. 131) point out that engineers "regard the production function as an economist's concept, and, as a matter of history, nearly all the production functions that have actually been derived are the work of economists rather than of engineers."3 Neoclassical economics generally is not concerned with the details of production; engineering specifications or other manufacturing processes are underlying explanations but not objects of interest. As Koopmans (1957, p. 70) observes with regard to operations research, "Economists have often regarded such management problems as outside the domain of economics and more properly entrusted to the production engineer or manager." Moreover, organizational aspects of the firm do not play an observable role in production-function analysis. The productionpossibilities set and the production-function analysis, while presenting an abstract and highly general picture of the firm, are directed primarily at representing manufacturing and agricultural production, and as such continue to be rooted in a nineteenth-century description of economic activity. While it certainly is true that a list of net inputs and outputs can be constructed for any firm engaged in any type of activity, very 1 2 3

See von Thunen (1966) and Marshall (1920). Elements D'Economie Politique Pure by Leon Walras was first published in 1874. See also Chenery (1953), Frisch(1965), and Dan0( 1966) on the engineering aspects of production models.

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different considerations can arise when production constitutes a small portion of the firm's activities. Having described the firm by its production possibilities, neoclassical theory makes two crucial behavioral assumptions. First, the firm takes market prices as given in its decision making; thefirmdoes not recognize the effects of its decisions on prices and so does not engage in activities to influence the price. Second, the firm chooses input-output vectors in its production-possibilities set to maximize profit. Debreu (1959, p. 37) defines the producer as "an economic agent whose role is to choose (and carry out) a production plan." The firm's input-output plans as functions of price are the output-supply and input-demand functions. The firm sells all its outputs at the market price, which obviates the need for marketing. Outputs are treated as homogeneous, so that individual firms need not differentiate their products or engage in research and development to devise new products. The firm obtains all necessary inputs at the posted price, so that more complex purchasing decisions are avoided. Inputs are treated in a homogeneous manner, whether capital, labor, or manufactured inputs, thus blurring the distinctions between financing of investment, hiring of personnel, and purchasing that are crucial for firms. Sales and purchasing decisions are immediate, so that contractual issues are avoided. If goods are deliverable in future periods and there is uncertainty about the state of the world, complete markets exist for state-contingent goods that effectively reduce the firm's supply and demand transactions to the case of immediate exchange. Feasibility and technological efficiency: the firm as operator of technology Neoclassical analysis of the economy begins with a complete list of commodities whose attributes (location, features, date of availability) are taken as given but not explicitly defined. The attributes of the commodities are implicitly defined by descriptions of consumer-preference rankings over commodity bundles. The characteristics of commodities also are defined implicitly by the production technology of firms that describes feasible input-output vectors, which must depend on the types of products used as inputs and created as outputs. Given the list of L commodities, the feasible production plans of a firm are represented by a production-possibilities set Y, which is a subset of the L-dimension space of commodities. An element of the productionpossibilities set, y, represents the firm's production plan, with positive terms for outputs and negative terms for inputs. For example, a firm that

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(0,0)

Figure 4.1. The firm's production-possibilities set.

uses x units of labor to produce q units of cloth would have a production plan y = (q, — x). A production possibilities set with one output and one input is represented in Figure 4.1. The production plan is a vector of net inputs and outputs, thus allowing some commodities to be used in the production of the same commodities. For example, some electricity is used as an input in the production of electricity. The production plan of the electric utility would show only the net electricity produced; see the appendix at the end of this chapter. The neoclassical firm stands between input suppliers and output purchasers. By transforming inputs into outputs, the firm intermediates between sellers and buyers. Through its technology and production services, the firm permits trade between input sellers and output buyers. Moreover, the firm is a technology owner and operates the technology to transform inputs into outputs. The firm has complete knowledge of its production possibilities, so that the neoclassical firm can be viewed as a repository of technological knowledge, which is embodied in the firm. The firm is more than the technology since the firm is a decision maker charged with selecting a feasible production plan. The production function provides a formal representation of technological efficiency. The firm's choice of production plans that maximize profits must be not only feasible but also technologically efficient. The production function is a building block in the derivation of profit, revenue and cost functions, which represent the firm's economically efficient decisions.

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Economic efficiency: thefirm'sprofit, cost, and revenue functions The neoclassical model of the firm combines a representation of technology with optimization, given market prices. The firm's objective function is profit, which is the product of the vector of market prices and the firm's production plan. The firm is assumed to take market prices as given. At market prices, p = (p\,..., pi). The firm's profit function is Tl(p) = max py subject to y e Y. y

The profit function exhibits a number of remarkable features. The first feature to be noted is the symmetry with which output and inputs are represented. Other than treating net outputs as positive and net inputs as negative, the roles of inputs and outputs in the profit function and production-possibilities set are not distinguishable. Moreover, diverse inputs are treated the same, so that capital services, labor services, and purchased inputs would be represented in the same way. Similarly, diverse outputs such as services and durable goods would appear in the same way in the profit function. The assumption of price-taking behavior has a number of implications for the profit function. First, the firm is not rationed, nor does it ration others, in input or output markets. Thefirmpurchases all that it demands in its input markets and sells all that it supplies in output markets. Thus production plans and purchasing and sales plans are identical. The input-output plan is chosen simultaneously so that problems of purchasing to stock, purchasing to order, and excess or insufficient inventory do not arise. The production-possibilities set and the profit function can be adapted to handle dynamic production decisions. Production lags, storage, and other temporal aspects can be incorporated by simply defining goods yj and their prices pj as referring to delivery or purchase at a particular date. Finally, note that all the firm's products are priced, so there are no externalities, such as pollution, received or generated by the firm. Moreover, the firm does not supply any unpriced goods, such as advertising or customer service. Suppose that the firm's profit-maximization problem has a welldefined, continuous solution y*(p) for all nonnegative prices p. 4 Suppose also that Tl(p) is continuously differentiate at p. The solution to the profit-maximization problem y?(p), / = 1 , . . . , L, represents the firm's supply or demand function for good /. The firm's supply of outputs and demand for inputs are the result of the assumption of pricetaking behavior. The firm's input supply and output demand are thus an 4

This holds if the production-possibilities set is compact and convex.

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essential feature of the neoclassical model. Hotelling's lemma, which is an application of the envelope theorem, states that dYl(p)/dpi = y?(p), which shows that the derivative of profit with respect to a price pi equals the firm's demand or supply function for good /. Given the solution y*(p), the firm's profit can be written as Tl(p) = py*(p). The neoclassical firm's profit-maximizing decisions include revenue maximization and cost minimization. Let (q, x) be a vector of outputs and inputs. Then the firm's cost function is defined by C{q\ w) = min wx

subject to (q, —x) e Y.

X

The cost function is the cost of the efficient combination of inputs needed to produce outputs q at input prices w. Similarly, the firm's revenue function is defined by R(x; p) = max pq q

subject to (q, —x) e Y.

The revenue function is the revenue generated from the efficient combination of outputs at output prices p that can be produced given the vector of inputs, JC. The firm's choice of inputs and outputs can be illustrated by the decisions of an oil refinery. The oil refinery can purchase various types of crude oil with different gravity (weight per unit volume) and sweetness (sulfur content). These factors affect the purchase prices. The refinery produces a number of products by cracking the crude oil, including jet fuel, gasoline, diesel fuel, kerosene, home-heating oil, liquified petroleum gas, asphalt, lubricants, and sulfur. For any given set of feedstocks JC, the relative amounts of the outputs q depend on the technology and the relative output prices. For any set of outputs q, the relative amounts of feedstocks purchased depend on the relative factor prices. The neoclassical firm has several distinctive features. First, the firm is fully described by its technology as represented by its productionpossibilities set. The characteristics of the firm's suppliers and the firm's consumers and other aspects of the firm's surroundings play no role whatsoever in this description. The information required by the firm also is quite basic. The only internal information needed is the shape of the production-possibilities set. The only external information needed is the vector of input and output prices. Second, the firm's actions are fully represented by a simple system of physical and monetary accounting. The physical accounting is a record of net outputs q and net inputs x. The monetary accounting keeps track of the firm's revenues pq and the firm's expenditures wx. The firm has

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no other activities that are recorded explicitly, although the productive activities involved in transforming x into q are implicit. Third, the firm's decisions consist entirely of tailoring production plans in response to relative prices. The firm's profit-maximizing output choices match marginal rates of output transformation to relative output prices. The input choices match marginal rates of technical substitution to input price ratios. The combination of input and output choices matches the marginal revenue products of inputs to their factor prices. Price adjustment in general equilibrium General-equilibrium analysis presents a complete picture of the economy that builds on the description of individual firms and consumers.5 The output-supply and input-demand functions offirmsare aggregated with consumer supply and demand functions to obtain total excess demand. Market equilibrium consists of a price for each good such that aggregate excess demands are zero. The general-equilibrium model does not formally specify a mechanism for establishing marketclearing prices. An appeal is made to the Walrasian auctioneer, which adjusts equilibrium prices in a tdtonnement process until excess demands equal zero. This process is represented in analyses of the stability of general equilibrium. Thus individual firms are atoms that make up the economy's aggregate supply. Prices are established centrally to clear all markets rather than to clear individual markets or to establish the terms of trade for individual transactions. The general-equilibrium model is an impressive representation of market interactions and simultaneous market clearing in the economy as a whole. Unlike partial-equilibrium models that examine individual markets, the general-equilibrium framework keeps track of the secondary market effects of production and consumption activities as well as the full effects of exogenous technological change or taxes. The centralization of economywide price adjustment and the decentralization of production and consumption decisions by price-taking consumers and firms drive the two theorems of welfare economics. The theorems state that market equilibrium is Pareto efficient and that any Pareto-efficient allocation can be achieved by market equilibrium after a suitable redistribution of initial endowments across consumers. In the first theorem, efficiency of market equilibria depends on the law of one price, with all economic agents taking the same price as their point of 5

See Arrow (1951), Arrow and Debreu (1954), and Debreu (1959) for the foundations of generalequilibrium analysis.

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reference. In the second theorem, attainment of a Pareto-efficient allocation depends on the separation of the decisions of consumers and firms who interact only through the centralized market-exchange mechanism, with redistribution of resources being carried out by a central planner. The model of general equilibrium decentralizes individual decision making while centralizing markets. The economic activities are established as follows. The general-equilibrium framework provides a decentralized analysis of consumer buying and selling decisions and producer input purchasing and output sales. Consumers and firms, taking prices as given, make consumption and production decisions, so that quantity choices are decentralized. In contrast, the general-equilibrium framework implicitly assumes that price setting and exchange are centralized. The price vector is established such that the economy as a whole is in equilibrium, as if by an auctioneer. Individual consumers and firms do not meet to exchange goods directly. Instead, aggregate supply is equated to aggregate demand, so that exchange appears to be centralized. The economy is described by L commodities, a set of / firms, and a set of / consumers. The commodities have fixed attributes that are implicitly defined by the technology of firms and the preferences of consumers. What is perhaps most remarkable about the general-equilibrium framework is the absence of joint restrictions on the characteristics of consumers and the firms. Assumptions about consumer preferences and endowments are separate from assumptions about firms. The consumers and the firms in the model function fully independently, free of externalities such as pollution, reputations, or bandwagon effects. There are no established trading relationships, since exchange takes place through market aggregation. This observation has implications for the welfare properties of the general-equilibrium model. Firms are represented by production possibilities sets Yj,j = 1 , . . . , / . Taking prices as given, firms maximize profit pyj subject to the production-possibilities constraint Yj. Firms' net production plans y*(p) are aggregated to yield total net production or supply:

.7 = 1

Consumers have preferences that can be represented by a utility function Ui(ii\ where consumption Zi takes values in a consumption set Z,-. Consumers have initial endowments of the L commodities, o>,-, and shares of the profits of each firm. Let sij denote consumer /'s share of firm y's profit, and let 5Z/=i SU = 1 f° r e a c ' 1 J- Taking prices as given,

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each consumer chooses nonnegative consumption plans zi to maximize utility subject to the budget constraint: j

7=1

Consumers' net consumption plans z*(p) are aggregated to yield total consumption or demand:

1=1

Let co = J2i=\ °>i represent total initial endowments. A Walrasian equilibrium is a price vector p = (p\,..., pi) such that markets clear. Market clearing is defined as the situation in which net consumption does not exceed net production plus initial endowments:

z*(p)
t(p) < 0. It is easy to demonstrate that Walras's law holds, that is,

pz\p) = 0; see the appendix at the end of this chapter. The key question is whether the price that drives excess demand to zero, that is, the price that equates demand to production plus initial endowments, describes a market equilibrium (other than by definition). How is the price arrived at within the economy? It is apparent that if the right price is chosen and communicated to consumers and firms, the equilibrium demands and supplies will be chosen. What is not clear is whether a mechanism for choosing the price can be imposed on the economy without fundamentally changing the nature of the equilibrium. Consider the mythical Walrasian auctioneer. No matter how the auctioneer is described, the equilibrium selection process is a deus ex machina, acting in a manner exogenous to the model. Arrow and Hahn (1971, p. 263) argue that, first, decentralized economies are often in a competitive equilibrium, and that, second, following Marshall, there are forces "that tend to drive an economy toward an equilibrium." They advance the notion of a tatonnement, which is a price-adjustment process with transactions taking place if and only if the equilibrium is attained. They postulate (p. 264) "the existence of a super-auctioneer who calls a given set of prices p and receives transaction offers from the agents

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in the economy. If these do not match, he calls another set of prices, following some rule." Arrow and Hahn (p. 266) propose an arbitrary price-adjustment rule that adjusts prices as a function of the value of excess demands, that is, pi does not change if p\ < 0 and zi(p) < 0, while the vector of prices is changed as a positive function of excess demands, say,

dp/dt = z(p). This rule changes prices if and only if the economy is not in equilibrium, and the adjusted prices remain positive if the initial price was positive. Not only does the story of the Walrasian auctioneer fail to correspond to any realistic market, but the abstract representation of price adjustment is devoid of economic content and inconsistent with the model itself. If all consumers and firms choose their plans by taking prices as given, which economic agents adjust prices? If the auctioneer is not an economic agent, who is the auctioneer? It would certainly be inappropriate to base an analysis of a decentralized competitive market on the notion that price adjustment is carried out by the government! Unfortunately, such a view seems implicit in the auctioneer story, since the auctioneer is presumed to act in the public interest and to set prices for the economy as a whole. What other institution could wield such economic power? If, on the other hand, the auctioneer is an economic agent, then it is necessary to spell out that agent's objective function and the compensation that the agent receives for price adjustment. It seems unlikely that an economic agent would choose to follow a price-adjustment rule that led to the competitive equilibrium price vector. In fact, trade is highly centralized in the general-equilibrium model, rather than being decentralized as is usually maintained. Although production and consumption decisions are decentralized, prices are established centrally, that is, they are adjusted by the Walrasian auctioneer, until all markets in the economy clear. Moreover, buying and selling are centralized, as all quantities produced by firms are aggregated, with purchases by consumers taken from the aggregate amount supplied. This contrasts, for example, with decentralized trade in which individual consumers transact directly with individual firms. The centralization of trade calls into question the interpretation of the two welfare theorems. The first theorem states that any Walrasian market equilibrium is Pareto efficient, that is, there is no feasible allocation that would make all consumers better off. The second welfare theorem states that any Pareto-efficient allocation can be attained as a Walrasian market equilibrium, after a suitable distribution of initial endowments and shares of firms. As the preceding discussion has demonstrated, at the Walrasian equilibrium consumers maximize utility subject to their

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budget constraints,firmsmaximize profits, and markets clear: z(/>*) = 0. These three elements prove the first theorem. If a feasible allocation (z, y) were to make all consumers better off than at the Walrasian equilibrium (z*, y*, p*), it would follow by revealed preference arguments that the allocation exceeded each consumer's budget constraint at the equilibrium prices. Summing across consumer budget constraints, this would imply that the value of consumption at equilibrium prices exceeded the value of equilibrium supply: p*z > pco + p*y*. Since the allocation is feasible, z = y + co, it follows that aggregate profits are higher, p*y > p*y*, which violates profit maximization. The second welfare theorem relies on a central planner, what Arrow and Hahn (1971, p. 94) term an omniscient state, choosing a price vector such that Walras's law holds and aggregate feasibility is satisfied. Moreover, the central planner chooses both initial endowments and shares of firms. For example, if (z°, y°) is the Pareto-efficient allocation and p is the equilibrium price, the planner could allocate to consumer / the proportion

1=1

of both the initial endowment and the firm profits. This allocation will guarantee that consumer budget constraints are satisfied at the Paretoefficient outcome. Suppose that the consumption set and the productionpossibilities set are closed and convex, consumer preferences are convex, and consumers are not satiated within their consumption sets. The separation theorem for convex sets then can be applied to establish the result. To illustrate the result, consider a one-output-one-input economy with a single consumer. Let Y be the aggregate production-possibilities set and let Z be the set of bundles in the consumer's consumption set that are preferred to consumption y\ and supply of input yi (say, labor). Then, at the price vector (p\, pi), the isoprofit line that separates the two is n = p\y\ + P2y2\ see Figure 4.2. The two welfare theorems strongly depend on the characteristics of the general-equilibrium model - in particular, the decentralization of individual decisions and the centralization of price setting and exchange. The welfare theorems rely heavily on the law of one price, with consumers and firms optimizing based on the same price vector, set costlessly by the Walrasian auctioneer. If trade were decentralized and prices varied

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(0,0)

Figure 4.2. The separation of the aggregate production-possibilities set from the preferred set of consumption bundles by the isoprofi t line, n = p\yi +pi >>2.

across transactions as a consequence of transaction costs, the welfare theorems might cease to apply. With decentralized trade, moreover, the transaction opportunities of individual consumers andfirmswould affect consumption and production plans. This would prevent the neat separation of consumption and production opportunities that is required for establishing the second welfare theorem. With decentralized trading, the demand and the supply sides of the market are not separable by prices, but are interdependent, as can be seen in search models.

4.2

Transaction costs and Walrasian equilibrium

The traditional theory of general market equilibrium not only depends on the presence of a Walrasian auctioneer but also costless markets. Foley (1970, p. 276) suggests that a weakness in the underlying assumptions of general equilibrium "is the absence from the theory of any real resource costs in information gathering and processing, or in the operation of "markets." The theory's predictive powers are limited as a conequence. Foley (1970, p. 276) observes that It is therefore disturbing that this theory, when applied to the complete problem of economic interaction over time, space, and in the presence of chance predicts the formation of numerous markets in timedated, place-tagged, contingent commodities which do not actually exist. Corollary to this embarrassment is the prediction by the theory that economic agents will choose

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one plan of action good for all time and all contingencies, which they clearly do not. How should transaction costs be incorporated into market models? The most basic approach to modeling transaction costs is to posit a constant per-unit cost k. If the intermediary is viewed simply as a producer of transactions and free entry is assumed, then the zero-profit bid-ask spread equals the transaction cost. If prices are determined by a Walrasian mechanism, then the ask and bid prices in the partial-equilibrium setting solve p - w = k, D(p) = S(p - k). This approach is reflected in a number of economic studies that introduce transaction costs into the Arrow-Debreu general-equilibrium model; see Foley (1970), Hahn (1971), Kurz (1974), Kurz and Wilson (1974), Winkler (1989), and Peck (1990). These approaches to intermediation are not satisfactory since prices in the model continue to be set by the Walrasian auctioneer. These models simply assign a cost to the allocation system. However, the price mechanism is not specified explicitly. For example, Foley (1970) distinguishes between buyer's and seller's prices. In his model, p > 0 and w > 0 are vectors of ask and bid prices and q > 0 and JC > 0 are vectors of purchases and sales. Then, given wealth GO, the consumer I'S budget constraint is pql — vox1 < col.

Firm j maximizes profit n = pqi — wxi = (p — w)qi + w{qi — JC7), where g7 — Jt7 is the net transaction carried out by the producer. Foley models costly production and marketing by requiring that (g 7 , qj — x 7 ) > 0. Foley shows that some markets may fail to exist as a result of transaction costs, particularly markets for contingent claims and forward markets. However, in his model, market clearing is obtained through standardfixed-pointtechniques rather than endogenously through intermediation activities of economic agents. Hahn (1971) presents a general, dynamic, pure-exchange model with transactions costs and shows that the market equilibrium can fail to be Pareto efficient if transaction costs are present. Foley (1970) suggests that such an efficiency analysis may be inappropriate and instead recommends comparing the transaction costs of alternative institutions of exchange, but he does not specify how this is to be done. Winkler (1989) models transaction costs by assuming that some households cannot trade

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with others and by requiring intermediation to be costly. Again, in Winkler's model, prices are selected through a Walrasian auctioneer and intermediation activities are not formally represented. In market game models, all agents send prices and quantities to an exogenous central mechanism that then allocates trades. These models do not resolve the problem of the Walrasian auctioneer either but merely change the types of messages the auctioneer receives (see, Dubey 1982; Simon 1984; and Benassy 1986). For example, Simon (1984, p. 214) observes that in his model, an arbitrage firm or a market maker is "a convenient fiction introduced because it facilitates the exposition of the outcome function." Decentralized price setting in a pure-exchange economy is introduced by Townsend (1983). He considers the sequential equilibrium of a two-stage game in which households first announce prices at which they can intermediate and then choose with whom to trade. Multiple equilibria are possible and any Walrasian equilibrium is attainable with or without the presence of trading restrictions.

4.3

Monopoly intermediation in general equilibrium

In Chapters 2 and 3, I presented economic models of intermediation within a partial-equilibrium setting. The role of intermediaries in price setting and market clearing bears examination within a general-equilibrium framework to determine whether the Walrasian auctioneer can be replaced by economic agents. The general-equilibrium framework requires close attention to the interrelation between output and input prices in the economy. The ask and bid prices offered by intermediaries have simultaneous impacts on both sides of the consumer budget constraint. The intermediation perspective shows that general-equilibrium analysis need not require sacrificing price-setting behavior by firms. Moreover, the institutions of market microstructure can be incorporated easily within the general-equilibrium framework. The two-consumer, one-firm, pure-exchange economy In this section, I consider the market equilibrum of a pureexchange economy with two consumers and two goods. A price-setting intermediary firm carries out the transactions between the two consumers. The features of market equilibrium in the partial-equilibrium setting are shown to carry over to the general-equilibrium framework. The traditional Edgeworth box presentation of the Walrasian equilibrium has several important features. The equilibrium is on the contract

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curve. The contract curve is the set of allocations that leave consumers as well off as they are at their initial endowments and equates the consumers' marginal rates of substitution. The equilibrium is on the budget line, which goes through the initial endowment point. In equilibrium, both consumers maximize utility subject to their budget constraints. Finally, at equilibrium prices, the purchases and the sales of the consumers are balanced and all initial endowments are consumed. The Walrasian market equilibrium in the pure-exchange economy raises the same questions, which I have already mentioned about how prices are established, but helps to shed additional light on the problem. If the two consumers can negotiate directly with each other, then no prices are necessary. The consumers negotiate a trade of some amount of one good for some amount of the other. The terms of trade implicitly determine a price ratio for the two goods. The allocation might correspond to market equilibrium but in the model the allocation is achieved through direct negotiation, not posted prices. However, suppose that there are many consumers of each type, thus replicating the pure-exchange economy with two consumers. Then, such decentralized bargaining is unlikely to be feasible because it will become difficult to find a suitable trading partner. Each type of consumer must somehow be matched up with the other type of consumer. Thus replacing the price mechanism with decentralized bargaining would require some mechanism for matching traders. Such a mechanism would entail costs of search and matching. If there were more than two types of consumers in the economy, the complexity would increase significantly because consumers would have to carry out exchange with multiple trading partners to reach the Walrasian equilibrium. The problem of the double coincidence of wants would soon arise. The problem of finding a trading partner would be compounded still further in an economy with more than two goods. If decentralized trade is costly because of the difficulty of finding trading partners and the costs of negotiation, the potential advantages of centralized trading become apparent. To realize the benefits of centralized trading while specifying the mechanism by which prices are established, suppose that there is a firm that purchases and sells both of the goods. I view the two consumers as representative, since the intermediation framework applies with many consumers of each type. The presence of many consumers helps to explain the intermediary's market power. With two goods, each consumer faces the choice of buying good one and selling good two, buying good two and selling good one, or consuming only their initial endowment. It might appear that the pureexchange economy with two goods requires four prices: an ask and bid

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price for each of the two goods. However, in choosing a consumption bundle, each consumer considers only two prices at a time. A consumer choosing to buy good one and sell good two considers the ask price of good one and the bid price of good two, (/?, /x). A consumer choosing to buy good two and sell good one considers the ask price of good two and the bid price of good one, (f, r). Since the consumer's demand is invariant to rescaling the price vector, the consumer will optimize in the same way if the two vectors are normalized. For example, let good two be the numeraire commodity; the consumer demand will be the same given the price vectors (p/fi, 1) and (1, r/f). Moreover, the comparison between the decisions to buy good one and sell good two, buy good two and sell good one, or buy neither will be unchanged. Therefore it is sufficient to treat good two as the numeraire and to specify only an ask price for good one and a bid price for good one, (/?, r). Generally speaking, if the economy has N goods, it is sufficient to have 2N — 1 prices, one of which is normalized to one. The initial allocations are co1-, where / denotes consumer 1 or 2 and j denotes good 1 or 2. The consumer utility functions are Ul(q, z), i = 1, 2, where q is consumption of good 1 and z is consumption of good 2. Suppose that, without trade, consumer one's marginal rate of substitution exceeds that of consumer two:

Then trade would enhance consumer welfare if consumer one provided good two and in exchange received good one. Thus consumer one would be a buyer of good one and consumer two would be a seller of good one. Accordingly, the intermediary will choose bid and ask prices for good one that separate the autarky marginal rates of substitution:

4)

r

Let n be the profit of the intermediary. Each consumer has a share sl,i = 1, 2, of the firm's profit. The profit is denominated in units of the numeraire. Assume free disposal of good one. Given consumer one's demand q(p) and consumer two's supply jc(r), the firm's profit is n = mdLx[pq(p) — rx(r)]

subject to q(p) < x(r).

The profit-maximizing prices solve the fundamental equation p* — r* = p*/rj + r*/£ and clear the market q(p*) = x(r*). Clearly consumer one will choose to buy at price p and consumer two will choose to sell at price r. Thus consumer one's demand q = q(p)

Intermediation and general equilibrium

99

solves — pq The consumer's first-order condition is

U\{a>\ +q,
pq+slU) pq+sxU) = P>

Consumer two's supply x = x(r) solves max U2(co\ - x, coj + rx + s2U), so that the consumer's first order condition is U2((o2 — x co2 + rx + s2Yl) U^ycoi — x, CO2 — rx + s 2 n )

The equilibrium is shown in Figure 4.3, where <2 = °)\ + ^(/7) and Z = &>2 — p^(p) + sl Ft1. The precise relationship between marginal rates of substitution at the equilibrium is obtained with the profit-maximization condition,

u\

-!/>?,

Consideration of the consumer decision problems and the firm's profit maximization shows that equilibrium marginal rates of substitution are

Figure 4.3. Equilibrium in the pure-exchange economy with intermediation.

100

Competition and market equilibrium

not equal. Thus, as a consequence of the intermediary's market power, the economy fails to reach a Pareto optimal allocation. As shown by Figure 4.3, the intermediated equilibrium Pareto dominates the autarky point. Moreover, consumers share the intermediary's profit. The market clears so that there is no excess demand or supply, and the consumers receive all the initial endowments of both goods at the equilibrium. The one-consumer, two-firm production economy To contrast price-takingfirmswith price-making intermediaries, consider a basic one-consumer two-firm economy. One firm, referred to as the supplier, is a primary good producer that acts as a price taker, buying labor from the consumer at the market wage and selling a good to the intermediary at the intermediary's bid price. The intermediary produces the final good, and acts as a monopoly-monopsony, choosing the input bid price and the final-output ask price. Thus both firms carry out technological intermediation, transforming productive factors into output. The intermediary also takes on the price-setting role, supplanting the Walrasian auctioneer. The consumer and the supplier take the wage rate W as given. The wage rate is determined by the consumer's budget constraint following Walras's law. The example can be extended by explicitly modeling clearing in the labor market, possibly through the activities of labor-market intermediaries. The consumer purchases the final output from the intermediary and supplies labor to the primary good producer. Let q denote the final good. Also, let L be the consumer's labor, co the initial labor endowment, and z the consumer's leisure, where z — co — L. The consumer takes the output price p as given. The consumer receives profits from the two firms, with n as the intermediary's profit and G as the supplier's profit. Let U{q,z) represent the consumer's preferences. The consumer chooses consumption and leisure to solve max U(q, z)

subject to pq < W(co - z) + n + G.

q,z

The consumer takes the profits of the two firms as given. At the solution to the consumer's problem, the consumer's budget constraint is strictly binding. The consumer's product demand q(p, W) and labor supply

L(p, W) = co- z(p, W) solve ) W ) p pq = W(o) - z) + n + G. The solution to the consumer's problem is shown in Figure 4.4.

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101

-W*/p*

Figure 4.4. Solution to the consumer's problem.

The supplier acts as a neoclassical firm and takes the wage W and the primary good price r as given. The supplier produces output x with a production function x = /(L), where f\L) > 0 and f"{L) < 0. The supplier chooses L to solve G(r, W) = max[r/(L) - WL]. At prices (r, W), the supplier's output supply is x(r, W) and the supplier's labor demand is L(r, W). The labor demand solves r/'(L) = W. The solution to the supplier's problem is depicted in Figure 4.5. The firm purchases labor from the consumer and sells the good to the consumer, taking as given the consumer's demand and supply functions. The firm not only acts as a purchaser of labor and a seller of output, but also uses labor to produce the good, with a production function q = h(x)9 which also is increasing with a diminishing marginal product, hf(x) > 0 and h"(x) < 0. The intermediary chooses prices p and r, taking the consumer's demand function q(p, W) and the supplier's supply function x(r, W) as given. The wage rate W also is taken as given. In this example, to simplify matters, the intermediary uses no labor. Therefore the

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Competition and market equilibrium

Slope = -W*/r*

-L(r*,W*)

Figure 4.5. Solution to the supplier's problem.

intermediary selects prices to solve

n = max [pq(p, W) - rx{r, W)] PS

subject to q(p, W) = h[x(r, W)]. Let p* and r* denote equilibrium values of the ask price for output and bid price for labor, respectively, and define n* as the maximum value of profit. Let x] = —pqi/q and £ = rx\/x\ the prices solve the fundamental equation with production and the production constraint h *h' - r * = P* ' r,*

r

*

+

Thus the equilibrium departs from Pareto optimality because p*h' > r*. Let W* be the equilibrium wage and let II* and G* be equilibrium profit levels. Denote equilibrium outputs and labor by q* = q(p*, W*), x* = jc(r*, W*) and L* = L(p*, W*). Because of the market power of the intermediary, the economy does not satisfy the Pareto optimal condition for efficiency because the consumer's marginal rate of substitution

Intermediation and general equilibrium

103

q

h(f(L))

Figure 4.6. The equilibrium in the one-consumer, two-firm economy.

is less than the marginal product of labor:

U2(q*,co-L*) < h\f(L*))f\L% Ui(q*,co-L*) Figure 4.6 shows the equilibrium. The slope of the consumer's indifference curve is not tangent to the curve representing the composition of the production functions. Consumer welfare could be enhanced by an increase in output along the production frontier. This distortion reflects the market power of the intermediary and is the cost of operating the price system. With competition between intermediaries, their market power would decrease, thus reducing pricing distortions, although this welfare increase would occur at the cost of establishing more firms. The intermediary is assumed to have market power because there are many small suppliers and many consumers, all of whom take prices as given. The supplier and the consumer in the model are representative economic agents. Other assumptions are consistent with price setting by firms. For example, suppliers may set their output price r, which intermediaries take as given, while intermediaries set their output price

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Competition and market equilibrium

p, which consumers take as given. This would cause the classic doublemarginalization problem to occur.

4.4

Monopolistic competition

In this section, I consider monopolistic competition between pricesetting intermediaries.6 The intermediaries' outputs are differentiated, representing differences in product branding, quality, performance, geographic location, and other factors that affect demand. The input purchases of intermediaries also are differentiated, representing variations in purchasing specifications, quality requirements, geographic location, and other factors that are reflected in supplier costs. As in the above oneconsumer, two-firm economy, there are three types of economic agents: consumers, suppliers, and intermediaries. Consumers purchase goods from intermediaries and provide labor to suppliers. Suppliers manufacture products that are sold to intermediaries. Each intermediary i produces output qt by using input JC,- and sets an ask price for output pi and a bid price for the input rt. As in the above example, the wage rate is determined by the consumer's budget constraint following Walras's law. Normalize the wage rate to equal 1. Consider an economy with identical consumers. A consumer purchases a set of goods qi at price /?,-, where i is an index of products that takes values in the unit interval. The consumer's product demand is parameterized by a constant elasticity rj. The consumer supplies labor L. The representative consumer's utility has the following form:

The representative consumer's budget constraint equates expenditures on goods to income, which is the sum of labor earnings and profits. The consumer takes distributed profits as given in making consumption and labor-supply decisions. Profits include both the profits of intermediaries and of input suppliers. The consumer's budget constraint is ptqt di = L + profits. //o' JO Maximizing utility subject to the consumer's budget constraint yields a set of product demands: qi=P;\

i €[0,1],

The consumer's labor supply is determined by the budget constraint. 6

The model extends the basic monopolistic competition example of Mankiw (1991) to allow for intermediation and input manufacturing without considering a money market and aggregate shocks. For a model of intermediation that includes these features, see Spulber (1998b).

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105

Suppliers also are identical. The representative supplier produces a vector of custom-made outputs, one for each intermediary, xi. The set of inputs is provided to intermediaries at prices b\, where / takes values in the unit interval. The supplier has the same production function for each product and carries out production independently: where £ is an elasticity parameter and L,- is the labor used to produce product i. Therefore the total labor used by the supplier is JO

l

~T- A/<

In equilibrium, labor demand and supply are equal. The supplier chooses outputs xt to maximize profit, taking as given prices b{. The representative supplier's profit is Gixiwfi = / riXi di - [1/(1 + i/§)] / x]+m Jo Jo The supplier's product supply functions are

di.

There is a continuum of intermediaries indexed by i that takes values in the unit interval. A type i intermediary sells output qt and purchases input X(. Thus each intermediary's output and input are differentiated from other intermediaries. The type i intermediary sets prices pi and r,-. The intermediary's profit is The intermediary maximizes profit by choosing output and input prices, given the output demand function and input supply function. The intermediary's technology allows free disposal: The intermediaries engage in Bertrand-Nash competition, choosing prices pi and r/. Let (/?*, r*) represent the Bertrand-Nash equilibrium. Each profitmaximizing intermediary adjusts prices to clear markets, so that in equilibrium qt = JC; . As a result, profit can be written as a function of qi with inverse demand and supply functions pt = qT /r/ ; the inverse supply is Ti = x(' : The profit-maximizing equilibrium output of the intermediary thus is

106

Competition and market equilibrium

Given the profit-maximizing output, calculate the equilibrium prices. Since the equilibrium is symmetric, the individual firm prices equal the consumer and the producer price indices for all i:

Therefore the equilibrium prices can be written as The price ratio is decreasing in both the supply and the demand elasticities since P* i + i/g r* l-l/ri' Compare the Nash equilibrium with the Walrasian equilibrium:

p* = l,

q"=xw = l.

The prices straddle the Walrasian equilibrium:

r* < pw < p\ Outputs are below the Walrasian levels for each i: q* < 1. The model demonstrates that competing intermediaries can carry out the Walrasian auctioneer's price-setting function. Consumers and suppliers are price takers, while intermediaries set profit-maximizing prices that clear markets. Thus the general equilibrium is consistent with monopolistic competition between intermediaries.

4.5

Conclusion

The neoclassical theory of the firm derives explanatory power from its focus on technology. Econometric estimates of cost functions provide a valuable picture of competitive firms. Empirical analysis of firm supply functions and factor demand functions often are accurate descriptions of firm behavior in markets with many small firms that fit the perfect competition framework. There are other areas of firm activity that the neoclassical model explains less well. Most firms cannot expect to sell all their output. Sales depend on pricing, advertising, sales strategy, customer service, and competition. Pricing is perhaps the most important activity undertaken

Intermediation and general equilibrium

107

by firms, but this activity is absent from the neoclassical setting because of the assumption of price-taking behavior. Most firms devote considerable attention to selecting prices or negotiating with customers and suppliers. Firms engage in strategic planning, evaluating the characteristics of customers and assessing the costs and capabilities of rivals. Firms differentiate their products by varying product features and continually creating new products. On the input side, firms engage in financial planning, choosing capital structure and sources of finance. Firms employ many different types of labor services and devise complex employment and personnel policies. Firms make strategic purchasing decisions that often involve long-term supplier relationships. These activities are not explained by the neoclassical theory of the firm. The neoclassical theory has its greatest success as a theory of market allocation, with the actions of firms represented by aggregate supply. The market-allocation framework yields important insights particularly in models of international trade, financial markets, and capital theory. Despite its descriptive strength, the general-equilibrium theory leaves much to be desired as a framework for understanding how markets work. The neoclassical model is at variance with actual markets in several respects. There is in practice no economywide auctioneer to adjust prices, nor should there be, given the disastrous results of government price controls. In most markets, transactions are highly decentralized, with terms of trade varying across buyers and sellers. This decentralization implies that the law of one price is misleading and overly restrictive. Firms usually play an important role in establishing prices. As a consequence of its focus on the production activities of firms, neoclassical theory fails to provide a price-adjustment mechanism and therefore cannot explain the many institutions of exchange in the economy, from stock markets to supermarkets. Price setting byfirmsis readily incorporated in the general-equilibrium setting. The models of monopoly intermediation and monopolistic competition between intermediaries are closely related to the monopoly and the competition models considered in Chapters 2 and 3. Equilibrium with price-setting intermediaries departs systematically from the Walrasian equilibrium, with buy and sell prices straddling the Walrasian price and output reduced below the Walrasian market-clearing output. These results emphasize that the Walrasian equilibrium is an ideal case that corresponds to a welfare optimum. The economy departs from this optimum when the price setting by firms is made explicit. In the following chapters, I consider various market frictions that determine the extent to which the economy departs from the Walrasian ideal.

108

Competition and market equilibrium

Appendix The firm's production function The properties of the production-possibilities set Y describe the firm's choices. The firm can shut down costlessly if the production plan of 0 is in the set Y. The production-possibilities set exhibits free disposal if y is in Y, and for all yr < y, yf is in Y as well. A production-possibilities set with one input and one output and a constant return-to-scale technology has the form Y = {(
<

min(axux2)}.

Thefixed-coefficientproduction technology represents a production process in which q units of output are produced with q/a units of input x\ and q units of input x2, so that, without redundancy, inputs are always used in the proportion a = x2/x\. The firm may have available several such fixed-coefficient production processes. In the limit, with average linear processes, the firm has available a smooth productionpossibilities set. The production-possibilities set allows for technological inefficiencies since it is possible to produce different output levels for a given level of inputs. The technological inefficiencies can be eliminated if attention is restricted to production functions, which describe the efficient boundary of the production-possibilities set. If the firm produces multiple outputs by using multiple inputs, the production function is defined by

H(y) = 0, where y satisfies H(y) = 0 if and only if there is no y' e Y such that yf > y.lf the firm produces only one output with multiple inputs, the general production constraint is where q = h(x\,..., xm) represents the highest output boundary of the production-possibilities set: h{x) = {q ; maxg such that (q, —x) e Y}. If the firm produces multiple outputs with one input, the general production constraint is

Intermediation and general equilibrium

109

where x = g(q\,..., qn) represents the input requirement function: g(q) = {x : minx such that (q, —x) e Y}. For example, a one-output-one-input production function is the upper boundary of the production-possibilities set in Figure 4.1. The Leontief production function is H(x) = min{ax\, xi). The linear production function is h(x) = ao + a\X\ + #2*2• The Cobb-Douglas production function is h(x) = x\x\. A linear input requirement function is

g(q\,qi) = bo + b\q\ + b2q2-

The production function, while restricting attention to technologically efficient input and output combinations, also provides a useful description of the neoclassical firm. The production function allows the definition of the incremental product of adding a factor: h(x\, X2) — h(0, X2). The additional product that is due to increasing a factor from x\ to x[ is h(x[, X2) — h(x\, JC2). If the production function is differentiable then as x[ approaches x\ in the limit, the change in output is the marginal product of the input x\, dh(x\, X2)/dx\. The production function is said to exhibit increasing (decreasing) returns to scale if h(kx) is greater than (less than) Xh(x), where X is a scalar greater than one. The production function is said to exhibit constant returns to scale if it is homogeneous of degree one in a positive scalar: h(Xx) = Xh(x). In this case, note that the output exactly equals the sum of the marginal products of inputs times input levels, by Euler's law: q = 7=1

This property implies that profits are zero if all factors are paid their marginal revenue products.7 The firm's cost and revenue functions The conditional input demand x(w, q) and the conditional supply q(p, x) represent the solutions to the firm's cost minimization and revenue maximization problems, respectively. Then Shephard's lemma implies that

dC(q\ w)/dwj =xj(w1 q), dR(x;p)/dpi=qi(p,x). These results represent applications of the envelope theorem. 7

Generally the production function is homogeneous of degree a if h(kx) = \ah(x) for all k > 0. A production function is homothetic if it is a monotonic transformation of a homogeneous function, that is, h(x) = f(g(x)) is homothetic if / is a monotonic function and g is homogeneous.

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Competition and market equilibrium

The firm's profit-maximization problem can be written with either the cost or the revenue functions: U(p, w) = max[/?(x; p) — wx] X

- C(q\w)].

The firm chooses inputs to equate the marginal revenue product of each input to its factor price: dR(x'9p)/dxj

= Wj,

7 = 1 , . . . , 7.

The solution to the profit-maximization problem yields input demands x*(p, w). The supply function can then be obtained when the input demand is substituted into the conditional supply function: q*(p,

w) = q(w, JC*(/?, w)).

Alternatively, the firm equates the marginal cost of each output to its sales price, Pi = Ci(q\w),

i = 1,...,/,

to obtain the supply functions q*(p, w). The input demand functions can then be obtained when the supply function is substituted into the conditional input demand

x*(p, w) = x(p, q*(p, w)). Cost minimization with two inputs and one output q involves equating the lowest isocost line C = w \ x 1+W2X2 with the isoquantg = h{x\,X2)\ see Figure 4.7. Revenue maximization with two outputs and one input x involves equating the highest isorevenue line R = p\q\ + P292 with the input requirement function x = g(q\, qi) or the production-possibilities frontier, see Figure 4.8. Suppose that the firm produces a single output with the production function q = h{x). Let p be the output price and let w = (w\,... ,wj) be the vector of input prices. Then the profit function can be written as FI(/7, w) = maxph(x) — wx. X

The firm purchases a vector on inputs x at price w and resells the inputs by combining and transforming them into output q and receiving total payment ph(x). Let the production function be differentiable and suppose that the solution to the firm's profit-maximization problem, JC*(/?, W), is interior. Then the firm maximizes profit by equating the marginal revenue product of each input to its price: ~ = Wj,

J =

l,...,/.

Intermediation and general equilibrium

111

Figure 4.7. Cost minimization.

The functions Xj(p, w) are the firm's input demands. The firm's profit maximization and the price-taking behavior assumption imply that the ratio of factor prices equals the ratio of marginal products, referred to as the marginal rate of technical substitution: dh{x*)/dxj = wj dh(x*)/dxi wi' 'y '••"• Similarly, the profit function with one input and many outputs and with an input requirement function x = g(q) is

n(/?, w) = maxpq - wg(q). q

The firm equates the marginal factor cost of each output to its price: Pi = tv-

The slope of marginal rate prices: Pi_ = Pi

i = 1,

the production-possibilities frontier, referred to as the of transformation, then is equal to the ratio of output dg(q*)/dqi dg(q*)/dqi'

x

i

112

Competition and market equilibrium

Figure 4.8. Revenue maximization.

Again, note that the firm's factor purchases g(q) are transformed and resold as output to the firm's customers. Walras's law and market equilibrium If consumers are not satiated, then their budget constraints hold with equality. Summing across consumer budget constraints yields /

i Z;(p)

=

p /

i o) + /

J

/

SijyAp).

Noting the definition of aggregate consumption and production, endowments, and the definition of excess demand, and 5Z/=i $ij = 1» immediately gives - a>] = o, which establishes Walras' law. Walras' law is an important building block in general-equilibrium existence theorems.

Intermediation and general equilibrium

113

A standard result (see Debreu 1959) is that an equilibrium exists for the economy given a set of assumptions on consumers and firms. Consumer preferences, consumption sets, and endowments satisfy the following assumptions: la. The consumption set for each consumer is closed, convex, and bounded below. lb. There is no satiation point in the consumption set. lc. For any consumption bundle in the consumption set, the set of bundles that are preferred or indifferent and the set of bundles that are less preferred or indifferent are closed. Id. For each consumer /, a convex combination of a consumption bundle zi and a bundle that is strictly preferred to it is strictly preferred to Zi. le. Each consumer / has an initial endowment cot that is the interior of the consumption set. Firm production-possibilities sets, Y}-, j = 1 , . . . , / , satisfy the following assumptions: 2a. 2b. 2c. 2d.

Firms can shut down costlessly, 0 € Yj. Production sets Yj are closed and convex. Yjn(-Yj) = {0}. Free disposal of inputs is possible.

The equilibrium price vector p* clears the market. Given p*, consumers choose consumption plans z* = z*(p*). Firms choose production plans y*. = y*j(p*). By Walras' law, the value of amount consumed equals the value of production plus the initial endowment: p*z* = p*y* + p*w. The proof that a market equilibrium exists shows that there is a price such that excess demands are zero; z*(p*) = 0.

Part III

Intermediation versus decentralized trade

Matching and intermediation by firms

Intermediaries compete with direct exchange to attract buyers and sellers. Consumers and suppliers choose between seeking each other out and bargaining over the terms of trade and exchange with the intermediary. Because consumers and suppliers must incur costs of search and bargaining under decentralized trade, intermediaries will be economically viable if they can carry out transactions at a lower cost. By demonstrating that intermediaries are profitable in equilibrium, the models examined in this chapter help to explain the role of firms as intermediaries. Firms will form in a pure-exchange economy if they are viable in competition with direct exchange. Models of matching and bargaining present a picture of markets as decentralized mechanisms with pairwise meetings of agents.1 Rubinstein and Wolinsky (1985, p. 1133) observe that such models contribute to "an understanding of the micro-mechanisms of price formation and their role in shaping market outcomes." In contrast, intermediated markets are more centralized because the intermediary deals with multiple buyers and sellers. Price-setting intermediaries provide an explicit mechanism of price adjustment that differs from pairwise bargaining. The intermediation models presented in Chapters 2 through 4 examined monopoly pricing, Bertrand-Nash competition between intermediaries and monopolistic competition in a general-equilibrium setting. These models emphasized price setting and market clearing by firms without explicitly allowing for direct exchange. This chapter presents several models with searching or matching costs in which intermediaries increase the likelihood of trade or improve the terms of trade relative to direct exchange. I begin in Section 5.1 with Gehrig's (1993) model of competition between an intermediary and a decentralized matching market. Buyers 1

See for example Diamond and Maskin (1979), Mortensen (1976, 1982), and Rubinstein and Wolinsky (1985, 1990). See the book by Osbome and Rubinstein (1990) for a survey and overview of the literature.

117

118

Intermediation versus decentralized trade

and sellers in the decentralized market engage in first-and-final-offer bargaining. The intermediary chooses a price spread in competition with the decentralized market. In equilibrium, the price spread offered by the intermediary depends on the efficiency of search and bargaining in the matching market. At the equilibrium price spread, high-willingness-topay buyers and low-opportunity-cost sellers trade with the intermediary. Buyers that have a moderate willingness to pay and sellers with moderate opportunity costs enter the matching market. Then, in Section 5.2,1 modify the basic model to allow for full information after a match is made. I also assume that buyers and sellers engage in alternating-offer bargaining in the matching market. I introduce transaction costs for the intermediary. In equilibrium, the intermediary's price spread and level of sales depend on the efficiency of the matching market. Bid and ask prices and sales also depend on the intermediary's transaction cost. Then, in Section 5.3,1 examine the intermediation model of Rubinstein and Wolinsky (1987), which involves random matching of buyers, sellers, and intermediaries. The size of the intermediary's market depends on the cost of delay in private search. As in Gehrig's model, the intermediary's customers and suppliers consist of these agents with high gains from trade. Competition between identical intermediaries again yields the Walrasian outcome. Finally, in Section 5.4,1 turn to Bhattacharya and Hagerty's (1987) model of intermediated exchange with production. This model does not address competition between an intermediary and a decentralized market. The model is of interest to our discussion because economic agents can choose between being a producer or an intermediary. Consequently the equilibrium returns to production and intermediation are equalized. The presence of intermediaries affects the equilibrium production in the economy. There is competition between intermediaries, but the bid-ask spread remains positive in equilibrium. In the model, suppliers face random costs and make production decisions after observing the realization of costs. The producer decision rule is summarized by the critical value of costs that depends on the discount rate. A higher discount rate lowers the critical-cost value, thus reducing expected production. A higher discount rate also reduces the number of agents who become intermediaries in equilibrium.

5.1

Intermediation versus a matching market

This section sets out the basic intermediation and search model of Gehrig (1993). Consumers and suppliers have two options. They can enter into

Matching and intermediation by

firms

119

a decentralized matching market where they meet randomly and bargain over the price of the good or they can transact with an intermediary. Section 5.2 extends the Gehrig model by altering the bargaining process and by introducing additional types of transaction costs. A buyer and a seller that meet in the marching market may fail to transact even if there are potential gains from trade. The failure to trade is due to the presence of asymmetric information about buyer willingnessto-pay levels and seller opportunity costs. The sequence of events is as follows. Intermediaries select prices and communicate those prices to buyers and sellers. After observing those prices, buyers and sellers decide whether to visit an intermediary or to go to the matching market. Some buyers or sellers may be quantity rationed by the intermediary and sent to the matching market. At market equilibrium with a monopoly intermediary, both the intermediated market and the decentralized market are active. If there are competing intermediaries, the bid-ask spread collapses to the Walrasian price, all consumers and suppliers transact through intermediaries, and the decentralized market does not operate. Buyer willingness-to-pay levels are represented by v. Thus, at price /?, the buyer's utility for a willingness-to-pay level v is

U(v) = v - p. There is a continuum of buyers whose willingness-to-pay levels are uniformly distributed on the unit interval. Given these assumptions, aggregate demand is linear and equals D(p) = 1 — p. Seller opportunity costs are represented by c. The seller's net benefit with opportunity cost c at price w is R(c) = w — c.

There is also a continuum of sellers whose opportunity costs are uniformly distributed on the unit interval. Given these assumptions, the aggregate supply is linear: S(w) = w. Buyer willingness-to-pay levels and seller opportunity costs are their private information, although aggregate demand and supply are common knowledge. This helps to explain the fundamental distinction between decentralized and intermediated markets. In the decentralized market, both search and bargaining are hampered by uncertainty about the characteristics of potential trading partners. Buyers and sellers are paired by the search process. Once they are matched, uncertainty persists about the type of trader they are dealing with: the buyer still does not know the seller's opportunity cost and the seller does not know the buyer's willingness to pay. The uncertainty in the bargaining

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Intermediation versus decentralized trade

process affects the search process by making the returns to search uncertain. The intermediary remedies the uncertainties associated with search and bargaining. Assume that the intermediary is able to post prices. The intermediary is able to select prices calculated by using aggregate information regarding the distribution of buyer and seller types because the intermediary expects to deal with many buyers and sellers. Even though individual buyers and sellers also know aggregate demand and supply, they are not able to make full use of this information because of the vagaries of the search and bargaining process. Consider first the decentralized matching process. The number of agents on the two sides of the market may differ. The matching technology is such that a market participant on the long side of the market is matched with an agent on the short side of the market with some probability k in the interval [0, 1]. The matching probability for an agent on the long side will depend on the relative number of agents on each side and will be less than or equal to k. Thus A is a parameter representing the efficiency of the matching process, in which k = 1 is a fully efficient matching market. Increasing the parameter k lowers transaction costs for buyers and sellers. The bargaining process for buyers and sellers in the matching market reflects information asymmetry. Once a match is made, one of the two traders, selected randomly, makes a take-it-or-leave-it offer. The other trader can choose to accept the bid and trade occurs, or the trader can reject the bid, whereupon further trading opportunities cease. Assume that only traders who expect positive gains from trade enter the matching market. Let (p(v) and \/f(c) represent the conditional distribution of trader types active in the matching market. Let the buyer bidding strategy equal z(v) and the seller bidding strategy equal y(c). Recalling that k is the probability of a match, the buyer and the seller expected utilities in the matching market are

(1)

U(v) = \ I ^ Jc
(2)

R(c) = \ f

( v - z(v)) dx/f(c) + \ I

( v - y(c)

^ Jy(c)
(y(c) - c) d
(z(v) - c) dcj>(v).

The intermediary sets an ask price p and a bid price w, in competition with the matching market. The intermediary randomly rations the long side of the market if the number of buyers and sellers that go to the intermediary are not equal. Let q equal the number of buyers and x the

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number of sellers. Then the intermediary's profit is (3)

n = (p - w) min(#, x).

The value to buyers of trading with the intermediary, v — p, and the value to sellers, w — c, are contingent on not being quantity rationed by the intermediary. Market equilibrium consists of three things: (1) a bid and ask price for the intermediary, (2) buyer and seller expectations about whether or not they will be rationed by the intermediary, and (3) buyer and seller choices of which market to enter, the matching market or the intermediated market. There are three stages to the market-clearing process. First, intermediaries select prices to maximize profit. Then buyers and sellers choose between the matching market and the intermediary. Those rationed by the intermediary can move on to the matching market. Finally, the matching market clears. For any positive bid-ask spread, there will be an active matching market. This is because buyers with willingness to pay such that w < v < p and sellers with opportunity costs such that w
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Intermediation versus decentralized trade

Consider the decision of buyers, as the case for sellers is the same. Suppose that a buyer with a willingness to pay i; chooses to enter the search market. Then any buyer with a higher willingness to pay would either search or trade with the intermediary rather than remain inactive because otherwise he could imitate buyer v and still obtain positive gains from trade. Suppose that a buyer v chooses to enter the matching market. Then it follows that any buyer with a lower willingness to pay also would enter the matching market (or be inactive). This establishes that the set of buyers visiting the intermediary comprises all those buyers with willingness to pay greater than v. I sketch out the basic argument. There are two cases: either the number of buyers visiting the intermediary is less than or equal to the number of sellers or the number of buyers visiting the intermediary exceeds the number of sellers. Consider the case in which the number of buyers visiting the intermediary is less than or equal to the number of sellers. (It is not necessary to review the other case, which is similar.) Since the number of buyers visiting the intermediary is less than or equal to the number of sellers, the intermediary does not ration buyers, so that the expected value to buyer v of visiting the intermediary is simply v — p. On the other hand, there may be more buyers than sellers on the matching market so that the buyer expects to be rationed on the matching market with some likelihood y. The expected returns from entering the matching market are

thus yU(v).

Since it is assumed that the type v buyer chooses the matching market, rather than being rationed by the intermediary, it must be the case that expected returns from the matching market exceed the surplus obtained by trading with the intermediary: yU(v) > v — p. Now consider now a buyer with a lower willingness to pay, v < v. Observe that the type v buyer would not have lower utility form by using the best bid strategy z(u), rather than z(v) by incentive compatibility arguments. To understand the implications of this, define U(v\ v) as the value of being of type v but bidding as some other arbitrarily chosen type i/:

£/(i/, v) = £ f 1

Jc
( v - z(v')) diKc) + £ / l

(v - y(c))
Jy(c)
Thus, since z(v) is a better strategy for consumer i; than is z(v), it must be the case that U(v) > U(v, v). Further, note that by the definition

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123

oft/(v),

U(v, v) > U(v) - 2 -1 I

L Jc
(v - v)d^c + f

Jy(c)
(B - v)dfc\ J

> U(v) - (8 - v). Multiplying both sides by y yields yU(v) > y[/(i)) — y(i) — v) > yU(v) — (v — v) > v — p. Thus type u also prefers the matching market for any v < v. This establishes that all buyers with willingness to pay above v choose to purchase from the intermediary. A similar argument shows that all sellers with costs below c choose to sell to the intermediary. Now that is has been shown that the critical values i>o, v9 Co, and c define the equilibrium, it remains to determine their magnitude. The sets of agents who are active in equilibrium are identical so that vo = c and c 0 = D, because a buyer with v < c or a seller with c > v will find no counterpart in the matching market. Thus the interval [c, v] defines the set of buyers and the set of sellers in the matching market. So, in equilibrium, no rationing occurs in the matching market (other than missed trades due to the limited efficiency of the matching mechanism represented by A). The distributions of agents in the matching market (v) and x//(c) are equal to the uniform distribution on [c, v]. The buyer's optimal bid strategy is the standard take-it-or-leave-it offer that maximizes dc fz I (v — z)-—rJc

V-C

Thus the buyer's offer strategy is z(v) = (v + c)/2. The seller's offer maximizes dv ' (y-c)- _, 'y v — c Jy so that the seller's offer strategy is y(c) = (v + c)/2. Substituting for the bid functions in U and R, we have

f

(4)

U(v) = £ T - ^ [ ( V " cf + (2v-v-

cfl

8v— c

(5)

R(c) = ^^-=[(c - vf + (2c-v-

cfl

8v- c Thus the critical pay-off levels U(v) and R(c) are equal: U(v) = R(c) = (A./4X8 " c). It can be easily shown (see Gehrig 1993) that the intermediary's prices are market clearing. This means that prices equate the demand and supply

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Intermediation versus decentralized trade

faced by the intermediary, /)(/?*) = S(w*), so that, given the form of demand and supply, Thus neither side of the market is rationed, and the value of visiting the intermediary is v — p* for buyers and w* — c for sellers. For the critical traders v and c, (6) (7)

R(c) =

w*-c.

Solving for v and c yields the value of trading volume: (8)

1 - D* = c* = [4(1 - p*) - A]/2(2 - X).

The intermediary's profit function is FI = (/?* — w*)c*, or (9)

n = (2/7* - l)c*.

The profit-maximizing prices that solve the intermediary's problem depend on the search-efficiency parameter: p*

= 3/4 - A/8,

u;* = 1/4 + A/8.

Trading volume equals 1 - D* = c* = 1/4. The intermediary trades with buyers in the interval [3/4, 1] and sellers in the interval [0, 1/4]. Buyers and sellers in the interval [1/4, 3/4] enter the matching market. The equilibrium beliefs of buyers and sellers are that they will not be quantity rationed by the intermediary. The equilibrium is illustrated in Figure 5.1. The prices are symmetric around the Walrasian price pw = 1/2. Also, the critical traders v and c are symmetric around the Walrasian quantity q w = 1 /2. As the matching market becomes increasingly efficient, that is, as X tends toward one, the price spread narrows: p*(l) = 5/8 and w*(l) = 3/8. Therefore, even with an efficient matching market competing with the monopoly intermediary, the intermediary still offers a price spread that straddles the Walrasian price. The remaining spread reflects the inefficiency due to the matching and bargaining process and the advantages offered by the intermediary's posted prices. The price spread is less than that of a monopoly intermediary, where pM _ 3^4 anc j WM _ 1^4 jkjg j s j u e t 0 competition from the decentralized matching market. However, as efficiency of the matching market vanishes, that is, as X tends toward zero, the intermediary's prices tend to the monopoly prices.

Matching and intermediation by

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125

1 S(w) = w \

p* /

pw= 1/2

w* 1 | 1/4

1/4 + A./8

q w =l/2

= 3/4

Figure 5.1. Equilibrium in the intermediated market and the matching market.

As Gehrig (1993) observes, there is a multiplicity of equilibria arising from the coordination problem between buyers and sellers and from their beliefs about the likelihood of rationing. The market equilibrium obtained in this section is appealing because it weakly dominates the no-trade equilibrium (and any other equilibrium). This occurs because visiting the intermediary is costless. Traders do not incur direct costs of visiting the intermediary nor does observation of the intermediary's posted price require foregoing the matching market. If it were costly to visit the intermediary and observe the posted prices, there might be a weakly dominating equilibrium with less trade or no trade with the intermediary, or possible indeterminacy in the model. The use of coordination mechanisms other than the intermediary's posted prices also could affect the equilibrium outcome. In addition, inventory holding by intermediaries could reduce buyer and seller concerns about being rationed, which could also alter the equilibrium outcome. Gehrig (1993) also considers Bertrand competition between two intermediaries. Again, trader beliefs about the possibility of being rationed affect the equilibrium outcome. The Walrasian equilibrium is a Bertrand-Nash equilibrium. If one intermediary offers the Walrasian price, the other cannot profitably offer a negative price spread, while a

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Intermediation versus decentralized trade

positive price spread would not generate trades. Moreover, any positive spread offered by one intermediary is subject to competition by the other intermediary's offering a lower ask price and higher bid price. At the Walrasian equilibrium, there are inactive buyers and sellers, and there is no active matching market. Consumers and suppliers are treated symmetrically. The lowestwillingness-to-pay consumer and the highest-cost supplier who deal with the intermediary have the same level of surplus: U(v) = R(c) = A/8. Moreover, the intermediary earns a surplus of p* — w* = 1/2 — k/4 from each unit bought and then resold. The total surplus earned from transacting with the marginal buyer and seller equals 1/2. The greater the efficiency of direct exchange, the higher the proportion of surplus going to the intermediary. With fully efficient matching in decentralized exchange, X = 1, so that the intermediary obtains half of the total surplus from transacting with the marginal buyer and seller. With fully efficient matching, therefore, the intermediary obtains less than half of the surplus of the buyers and the sellers who transact with the intermediary.

5.2

Costly intermediation

This section extends the basic model of competition between the intermediary and a matching market in several ways. First, the intermediary has a per-unit transaction cost k. The comparative static effects of the transaction cost on the equilibrium outcome are examined. Also, the prices in the decentralized matching market are established by use of full-information alternating-offer bargaining between the buyer and the seller, as in Rubinstein (1982), thus eliminating the disadvantage of the matching market that is due to asymmetric information bargaining. The uncertainty of the matching process remains. It is assumed that the matching process is fully efficient. As before, consumers purchase at most one unit of the good and have a reservation value v. The reservation values of the population of consumers are distributed over the unit interval according to the cumulative distribution function F(v) with continuous positive density f(v), and F(0) = 1 - F(l) = 0. Suppliers sell at most one unit of a good and have a production cost c. The production costs of the population of suppliers are distributed over the unit interval according to the cumulative distribution function G(c), with continuous positive density g(c), and G(0) = 1 — G(l) = 0. Both consumers and suppliers discount future benefits with a discount factor 8 > 0. The trader's discount factor affects the equilibrium negotiated price and thus alters the intermediary's price spread.

Matching and intermediation by

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127

Consumers and suppliers who choose to search are matched randomly only once. After a match is made, the consumer's reservation value and the supplier's production cost are observed by the other party. If the consumer's reservation value is less than the supplier's cost, no exchange takes place. If the consumer's reservation value is greater than or equal to the supplier's cost, alternating-offer bargaining takes place. Assume that the supplier makes the first offer. Then, as shown by Rubinstein (1982), exchange takes place at the supplier's first offer. Therefore, if a consumer of type v is matched with a supplier of type c, the consumer obtains a share of the gains from trade equal to (v — c)[S/(l + 8)] and the supplier obtains (v — c)/(l + 8). Note that a higher discount factor 8 tilts the allocation of gains from trade in favor of the buyer. There are no transaction costs after a match has been made. Since there is no asymmetric information between a matched buyer and seller, exchange always occurs as long as there are gains from trade. Moreover, since no delay occurs in exchange, all gains from trade are captured by the consumer and the supplier. Therefore the only transaction costs are due to asymmetry of information before matches are made. The asymmetry of information is due to the random matching process. This framework is adapted to contrast matching markets with posted prices. Allowing parties to a match to capture all potential gains from trade provides a benchmark for intermediaries. The equilibrium has the same properties as that in Section 5.1. In equilibrium, consumers and suppliers in the interval [c, v] enter the matching market. The intermediary trades with high-value buyers in (v, 1] and low-cost sellers in [0, c). Buyers in [0, c) and sellers in (v, 1] are inactive. As before, the critical values c, v are those that balance the market, so that there is no quantity rationing in equilibrium:

(10)

1 - F(v) = G(c).

The consumer's reservation value is

(11)

I/( V ,C) = - 4 T

[(v - c) dG(c).

1 +0 Jc

The consumer buys from the intermediary if and only if

v - p > U(v,c). The critical-reservation value solves (12)

p = v-U(v,c)

for v in [c, 1) and v = 1 for p > 1 — C/(l, c).

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Intermediation versus decentralized trade

Similarly, the supplier sells to the intermediary if and only if the net benefits w — c are greater than or equal to the expected returns from a match. The expected returns from a match for a supplier with cost c < v are (13)

R(v,c) =

/ (v-c)dF(v). I +8 Jc The critical cost for suppliers, given v and w, solves (14) w = c + R(v, c) for c in (0, v] and c = 0 for w < R(v, 0). The firm's equilibrium bid and ask prices are functions of the criticalreservation values and opportunity cost, p(v, c), w(v, c), respectively, derived from Eqs. (12) and (14). The prices are increasing in the critical values: Pl(v,

c) = 1 - T^—AG(V) - G(c)] > 0, 1+0 $ P2(V, C) = 7—r(u - C)g{c) > 0, 1+0

, c) = ——:(v - c)f(v) > 0, l+o , c) = 1 - ^—AF(v) - F(c)] > 0. l+o Thus an increase in the number of suppliers selling to the intermediary (higher c) is associated with higher bid and ask prices. Similarly, the fact that fewer consumers are buying from the intermediary (higher v) is associated with higher bid and ask prices. It is easy to demonstrate that a higher v is associated with a higher bid-ask spread, while a higher c is associated with a lower bid-ask spread: (p\ — w\) > 0and(/?2 — ^2) < 0. Consider the intermediary's choice of prices. The monopoly intermediary chooses p, w to maximize profit defined by (15)

n(p, w) = (p-w-

k)G(c),

subject to the constraints (10), (12), and (14). The consumer's critical reservation level can be expressed as a function of the critical-cost level, from Eq. (10): v = V(c) = F~l(l - G(c)). Furthermore, by substituting from constraints (12) and (14) into the intermediary's profit function (15), profit can be written as a function of the critical-cost level: (16)

n(c) = [p(V(c), c) - w(V(c), c) - k]G(c).

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If c > 0 solves the intermediary's optimization problems, the first-order condition is (17)

n\c) = (p-w= 0.

k)g(c) + [(pi - wi)V'(c) + (p2 - w2)]G(c)

Observe that increasing the size of the market by an increase in c lowers the markup since (p\ — w\)V'(c) + (p2 — wi) < 0. The existence of an interior solution depends on the size of the intermediary's transaction cost. There exists a critical value of the transaction cost k such that intermediation is profitable for any k in the interval [0, k). The critical value is equal to k

i

To derive the critical value k, substitute pi(v, c),i = 1,2 and w,(v, c), i = 1, 2 for pi and w, in Eq. (17):

n'{c) =\v- -^-\

£ G(c)dc - (v - c)G(c)j - c)F(v) - JV F(v)dv] - k\

- j^\(v r l+o

f(v)

1+. The intermediary chooses c > (Hf^O) > 0. Evaluating marginal profit at c = 0 yields

(20)

7r'(0) = ji -

[YTS(1

" Ec)

+

T+8Ev\ "" kk \\g ( 0 ) '

Thus 7r'(0) > 0 for k < k. Since 5/(1 + S) + 1/(1 + 8) = 1, Ec < 1, and Ev < 1, the critical transaction-cost parameter takes values in the unit interval 0 < k < 1. As long as the intermediary's unit costs do not exceed k, the monopoly intermediary will operate. The critical value of the intermediary's transaction cost has a number of interesting properties. The critical value k is decreasing in the mean of consumer willingness to pay and increasing in

130

Intermediation versus decentralized trade

the mean of supplier cost. The critical value k is increasing (decreasing) in the discount factor S if 1 — Ev < (>)Ec. Consider the solution when F and G are uniform distributions. Then the critical-cost parameter is k — 1/2, and c = [(1 - 2fc)/12]1/2, so that c < 1/3 and v > 2/3. From Eqs. (11)—(14), it follows that

An increase in the firm's transaction cost k lowers c, raises /?, and lowers w, thus raising the spread p — w.Ask approaches 1/2, c goes to zero and the markup (p — w — k) tends to zero. As k approaches zero, c goes to (1/12) 1 / 2 and the price spread goes to p — w = 1/3. Finally, an increase in the discount factor S lowers both the equilibrium bid and ask prices. Competition between intermediaries need not yield the Walrasian equilibrium outcome when transaction costs vary across firms. When there are two intermediaries, the low-cost intermediary can deter the entry of the high-cost intermediary and still obtain a positive markup over k. Moreover, when transaction costs k are unobservable, intermediaries can be expected to set positive markups. The results obtained for auction-type competition between intermediaries in Chapter 3 should continue to hold when consumers and suppliers also have the option of going to a decentralized matching market.

5.3

Intermediation with random matching

This section summarizes the model of Rubinstein and Wolinsky (1987) in which trade frictions associated with random matching also create a role for intermediaries. In their model, buyers, sellers, and intermediaries are randomly matched. Intermediaries participate on equal terms with buyers and sellers in the decentralized market because a buyer or a seller cannot deliberately choose to visit an intermediary. The matching process is time consuming, and all agents discount future benefits. Thus intermediaries play a role simply by increasing the number of agents that can buy or sell the good, as long as the likelihood of a buyer's or a seller's encountering an intermediary whom they can trade with is at least as great as the likelihood of encountering each other. Both Gehrig's model, as presented in Section 5.1 and extended in Section 5.2, and the Rubinstein and Wolinsky model address how

Matching and intermediation by

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131

uncertainties in matching and bargaining generate returns to intermediation. In contrast with Gehrig's static framework, the steady-state matching probabilities in Rubinstein and Wolinsky do not depend directly on the choices of buyers and sellers. The matching probabilities are the result of an exogenous matching process. The probability that buyers and sellers will meet each other or that they will meet an intermediary are constant and exogenous. The probability that any individual intermediary will meet a buyer or a seller is determined within the model by the number of intermediaries that enter the market. In Gehrig's model the proportion of buyers and sellers whom an intermediary meets is determined by the equilibrium bid-ask spread. The matching market in Gehrig's model has an exogenous efficiency parameter, but the proportion of buyers and sellers that enter the matching market depends on buyer and seller reactions to the equilibrium bid-ask spread. There are three types of economics agents: buyers, sellers, and intermediaries. There are an equal number of buyers and sellers, normalized to equal 1. There is a pool of K intermediaries, and at any time there are K intermediaries who have a unit of the good to sell and K other intermediaries seeking to purchase a unit of the good, with 2K < K. Buyers and sellers exit the market when they have purchased or sold a unit and are replaced at a constant rate. Define the following transition probabilities for economic agents: a: Probability of a buyer meeting a seller or a seller meeting a buyer; /}: Probability of a buyer or a seller meeting an intermediary; y: Probability of an intermediary meeting a buyer or a seller. The probability y depends on the number of intermediaries. Consider the steady-state equilibrium of the matching process. All agents discount future benefits with a factor S. They buy or sell at most one unit of the good. Market equilibrium consists of an intermediary ask price /?, an intermediary bid price w, and a buyer-seller transaction price z. A seller's expected utility is tfw and a buyer's expected utility is 5^(1 — p) if a transaction occurs after t periods. The intermediary obtains from each pair of transactions with a purchase lag of t and a sale lag ofT. Let the indices B, 5, M, and N indicate buyers, sellers, intermediaries with a unit of the good, and intermediaries without a unit of the good, respectively. Further, let V/, i = B, S, M, N, indicate the steady-state

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Intermediation versus decentralized trade

equilibrium values of being in the unmatched pool. These are the opportunity costs of exchange. On meeting, economic agents agree to divide gains from trade equally or disagree and return to the unmatched pool. The total gains from trade for a buyer and a seller equal one, which is the buyer's utility. The gains from trade for a seller and intermediary (without the good) equal the intermediary's value of having a unit Ww The gains from trade between a buyer and an intermediary equal the buyer's utility from having a unit plus the intermediary's value of returning with the good to the unmatched pool: 1 + V#. At market equilibrium (p, w, z), the following conditions define the outcome. First, if a seller and an intermediary transact and Vs + V# < VM, the bid price is the value to the seller plus half of the surplus: (21)

w = Vs + (1/2)(VM -VS-

VN).

If a seller and a buyer transact and Vs + VB < 1, the negotiated price equals the value to the seller plus half the surplus: (22)

Z = VS +

(1/2)(1-VS-VB).

Finally, if a buyer and an intermediary transact and VM + VB < 1 + V#, the ask price that gives the consumer VB plus half the surplus (1 + V# — VB - VM) is (23)

p = (1/2)(1 + VM - VB - VN).

The values of being in the unmatched pool depend on whether intermediaries are active and buyers and sellers participate in exchange. Individual rationality requires that VB > 0,

Vs > 0,

and VN > 0.

Participation in exchange requires that either w or z be greater than or equal to the seller's opportunity cost Vs and that either 1 — p or 1 — z be greater than or equal to the buyer's opportunity cost VBIf intermediaries are active, the opportunity costs V, are the unique solution to the following system of recursive equations: (24) (25) (26) (27)

Vs = 8[az + Pw + (l-a VB = 8[a(l - z) + j8(l - p) + (1 - a - 0)VB], VM = 8[y(p + VN) + (1 - y)VMl VN = 8[y(VM - w ) + (ly)VN].

Substitute for p, w, and z from Eqs. (21), (22) and (23) to solve for Vh i = B, 5, M, N in Eqs. (24)-(27). The main result shown by Rubinstein and Wolinsky is that if an equilibrium exists with active intermediaries (that is, K > 0 and VN > 0),

Matching and intermediation by

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133

then the solution satisfies the individual rationality and participation constraints only if

y(K) > a. Thus the likelihood of a meeting between an intermediary and a buyer or a seller is at least as great as the likelihood of a buyer and a seller meeting if intermediaries are active in equilibrium. Rubinstein and Wolinsky show that if intermediaries are not active, then y(0) < a and p = 1/2. The intermediary captures only half of the potential profit. To see this, note from Eqs. (21) and (23) that the markup is (28)

p-w

= (1/2)(1 - VB - Vs).

Also, the price spread (p — w) is less than 1/2. This means that the intermediary obtains less than half of the buyer-seller gains from trade. This result is similar to the situation in the Gehrig model. Buyers are better off than sellers as a result of intermediation if and only if z < 1/2. To see this, observe from Eq. (22) that (29)

VB - Vs = 1 - 2z.

Alternatively, from Eqs. (24) and (25), (30)

W [1 - (p + w)]. 1 — o(l — p) Therefore VB > Vs if and only if p + w < 1. To investigate the value of p + w, add Eqs. (21) and (23) to obtain p + w as a function of the steady-state equilibrium values. Then, substitute into that expression using the steady-state equilibrium values from Eqs. (24)-(27), (31)

VB - VS =

. 2{(1 - 5y)/[l - 5(1 - 2y)]} - 5y/[l - 5(1 - yS)] It is easy to verify that 8 < 1 implies that p + w < 1. Thus buyers are less well off than sellers, VB < Vs, and the buyer-seller negotiated price z is less than 1/2; compare this with the Gehrig model in Section 5.1 in which buyers and sellers are treated symmetrically. The asymmetry between buyers and sellers is eliminated if intermediaries sell on consignment, acting more as brokers than merchants. If the intermediaries broker one unit at a time, selling at /?, but paying the seller a predetermined price wo, the asymmetry is removed and buyerseller bargaining splits the surplus.2 The reason is that a predetermined 2

p+ w=

y

The system of Eqs. (24)-(27) changes to:

Vs = 8(az + Pwo{8y/[\ - 8(\ - y)]} + (1 - a VB = S[a(l VM = 8[y(p + VN- w0) + (1 - y)VM], VN=8[yVM+(l-y)VN].

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Intermediation versus decentralized trade

bid price commits the intermediary to a price, but the payment itself is not a sunk cost. Thus the value of a match between an intermediary and a buyer is reduced by wo: l + VN-

w0.

As above, the buyer-seller negotiated price is z = (1 + Vs — V#)/2, and the intermediary's ask price is p = (1 + VM + wo — VB — VN)/2. The discounted bid price equals the value to the seller plus half the surplus: (32)

wo- ^ 7 = Vs + (1/2)(VM -VSVN). 1 - 5 ( 1 -y) Rubinstein and Wolinsky show that in this case VB tends to Vs in the limit as the length of time periods and the discount rate go to zero, so that buyers and sellers have the same opportunity costs in the limit.

5.4

Intermediation and matching with production

Peter Diamond (1982) presents a search model with production in which there are problems in coordinating production with transactions. The likelihood of trade affects production decisions, which in turn affect the likelihood of trade by determining the proportion of producers that have goods to sell. This section examines a related model due to Bhattacharya and Hagerty (1987) that introduces intermediaries into Diamond's search model to determine whether prices mitigate the trading externalities that result from decentralized bargaining. The model does not allow direct interaction between buyers and sellers so that there is no decentralized market that competes with intermediaries. However, I consider this model because agents can choose whether to be producers or intermediaries, so that the relative number of producers and agents is determined endogenously. Agents are infinitely lived, risk neutral, and identical ex ante. They discount benefits with a factor of 8 = 1/(1 + r). There are two types of agents: consumer-producers and intermediaries. A consumer-producer makes a unit of the homogeneous good JC, but can consume it only after exchanging it with another consumer-producer. This is a modeling convention that has the same agents playing the role of buyers when they have not produced a unit and suppliers when they have produced a unit. The cost realization determines whether an agent chooses to be a consumer or producer, with high-cost agents becoming buyers and low-cost agents becoming suppliers. In this way, the model is similar to those considered in the preceding sections of the chapter in which the

Matching and intermediation by

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135

proportion of buyers and sellers is determined exogenously. Hereafter, these agents are simply called producers. Intermediaries carry out trades between producers, with a normalized ask price equal to 1 and a bid price w. Intermediaries visit multiple producers, and producers trade with only one intermediary. After the production decision is made, all buyers are identical and all sellers are identical. As in Rubinstein and Wolinsky, the number of intermediaries is determined by entry. The producer's problem is as follows. The producer obtains utility x from consuming x units and incurs production cost c, which is uniformly distributed on the unit interval. The producer's expected benefit from having a unit of the good is V\ and the expected benefit from not having a unit of the goods is Vo. The producer makes a unit of the good if realized cost is below a critical value c*. The value of not having a unit of the good is the present value of expected returns. The producer without a unit of the good will either produce a unit of the good in the next period or wait another period. Thus the value of not having a good solves the recursive equation

(33)

Vo = max s\ T (Vi - c)dc + (1 - c*)Voj.

The critical-cost value is therefore c* =

The intermediary visits the producer with probability y. Therefore V\ is defined by the expected discounted value of selling the good or holding it for another period: (34)

Vi = 8[y(w + VO) + (1

When the critical value c* is used, Eq. (34) becomes (35)

Vx = (y/r)(w - c*).

Integrating Eq. (33) by parts, substituting V\ — Vb for the critical value c*, and using Eq. (34) yields (36)

(r + y)c* = yw-(c*)2/2.

Thus Vo, Vi, and c* solve Eqs. (34)-(36). Consider the intermediary's profit maximization problem. The steadystate likelihood of trade can be shown to equal c*/(c* + y), where c* is the probability that the agent has drawn a cost value below the critical level c < c* and y is the probability the intermediary visits the

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Intermediation versus decentralized trade

agent.3 The intermediary's expected profit with an infinite horizon then is simply (37)

Tl(w,y;c*) = ^—-a-w). c* + y r The market equilibrium is a symmetric Nash equilibrium represented by (w*, y*9 c*) in which all intermediaries choose the same w* and y* and all producers choose the same c*. The Nash equilibrium is defined by the following three conditions: 1. The producer chooses the critical value c* to maximize expected net benefits, given JC* and y*. 2. The intermediary chooses the bid price w* and the probability of a visit y* to maximize profit n , given the critical-cost value c*, subject to the condition that they are drawn from the set of w, y that produce the same c*. 3. Since agents choose whether to be a producer or an intermediary, an intermediary's expected discounted profit equals the expected discounted benefit of a producer that has a unit of the good:

In equilibrium, the equality of returns to production and intermediation implies that

(38)

-£—l(i-w)

=

L(w-c*)m

c* + y r r In equilibrium, the marginal rates of substitution over (w, y) are equalized across intermediaries and producers: dn/dw Therefore, when the forms of the profit function and the value function are used, (40)

\ —w c* + y

w — c* y

Thus the equilibrium (c*, y*, w*) solves Eqs. (36), (38), and (40). Solving for c* gives the characteristic equation (41) 3

1 = (1 + r)c* + (c*)2/2 + (c*) 3/2 + r(

See Bhattacharya and Hagerty (1987) for the derivation.

Matching and intermediation by firms

137

By continuity, there exists a solution to Eq. (41) between zero and one. The reservation cost c* satisfies 0 < c* < 1. Since the right-hand side of Eq. (41) is strictly increasing in c*, the equilibrium is unique.4 FromEqs. (36) and (40), c* = (y*) 2 . Thus the equilibrium probability of a meeting between a producer and an intermediary y * also lies strictly between zero and one. The equilibrium of the dealer market has a number of properties. A higher interest rate lowers both the critical value c* and the periodic visit probability y*. This means that as the interest rate increases, expected production (by a producer without inventory) increases. Correspondingly, a higher interest rate raises the difference between the value of having and not having a unit of the good since c* = Vi — Vb- The equilibrium bid-ask spread is positive by Eq. (40), 1 > w*. The proportion of agents who become dealers is determined endogenously. Each intermediary has n* customers, where n* = 1/y* by definition. The equilibrium proportion of intermediaries in the population of agents is l/(w* + 1). Since y* < 1 in equilibrium, each intermediary has multiple clients. A higher interest rate lowers the number of intermediaries, raising the number of clients per intermediary. Because the bid-ask spread is strictly positive in equilibrium, the intermediary's profit and that of a producer holding a unit of the good are strictly positive: n* = Vi > o. Since V\ = Vo + c* > VQ9 sellers are better off than buyers, in contrast to the Gehrig model, in which buyers and sellers are treated symmetrically and in contrast to the Rubinstein and Wolinsky model, in which buyers are better off than sellers. The reason is that sellers enjoy the benefits of a low-cost realization. The total surplus obtained by a buyer, seller, and an intermediary equals (2V\ + Vb)- Since II* = V\, intermediaries are as well off as sellers and each captures less than half of the total surplus.

5.5

Conclusion

The economic value of intermediation is illustrated by the returns to intermediation when economic agents have a decentralized trade alternative. Decentralized trade carries risks for buyers and sellers who must search for trading partners and bargain over the terms of exchange when a match is made. The intermediary can alleviate these uncertainties by providing a trading focal point and by posting buy and sell prices. 4

Bhattacharya and Hagerty (1987) explore more general sufficiency conditions for uniqueness based on general forms of the probability distribution of cost uncertainty.

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Intermediation versus decentralized trade

When an intermediary posts prices in competition with a decentralized matching market, the intermediary serves high-value buyers and lowcost sellers with intermediate-value buyers and intermediate-cost sellers entering the decentralized market. Thus those buyers and sellers with the highest gains from trade at the posted prices trade with the intermediary. These results also hold if there is only uncertainty in the matching process, with full-information bargaining after a match is made. If the intermediary incurs a per-unit transaction cost, the critical-cost value below which the intermediary is feasible depends on the expected buyer value, seller cost, and the discount factor. The lower the intermediary's per-unit transaction cost, the greater the intermediary's share of active buyers and sellers. When buyers, sellers, and intermediaries are randomly matched and all terms of exchange are determined competitively, intermediaries continue to have an economic function in comparison with the decentralized trade alternative. The presence of intermediaries increases the likelihood of meeting a trading partner for both buyers and sellers, thus remedying the inefficiencies of the matching process. If buyers and sellers discount future returns, then the cost of inefficient matching is due to delays in obtaining gains from trade. By reducing these costs, intermediaries earn a positive bid-ask spread that equals half of the potential buyer-seller gains from direct trade. In an economy with production, Peter Diamond (1982) has identified a trading "externality" that results from search uncertainty. Search uncertainty is due to there being only a fraction of agents having goods to trade. In turn, agents' production decisions depend on the likelihood of meeting a trading partner. The concern with uniqueness of equilibrium stems from Diamond's (1982) observation that, with multiple equilibria, public policy might play an active role in the economy. If equilibria could be ranked, then government planners presumably would attempt to move the economy from an equilibrium to a Pareto superior one. Moreover, in either the Diamond model or the Bhattacharya-Hagerty model, the Pareto-dominant equilibrium is inefficient, leading these authors to suggest some further scope for government intervention. Whether such regulatory intervention is desirable appears doubtful, given the apparent difficulties of evaluating what equilibrium state the economy is in and then of applying policy instruments to change from one equilibrium to another. Instead of public-policy implications, what I wish to emphasize is that the presence of intermediaries would appear to alleviate the trading externality by providing market-making services to buyers and sellers. Standing ready to buy and sell then should reduce trade uncertainty

Matching and intermediation by

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139

for buyers and sellers and thus increase equilibrium production. Bhattacharya and Hagerty observe that the proportion of agents choosing to be intermediaries is less than the socially optimal level. This need not suggest public subsidies for intermediation since the model does not allow for free entry of intermediaries, only the choice between production and intermediation for existing entrants. What the result does suggest, however, is that the presence of intermediaries improves social welfare at the market equilibrium.

6

Search and intermediation by firms

In the Walrasian market model, consumers, suppliers and firms are price takers, and the selection of market-clearing prices is ascribed to an exogenous Walrasian auctioneer. In practice, however, while some firms act as price takers, many other firms act as price makers, often setting both output prices and input prices to balance their purchases and sales. Certainly one cannot enter a store or view an advertisement without observing that firms post prices for their products. Furthermore, both large and small companies bid for capital, labor, manufactured inputs, resources, and technology. By setting ask and bid prices, wholesale and retail firms act as intermediaries, coordinate transactions, clear markets, and establish relative prices in the economy; see Spulber (1996b). Manufacturing firms often combine production with related market-making activities. These observations suggest that markets are created and operated through the price-setting activities of firms. The question is how market equilibrium with endogenous price setting by firms differs from the frictionless Walrasian framework. The purpose of this chapter is to present a search model that allows an explicit comparison between market equilibrium with endogenous price setting by competing intermediaries and the traditional supply and demand model. I examine market making by price-setting firms with consumers searching for the lowest ask price and suppliers searching for the highest bid price. Contrary to the law of one price and consistent with some search models, equilibrium with price setting by firms features nondegenerate distributions of buyer and seller prices. Moreover, trade frictions give firms market power, so that in my model the buy and sell prices offered by afirmare not equal in equilibrium. Instead, marketmaking firms set buy and sell prices with ranges that are respectively above and below the Walrasian market-clearing price. Furthermore, as a consequence of market frictions, total output lies below the Walrasian output. The market equilibrium is also compared with monopoly intermediation. The equilibrium buy and sell pricing policies are respectively 140

Search and intermediation by

firms

141

below and above those of a monopoly intermediary, and total output lies above the expected monopoly level. The model highlights the role of time as a transaction cost. There are no explicit costs of search. Rather, since search is time consuming, and buyers, sellers, and firms discount future returns with a common discount rate, a buyer may settle for a higher price or a seller may accept a lower offer instead of continuing to search. Firms examine the trade-off between current and future sales in committing to a price. The equilibrium depends on the discount rate in a crucial way. I show that as the discount rate goes to zero, thus eliminating the time cost of search, output at the market equilibrium with price-setting firms approaches the Walrasian outcome. Conversely, as the discount rate becomes large, thus increasing the time cost of search, output at the equilibrium with price-setting firms approaches the monopoly intermediation outcome. Increases in the discount rate lead to an increase in the equilibrium number of active firms, profit per firm, the mean spread between ask and bid prices, and the variance of ask and bid prices, while lowering the number of active consumers and suppliers. To emphasize further the role of time as a transaction cost, I examine one-time entry of consumers and suppliers and then I extend the model to derive the steady-state equilibrium with continual entry of consumers and suppliers. In the basic model, consumers and suppliers enter the market in the initial period and exit when they have purchased or sold the good. I assume that firms commit to stationary pricing policies and choose prices before search begins, as in most search models. The discount rate directly affects the firms' decision problem since demand is nonstationary. Firms are concerned about the trade-off between pricing for high demand in the early periods, when there are many searchers, and pricing in the later periods when there is low demand since many searchers have left the market. I show that there is a unique symmetric equilibrium and characterize the firms' bid and ask pricing policies. I then allow continual entry of consumers and suppliers in each period and the possibility of exit before making a purchase or sale, respectively. In the steady-state market equilibrium, I also assume that firms choose stationary prices. As a consequence, demand is stationary and firms maximize current period profits so that here the discount factor does not directly affect the firm's decisions. Unlike the basic model, a closed-form solution is difficult to obtain. I show the existence of a symmetric steadystate equilibrium with continuously differentiable pricing policies. I do not consider direct trade between consumers and suppliers. Instead, I assume that firms have some advantage over either consumers

142

Intermediation versus decentralized trade

and manufacturers. For retailers and wholesalers, this advantage could consist of specialized technologies for effecting transactions that yield absolute cost advantages, such as computer processing of transactions, bar-code scanners, automated warehousing, and transportation. George Stigler, in his classic 1961 article "The Economics of Information," recognized that because the efficiency of personal search is low for both buyers and sellers, there arises a need for specialized traders. For manufacturers, the advantage could include not only lower transaction costs but also knowledge of manufacturing technology that is not readily available to consumers and suppliers. My purpose is to explore competition between intermediaries rather than comparing intermediation with direct transactions between consumers and suppliers. There are several types of heterogeneity in the present model. Consumers differ from each other in terms of their willingness to pay for the final good, so that reservation values differ. Suppliers differ from each other in terms of the opportunity costs of supplying their good or service so that their reservation values differ as well. This heterogeneity of consumers and suppliers has the advantage of making it possible to derive the traditional supply and demand curves and to compare the results with the Walrasian framework. The search framework is particularly useful in that it makes clear the connection between transaction costs and market equilibrium. Finally, firms differ from each other in terms of transaction or production costs. The analysis shows how heterogeneity leads to market-equilibrium distributions of bid and ask prices. My model contrasts with standard search models that differentiate between agents on the search side of the market strictly in terms of the costs of search so that consumers have the same demands or workers have the same outside opportunities. The exception to this approach is that of Peter Diamond (1987), who examines a search model in which consumers can differ in their willingness to pay for the good. In Diamond's model, search is costly because it takes time and consumers discount future returns. Search models with bilateral heterogeneity have been given limited attention. My search analysis is closely related to that of MacMinn (1980) and the extension by Benabou (1993), who study a search model in which consumers have different search costs while price-setting firms have different production costs, although they do not consider intermediation. In a search model, Hogan (1991) introduces a monopoly arbitrageur that competes with producers and shows that arbitrage may reduce efficiency. His model does not address competition between intermediaries or search across intermediaries as in the present model. Gehrig (1993) presents an intermediation model in which there are heterogeneous consumers and suppliers who have the opportunity to

Search and intermediation by

firms

143

be randomly matched with each other or to visit intermediaries whose posted prices are commonly observable. In contrast to the present model of time-consuming search, Gehrig allows consumers and suppliers to meet costlessly and to trade based on first-and-final offers. He finds that the intermediary trades with a set of consumers with high willingness to pay and suppliers with low cost, which is similar to the set of active consumers and suppliers in my model. Gehrig's model is similar to the present one in that consumers and suppliers are heterogeneous and the monopoly intermediary posts both ask and bid prices. Gehrig's model differs from the present one in that his matching process is static, and since posted prices are commonly observable, there is no search across intermediaries. Unlike the present model, Gehrig is concerned with price setting by a monopolist competing with direct matches between consumers and suppliers. Gehrig further shows that Bertrand competition between identical intermediaries results in Walrasian prices. This contrasts with the market equilibrium in my model in which search across heterogeneous intermediaries results in a departure from the ideal Walrasian outcome, but corresponds with an important limiting case. Rubinstein and Wolinsky (1987) observe that, "Despite the important role played by intermediation in most markets, it is largely ignored by the standard theoretical literature." They present an intermediation model based on a stochastic, time-consuming matching process. In their model the terms of trade are the result of a split-the-difference bargaining process between buyers, sellers, and intermediaries, rather than the search and price setting considered here. The advantage of my model is that relative prices are set by intermediaries. In their model, as in mine, the matching process is exogenously determined and buyers and sellers form reservation values. In my model, consumers and suppliers make optimal search decisions based on the market-equilibrium distribution of ask or bid prices. Finally, in their model, consumers, suppliers, and intermediaries are each identical. This has the advantage of permitting simple stochastic matches of consumers and suppliers with each other or with the intermediaries. The assumption of identical agents does not permit the general demand and supply framework developed here that allows a comparison with the Walrasian framework. Moreover, my framework emphasizes that firms perform a dual role of making markets and transforming inputs into outputs. Thus their role is not simply reduction of market frictions. Models of financial market microstructure generally obtain a bid-ask spread by assuming commonly observable prices, that is without search, either in a perfect competition setting (e.g. Copeland and Galai 1983, and Glosten and Milgrom 1985) or a monopoly setting (e.g., Garman

144

Intermediation versus decentralized trade

1976). Similarly, Dennert (1993) presents a static-equilibrium model of oligopoly competition between dealers in financial markets when there are informed insiders and uninformed liquidity traders and shows that only randomized pricing strategies exist in equilibrium. While the present search model is substantially different, the heterogeneity of intermediaries plays a related role in generating equilibrium price distributions. Also, Yanelle (1989a,1989b) presents a static,financialintermediation model without search in which the intermediary has an advantage over direct transactions because of economies of scale. Bhattacharya and Hagerty (1987) extend the model of Peter Diamond (1982) to examine bid-ask price setting by identical dealers who set prices and choose the number of permanent clients whom they will visit. Their setting, and the other financial intermediation models, are substantially different from the present one. This chapter is organized as follows. Section 6.1 presents the basic market model and describes consumers, suppliers, andfirms.Section 6.2 examines market equilibrium with a one-time entry of consumers and suppliers. Section 6.3 compares the intermediated market equilibrium with the Walrasian equilibrium and the monopoly outcome and characterizes the effects of the discount rate on the intermediated market equilibrium. Section 6.4 considers the steady-state market equilibrium with continual entry and exit of consumers and suppliers. Section 6.5 presents the main conclusions.

6.1

The market model

In this section, I present a model of a market in which competing pricesetting firms act as intermediaries, purchasing a good from suppliers and reselling the good to consumers. Firms post constant ask prices p for sales to consumers and constant bid prices w for purchases from suppliers. The ask and bid prices can be observed only after time-consuming search. Consumers search across firms for the best ask price while suppliers search across firms for the best bid price. I begin by characterizing the three kinds of economic agents and deriving the supply and demand functions faced by individualfirms.Then I set out the firms' optimization problem and define the market equilibrium. All economic agents discount future net benefits at a positive rate 8. There are no explicit costs of search. Since search is a time-consuming process for both consumers and suppliers, the only cost of search is due to the time spent searching and the discounting of delayed benefits. In each period, consumers and suppliers visit one firm and observe the firm's posted ask or bid price, respectively. Thus the cost of search

Search and intermediation by firms

145

for consumers and suppliers is due to discounting future gains from trade. Firms discount future earnings as well, which affects their pricing policies in the case of price commitment. Firms, such as large retailers, typically deal with millions of consumers and thousands of suppliers. The purchases of consumers from such firms and the sales of suppliers to such firms typically are very small relative to the firm's overall sales and purchases. To represent this and to facilitate aggregation, the model assumes that consumers have unit demands and suppliers have unit supplies, while firms purchase multiple units from suppliers and sell multiple units to consumers. By setting ask and bid prices and by purchasing inputs from suppliers and selling outputs to consumers, firms make the market. They stand ready to sell products and to buy inputs at their posted prices. Firms establish and operate the market mechanism by sending price signals to suppliers and consumers that determine their search decisions and their production or consumption choices. The firm is restricted to posting prices and cannot ration consumers or suppliers by quantity. Free disposal is allowed so that the firm can overstock. Firms cannot hold inventories across periods (inventory costs are too high or the goods are perishable). Thus prices must be set such that the quantity purchased is greater than or equal to the quantity sold in each round. The market equilibrium consists of distributions of ask and bid prices across firms. The equilibrium distributions of ask and bid prices are represented by cumulative probability distributions F{p) and G(w) that are defined on the nonnegative real line. Assume that firms choose stationary bid and ask prices. The assumption of stationary price paths is made to simplify the analysis and implies that the market-equilibrium price distributions are also stationary. The equilibrium of the model without the assumption of constant price paths would lead to complex nonstationary price distributions and nonstationary decision problems for consumers and suppliers as well. In the model with a one-time entry of consumers and suppliers, this assumption corresponds to most search models in which prices remain constant until the search process is completed. In the model with continual entry and exit of consumers and suppliers in Section 6.4, it is sufficient to restrict attention to stationary prices along the equilibrium path without restricting strategies. Consumers and suppliers are assumed to be price takers while the firms acting as intermediaries are price makers. In particular, I assume that consumer and supplier decisions are not based on the solvency of the intermediary or the possibility of being rationed. This rules out situations in which sellers might refuse to supply a low-cost intermediary,

146

Intermediation versus decentralized trade

resulting in an intermediary's rationing buyers more than anticipated. This further eliminates the possibility of bankruptcy for the intermediary resulting from buyers' not making purchases. Given the continuum of buyers and sellers, I do not consider-off equilibrium behavior that might arise in other settings. Thus intermediaries set prices based on their supply and demand functions, which depend on equilibrium market price distributions. To highlight the competition between firms acting as market makers, I assume that consumers and suppliers do not trade directly with each other. As noted above, this is due to the intermediary's cost advantages in managing transactions. If the firms are manufacturers, then they may use production technology that is not readily available to customers and suppliers. The purpose of the analysis is not to explain the existence of intermediaries compared with decentralized trade but rather to show the effects of costly search on the market equilibrium with competing intermediaries. Consumers Consumers have a willingness to pay v for the good purchased from a firm. The population of consumers is represented by a uniform distribution of willingness-to-pay levels on the unit interval. Differences in willingness-to-pay levels represent differences in consumer tastes. This representation of consumer preferences differs from most search models in which consumers have an identical willingness to pay for the good but differ in terms of the cost of search. In these search models, price distributions are obtained on the basis of varying search costs. The present model, by assuming heterogeneous tastes, addresses the basic issue of how to allocate goods across consumers with differing valuations and allows a comparison with traditional market models. Since consumers have differing valuations of the good and since the costs of search are deferred gains from trade, it follows that consumers will also have differing costs of search. Consumers know the equilibrium distribution of ask prices F(p) but not the particular firms associated with each price. Depending on the consumer's willingness to pay and on the distribution of ask prices, some consumers will choose to refrain from search. Active consumers search acrossfirmsand observe a single asking price in each period. After observing a price, an active consumer decides whether to purchase the good or to continue searching. The consumer's optimal search rule is to compare the net value of current consumption with the returns to search. The consumer purchases the

Search and intermediation by

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147

good if and only if the ask price p is less than or equal to the reservation value. The reservation value is defined by a standard recursive equation,

(1)

v-r = -^-\j

(v-p)dF(p) + j

(v-r)dF(p)\

where a solution exists. Simplifying the recursive equation with integration by parts yields

= r + \ f F(p)dp.

(2)

o Jo

Consumers with a higher willingness to pay engage in less search.1 A consumer with willingness to pay equal to 1 has the maximum reservation value ?} For any given F, a less-patient consumer engages in less shopping. Suppliers Suppliers' unit supplies represent labor, capital, land, resources, or a manufactured input. Suppliers have an opportunity cost c for the good or service supplied to a firm. The population of suppliers is represented by a uniform distribution of opportunity costs on the unit interval. Different opportunity costs can represent differences in suppliers' outside opportunities, disutilities of effort, or abilities. The model addresses the question of how the market allocates production across suppliers with differences in opportunity costs. Since suppliers have different opportunity costs and since the costs of search are deferred gains from trade, it follows that, like consumers, suppliers will have differing costs of search. Suppliers know the equilibrium distribution of bid prices G(w) but not the particular firm associated with each price. The suppliers' decision problem parallels that of consumers. The supplier sells a good or service to a firm if and only if the firm's bid price w is greater than or equal to the supplier's reservation value. Suppliers have a reservation value t defined by (3) 1 2

- c = j^I" j\t - c)dG(w) + j°°(w - c)dG(w)\,

This follows because the function L(r) is continuous and strictly increasing on [0, oo]. Since the function L(r) is continuous and strictly increasing on [0, oo], it has an (increasing) inverse R. For any v in [0, 1], Eq. (2) has a unique solution r = R(v;8, F) for every 8 and F. The maximum reservation value is r = R{\\ 8, F).

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Intermediation versus decentralized trade

where a solution exists. The recursive equation simplifies to (4)

1 f°° c = Y(t) = t - - / [1 - G(w)] dw.

A higher-opportunity-cost supplier engages in more search. The lowestcost firm has a minimum reservation value of i? For any given G, a less-patient supplier engages in less search. Intermediaries The population of potentially active firms is represented by a uniform distribution of transaction costs k on the unit interval. Differences in transaction costs across firms represent differences in technology and managerial ability. The firms could be either merchants or manufacturers. As merchants, thefirmssell the same number of units that they purchase. As manufacturers, it is assumed that the firm's technology exhibits constant returns to scale. Then, without loss of generality, it can be assumed that the technology converts inputs to outputs on a one-to-one basis. Firms have a constant marginal cost k of carrying out a transaction and stocking or manufacturing a unit of output. I do not consider the entry of additional intermediaries. The intermediaries cannot operate multiple firms. The model with a given number of firms could be interpreted as follows. There is a nonrecoverable cost of entry. This cost must be incurred before the firm observes its technology parameter k. The entry of firms will continue until the expected returns from additional entry would be driven below entry costs. Thus entry determines the density of firms in the economy, but not the distribution of technology types. Since matching probabilities are not affected, this form of entry does not change the analysis, so that the density of firms can be taken as a given. Consider now the actions of market-making firms. Assume that firms post constant ask and bid prices before the search process begins. The rigidity of prices during search is a standard assumption in search models. Firms set prices to maximize the present discounted value of profits, trading off net revenues from current and future transactions. Thus the firm's pricing policy depends directly on the discount rate, as well as indirectly through the demand and supply decisions of consumers and suppliers. 3

The function Y(t) is continuous and strictly increasing in t on [0, oo) so that it has an (increasing) inverse T. For any c in [0, 1], Eq. (4) has a unique solution t = T(c; 8, G) for every 8 and G. The minimum reservation value is i = 7\0; 8, G).

Search and intermediation by

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149

The density of consumers with reservation value r can be represented by /i(r), which is given by (5)

h(r) = dL(r)/dr = 1 + F(r)/S.

Let TV represent the endogenous density of active firms, so that the perfirm density of consumers equals h(r)/N. Each active firm receives an equal share of searchers. By the law of large numbers, the number of active consumers with reservation value r who visit the firm can be calculated. The number of consumers with reservation value r who visit the firm equals the density of consumers per firm times 1 for thefirstround of searches, 1 — F(r) for the second round of searches, [1 — F(r)]2 for the third round of searches, and so on. The firm's demand in the ith round of searches is obtained by integration over the set of consumers with reservation values higher that the firm's ask price for all p < r: (6)

Di(p)= f [l-F(r)]'"^dr.

JP

N

The situation is similar on the supply side. The density of suppliers with reservation value t is represented by Z(f), which is given by (7) l{t) = dY(t)/dt = 1 + [1 - G(t)]/S. The per-firm density of suppliers thus equals l(t)/N. The supply in the ith round of searches for all w > i is

Define weighted demand and supply functions D(p) and S(w), respectively:

These functions will be useful in characterizing the market equilibrium. Given constant posted prices, the price-distribution functions F(p) and G(w) are the same in each period. Substitute for h(r) from Eq. (5) into Eq. (6) and apply the convergence of the sum of a geometric series to Eq. (9). For any market price-distribution functions, the weighted demand has a linear form:

(1!)

flw_."-.".-*M]'H'

+ *M],-

~

-.« + »

150

Intermediation versus decentralized trade

Substitute for l(t) from Eq. (7) into Eq. (8) and apply the convergence of the sum of a geometric series to Eq. (10). For any market pricedistribution function, the weighted supply also has a linear form:

dr(u;

P + 1 - G(t)] A

v T W I N

d r ( u ;

°

°

,,(1+3)

The firm's present discounted value of profits II is defined as

Because firms cannot ration customers or hold inventories, prices must be set such that Dl(p) < Sl(w). The firm chooses prices /?, w to solve the following program: (14)

max n(/?, w, k)

6.2

Market equilibrium

p,w

subject to D\p) < S\w),

i = 1, 2 • • •.

The market reaches equilibrium as a result of the pricing policies of firms acting as intermediaries between consumers and suppliers. This section solves the firm's optimization problem and characterizes the equilibrium price distributions. The constraints in expression (14) are difficult to handle. Accordingly, I solve a relaxed program in which the constraints are replaced by a single less restrictive constraint. I characterize the equilibrium, given the firm's optimal actions in the relaxed program. Then I show that the constraints in original program (14) are satisfied at equilibrium. This establishes that equilibrium applies to firm behavior in the original problem. When the weighted demand and supply functions in Eqs. (11) and (12) are used, the firm's relaxed program is (15)

max Tl(p, w, k) p,w

subject to D(p) < S(w).

The profit-maximizing firm that solves the relaxed program chooses prices such that the weighted demand and supply are equal. Otherwise, the firm could increase its profit by lowering the bid price w. Therefore the constraint in expression (15) is strictly binding. Since D{p) is continuous and downward sloping it has a unique inverse p = P(q). Also, the weighted supply S(w) has a unique inverse w = W(q). Then the firm chooses q to maximize profit: (16)

Tl(q) = [P(q)-W(q)-k]q.

Search and intermediation by firms P,w

151

S(P)

w(k)

Figure 6.1. Profit-maximizing price setting by firms.

Each firm equates the price-spread net of transaction costs with the sum of the reciprocals of the elasticities of demand and supply times the ask and bid prices, respectively.4 Define r](p) = —pD\p)/D{p) and %(w) = wS'(w)/S(w) as the elasticities of the weighted demand and supply functions. The firm's profit-maximizing ask and bid prices p(k) and w(k), respectively, satisfy the following fundamental equation: (17)

p(k) - w(k) -k

=

p(k)

w(k)

ri(p(k))

The solution is represented in Figure 6.1. At the profit-maximizing ask and bid prices, weighted demand and supply are equal: (18)

D(p(k)) = S(w(k)).

To obtain the equilibrium pricing policies, I derive the pricing policies that solve the firm's relaxed program (15) and then show that the 4

The problem of prices bunching at some price as in Diamond-type equilibria does not occur here in equilibrium. Since there are no explicit costs of search, consumers have different willingness-topay levels so that a lower ask price increases demand. A higher bid price raises the amount offered by suppliers who have different opportunity costs. In this setting, differences in transaction costs of firms leads to different prices. Bunching of equilibrium prices in search models is discussed by Reinganum (1979), Stiglitz (1987a), and Benabou (1993).

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Intermediation versus decentralized trade

constraints in general program (14) are satisfied in equilibrium. Given Eqs. (11) and (12), the profit function in Eq. (16) has the form

U(q) =

{f-t-k-

which is strictly concave with a unique maximum at

q(k) = (r-t-k)(l+8)/(48N) for all k < r — i. This is strictly decreasing in k for k < f — i. Prices are given by

p(k)=P(q(k))=(3r + t + k)/4, w(k) = W(q(k)) = (r + 3? - k)/4. The firm's pricing policy is unique. The profit of the firm is strictly decreasing in the transaction cost k since Tl(q*(k)) = (r-i-

kf{\ + 8)/(S8N).

Therefore the set of activefirmsis convex. No consumer is willing to pay more than r and no supplier will sell for less than i so that N = k = r — t is the marginal firm. Given the pricing policies, a unique closed-form solution is obtained for the equilibrium distribution.5 Substitute fork = k and k = 0 so that p = (3r + f)/4, p = r, For p G [/?, p] and w e [w, w], the equilibrium ask and bid price distributions are obtained as follows: 4p 3r

(19)

F(p) = Pr{p*(k)
(20)

G(w) = Pr{w*(k) < w] = 1 -

~ ~\

r—t

r—t Now substitute the equilibrium ask and bid price distributions into the consumer and supplier conditions (2) and (4) to calculate the highest reservation value for consumers and the lowest reservation value for 5

The market equilibrium consists of ask and bid price distributions (F,G) defined by the functional mappings H(p; F, G) = Pr{p*(k) < p} for p < r, H(p; F, G) = 1 for p > r, J(w\ F, G) = Pr{tu*(&) < if} for w > t, and J(w; F, G) = 0 for w < i. The firm pricing policies p(k) and w{k) depend on the equilibrium price distribution through the values of r and t. The pair of price distributions is a market equilibrium if and only if it is a fixed point of the functional mapping (H, / ) : (F, G) - • (H(•; F, G), J{-; F, G)).

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suppliers. From Eq. (2), for v = 1, and r = /?(1),

p

Ap — 3f — r

l(3r+t)/4

—t

_ (1 + 85)r - i ~ 85 ' From Eq. (4), for c = 0 and i = 7\0), A

= t--

1 / Ifi 'r + 3 f 8 J{

= =— d r-t r-t

w

_ (1 + SS)i - r ~ 85 ' Solving for r and i yields r = (1 + 8<5)/(2 + 85),

? = 1/(2 + 85).

Therefore the price ranges are p = (1 + 65)/(2 + 85), w = 1/(2 + 85),

p = (1 + 85)/(2 + 85), u> = (1 + 25)/(2 + 85).

Since the weighted demand and supply are equal, D(p(k)) = S(w(k)), it follows that

p(k) + w(k) = r + i. Substituting for w in Eq. (20), note that

1 - G(w(k)) = [4p(k) - 3f - t]/(r - t) = F(p(k)). Therefore Dl(p(k)) = Sl(w(k)) for all /, so that the firm's equilibrium strategies satisfy general optimization problem (14). The unique symmetric-equilibrium-pricing policy functions for k < r — fare p(k) = (1 + 6<5)/(2 + 88) + Jfc/4,

w(k) = (1 + 28)/(2 + 85) - k/4. The equilibrium set of active firms is the convex set [0, k], with the transaction cost of the marginal firm equal to the difference between the highest consumer reservation value and the lowest supplier reservation value: N = k = r — f.

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Intermediation versus decentralized trade

The unique market-equilibrium ask and bid price distributions are as follows. The distribution of ask prices is (21)

F(p) =

— Zo

forp € [p, p],

with F(p) = 0 for p < p and F{p) = 1 for p > p, where p = (l + 6S)/(2 + 85),

p = (l + 85)/(2 + 85).

The distribution of bid prices is (22)

G(w) =

W(2 + 8 )

. / ~ * for 28

we[w,w],

with G(w) = 0 for w < w and G(w) = 1 for w > w, where w = 1/(2 + 85), w = (1 + 2<5)/(2 + 85). At market equilibrium, both the bid and the ask prices have nondegenerate distributions. The price distributions are functions of the rate of discount. This serves to emphasize the role played by time-consuming search in price setting. A consumer is active if and only if the consumer's willingness to pay is greater than or equal to the minimum support price of the price distribution. Therefore, if a consumer is active, so are consumers with a greater willingness to pay. Active consumers thus have high reservation prices in the convex set [0, 1], where v > 0 is the marginal consumer. From Eq. (2), v = p = R(i)) = f. For suppliers, from Eq. (4), c = w = T(c) = t, and active suppliers have low opportunity costs [0, c]. In equilibrium, the number of active consumers and suppliers and total output Q is 85). The number of active firms is £ = 45/(1+4(5). The equilibrium is illustrated in Figure 6.2.

6.3

Comparison with Walrasian equilibrium and with monopoly

I now compare market making by price-setting firms with the Walrasian and monopoly equilibria. These benchmarks are represented in Figure 6.3. I also examine the effects of the discount factor on the market equilibrium.

Figure 6.2. The market equilibrium with stationary pricing. p,w

pM = 3/4

D w (p)=l-p

Figure 6.3. The Walrasian equilibrium and monopoly intermediation equilib-

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Intermediation versus decentralized trade

Comparison with Walrasian equilibrium Consider first the Walrasian framework, which assumes a frictionless economy with exogenous price setting. In the Walrasian equilibrium, supply and demand are equalized at a single price and transaction costs are zero. A consumer is able to observe the market-equilibrium price without engaging in search. A consumer thus purchases the good at the market-equilibrium price if and only if the price is less than the consumer's willingness to pay for the good. It is interesting to determine whether this is a limiting case of market equilibrium with price-setting firms. Given a uniform distribution of consumer willingness-to-pay levels on the unit interval, the number of consumers willing to purchase the good is given by those consumers with willingness to pay between p and 1. Thus aggregate demand is simply Dw(p) = 1 — p. Similarly, given a uniform distribution of supplier opportunity costs on the unit interval, the aggregate supply is Sw(p) = p. Equating demand and supply, we find that the Walrasian price and quantity are pw = 1/2 and Qw = 1/2. The equilibrium price ranges for bid and ask prices straddle the Walrasian price for all positive S: w < w < pw < p < p. Thus the properties of the bid-ask spread that are observed in financial market-monopoly models (Garman, 1976) carry over to search markets with competing intermediaries. Thus competition between intermediaries does not lead to the Walrasian outcome. Moreover, the spread of prices around the Walrasian price is not due here to inventory costs, but rather is due to the local market power of firms as a consequence of consumer search costs. Bid and ask prices that straddle the Walrasian price implies that the total output with price-settingfirmsis strictly less than the Walrasian output levels for all positive 8: Q(S) < Qw. This shows that transaction costs cause aggregate output to fall below the perfectly competitive output. As the discount rate goes to zero, the range of bid prices and the range of ask prices converge to the Walrasian price: lim w = lim w = lim p = lim p = pw. 8^0

8^0

8^0

8-+0

Also, the aggregate output with price-setting firms converges to the Walrasian equilibrium output: l i m ^ o Q(S) = Qw. This result illustrates the effects of the time costs of search on the market equilibrium. When the cost of time becomes very low (that is, the discount rate falls), total output rises toward the Walrasian equilibrium. However, with a low cost of time, search costs are lowered, so that only firms with very

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low transaction costs remain active. This means that there are relatively fewer firms in an equilibrium with a lower discount rate. Since consumers search more, price competition between firms becomes much more vigorous and the spread between the ask and bid prices approaches zero. Thus the market equilibrium with price-setting firms approaches textbook market equilibrium. In the limit, the only active firms are lowtransaction-cost firms posting prices in a manner that resembles that of the Walrasian auctioneer. Comparison with monopoly In the monopoly equilibrium, there is a single price setter and the market clears in the first period without search taking place. The costs of market clearing are just monopoly profits and do not include search costs. A monopoly with transaction cost k sets prices such that demand and supply are equal, Dw(pM) = Sw(wM), and the markup satisfies fundamental equation (17). The firm equates the markup over cost to the sum of the reciprocal of the demand elasticity times the ask price and the reciprocal of the supply elasticity times the bid price: pM __ WM _k — pM^w^pM^

_^_ WM/{:W(WM).

N o te that, in contrast to

the firm's optimization condition that was already derived, the monopolist's prices are based on the Walrasian supply and demand functions. The monopolist's optimal ask and bid prices are therefore equal to pM(k) = (3 + k)/A and wM(k) = (l - k)/A. The monopoly output is QM(k) = (1 - k)/A so that expected output is QM = 1/8. For any finite discount rate 8, the price spread for each firm is within the monopoly price spread for the same transaction cost k: wM(k) < w(k) < p(k) < pM{k). For any finite discount rate 8, the total output with price-setting firms is strictly greater than expected output under monopoly: QM < Q(8). Thus, for any finite positive 8, each competitive firm offers a lower ask price and a higher bid price than the monopoly and the total output with price-setting firms lies between the monopoly and the Walrasian output levels: QM < Q(8) < Qw. As the discount rate goes to infinity, all firms are active, with each firm's pricing strategy tending toward the monopoly pricing policy, lim p(k) = pM(k)

and

lim w(k) = wM(k).

Also, as the discount rate goes to infinity, the aggregate output with

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Intermediation versus decentralized trade

price-setting firms converges to the expected monopoly output: Q(S) =

QM.

As the discount rate rises, the cost of search to consumers and suppliers rises as well. This causes the equilibrium output to fall toward the monopoly output. With high costs of time, search costs increase for consumers and suppliers, so that firms with higher transaction costs can operate profitably. This implies that when search costs are high many firms will operate in equilibrium but price competition will be less vigorous. The spread between ask and bid prices increases as a consequence of reduced price competition. Characterization of the market equilibrium The equilibrium spread between a firm's ask price and bid price exceeds the firm's per-unit transaction cost for all but the marginal firm:

p(k) - w(k) -k = (k- k)/2 > 0, for all k < k . This result is important since it demonstrates the existence of positive arbitrage profit in equilibrium. This occurs because firms set prices and face downward-sloping demand functions and upwardsloping supply functions as a consequence of the time costs of search. This result demonstrates that arbitrage profit is observed in equilibrium with a continuum of competitive price-setting firms. The form of the firm's pricing-policy functions is particularly interesting since it shows that the less efficient firms offer a higher ask price and a lower bid price. Thus the firm's ask and bid prices are inversely correlated, and a firm with a higher transaction cost k has a higher price spread. This testable proposition shows that high prices and low factor payments are due to inefficiency rather than to market power. Moreover, the markup p(k) — w(k) — kis decreasing in k, so that less-efficient firms have smaller markups. Consider now the effect of the discount rate on the market equilibrium. The discount rate affects consumers' and suppliers' search decisions and determines the firm's pricing policy. A higher rate of discount lowers the number of active consumers and suppliers and raises the number of active firms. The intuition is that a higher rate of discount raises the costs of additional search to consumers. This increases the returns to intermediation by firms, thus increasing the marginal transaction cost at which firms can operate profitably, which increases the number of firms that are active in equilibrium. The means of the ask and bid price distributions are Ep = (1 + 7<5)/(2 + 85), and Ew = (1 + S)/(2 + 85). The variances of prices are

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159

equal in the input and the output sides of the market: The price means and variance have the following properties. An increase in the discount rate raises the mean ask price, lowers the mean bid price, and raises the variance of the ask and bid prices. The expected spread between ask and bid prices thus is increased by a higher discount rate. A higher discount rate, by raising the cost of search, also increases price dispersion. Since a higher rate of discount also raises the number of active firms, it follows that the number of active firms is positively correlated with the expected bid-ask spread. This means that increased competition is associated with greater expected spreads and higher variance. The reason for this correlation is that a higher cost of search raises the returns to intermediation. The equilibrium price spread and profit perfirmare now characterized. The net equilibrium price spread is p(k) - w(k) -k = [48- k{\ + 4<5)](1 + S)/(16S2). A higher discount rate increases the markup for all active firms k < k. This result reflects the value of information. A higher discount rate increases the cost of time-consuming search for consumers and suppliers. Firms raise ask prices and lower bid prices because consumers and suppliers are willing to pay a premium to avoid further search. The effect of the discount rate on profit per firm depends on the firm's level of cost.6 The reason is that while a higher discount rate increases the markup for all firms, the effect on quantity sold per firm differs. A higher discount rate raises quantity sold for higher-cost firms and lowers quantity sold for lower-cost firms.

6.4

Market equilibrium with continual entry of consumers and suppliers

This section introduces entry and exit by consumers and suppliers in each period and characterizes the steady-state market equilibrium. Assume now that a set of consumers and a set of suppliers, each uniformly distributed on the unit interval with unit density, enter the market in each period. In any period, consumers and suppliers exit the market without making a purchase with probability a, where 0 < a < 1. Consumers and suppliers remaining in the market continue searching until they have made a transaction, at which time they voluntarily exit the market. 6

Profit for a firm with transaction cost k is U(k) = [(1 + 8)/(2 + 8<$)16<52][4<$ - k{\ + 48)]2.

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Intermediation versus decentralized trade

To avoid a multiplicity of equilibria, I restrict attention to stationary pricing policies on the equilibrium path without restrictions on pricing off the path; see Benabou (1993) for a similar argument. It is necessary to consider only histories that do not involve simultaneous deviations by a positive measure of players (see Benabou 1993 and Gul, Sonnenschein and Wilson, 1986). The steady-state market equilibrium is represented by a pair of stationary ask and bid price distributions, F(p) and G(w), respectively. Consumers and suppliers need consider only stationary ask or bid price distributions in selecting their search strategies. Since this generates stationary demand and supply functions, so that firm profit functions are stationary, it follows thatfirmshave no incentive to deviate from stationary pricing strategies. The entry and the exit of consumers and suppliers alter the firm's demand and supply functions. The exit probability acts as a discount factor and modifies the consumer and supplier recursive equations: (23)

v = L(r) = = rr ++\\^^ - II F(p) dp,

(24)

c = Y{t) = t

1 -a

r°° / [1 - G(w)] dw.

8 + a Jt

The density functions are h{r) = 1 + [(1 - a)/{8 + a)]F(r) and l(t) = The single-period supply and demand functions are stationary as a consequence of the stationary-equilibrium price distributions. In any period, the number of consumers with reservation value r visiting the firm equals the per-firm density h(r)/N times 1 for consumers just entering the market, times 1 — F(r) for consumers already in the market for one period who are on their second search, times [1 — F(r)]2 for consumers already in the market for two periods who are on their third search, and so on. Therefore a firm's demand function in any period for p < f is obtained by integration from p to r and summing across consumers. Then using for the density function h(r) and the sum of a geometric series, we obtain the steady-state demand function for p < r

(25)

D{p) =

£ { ( 1 - a)[l - F(r)]Y - ^ dr J

p

i=o i

=

/»r r

N(8 + a) Jp [a

c

- a)F(r)

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Using the density function l(t) and the sum of a geometric series we obtain the steady-state supply function with w > i (26)

S(w) = f

h

Y"[(l - a)G(f)]'' — dt N ;=o H w f

S

l\dt.

Since the supply and demand functions are stationary, firms choose prices to maximize their single-period profit functions subject to D(p) < S(w). The firm chooses prices /?, w to solve the following program: max n(/?, w, k) p,w

subject to D(p) < S(w).

The profit-maximizing bid and ask prices p(k) and w(k) satisfy fundamental Eq. (17), and supply and demand are equal: D(p(k)) = S(w(k)). The firm will not set prices such that purchases exceed sales, because otherwise, the firm could increase its profit by lowering the bid price w.1 There exists a continuously differentiable symmetric-equilibrium pricing policy, p(k), w(k), with p(k) increasing in k and w(k) decreasing in k for all k < k (see Appendix). For the steady-state equilibrium, the equilibrium price ranges for bid and ask prices straddle the Walrasian price for all positive <5; w < w < pw < p < p. The total output with price-setting firms is strictly less than the Walrasian output levels for all positive S\ Q(S,a)
With integrable price-distribution functions, the firm's demand curve D(p) is continuous and decreasing on [0, r] so that it has a continuous and decreasing inverse P{q) on [0, D(0)]. The supply function S(w) is continuous and increasing on [i, 1] so that it has a continuous inverse W(q) on [0, 5(1)]. The firm chooses output q < 0 to maximize the profit function U(q,k) = [P(q)-W(q)-k]q, where P is inverse demand and W is inverse supply.

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Intermediation versus decentralized trade

Thus the possibility of exit creates a cost of search as well. As the discount rate and the likelihood of exit go to zero, the costs of search fall and the steady-state equilibrium then approaches the Walrasian equilibrium. Next compare the steady-state equilibrium with search and pricesetting firms with monopoly. For any finite discount rate 8 and exit probability 0 < a < 1, the steady-state price spread for eachfirmis within the monopoly price spread for the same transaction cost k: wM(k) < w(k) < p(k) < pM(k). From Eqs. (A2) and (A6) in the Appendix, p(k) < (1 + k)/2 + r- p(k). Since r < 1, p(k) < pM(k) and w(k) > wM(k). As the exit probability approaches one for any discount rate 8, all firms are active in the steady-state equilibrium, with each firm's pricing strategy tending toward the monopoly pricing strategy pM (k) = (3 + M

lim p(k) = pMM(k) (k) l

and

lim w(k) = wwMM{{k). 1

This holds because lim^^i r = 1 and limo^i p(k) — (3 + k)/4. The discount rate 8 approaching infinity is no longer sufficient for the steady-state firm pricing policies to approach the monopoly equilibrium. A high discount rate is also not necessary for monopoly. The exit probability a approaching one is sufficient for the steady-state equilibrium pricing policies to approach the monopoly equilibrium. This is because a high exit probability is sufficient to raise the cost of search to consumers and suppliers.

6.5

Conclusion

The model of firms presented here combines intermediation between input and output markets with price setting. Intermediation between customers and suppliers often is the primary economic activity of firms, whether they are merchants or manufacturers. The neoclassical model of the firm implicitly recognizes that, as intermediaries, firms coordinate input purchases, production, distribution, and output sales. However, since the neoclassical firm takes prices as given, the firm intermediates on only the quantity side by transforming inputs into outputs. In the neoclassical framework, market making takes place outside the firm through exogenous price adjustment represented by the Walrasian auctioneer. On the other hand, models of imperfect competition in the field of industrial organization have brought the price-setting role of firms to center stage, but ignore the intermediation role of firms by emphasizing competition in product markets. The analysis presented here shows

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163

how price-setting firms make the market by acting as intermediaries between consumers and suppliers. It shows that market clearing can involve distributions of both ask and bid prices when price-settingfirmsact as intermediaries and establishes conditions under which the standard model of supply and demand is a limiting case of a market with costly search. Consumers and suppliers have incomplete information about ask and bid prices. Search is costly since search acrossfirmsis a time-consuming process and economic agents discount future returns. Equilibrium bid and ask prices set by firms depend on the discount rate. The level of the discount rate can be viewed as a determinant of the value of information. A higher rate of discount raises the cost of search and increases the spread between bid and ask prices as well as the dispersion of ask and bid prices. This in turn raises the profits of firms. In the equilibrium of the singleentry model with stationary pricing policies, the number of active firms is increasing in the discount rate. This result demonstrates that there are greater returns to intermediation when search is more costly. The time cost of obtaining price information thus creates economic rents for firms acting as market-makers. Microeconomic and finance models often assume that a price spread cannot be sustained because of the incentives for unlimited purchase and resale. The no-arbitrage condition is predicated in part on the assumption thatfirmsare price takers with prices set by a Walrasian auctioneer. In the present model, with market making by competing price-setting firms, the price spreads set by firms are positive at the market equilibrium. The equilibrium with competing intermediaries is compared with the standard Walrasian supply and demand framework. For any rate of discount, the market clears in the sense that supply equals demand. The range of ask prices is above the Walrasian price and the range of bid prices is below it, and total output is less than the Walrasian output. As the discount rate goes to zero, thus lowering the time cost of search, the market equilibrium with price-setting firms approaches the Walrasian equilibrium. This result confirms the familiar textbook characterization of supply and demand as an ideal or limiting case of a market with price-setting firms. The competitive equilibrium with price-setting firms is also compared with the case of a monopoly intermediary. As the discount rate becomes large, thus raising the time cost of search, the market-equilibrium output falls, reaching the monopoly equilibrium in the limit. With a continuum of firms, more firms operate as the discount rate increases, and each firm's ask and bid prices converge to the monopoly ask and bid prices. This demonstrates the trade-off between costly search activities

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Intermediation versus decentralized trade

by consumers and suppliers and the economic rents earned by firms acting as intermediaries.

Appendix Proposition Al. (i) Along the equilibrium path with stationary pricing, the ask price function p(k) is nondecreasing and the bid price function w(k) is nonincreasing. (ii) The equilibrium price-distribution functions F(p) and G(w) are nondecreasing. (iii) The set of active firms is a convex set [0, k]9 and the transaction cost of the marginal firm is equal to the difference between the highest consumer reservation value and the lowest supplier reservation value: k — r — t Proof, (i) I first show that if q(k) is an equilibrium output, it is nonincreasing. Define the profit function Tl(q(y), k) = [P(q(y)) — W(q(y)) — k]q(y), for k, y in [0, k]. For q(k) to be an equilibrium strategy it must be the case that U(q(k), k) > U(q(y), k) for all y, k in [0, jfc]. Therefore

(k - y)q(y) > U(q(y), y) - U(q(k), k) > (k - y)q(k), so that k > y implies that q(y) > q(k) and q(k) is nonincreasing in k. Therefore the ask price function p(k) = P(q(k)) is nondecreasing in k, and the bid price function w(k) = W(q(k)) is nonincreasing in k. (ii) The price distributions for p < r and w > i are defined by F(p) = Pr{/?(&) < p] and G(w) = Pr{w(k) < w}. Since k is uniformly distributed and p(k) is nondecreasing, then for p" > pf, F(p") = Pr{p(k) < p"}> Vr{p(k) < p'} = F(pf). The same argument holds for G(w). (iii). Because consumers do not purchase above r and suppliers do not sell below i, the density of firms is k = r — i, for f > i. Q. E. D. Derivation of equilibrium pricing policies for the steady-state case The steady-state demand and supply functions in Eqs. (25) and (26) do not have the simple linear form as in the nonstationary case, so that it is difficult to establish uniqueness of the equilibrium or to derive closed forms of the equilibrium price distributions. If attention is restricted to continuously differentiable pricing policies, it is possible to characterize an equilibrium, although the equilibrium need not be

unique. Define X(k) = [a + (1 - a)k/k] and Y(k) = X(k)/[S + X(k)].

Proposition A2. There exists a continuously differentiable symmetricequilibrium pricing policy p(k), w(k) with p(k) increasing in k and w(k) decreasing in k for all k < k. The pricing-policy functions for k < f — f

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165

satisfy

(Al)

p(k) = Y(k)

(-n^*\

x a+s)

V -i

fk\

[

l

(l+z)8(l-a)/k

(A2) w(k) = l The corresponding equilibrium price distributions are defined by F(p) = p~l(p)/k for p G [p, p] and G(w) = 1 — w~l(w)/k for w e [A, tu]. Also, r and f solve Eqs. (A3) and (A4), where p(k) and w(k) are given by Eqs. (Al) and (A2), with k = r - i = If - 1 = 1 - It:

1 (A4)

0=f

i^p ^ 1 - O f 1 /•*

- / w(k)dk. o + 1 k Jo

Proof. Given that p(k) and w{k) are continuously differentiable, with p(k) increasing and w(k) decreasing in k, and the definition of F and G, it follows that the price distributions F and G are continuously differentiable. Thus P(q) and W(q) are twice continuously differentiable, so that the profit function Y\(q,k) is twice continuously differentiable in q as well. By the classical necessary conditions for q{k), where p{k) = P(q(k)) and w(k) = W(q(k)\ Tli(q, k) = 0 and Un(q, k) < 0. Note that ni(0, k) = r-i-k > Oforf > i andfc < k. Since F(p(k)) = k/k = 1 — G(w(k)), the first-order condition defined at q(k) is (A5) Substituting for q(k) = D(p(k)) into Eq. (A5) specifies the firm's markup: p(k) - w(k) - k (A6)

- a)fe/fc] r

g + g + (l-g)F(r)

-a)k/k]m

a + (l-a)F(r)

Differentiating Eq. (A6) yields a differential equation for the ask price p(k). Rearranging terms places the equation in the standard format, , 8(l-a)/k l+k 8(l-a/k) = 1 I ) P() P( >X(k)[8 + X(k)] 4 4 X(ik)[« + X(ifc)]' The differential equation has a unique, continuously differentiable solution p(k) that satisfies Eq. (Al). The bid price function w(k) can be derived in the same way.

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Intermediation versus decentralized trade

To solve for r and i, perform a change of variables by using the distribution functions in the consumer and supplier recursive equations (23) and (24) and note that F(p(k)) = k/k for p < r and (1 - G(w(k))) = k/k:

i 1=f+jii/'f(,)d,.,+
(A8) (A9)

I — a f™ [l- G(w)]dw 0=? - — - 8 + a Ji

1 — a f* k = t + -— jw' 8 + a Jo k

Integrate by parts to obtain Eqs. (A3) and (A4). Further, since D(p(k)) = S(w(k)) for all k < k and Df(p(k)) = -S'(w(k)\ it follows that p'(k) = -w\k) for all* < k. So r + i = 1. Also, k = r - i = 2r - 1. Since p(k) = r and w(k) = f, it follows that p(k) + w(k) = 1 for all k < k. Note that p = p(0) and fc = u;(0) = l - p ( 0 ) . The price functions p(k) and w(k) are thus parameterized by k, since £ = 2? — 1 and £ = 1 — 2?. To obtain the value of £, which determines the form of the pricing functions, it is sufficient to solve Eq. (A3). Rearranging terms, write Eq. (A3) as (MO) l

=

^£

1 +

^

(8 + 1) (8 + 1) k There exists a k (not necessarily unique) that solves Eq. (A 10) since the function $(k) is continuous and maps the unit interval into itself. Since p(k\ k) < 1 for all k in [0, 1], it follows that 0(fc) < 2(8 + a)/(8 + 1) 1 + 2(l-a)/(8 + 1) = 1. Also, since p(k\ k) > p(O;ik) > l/2foralU in[O,l],0(A:) > (8 + a)/(8 + 1) > O.SothereisaitthatsolvesEq.(AlO). Let (F*, G*) be the price distributions that correspond to the pricing policies p*(k), w*(k) defined by Eqs. (Al) and (A2): F*(p) = p*~l(p)/k(F*, G*) for p < r and G*(w) = 1 - w*-\w)/k(F*, G*) for w >i. Since F* and G* are continuously differentiate, the pricing policies p*(k) and u;*(^) in Eqs. (Al) and (A2) are obtained by profit maximization, given F* and G*. The profit-maximizing output q*(k) given (F*, G*) is the global maximum on the interval [0, g*(0)]. To see this, differentiate the first-order condition: Tln(q*(k), k)q*'(k) + nn(q*(k), k) = 0. Since rii 2 = - 1 and q*f(k) < 0, nn(q*(k), k) < 0 for all 0 < k < k. Note that q*(k) = 0. Since Flu does not depend on k, it follows that n n < 0 for all 0 < q < q(0) for all k. The pricing policy chosen by firms depends on the form of the equilibrium ask and bid price distributions since the demand and supply functions depend on the distribution of ask and bid prices; D(p\ F) and

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S(w; G), as do the inverse demand and supply functions, P(q; F) and W(q\ G). Define the revenue net ofpayments to suppliers, n(q; F, G) = [P(q\ F) — W(q\ G)]q, and note that the first-order condition for profit maximization is iz'(q\ F, G) = k. Since k depends on the form of the equilibrium pricing policy, let k(F, G) be the number of active firms operating, given the distributions (F, G). The distributions (F, G) are an equilibrium if and only if they satisfy the fixed-point conditions for

p < r(F, G) and w > t(F, G):

G(w)=l-

k(F, G) nf(S(w\G)\F,G)

and F(p) = 1 for p > f (F, G) and G(w) = 0 for w < t(F, G). To verify that (F*, G*) is an equilibrium, choose any p in the interval [0, r(F*, G*)]. For that /?, there exists a unique k such that p = /?*(/:).Therefore, by the definition of p*(k) and the first-order condition for q(k\ F*, G*), n\D{p\k\ F*, G*); F*); F*, G*)/k(F*, G*) = 7T V ( £ ; ^*. G*); F*, G*)/Jfe(F*, G*) = ik/ifc(F*,G*)

The demonstration for G* is similar. Therefore (F*, G*) satisfies the fixed-point conditions and is a market equilibrium. Q. E. D. Proposition A3. For the steady-state equilibrium, the following hold, (i) The equilibrium price ranges for bid and ask prices straddle the Walrasian price for all positive 8: w < w < pw < p < p. (ii) The total output with price-setting firms is strictly less than the Walrasian output levels for all positive 8: Q(8, a) < Qw. (iii) As the discount rate goes to zero and the exit probability approaches zero, the range of bid prices and the range of ask prices in the steady-state equilibrium converge to the Walrasian price pw = 1/2. Proof, (i) From Eqs. (A2) and (A6), p(0) = 1 - w(0) > 1/2. (ii) Note that with I/a consumers and suppliers, the Walrasian output equals I/(2a). With Eqs. (A2) and (A6) and terms rearranged, the steady-state

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Intermediation versus decentralized trade

equilibrium output is

fk rk

Q(8,a)= / D(p(k))dk Jo

p(k)

[ ~

The second bracketed term is less than (8 + a)/a. Also, Ep(k) = f (1 + S)/(l -a)-(8 + a)/(l - a). Thus Q(8, a) < I/(2a) = Qw. (iii) From Eq. (A7), lim^o p'(k) = 1/4, and from Eq. (A5), lim^^o r = (1 + 7a)/2(l + 3a). Also, lim^ 0 p(0) = 1/4 + (1 + 7a)/4(l + 3a). Thus lim lim w = lim lim w = lim lim p = lim lim p = pw, which establishes (iii). Q. E. D.

Part IV

Intermediation under asymmetric information

Adverse selection in product markets

This chapter considers allocation of goods by intermediaries under asymmetric information. Consumers have private information about their willingness to pay for the good. Suppliers have private information about their opportunity costs. This creates information asymmetries that complicate the process of exchange between consumers and suppliers as well as supplier production decisions. Incomplete information creates a role for intermediaries as designers of trading mechanisms that give consumers and suppliers incentives to reveal their private information. Intermediaries generally are subject to the same information asymmetries as buyers and sellers. They do not know consumer willingness-topay levels or supplier opportunity costs. However, intermediaries have a number of potential advantages over other market participants. The intermediary can achieve cost advantages from specialization as a mechanism designer. Intermediaries can gather additional information by dealing with multiple buyers and sellers. Also, intermediaries have greater latitude in the design of mechanisms as they can tax or subsidize individual transactions, since they are not subject to the implicit budget balancing that direct exchange requires. To address basic exchange under asymmetric information, I begin in Section 7.1 with the basic intermediated bargaining model of Myerson and Satterthwaite (1983). In the model, an intermediary designs a trading mechanism for a buyer and a seller who are exchanging a single object. By the revelation principle, a direct mechanism can represent the outcomes of bargaining under asymmetric information.1 The direct mechanism determines the payment and the likelihood of trade given the announcements by the buyer and the seller of their respective private information. The direct mechanism represents the outcome of such bargaining procedures as first-and-final offers by either the buyer or the seller or alternating offers. It also encompases double auctions, in which 1

See Myerson (1979) and Dasgupta, Hammond, and Maskin (1979).

171

172

Intermediation under asymmetric information

the good is exchanged at some average of buyer and seller bids, as long as the buyer's bid exceeds that of the seller. An intermediary modifies the bargaining process by designing a profitmaximizing mechanism that taxes the exchange. The intermediary's direct mechanism creates a spread between the payment to be made by the buyer and the payment to be received by the seller. As with direct bargaining, intermediated exchange also can fail to take place under asymmetric information, even when the buyer and the seller would realize gains from trade. Because the buyer and the seller have an incentive to conceal their private information, they must be compensated by information rents to induce them to reveal their information. If the gains from trade are not sufficiently large to cover these rents, even intermediated trade will break down. In Section 7.2,1 generalize the model of basic exchange of an indivisible object to allow for production of multiple units by the supplier. I consider intermediated exchange when the consumer has a downwardsloping demand and the supplier has an upward-sloping supply function. I characterize the intermediary's profit-maximizing mechanism when the consumer's willingness to pay and the supplier's production cost are unobservable by the intermediary. Asymmetric information results in a lowering of output below the Walrasian level and can still result in the breakdown of exchange. Next, in Section 7.3,1 extend the production model to allow for multiple buyers and sellers. The problem is made more difficult for the intermediary because aggregate demand and supply are unknown. Therefore the intermediary faces the additional problem of market clearing. The optimal mechanism must assign output to individual consumers and production to individual sellers while balancing total production and consumption. I show how the intermediary's optimal mechanism can be characterized by deriving virtual demand and supply functions that are adjusted for asymmetric information. I derive a shadow price for the intermediary's market-clearing problem that is used to determine the allocation of the good. With many buyers and sellers, the intermediary's information about aggregate demand and supply is improved by larger samples. The intermediary's problem is then to induce individual consumers and suppliers to reveal their demand or cost information. This allows the intermediary to use simpler dominant-strategy mechanisms such as nonlinear pricing and constant prices per unit without significant losses in efficiency. Thus standard pricing mechanisms such as quantity discounts or posted prices can work relatively well, even when individual demand and supply functions are unobservable.

Adverse selection in product markets

173

In Section 7.4,1 examine the role of intermediaries as experts. Asymmetric information about product quality can hinder bilateral trade, as in Akerlof's (1970) well-known model of a market for lemons. Akerlof showed that a market for a product could fail to exist if customers were less well informed than suppliers about product quality. In equilibrium, low-quality used cars drive out high-quality used cars, since consumers are willing to pay only an average price for cars of unknown quality, and only sellers of low-quality cars can trade at that price. As a result of unobservable product quality, there can be returns to centralized quality certification by intermediaries. Since there are foregone gains from trade, there are economic returns to investment in capital equipment or expertise needed to certify the quality of the product. By investing in the technology needed to verify product quality and by certifying product quality, intermediaries can supply useful information to the market. Biglaiser (1993) shows that introducing a monopoly intermediary into a market with adverse selection enhances efficiency.2 His analysis suggests that the intermediary has a greater incentive to invest in monitoring quality than does an individual buyer, since the intermediary buys more goods. In addition, the intermediary's incentive to report accurately the quality of goods stems from the returns to building a good reputation. Biglaiser's model has three types of agents: buyers, suppliers, and an intermediary. When two agents meet, they bargain over the terms of trade. A buyer entering the market decides whether to go to a seller or to an intermediary. In equilibrium, the intermediary has no incentive to sell a low-quality good as a consequence of the returns to reputation. All highquality suppliers sell through the intermediary, while most low-quality suppliers sell directly to consumers, so that a separating equilibrium exists. The chapter is organized as follows. Section 7.1 considers intermediated trade between a single buyer and seller. Section 7.2 examines intermediated trade with production. Section 7.3 examines market clearing by an intermediary and derives the intermediary's optimal mechanism when there are multiple buyers and sellers. Section 7.4 considers intermediation in the market for lemons by experts who can evaluate and certify product quality. Section 7.5 concludes the chapter.

7.1

Intermediated trade

In this section, I consider intermediated trade between a buyer and seller under asymmetric information. A profit-maximizing intermediary 2

See also Garella (1989).

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Intermediation under asymmetric information

designs a trading mechanism for the buyer and seller. I consider the efficiency of the trading mechanism and other properties. For the simple problem of exchange of a single good, the mechanism is said to be ex post efficient if trade takes place whenever there are gains from trade. In other words, trade occurs if the buyer's valuation is greater than or equal to the seller's opportunity cost. Myerson and Satterthwaite (1983) characterize the set of efficient mechanisms for bilateral trading. They build on the insight of Vickrey (1961) who showed the impossibility of designing a mechanism such that three of the following conditions hold: (1) revelation of supply and demand is a dominant strategy for all individuals, (2) no subsidy is needed, and (3) the allocation of goods is Pareto efficient ex post. D'Aspremont and Gerard-Varet (1979) showed that Bayes-Nash mechanisms could achieve efficient allocations without outside subsidies. As part of their analysis, Myerson and Satterthwaite examine trade with a broker, who selects the trading mechanism but cannot own the object being traded. They show that if a welfare-maximizing broker were to subsidize trade, then an individually rational mechanism could achieve ex post efficiency. A broker can tax or subsidize the buyer and seller exchange so that the payment made by the buyer need not equal the payment received by the seller. A profit-maximizing broker taxes the exchange by setting a bid-ask spread. In what follows, I confine attention to their model of a profit-maximizing broker. Both the buyer and the seller have private information. The buyer's willingness to pay v takes values on the interval [uo, v\] with cumulative distribution function F and a density function / that is continuous and positive on the interval. The seller's opportunity cost c takes values on the interval [co, c{\ with cumulative distribution function G and a density function g that is continuous and positive on the interval. Define the buyer's virtual valuation and the seller's virtual cost:

J(v) = v - [(1 - F(v))/f(v)l

H(v) = c + G(c)/g(c).

Assume that both J(v) and H(v) are monotonic functions.3 By the revelation principle, it is sufficient to consider incentivecompatible direct mechanisms without loss of generality. A direct mechanism is one in which the buyer and the seller report their respective valuations to the broker who determines the buyer's payment and the seller's revenue and whether or not the good is transferred. Let (fi,a,b) represent the direct mechanism; /3(v, c) is the probability of transfer, 3

For techniques that apply when these functions are nonmonotonous, see Myerson (1981).

Adverse selection in product markets

175

a(v, c) is the expected value of the payment to be made by the buyer to the broker, and b(v, c) is the expected value of the payment to be made by the broker to the seller. The expected payments reflect the probability of the good being transferred. Let E(,i = v, c, be the expectation operator associated with F and G, respectively. Then, the mechanism, expressed as marginal densities, is defined as Pi(v) = Ecp(v, c), &(<;) = Ev/3(v, c), a\(v) = Eca(v, c), a2(c) = Eva(v, c), bi(v) = Ecb(v, c), b2(c) = Evb(v, c). The buyer's and the seller's expected net benefits from trade of the object are now defined: (1) (2) The mechanism is said to be incentive compatible if truth telling is the preferred strategy for both the buyer and the seller of any type: (3) (4)

U(v) > v/3\(v') — a\(vf) for every v, vf in [vo, v\], W(c) > b2(cf) - cfcic') for every c, c' in [c0, c\\.

The mechanism is said to be individually rational if both the buyer and the seller of any type receive gains from trade: (5) (6)

U(v) > 0 for every v in [DO, V\], W(c) > 0 for every c in [co, c\ ].

The broker selects the mechanism ()8, a, b) to maximize profits subject to the constraints imposed by incentive compatibility and individual rationality. The broker communicates the mechanism to both buyer and seller. The buyer and the seller choose to participate in the trading mechanism, and they communicate their respective type to the broker. Then the broker determines the likelihood of trade and the expected payments by using the realization of the mechanism. Subject to relations (3)-(6), the broker chooses (/3,a,b)to maximize profit defined by (7)

n = EvEc[a(v,c)-b(v,c)].

The broker's expected profit is the spread between the buyer and the seller payments. To solve the broker's problem, it is useful to begin by characterizing the properties of incentive-compatible, individually rational mechanisms. Given incentive compatibility and individual rationality of the mechanism, it follows that fi(v) is nondecreasing in willingness to pay and

176

Intermediation under asymmetric information

fi(c) is nonincreasing in opportunity cost. To see why this is so, note that, by incentive compatibility, (8)

(v - vf)^(v)

> U(v) - U(v') >(v-

v'

for all v, vr. Clearly, for v > v\ it follows that Pi(v) > £1(1/), so that the function is nondecreasing in willingness to pay. A similar argument shows that the expected marginal likelihood of trade /^(c) is nonincreasing in opportunity cost. Now, dividing through relation (8) by (v — i/), consider the limit as vf approaches v. The marginal effect of the buyer's willingness to pay on the buyer's net benefit is (9)

U'(v)

So, by integration,

(10)

U(v) = U(vo)+ f Pi(t)dt.

The second term on the right-hand side of Eq. (10) represents the buyer's information rent. Similarly, for the seller, the effect of the seller's opportunity cost on the seller's net benefit is (11)

W'(c) = -P2(c),

so that, by integration, (12)

W(c) = W(Cl)+

I * /32(t)dt. Jc

The second term on the right-hand side of Eq. (12) is the seller's information rent. These forms of the buyer's and the seller's net benefits show their dependence on the likelihood of trade. The net-benefit functions are useful in characterizing the broker's profit function. Taking expectations with respect to v and to c, integrate Eqs. (10) and (12) by parts and apply the definitions of virtual willingness to pay and virtual opportunity cost to obtain (13) (14)

EvU(v) = U(v0) + EvPi(v)(v EcW(c) = W(ci) + Ec/32(c)(H(c) - c).

The second term on the right-hand side of Eqs. (13) and (14) represent the expected information rents for buyers and sellers.

Adverse selection in product markets

177

From the definition of buyer and seller net benefits from trade, the expected buyer payment and the seller revenue are (15)

EvEca(y, c) = Evvpx(v) -

(16)

EvEcb(v, c) = EcW(c) + Ecc/3(c).

EvU(v),

Simplify the broker's profit function in Eq. (7) by using Eqs. (13)—(16): (17)

n = EvEc/3(v, c)(J(v) - H(c)) - U(v0) - W{cx).

Therefore, given incentive compatibility and individual rationality, it follows that fi\ (v) is nondecreasing, faic) is nonincreasing, and the profit function has the form given in Eq. (17). It can be shown that incentive compatibility and individual rationality also are necessary conditions.4 Given the simple form of the broker's profit function, the profitmaximizing mechanism is easy to obtain. The broker's profit is maximized by raising the buyer's payment at least until the buyer with the lowest willingness to pay has no surplus. Also, the broker will lower the payment to the seller at least until the highest-cost seller has no surplus: U(v0) = W(Cl) = 0. This leaves the broker with the expected value of the likelihood of trade multiplied by the difference between the buyer's virtual willingness to pay and the seller's virtual opportunity cost:

n = EvEcp(v, c)(J(v) - H(c)). The difference between J(v) — H(c) and the actual gains from trade v—c is a distortion due to the information rents necessary to compensate the buyer and the seller for revelation of their true types. The broker chooses the profit-maximizing likelihood of trade. When J(v) > H{c), profit is maximized by setting /3(v, c) = 1, that is, by transferring the good from seller to buyer. When J(v) < H(c), the gains from trade are not sufficiently great to compensate for the payment of information rents. In that case, profit is maximized by setting /J(u, c) — 0, that is, by not transferring the good. A simple example illustrates the optimal mechanism. Suppose that i; and c are uniformly distributed on the unit interval. Then, given the profit-maximizing mechanism, gains from trade are sufficient to transfer the good if and only if v-c> 4

1/2.

The broker chooses ft to maximize profit n in Eq. (17) subject to individual rationality, with ^i (v) nondecreasing and ^ ( c ) nonincreasing. It can be shown that the mechanism derived from the unconstrained maximization of II satisfies the incentive-compatibility constraints. Setting U(VQ) = W(c\) = 0 satisfies individual rationality.

178

Intermediation under asymmetric information

Buyers with willingness to pay less than 1/2 and sellers with opportunity cost greater than 1/2 are inactive. The buyer of type v > 1/2 has utility U(v) = (v-

l/2) 2 /2.

The seller of type c < 1/2 has utility W(c) = (1/2

-cf/2.

Expected payments are a\(v) = v2/2 - 1/8 and b2(c) = 1/8 - c2/2. The expected likelihood of trade is EvEcfi(y, c) — 1/8. The broker's profit is n = 1/24. Compare the broker's profit-maximizing mechanism with the outcome when the broker posts profit-maximizing bid and ask prices. Trade occurs if and only if the buyer agrees to the ask price p and the seller agrees to the bid price w. The mechanism that corresponds to this procedure is jg(t>, c) = 1 if and only if

v > p and w > c,

and fi(v, c) = 0 otherwise. The seller's profit when this mechanism is used is simply the price spread multiplied by the likelihood that the buyer will agree to trade and the likelihood that the seller will agree to trade: 7, w) = (p - w)(l - p)w. The profit-maximizing prices are p = 2/3 and w = 1/3, the likelihood of trade is 1/9, and the broker's profit is n = 1/27. As expected, the broker does better with the profit-maximizing mechanism described above than by using posted prices. The reason is that, by not posting prices, the broker can adjust the likelihood of trade to reflect the reports of the buyer and the seller, increasing the likelihood of trade. This result accords with the observed use of bargaining rather than posted prices when small numbers of economic agents are involved. Posted prices commonly are observed in markets with large numbers of buyers and sellers. When there are many buyers and sellers, the broker's knowledge of the distribution of buyer and seller types more accurately mirrors the population distribution of types. Given the restriction that the broker cannot own the good, the likelihood that purchases and sales will balance by use of posted prices is increased by a greater number of agents whose types are samples from the cumulative distribution of agent types. The preceding discussion focused on deriving profit-maximizing Bayesian mechanisms for the intermediary. The Bayes-Nash equilibrium consisted of truthful revelation of types by buyers and sellers. However, the intermediary need not be restricted to Bayesian mechanisms.

Adverse selection in product markets

179

Mookherjee and Reichelstein (1992) point out that any risk-neutral broker, whether maximizing profit or some welfare measure, can implement the optimal mechanism with dominant strategies for the buyer and the seller. The transfers in the welfare-maximizing dominant-strategy mechanism need be balanced only in expectation. Then truthful revelations of types by buyers and sellers are dominant strategies.

7.2

Intermediated trade with production

An intermediary contracts with a buyer and a producer. The intermediary designs a mechanism that induces the buyer to reveal a willingness-topay parameter and the producer to reveal a cost parameter. The mechanism establishes the level of production, the buyer's payment to the intermediary, and the intermediary's payment to the producer. The model generalizes the Myerson and Satterthwaite (1983) model of the monopoly broker considered in Section 7.1. The model is based on Spulber's (1988) analysis of mechanism design with downward-sloping demand and upward-sloping supply. The intermediary cannot hold inventories of the good. Since the intermediary's mechanism establishes the quantity to be produced, the formal analysis is the same whether the intermediary is a broker who is reselling the good without owning it or whether the intermediary purchases and resells the good. The buyer has benefit B{q, v) from output q, where v is a preference parameter. Assume that B(q,v) is increasing and concave in q, increasing in v, and marginal benefit B\ is increasing in v. The producer-seller has cost C{q, c), where c is a cost parameter. Assume that C(q, c) is increasing and convex in q, increasing in c, and marginal cost C\ is increasing in c. The parameters v and c are private information for the buyer and the seller, respectively. The preference parameter v is distributed on the interval [i>o, v\] with cumulative distribution function F and density function / . The producer's cost parameter c is distributed on the interval [co, c\] with cumulative distribution function G and density function g. Let (q,a,b) represent the intermediary's mechanism, where q(v, c) is the output to be produced, a(v, c) is the buyer's payment to the intermediary, and b(v, c) is the payment made by the intermediary to the seller. Define the expectation operators Ec and Ev as in Section 7.1. The terms a\(v), a2(c), b\(v), and b2(c) are defined as above. The buyer's and the seller's expected net benefits from trade are (18) (19)

U(v) = EcB(q,v)-al(v)i W(c) = b2(c)-EvC(q,c).

180

Intermediation under asymmetric information

The intermediary selects the mechanism (q,a,b)to maximize profits subject to the constraints of incentive compatibility and individual rationality. The intermediary's profit is the same as in the single-unit case: (20)

n = EvEc[a(y, c) - b(v, c)].

By incentive-compatibility arguments similar to those of Section 7.1, the marginal buyer and seller value functions are (21) (22)

U'(v) = W'(c) =

EcB2(q,v) -EvC2(q,c).

By integration of the marginal value functions of the buyer and the seller, the value functions can be expressed as (23)

f EEc B (q(t,

U(v) = U(v0) + f

c 2

c), 0 df,

JVQ

(24)

W(c) = W(c!) + [ ' EvC2(q(v, t), t)dt. Jc

Taking expected values and integrating the value functions by parts yields the following expressions: (25) (26)

EvU(v) = U(v0) + EvEc{B2(q, v)[v - J(v)]}, EcW(c) = W(ci) + EvEc{C2(q, c)[H(c) - c]}.

The monopoly intermediary will raise a and lower b so that at least the lowest-value buyer vo and the highest-cost seller will have no surplus: (27)

U(v0) = W{cx) = 0.

Rewrite the intermediary's profit function in Eq. (20) by using Eqs. (18), (19), (25), and (26) to obtain profit as a function of output: (28)

n = EvEc[B(q, v) - B2(q, v)(v - J(v)) - C(q, c) -C2(q,c)(H(c)-c)].

The intermediary maximizes profit subject to incentive-compatibility and individual-rationality constraints. It can be shown that this entails q\(y) nondecreasing, q2(c) nonincreasing, and U(vo) > 0, W(c\) > 0. The first-order condition for the intermediary's unconstrained optimization problem at each v and c is for q > 0:

(29)

Bi(q, v) - Bn(q9 v)(v - J(v)) - d(q, c) -Cl2(q,c)(H(c)-c) = 0.

It can be shown that the mechanism q(v,c) that solves Eq. (29) satisfies incentive compatibility and individual rationality. At the profit-maximizing output, marginal consumer benefit exceeds marginal

Adverse selection in product markets

B,C

181

C,(q,c)

B,(q*,v)

B,(q,v) q*(v,c)

Figure 7.1. Profit-maximizing mechanism design for intermediation between a consumer and a supplier.

supplier cost: B\(q, v) > C\(q, c). For each pair of types (v, c), output is less than the Walrasian output; see Figure 7.1. Based on consideration of Figure 7.1, note the similarity of the solution to the full-information pricing problem for a monopoly intermediary. To implement the optimal mechanism, the intermediary requires announcements from both the buyer and the seller to calculate the equilibrium output. I now characterize the solution by using an example. Let v and c be uniformly distributed on the unit interval. Let consumer benefit and seller cost have the respective forms ) = vq-q2/2, ) = cq+q2/2. The optimal mechanism is then simply q(v, c) = v — c — 1/2

if v—c—1/2 > Oandg(i>, c) = 0 otherwise. Consumers with preference parameter v < 1/2 and sellers with cost parameter c> 1/2 are inactive in equilibrium. Compare this example with the single-unit example in Section 7.1, in which the good is exchanged if and only if v—c—1/2 > 0.

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Intermediation under asymmetric information

Also, compare the equilibrium output level with the Walrasian output: qw(v, c) = (v — c)/2. Clearly, q(v, c) < qw(v, c), as illustrated in Figure 7.1. Marginal consumer benefit and marginal supplier cost straddle the Walrasian price pw = (v + c)/2:

Bl(q,v)> pW

>d(q,c).

Note also that, with asymmetric information, trade breaks down for v — c < 1/2, while the Walrasian output is positive as long as there are gains from trade, that is, for v greater than c. In the exchange of a single unit, asymmetric information can cause trade to break down even with intermediation by a broker. In the case of production and exchange of multiple units, asymmetric information reduces the equilibrium output below the Walrasian output level. As in the case of a monopoly intermediary who uses linear pricing, the marginal consumer benefit exceeds marginal supplier cost, but the source of the distortion differs. In the present setting, the intermediary is not restricted in terms of pricing policies. Thus, under full information, the intermediary could choose prices such that buyer marginal benefit equaled seller marginal cost. This would maximize the gains from trade from the transaction, and the intermediary could extract the rents by using lump-sum fees. The output distortion under asymmetric information is due to the need to compensate buyers and suppliers for revelation of demand and cost information. In Section 7.3,1 compare allocation under asymmetric information with full-information, first-degree price discrimination in the case of many consumers and suppliers.

7.3

Market clearing by intermediaries

Intermediaries not only face the problem of incomplete information about individual buyers and sellers, but in many types of markets, they may not know aggregate demand and supply. Incomplete information about aggregate demand and supply significantly complicates the problem of providing immediacy to buyers and sellers and balancing supply and demand. In Sections 7.1 and 7.2,1 considered how an intermediary transfers a good from a seller to a buyer. I now turn to allocation of goods across multiple buyers. The analysis can be generalized to incorporate an intermediary who allocates purchases among multiple suppliers and sales among multiple consumers. As noted earlier in Chapter 2, firms use both prices and quantity rationing to clear markets. In the short run, most manufacturing firms are

Adverse selection in product markets

183

constrained by their productive capacity. Retailers and wholesalers are constrained by inventories and the speed of ordering additional supplies. In markets for electricity generation and transmission, naturalgas transportation, capital equipment manufacturing, job-shop services, computer services, and club facilities, firms directly allocate scarce capacity across a set of buyers. When preferences differ across buyers, the profit-maximizing intermediary may adopt pricing policies that allocate the good to those consumers for whom the good has the highest value. This problem is complicated by the presence of asymmetric information about consumer preferences. In addition to not knowing the preferences of individual consumers, the intermediary may not have complete information about aggregate demand. As one might expect, the firm's pricing and supply strategies are highly sensitive to the information the firm has about consumer demand. The profit-maximizing output allocation I begin with the problem of allocating scarce capacity without precise knowledge of aggregate demand. As I show in the next subsection, nonlinear pricing methods such as quantity discounts are useful for revealing individual demand levels. However, given capacity constraints or increasing marginal cost, the shadow price of capacity will depend on the demands of all the firm's customers, so that nonlinear pricing is no longer optimal. Moreover, standard auction methods cannot be used if consumers have multiunit demands. The consumer marginal willingness to pay is u(q, /x;), where q is consumption and /x, is a demand parameter for consumer /. Assume that marginal willingness to pay is twice continuously differentiable in q and /x. Also, marginal willingness to pay is strictly decreasing in q so that demand is downward sloping. Marginal willingness to pay is increasing and concave in /x. Consumer absolute risk aversion is nonincreasing in /x, so that higher-demand types have a lower level of absolute risk aversion: d(-Ui/u)/d/JL < 0.

Aggregate demand is unknown to the firm because it observes only a finite number of consumer types /x;, i = 1 , . . . , n, that are drawn independently from the population distribution F(/x). Assume that (1 — F(/x))//(/x) is nonincreasing. The preference parameter /x takes values in the unit interval / = [0, 1]. Suppose that the firm's marginal costs of production are increasing, so the firm must allocate scarce capacity across consumers. Let C(Q)

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Intermediation under asymmetric information

represent the firm's total cost function, with marginal cost c(Q). The production side of the firm's problem could be replaced by the purchase of inputs from suppliers. This aspect of the firm's problem is set aside to simplify the presentation of allocation on the buyer side. According to the revelation principle, the firm's allocation procedure can be represented by direct-revelation mechanisms for which truth telling is an optimal strategy for consumers.5 The mechanism is represented as an output and payment pair (#(/x;, /X(/)), pifii)) that assigns outputs and payments to each consumer on the basis of consumer announcements of parameter values. Thefirmcommunicates the mechanism to each consumer. Then each consumer reports a parameter value pit to the firm. Finally, the firm allocates outputs and payments on the basis of the reported parameter values. As a consequence of increasing marginal cost, the output allocation to consumer /, which is represented by #(/x;, //,(,-)), depends on consumer f's announced parameter value /z; and the announcements of all other consumers /X(/). As a result of the symmetric representation of consumer preferences, all consumers face the same direct-revelation mechanism.6 Also, since income effects are absent, attention can be restricted to payments that only depend on each consumer's parameter report. Given Bayes-Nash implementation, consumer /'s net benefit from reporting /i; when the true parameter value is /x; is (30)

V(in, £«) = I

U(q(fih jLi(0), /x(/)) dF ( 0 - /?(£;),

where V(/x,) = V(/x;, /x,). Incentive compatibility requires that consumers prefer to reveal correctly their parameter value, V(/x;)> VOx,-, £i) f° r a ll Mi» Ai i n [0,1]. Individual rationality requires that each consumer has nonnegative gains from trade, V(/x,) > 0. Suppose that the firm is a monopolist. The firm chooses a direct mechanism (q, p) to maximize expected profit subject to the constraints imposed by incentive compatibility and individual rationality. The 5

6

The direct mechanism involves two-stage communication as defined by Dasgupta et al. (1980). In the first stage of the model, the monopolist announces the mechanism and consumers report their types. In the second stage, the monopolist announces the output allocation and payment levels. It can be shown that for the present model there is no loss to the monopolist from replacing Bayesian incentive compatibility by the dominant-strategy requirement; see Mookherjee and Reichelstein (1992). Define/i(o = (AH, . . . , tn-uin+i,..., fin), F(i) = (F(m),..., F(jn-i), F(M«+I), ••. ,Ffan)) and F = (F(m),..., F(/x n)). Also, let Im = [0, l ] m for any integer m, 1 < m < n. The analysis can be generalized to allow nonidentical distribution of consumer types and nonsymmetric mechanisms without changing the basic results.

Adverse selection in product markets

185

monopolist's expected profit is given by

(31)

U(q,p) =

dF. i=\

The firm's optimization problem can be solved by standard methods. By using Eq. (1) and incentive compatibility, we can substitute for the payments p in the expected profit equation and maximize profit to obtain the optimal output schedule. Rather than going through the optimization exercise, it is useful to characterize the solution with more familiar supply and demand tools. Suppose that (#*, p*) is the incentive-compatible and individually rational mechanism that maximizes profit. Then, with the optimal output schedule #*(/z;, //,(,•)), the profit-maximizing payment schedule is derived as follows: (32)

p*(in) = f

\u(q*(in, /•Mi

-

/

/X(0), fit) "I

U2(q*(fi, At(l-)), fi) d/x d F ( 0 .

The expected payment can be obtained from Eq. (32) by integration by parts and the assumptions on consumer preferences: / «Jo -[(1 The term in braces represents consumer i 's virtual marginal willingness to pay. The key step in understanding how the optimal mechanism works is to introduce a shadow price for scarce production capacity. The shadow price represents the firm's marginal cost at the optimal allocation. It is also a guide to the allocation of output across the firm's customers. Let p be the shadow price representing the implicit capacity constraint on the sum of individual output allocations. Now equate the consumer's virtual marginal willingness to pay to the shadow price p: (34)

uiqu fit) - [(1 - F(/x / ))//(^)]w2fe, tn) = p.

This is the asymmetric-information analog to equating marginal willingness to pay to the price. The result is a set of output levels qi that depends on the consumer's own type and the shadow price. Next, define a virtual demand function or equivalently an allocation function D* to represent the output levels that equate willingness to pay to the shadow

186

Intermediation under asymmetric information

price in Eq. (34): (35)

ft

= D*(p, W ),

The function D allocates output to an individual of type /x,, given the shadow price p, and corresponds to a virtual demand function. Given each consumer's virtual demand function, we can choose the price that equals the firm's marginal cost evaluated at the total of virtual demands, just as in the traditional supply and demand analysis. Define p* = p*(/x) as the equilibrium shadow price, given the output allocation rule qt = D*(p, /x;). The shadow price equals marginal cost evaluated at total output: (36) This formulation makes clear how asymmetric information about consumer demands affects the estimated marginal value of capacity in equilibrium. To obtain the monopolist's direct mechanism, use the allocation rule for each consumer evaluated at the equilibrium shadow price of capacity: (37)

q*(to, /x(0) = £*(p*(A), to), i = 1, • • •, n.

The solution to Eq. (37) is the mechanism that solves the firm's profitmaximization problem. Because the firm's marginal cost is increasing, it is evident from Eq. (36) that a higher value of /x,- for a given consumer crowds out the output allocation to other consumers even though total output increases. In particular, note that both aggregate output and the shadow price are increasing in /x;, i = 1,.., n. Moreover, the firm's output allocation for any individual consumer is decreasing in other consumers' taste parameters. To see why, differentiate Eq. (36) with respect to /x;- to obtain 3p* where c' = c'(£1=1 D*(p*, /z,)) > 0 denotes the slope of marginal cost. Since D* < 0 and D\ > 0, it follows that 3p*/9/x ; > 0 for every /. Because the shadow price is increasing in the preference parameter, it follows from Eq. (36) and increasing marginal cost that aggregate output also is increasing in \X[. The effect of increasing the taste parameter is equivalent to an outward shift of the virtual demand curve. Furthermore, since the output allocation rule I>*(p*, /x,-) is decreasing in the shadow price, the output allocation for any individual consumer is decreasing in

Adverse selection in product markets

187

every other consumer's taste parameter. The increase in any consumer's allocation from raising that consumer's taste parameter outweighs the reduction in the total output allocated to all other consumers. The output allocation mechanism generalizes easily to a market intermediary dealing with both suppliers and customers. As already shown, the intermediary offers consumers the direct mechanism (#(/x;, /X(/)), pifii)) that assigns outputs and payments to each consumer on the basis of consumer announcements of parameter values. Suppose that suppliers are characterized by marginal cost functions C(JC, OJ), where x is production and Oj is a cost parameter for supplier j . The intermediary purchases x from suppliers with payment w and offers suppliers the direct mechanism (JC(0/, 9(j)), w(0j)). The intermediary balances total purchases and sales and derives the mechanism by using a shadow ask price and a shadow bid price. Comparison of the output allocation mechanism with price discrimination Under asymmetric information, the monopolist is unable to extract all consumer surplus, resulting in second-degree price discrimination. In contrast, with full information, the monopolist would be able to practice first-degree price discrimination. The case of full-information price discrimination provides a useful benchmark for describing the asymmetric-information case. To describe the full-information benchmark, let qt = D(p, /x,-) represent consumer I'S standard demand function, which solves (38)

Under first-degree price discrimination, the monopolist allocates output such that each consumer's marginal willingness to pay equals the shadow price. The profit-maximizing shadow price under full information pF then equals marginal cost evaluated at total demand: (39) where pF depends on the vector of consumer taste parameters. Under asymmetric information, the incentive-compatibility restriction can be represented as a reduction in the consumer's marginal willingness to pay, as shown in Eq. (34). The reduction in the consumer's marginal willingness to pay ensures that the consumer obtains rents in return for disclosing to the monopolist private information regarding the taste parameter. Therefore, for each realization of consumer taste

188

Intermediation under asymmetric information P

c(q)

PF

(AMi) i=\

Figure 7.2. Comparison of monopoly pricing under asymmetric information with first-degree price discrimination.

parameters /x, the monopolist's total output is lower under asymmetric information than under full information. This result can be illustrated with Figure 7.2 and Eqs. (36) and (39). Fix /x arbitrarily. For any /x, in [0,1] and for any price p, D*(p, /x,) < D(p, /jii) since, by definition and given U2 > 0, u(D*(p, /x,-), /x;) > p — u(D(p, /Mi), /Xi). Thus, since the total output line under asymmetric information is below the total output line under full information, and marginal costs are increasing, output is lower with asymmetric information. Figure 7.2 illustrates how second-degree price discrimination in the asymmetric-information case leads to a lower total monopoly output. However, output for each consumer need not be lower under asymmetric information. Since marginal cost is increasing in output, the equilibrium shadow price also is lower under asymmetric information, as shown in Figure 7.2. This may raise some consumers' allocations above the fullinformation level. Note that if marginal costs were constant, the shadow price would equal marginal cost, so that each consumer's allocation would be lower under asymmetric information. Nonlinear pricing Nonlinear or quantity-based pricing is a widely used pricing technique; see Spence (1977b), Mussa and Rosen (1978), Spulber

Adverse selection in product markets

189

(1981b), Maskin and Riley (1984b), and Wilson (1993). Nonlinear pricing is useful for inducing individual consumers to reveal their private information. If the firm knows the population distribution of customer types, then nonlinear pricing can be applied to allocate goods and to clear markets. However, nonlinear pricing is difficult to apply when the firm does not know aggregate demand or supply. However, as the number of consumers served by the firm increases, the firm's knowledge of aggregate demand improves since the group of customers served is a larger sample from the population. This means that with many buyers and sellers, the firm may apply simpler pricing techniques that are approximately optimal. Suppose that the firm offers to all consumers a schedule of contracts specifying output and payment levels. Equivalently, the firm can offer a set of two-part tariffs composed of a linear price and afixedfee. I characterize the firm's optimal contracts for the simple case of two consumer types in the appendix to this chapter. Suppose that consumers are continuously distributed on the unit interval with cumulative distribution F(/x), where F(0) = 1 — F(l) = 0. To find the payment schedule, take the limit of the payments in the discrete-types cases as /x, approaches /x,-i: (40)

P(fit) = / u(q, m)&q - / / u2(q, Jo Jo Jo where the contract chosen by a type /JL consumer is qi — Integrating Eq. (40) by parts, the firm's expected profits are (41)

nn = = max/ max/

/

M Jo J LJ vM

-1

u(q,fi)dq-cq(fi)

u2(q, £t)d<7

j - ~ —

dF(/x).

The firm maximizes profit subject to the constraints imposed by incentive compatibility and individual rationality. Under some conditions the solution to the unconstrained profit-maximization problem satifies the incentive compatibility and individual-rationality conditions. The firstorder condition for the firm's optimal output schedule therefore equates the consumer's virtual marginal willingness to pay to the firm's marginal cost:

(42)

u(q\ n) -

l

/[^u2(q\

/(A0

/x) - c.

Given the assumptions on marginal willingness to pay and on the distribution of the preference parameter, the virtual marginal willingness to pay q(jji) is nondecreasing in the taste parameter so that the mechanism

190

Intermediation under asymmetric information

is incentive compatible.7 The consumer's net benefit U(/JL) is zero below some critical value of the taste parameter that is greater than or equal to zero and the consumer's net benefit is positive and increasing for all higher values of the taste parameter. By a change of variables, the nonlinear price schedule offered by the firm has the form

(43)

P(q)= I u(y,ii*(y))dy, Jo

where /x*(j) = min{/x : g*(/z) = y}. Comparison of the output allocation mechanism with nonlinear pricing when the number of buyers and sellers is large The firm's optimal mechanism derived at the beginning of this section used information about all consumer demands in determining each consumer's allocation. Each consumer's report affected aggregate demand which in turn affected the firm's marginal cost and thus raised the equilibrium shadow price, thereby changing the optimal allocation of the good across consumers. The profit-maximizing allocation just described contrasts with a situation in which thefirmuses nonlinear pricing, such as quantity discounts to allocate the good. In that case, each consumer chooses an allocation independently, and payment levels only are based on the consumer's purchase. Since the profit-maximizing allocation of the good across consumers depends on each customer's type, any allocation achieved with nonlinear pricing generally would be suboptimal. Are there any conditions under which a basic nonlinear price schedule would maximize the firm's profits? Clearly, if the firm has constant marginal costs, each consumer's allocation can be produced independently, and nonlinear pricing would implement the firm's optimal mechanism. Suppose that marginal costs are increasing, or equivalently, the firm experiences a short-run capacity constraint. Then nonlinear pricing is suboptimal as a consequence of the monopolist's incomplete information 7

Differentiate the optimal mechanism g(/z): dq* _

u2{q\ fi) -

l

-^u22(q*,

fi) - u2(q*, M ) ^ ^ ^

The numerator is positive since ui > 0, W22 < 0, and (1 — F(/u,))//(/z) is nonincreasing in 11. The denominator is negative if M21 > 0. If M21 < 0 the numerator is negative by the assumption that the absolute rate of risk aversion is nonincreasing. See Maskin and Riley (1984b).

Adverse selection in product markets

191

about the state of aggregate demand. This suggests that as the monopolist's information about aggregate demand improves so does the optimality of nonlinear pricing. Speaking informally, the monopolist's information about demand improves as the number of consumers rises since this increases the number of samples from the cumulative distribution of consumer preference parameters. The approximate efficiency of nonlinear pricing by the monopolist is demonstrated by showing that profit with nonlinear pricing approaches maximum profit as the number of consumers becomes large; see Spulber (1993a). The return from nonlinear pricing n is given by Eq. (41) evaluated at the nonlinear pricing schedule given by Eq. (43). The maximum profit is the monopolist's profit evaluated at the optimal mechanism n((2*, p*) as defined by Eqs. (31) and (32). The proof involves replicating consumer types. Suppose that there are m consumers of each type jii,i = 1 , . . . , n. Then the profit from nonlinear pricing approaches the maximum profit as m becomes large. The proof that nonlinear pricing is approximately optimal in the limit is related to the standard proof of the weak law of large numbers but differs in two important respects. First, the problem is complicated by the dependence of output on the number of consumers. The monopolist's direct mechanism, given by Eq. (37), is an optimal allocation rule for each consumer evaluated at the equilibrium shadow price of capacity. That allocation depends on the (normalized) size of the sample. Second, concavity of the virtual utility, convexity of costs, and Jensen's inequality play a role in developing the upper bound on the efficiency loss from nonlinear pricing. These results have implications for intermediation. An intermediary can offer a nonlinear price schedule P (q) to its customers and a nonlinear price schedule W(x) to its suppliers when the firm has many customers and suppliers. The profit obtained by an intermediary offering nonlinear prices will approach the maximum profit when there are many customers and suppliers. Consider now the limiting case of the output allocation mechanism with unit demands. As the number of consumers becomes large, the output allocation mechanism converges to posted pricing. In other words, profit from simply posting a constant per-unit ask price p* and bid price if* is approximately optimal for the firm. Thus it follows that, given a large number of consumers, each making purchases of afixedsize, firms will choose to post unit prices. With increasing marginal costs or a binding production capacity contraint, the optimal allocation rule would require charging customers different prices based on the likelihood that they would obtain a unit of the

192

Intermediation under asymmetric information

good. Allocation under such a priority pricing scheme would depend on the demands of all consumers. In contrast, as the number of consumers becomes large, the firm's information about aggregate demand improves, so that the firm will do quite well by posting constant prices. Suppose that individual consumers have a unit demand function given by D(p, fit) = 1 for p < /x, and D(p, /x,-) = 0 otherwise. The quantity q represents the probability that the customer receives a unit of the good. Consumers therefore announce the probability of service that they desire and the nonlinear price schedule R(q) is the cost of being served with reliability q.s Define the optimal output allocation by

if J(fii)>p otherwise

where 7(/x) = /x — (1 — F(/x))//(/x) is the consumer's virtual willingness to pay. Using the allocation qi = D*(p, /x,), define the equilibrium shadow price p = p{q\, ...,#«) as follows: p = inf{p : p > c(Y^i=\ D*(p, fi*(qi)))}. The monopolist's output allocation rule is otherwise The consumer's expected benefit is no longer a function of the announcement of other consumers. This is because utility is linear in output: Vi = ixtqi — R(qt). The monopolist's optimal pricing rule with unit demands is thus R*(q) = H*(q)q

-

/

Jo The optimal pricing schedule with unit demands has a quantity premium, that is, the average payment R*(q)/q increases with expected output. Consumers pay more at the margin for increased reliability of service. Compare this rule with constant per-unit pricing. Since consumer types are distributed according to F(/x), the limit market demand with many consumers is simply

(44)

D(p) = 1 - F(p).

The profit-maximizing price, according to the inverse elasticity rule, is (45)

,

The monopolist's profit with constant per-unit pricing is

(46) 8

11* = p*(l - F(p*)) - C{\ - F(p*)).

See Harris and Raviv (1981) and Spulber (1992c).

Adverse selection in product markets

193

Define the output allocation rule as q *(/>i) = 1 if \x > p* and #*(//,) = 0 otherwise. Then, by the definition of integration, profit can be rewritten as (47)

n* =

where /(/x) = \x — ((1 — F(/z))//(/i) is the consumer's virtual willingness to pay. As the number of customers becomes large, the profit obtained from the optimal pricing rule with unit demands approaches the full-information profit with constant per-unit pricing II*. The analysis applies readily to an intermediary who sells to consumers with unit demands while purchasing from suppliers with unit supply functions. This implies that it is approximately optimal to post constant bid and ask prices as the number of consumers and suppliers becomes large. Therefore, in large markets, a profit-maximizing firm will post constant per-unit ask and bid prices p* and w* because doing so is approximately efficient.

7.4

Product quality and guaranties by experts

The classic adverse selection problem is Akerlof's market for lemons in which suppliers know product quality but buyers do not. Sellers of low-quality goods have an incentive to overstate quality. Biglaiser (1993) introduces an intermediary who plays the role of an expert in determining product quality. The intermediary has an incentive to invest in skills to detect the quality of the product because he buys many more goods than an individual buyer. In addition, the intermediary has a greater incentive to report accurately the quality of the good than does a supplier who sells only a few goods. Therefore the intermediary becomes an expert because of the returns to investment in detecting quality and the returns to investment in reputation. In this section, I review some of the main conclusions of Biglaiser's analysis, without reproducing the full details of his model. There are three types of agents in the market: buyers, sellers, and a monopoly intermediary. All agents are infinitely lived and discount returns with a factor 8 = e~r, where r is the rate of discount. Each seller is endowed with one unit of the good, which can be of two quality levels, high or low. The seller knows the quality of the good, but the quality is unobservable to buyers. The intermediary is able to discern the quality of any seller's good by becoming an expert at a one-time entry cost of K. For ease of discussion, I normalize to zero the cost of meeting a buyer or seller and the cost to the intermediary of testing individual goods.

194

Intermediation under asymmetric information

The intermediary does incur a cost of verifying product quality in that testing delays the sale of the good by one period. A buyer or a seller that has the good receives a return equal to its value in each future period. A buyer values a low-quality good at VL and a high-quality good at VH, where 0 < VL < VH •A seller values the low-quality good at zero and the high-quality good at w#, where UH < VH> This implies that there are always gains from trade between a buyer and a seller, regardless of the quality of the good. In each period a measure i of sellers and buyers enter the market. A proportion k of sellers has a high-quality good while a proportion 1 — k has a low-quality good. The analysis is restricted to a steadystate equilibrium in which the measure of agents entering and leaving the market is equal. Furthermore, each player's strategy maximizes that player's utility, given the strategies of other players, and all players of the same type use the same strategies. Following Akerlof (1970), assume that a buyer values the average quality of goods less than a high-quality seller's valuation: (48)

(l-k)vL+kvH


This market-for-lemons condition (48) makes it impossible for highquality goods to be in the market when the price for all goods is the same. Note that the condition implies that vi < UH- The condition is more likely to hold if the proportion of low-quality goods is high. Consider first the market without an intermediary. Suppose that buyers and sellers are matched randomly and bargain over the price of the good. The bargaining game is not specified. However, assume that if the buyer thinks that the seller has a low-quality good and if that belief is accurate, then the buyer and the seller immediately come to an agreement. The buyer and the low-quality seller trade at some price p. Otherwise, bargaining is subject to asymmetric information. A seller can signal that he or she holds a high-quality good only by waiting to trade. Given these assumptions, two outcomes are possible: there are only low-quality goods in the market or there are both low- and high-quality goods. Suppose that both goods are traded in the market. What is the highest possible price of the low-quality good? The price must be such that the low-quality seller does not have an incentive to delay and thereby represent the good as a high-quality good. To determine the value of representing the good as being of high quality, let t be the delay in trading with a high-quality seller. Suppose that high-quality sellers receive the lowest possible price that keeps them in the market, namely UH> The low-quality seller will reveal truthfully the quality of the good if and

Adverse selection in product markets

195

only if the price p is less than or equal to the present discounted value of what the high-quality seller receives, 8*UH> The incentive-compatibility condition is strictly binding if (49)

p = 8fuH.

Again assuming that the high-quality seller receives exactly UH with delay t, the highest price that can be paid for the low-quality good and still keep the buyer in the market equates the buyer's expected net benefit to zero: (50)

(1 - X){vL -p) + k8\vH - uH) = 0.

Solving Eqs. (49) and (50) yields an upper bound on the price for the lowquality good and a delay in trading the high-quality good such that there are both low- and high-quality goods in the market. The equilibrium delay t solves (51)

8* =

{\-X)vL/(uH-\vH).

From the market-for-lemons condition (48) it follows that 8* is between zero and one. Also, p = 8lun < UHIf low-quality goods drive out high-quality ones, that is, if only lowquality sellers enter the market, social welfare will be (52)

WL = [1/(1 - <5)][(1 - k)vL + XuHl

If both types of sellers enter the market, then social welfare will be (53)

WH = [1/(1 - <5)]{(1 - X)vL + \18\VH

- uH) + uH]}.

There may not be an equilibrium with high-quality goods in the market. Now compare the market outcome with an infinitely lived intermediary. Assume that the intermediary has no more bargaining power than buyers. The intermediary can offer a warranty. Suppose that it is common knowledge whether or not the intermediary has honored warranties in the past. Also, suppose that another intermediary always can enter the market and supplant the incumbent. Although the warranty is not enforceable, the offer is credible because the intermediary is concerned about the consequences of a reputation for not honoring warranties. Assume that the expected time when a buyer and a low-quality seller will trade is the same whether or not the intermediary is in the market if the buyer's belief about the seller's type is the same. The price at which they trade may vary, depending on the presence or absence of the intermediary within the market.9 9

Biglaiser (1993) also assumes that when bargaining with a low-quality seller, the buyer and the low-quality seller will agree to a price that makes the buyer indifferent between purchasing from the low-quality seller or from the intermediary.

196

Intermediation under asymmetric information

Biglaiser (1993) constructs a market equilibrium with the following properties. The market is segmented. All high-quality sellers sell their goods through the intermediary and most low-quality sellers sell their goods directly to buyers. Sellers of low-quality goods need not go through the intermediary since their claim to have a low-quality good is credible. The intermediary receives a high-enough payment for the good so that he accurately represents the quality of the goods he sells. The intermediary's profit is (54)

n = [1/(1 - 8)]X(8pH - wH) - K,

where pn is the ask price of the high-quality good and WH is the bid price of the high-quality good. The intermediary's profit is positive for 8 sufficiently close to one. Social welfare at this market equilibrium with an intermediary is (55)

W* = [1/(1 - 5)][(1 - X)vL + X8vH] - K.

The value of the high-quality good is discounted because of the delay due to testing the good. Compare welfare in the intermediated market equilibrium with the case of decentralized exchange. Consider the difference between welfare in the intermediated market and welfare in the decentralized market for the case in which only low-quality sellers enter the decentralized market, (56)

W* - WL = [1/(1 - 8)]X[8vH - uH] - K.

Compare welfare in the intermediated market with welfare in the decentralized market for the case in which both types of sellers enter the decentralized market, (57)

W* - WH = [1/(1 - 8)]X[8vH - 8\vH - uH) - uH] - K.

Consideration of Eqs. (56) and (57) shows that in either case, as 8 approaches 1, welfare is higher with an intermediary. The reason is that the discounted value of the gains from trade of the high-quality good, VH — UHI exceeds the setup cost that the expert incurs to enter the market. The greater the gains from trade of the high-quality good, the higher the value of the intermediary's intervention. Moreover, the greater the proportion of low-quality goods, the more likely the market-for-lemons condition is satisfied and thus the more likely an expert will enter the market. With a relatively low discount rate or a relatively low setup cost for experts, the intermediary will be profitable and the welfare gain from quality certification by the intermediary will be increased. Biglaiser's analysis shows that in markets in which goods are sold directly both by producers and by intermediaries that certify their quality, the intermediary's goods will have a higher average price and a higher

Adverse selection in product markets

197

average quality. Thus quality certification by experts in markets with adverse selection helps to explain part of the commonly observed bidask spread between wholesale and retail prices. It also explains the presence of retail guarantees for some manufacturers' products because consumers in the model have the choice of whether to purchase the good directly from the manufacturer or through an intermediary. In a dynamic setting, Biglaiser and Friedman (1994) consider intermediaries as guarantors of the product quality of their suppliers. Since intermediaries handle the products of two or more suppliers, their incentives to sell a lower-quality good differ from those of individual suppliers. The intermediary that sells a low-quality product suffers a loss of reputation and thus loses customers for all other products. They characterize the long-run equilibrium of a competitive market in which the presence of intermediaries lowers the threshold prices that are required for sustaining high quality production. Biglaiser and Friedman (1997) extend the analysis of adverse selection to allow for free-entry competition between experts. Intermediaries have an infinite time horizon, unlike buyers and sellers who are active for, at most, one period. This gives intermediaries incentives to learn from experience, to invest in expertise, and to earn returns to building a reputation for truthfulness. Through these activities, intermediaries alleviate adverse selection relative to decentralized trade between short-lived buyers and sellers. Intermediaries address adverse selection by offering nonlinear price schedules to buyers and sellers. Nonlinear pricing induces buyers to reveal their valuation through purchases of higher-quality goods and induces sellers to reveal product quality though premiums for higher quality. They show that decentralized trade cannot yield an optimum allocation, and they provide conditions under which intermediated trade achieves the optimum.

7.5

Conclusion

Adverse selection is a common feature of transactions and contracts in any market. Buyers have unobservable characteristics such as income, location, risk aversion, impatience, and valuation of quality that affect willingness to pay. Sellers have unobservable characteristics such as opportunity costs, production costs, and product quality that affect their supply decisions. Dealing with the effects of incomplete information creates costs for both buyers and sellers. This chapter has presented an array of models in which a profitmaximizing intermediary allocates goods under asymmetric information. Generally, asymmetric information creates distortions such that the

198

Intermediation under asymmetric information

output is below the Walrasian quantity. With production, the marginal benefits obtained by buyers and the marginal costs of sellers straddle the price that would be observed at a Walrasian equilibrium. With multiple buyers and sellers, the intermediary faces the difficult problem of clearing the market when aggregate demand and supply are unknown. The profit-maximizing direct mechanisms entail Bayesian strategies for consumers and suppliers announcing their private information. These mechanisms are relatively complex and appear to differ from commonly observed pricing rules. As the number of buyers and sellers served by the intermediary increases, information about aggregate demand and supply improves. This implies that dominant-strategy mechanisms that determine each buyer or seller allocation individually are approximately efficient as the number of buyers and sellers becomes large. The analysis suggests that intermediaries will use bargaining and other complex allocation procedures when dealing with small numbers of buyers and sellers. With many buyers and sellers, intermediaries use standard nonlinear pricing or linear posted prices without significant inefficiency. Product market intermediaries also address adverse selection by evaluating product characteristics and by certifying product quality. By dealing with a greater number of buyers and sellers, as compared with decentralized trade, intermediaries have incentives to invest in product testing and in reputation. Similarly, in a dynamic setting, longer-lived firms have incentives to test products and to build a reputation for accurate representation of product quality.

Appendix Consider the simple case in which the firm has constant marginal cost c. I return to the case of increasing marginal cost shortly. Suppose for now that there are only two types of consumers, with demand parameters /xo and /xi. Then the firm need offer at most two contracts, (go, ^o) and (<7i» ^i)- As before, let u(q, /x) be the type /x consumer's marginal willingness to pay for consumption q. The individual demand q = £>(/?, /x) is defined by equating marginal willingness to pay to a per-unit price u(q, /x) = p. Assume that there exists q > 0 such that u(q, 1) = c so that consumption is bounded above. Consider first a contract that consists of output at the marginal cost price and a payment that extracts all the consumer's net benefits, as with

Adverse selection in product markets

199

c —

Figure 7.3. The high-demand consumer has greater surplus at any output level by an amount equal to the shaded area A.

first-degree price discrimination under full information: (Al) (A2)

P* = /

D(p, tii)dp + cql

i = 0, 1.

J c

Note that qo < qi and Po < blunder asymmetric information, the first-degree price-discrimination contracts would not separate consumers since both types would prefer the low-priced contract. Adverse selection would occur. The high-demand consumer would obtain no gains from the high-payment high-output contract but would obtain positive gains from the low-payment lowoutput contract since the high-demand consumer's surplus at any output is greater than that of the low-demand consumer, see Figure 7.3. To induce the high-demand consumer to choose the marginal-cost price output q\, the firm must lower the fixed payment by the consumer surplus gained from the low-output contract:

where A is the shaded area in Figure 7.3. This will result in consumers self-selecting, with low-demand consumers choosing (q£, P£) and highdemand consumers choosing (q*, P\).

200

Intermediation under asymmetric information P

Figure 7.4. Adjusting the nonlinear price schedule to maximize profits.

The monopolist can easily obtain higher profits, however. By slightly lowering the quantity offered to the low-demand consumers, the firm loses very little in terms of the fixed fee. This allows the firm to raise the fixed fee substantially to higher-demand consumers. This is illustrated in Figure 7.4. By lowering the quantity below q£ to qo, the fixed fee charged to low-demand consumers must be reduced so that profit earned from lowdemand consumers falls by E. At the same time, the fixed fee can be raised to high-demand consumers by an amount equal to 2?, which is always greater than E. The profit gained by the firm is the difference between thefirst-ordereffect on thefixedfee of the high-demand consumer B and the second-order effect on the profit earned from the low-demand consumer E. The area B represents the decrease in the shaded area A, which was the reduction in the fixed payment required for keeping the high-demand consumer indifferent between the two contracts. Moreover, the low-demand consumer continues to be charged a fixed fee equal to that consumer's benefit from output qo. The firm's profit-maximizing contracts are connected by the problem of adverse selection, that is, consumers may select contracts that were designed for others. The firm's contracts must be chosen to form a schedule that induces consumers to self-select the contract intended for them.

Adverse selection in product markets

201

The fixed payment that leaves the low demand consumer indifferent between purchasing from the firm and not purchasing the good is (A3)

= / Jo

The fixed payment that leaves the high-demand consumer indifferent between the two contracts is (A4)

f q* i= /

r fqo u(q, fi\)dq -

/

i

u(q, tn)dq - Po .

Suppose that a proportion fi are low-demand consumers, while the rest, 1 — /J, are high-demand consumers. The firm's profit is n = /3(Po - cqo) + (1 - j8)(Pi - cq\). After substituting the expressions in (A3) and (A4) for the payment schedules Po and Pi, the firm's profit-maximization problem is rvo P / u(q,iJLo)dq - ficqo

[

Jo

fq* u(q, ljL\)dq — (1 — fi)cq\ Jo/•/iii rqo "I

+ (1 — /}) /

— (1 — )8) I

/

U2(q, /x) dq d/x .

J/jio Jo J The firm's first-order condition for the low-demand consumer's output is (1 _ £ ) r»>\ (A6) M(^ 0 , /XO) = c H — / u 2(qo, /x) d/x. Clearly the low-demand consumer's output is less than the first-degree price-discrimination output level at which marginal willingness to pay equals marginal cost. The marginal price for the low-demand consumer is thus above marginal cost, u(qo, /xo) > c, while that of the high-demand consumer equals marginal cost; see Figure 7.4. Suppose that there are many consumer types distributed on the unit interval /x/, / = 0, 1 , . . . , /, with /xo = 0. The firm chooses contracts such that each consumer is exactly indifferent to the contract offered to the next-lowest type: (A7)

rqt

P t= /

u(q, fii)dq -

/ = !,...,/.

r

rqi-i

/

u(q,

202

Intermediation under asymmetric information

Substituting into (A7) recursively using the expressions derived in (A7) for Pi-i, P(-2 and so on yields (A8)

Pi =

u(q,fii)dq-} JO

since Po = f£° u(q,

J^Q

/ I Juj JO

u2(q, li)dq dfi

8

Adverse selection in financial markets

Intermediaries supply many types of information to their customers and suppliers. Often the information is bundled with the other services that are provided to customers and suppliers. Intermediaries, such as retailers, inform their customers about product characteristics. Intermediaries also relay information about market demand and customer requirements to their suppliers. If there are returns to scale in producing and distributing this information, there are benefits from consolidating transactions through intermediaries. In this chapter, I examine how intermediaries cope with and alleviate adverse selection. Asymmetric information affects the returns to intermediation activities in several crucial ways. Asymmetric information about willingness to pay and opportunity costs creates inefficiencies in bilateral trade, causing efficiency distortions in the amount traded or even the breakdown of trade that would have been mutually beneficial. In this case, there are returns to intermediation by the firm as a designer of allocation mechanisms as observed in Chapter 7. The returns to intermediation are reduced by the information rents that must be given to buyers and sellers to induce truthful revelation. Intermediaries, after all, often face the same asymmetries of information that trouble individual sellers. Asymmetric information can create losses for the intermediary if some agents are better informed about the value of the assets that are being exchanged. The intermediary compensates for expected losses by extracting rents from less-informed agents. Adverse selection has a specific effect on the bid-ask spread in financial markets; see Copeland and Galai (1983) and Glosten and Milgrom (1985). The market maker must deal with informed and uninformed traders. The informed traders may have better information than the intermediary about the value of the asset. Thus the informed traders may know that the value of the asset is above the ask price or below the bid price. In this case, trading with informed traders results in losses for the intermediary. Uninformed traders are said to trade for liquidity and purchase at the ask price or sell at the bid price, depending on their estimates of the asset value of 203

204

Intermediation under asymmetric information

liquidity requirements. The intermediary sets bid and ask prices to recover losses from trades with informed agents through trades with uninformed agents. The returns to dealing with informed and uninformed agents are affected by competition between intermediaries. Dennert (1993) considers a market for a risky asset with competing intermediaries setting bid and ask prices. See also the related results of Kyle (1989) in which uninformed speculators take the role of market makers. In Dennert's model, each intermediary is required to trade up to one unit of a divisible asset. After prices are posted, the value of the asset is realized. Informed traders observe all the bid-ask spreads and determine the quantities to be traded with each market maker. Uninformed traders do not observe the value of the asset and buy one unit from the intermediary with the lowest ask price (or, if the trader is a seller, the trader sells one unit to the intermediary with the highest bid price). Given the framework, the bid price competition is independent of the ask price competition. Thus the model reduces to Bertrand-Edgeworth price competition between intermediaries. A pure-strategy equilibrium fails to exist, but there is a symmetric mixed-strategy equilibrium with positive bid-ask spreads that depend on the number of competitors. An increase in the number of traders increases the bid-ask spread, thus raising transaction costs for all traders. Again, this occurs because the intermediary must offset the losses from dealing with uninformed traders. In contrast, Laffont and Maskin (1990) present a model in which the market maker is the informed trader while all other traders are uninformed. Moreover, the market maker has market power while uninformed agents are small traders. The market maker sets the bid-ask spread based on his inside information. However, when the possible variation in the informed trader's information is not too large, the informed trader has an incentive to conceal that information. In that case, the market equilibrium will be a pooling one and the bid-ask spread will not reflect the informed trader's information. This is a departure from the informational efficiency observed in models in which the market maker is uninformed. When there is substantial potential variation in the informed trader's information, a separating equilibrium will emerge, suggesting that the information inefficiencies in the market associated with a pooling equilibrium occur only when the efficiency losses from pooling are not too large. The problem of adverse selection in markets suggests that there may be returns to centralized information processing by an intermediary who sees a greater proportion of transactions than would individual traders.

Adverse selection in financial markets

205

The intermediary can supply information to the marketplace by various mechanisms to screen traders. I consider two models that examine such screening mechanisms. Asymmetric information about borrower characteristics creates adverse selection problems in trade between borrowers and lenders. This creates a role for financial intermediaries such as banks who take deposits from savers and make loans to consumers andfirms.Such financial intermediaries use various screening and rationing devices to alleviate adverse selection problems that they encounter in writing loan contracts. In their well-known model of credit rationing, Stiglitz and Weiss (1981) examine the role of interest rates set by banks when the characteristics of borrowers are unobservable. They show that banks use interest rates as a screening device to separate high-risk from low-risk borrowers. Banks face a trade-off in setting interest rates. Higher interest rates raise the return from making a loan but change the average characteristics of the bank's borrowers. Because they can default, higher-risk borrowers are willing to borrow at higher rates of interest. Similar effects occur with other screening devices such as collateral requirements. Because of adverse selection, credit can be rationed at the competition market equilibrium. The chapter is organized as follows. I begin in Section 8.1 by considering intermediation by specialists who have less information than market insiders. In Section 8.2,1 examine competition between specialists. In Section 8.3,1 turn to the case of a monopoly specialist's setting the bid-ask spread, in which the specialist is the only informed trader. In Section 8.4,1 consider the equilibrium bid-ask spread in the market for loans when the characteristics of borrowers are unobservable. Section 8.5 concludes the discussion.

8.1

Insiders, liquidity traders, and specialists

Market makers in financial markets provide liquidity to traders by standing ready to buy and sell a financial asset. Traders can convert the asset to cash and vice versa at the prevailing bid-ask spread. Market makers earn a return to providing liquidity services based on the size of the bid-ask spread and the volume of transactions. Traders may have different information about the future returns to the financial assets being bought and sold. To take a simple example, some traders may be insiders who are fully informed about the value of the assets while others, who trade only for liquidity, are uninformed about the value of the assets; see Bagehot (1971), Logue (1975) and Jaffe

206

Intermediation under asymmetric information

and Winkler (1976). In this simple two-type market, the market maker encounters classic adverse selection problems. Suppose that the market maker cannot distinguish between insiders and liquidity traders. Then, if bid-ask prices reflect an average valuation of the assets by traders, those traders who have assets to sell and value those assets above the bid price will leave the market. Those traders who are seeking assets and value the assets below the ask price also will exit the market. Thus a pooling contract based on average valuations can be problematic for the market maker. After adverse selection occurs, the market maker no longer will face the average trader and the contract no longer will be economically feasible for the market maker. The adverse selection problem just described reflects asymmetric information about the characteristics of individual traders. This problem is compounded by the market maker's imperfect knowledge of the value of the financial asset. Insiders may have better information about the asset's value than does the market maker. Informed traders will buy the good from the market maker or sell the good to the market maker only if the value of the asset lies outside the bid-ask range. Thus the market maker makes losses in dealing with the informed traders. Therefore the profitability of the dealer depends on the returns to providing liquidity services, which must be sufficient to offset the losses from dealing with better-informed traders. I begin by examining how an uninformed intermediary selects a bidask spread based on the relative proportions of similarly uninformed liquidity traders and informed insiders. Then I look at how such an intermediary updates the bid-ask spread over time in response to information revealed by completed trades. The bid-ask spread To illustrate the basic adverse selection issues in financial markets, I consider a model adapted from Copeland and Galai (1983) in which the price spread chosen by market makers depends on the relative proportion of informed insiders and uninformed liquidity traders. The analysis highlights the relative returns to market makers that transact with both types of traders. Let p be the market maker's ask price and w the bid price. All informed traders are identical. Let v be the informed trader's valuation of the asset. The market maker's beliefs about the valuation v are represented by a uniform distribution on the unit interval. An informed trader sells a unit of the asset to the market maker if and only if 0 < v < w and buys a unit of the asset from the market maker if and only if p < v < 1. Thus

Adverse selection in financial markets

207

the market maker's expected loss from dealing with an insider is (1)

H(p,w)=

pi

pw

/ (v-p)dv+

/

Jp

(ti;-

J0

The expected preferences of a representative liquidity trader are decomposed into two components. The liquidity trader's expected demand for the asset is D(p) = 1 — p. The liquidity trader's expected supply of the asset is S(w) = w. Since the market maker's beliefs about the value of the asset are represented by a uniform distribution on the unit interval, the market maker's expected value of the asset is Ev = 1/2. So the market maker's expected revenue from dealing with an uninformed liquidity trader is (2)

/(/?, w) = (p- 1/2)(1 -p) + (1/2 - w)w.

Normalize the number of traders to equal one. Let a be the proportion of insiders and (1 — a) be the proportion of liquidity traders in the population of traders. The market maker's expected profit is (3)

TI(p, w) = (1 - a)J(p, w) - aH(p, w).

The market maker is restricted to pricing such that the expected demand and supply of the asset balance: pi pw (4) (l-a)D(p) + a dv = (1 - a)S(w) + a / dv. Jp Jo This implies that prices satisfy (5)

l-p

= w.

Since demand and supply are equal only in expectation, the market maker must have a stock of the asset on hand sufficient to cover any realized excess demand. The market maker maximizes profit subject to market-clearing condition (5). Substituting for w = 1 — /?, profit can be written as a function of the ask price: no?, l - P) = (l - p)(2p -aP-

i).

The profit-maximizing ask and bid prices are functions of the proportion of insiders: ,

w*= w

. 2(2-a) 2(2-a) So the spread is p* — w* = 1/(2 — a). An increase in the proportion of informed traders raises the ask price and lowers the bid price, thus widening the spread. This lowers profits P F

208

Intermediation under asymmetric information

from liquidity traders while lowering the losses from informed traders. The market maker's profit is

For the market maker to be profitable, the proportion of informed traders cannot exceed 2/3. Otherwise the losses from the informed traders overwhelm the gains from liquidity traders. An increase in the proportion of informed traders always lowers the market maker's profit as long as profit is positive. Thus adverse selection reduces the market maker's profit. Compare the profit-maximizing prices with the zero-profit prices in the free-entry perfect-competition case: pc = 1/(2 - a),

wc = (1 - a)/(2 - a).

The monopoly price spread straddles the zero-profit price spread:

w* < wc < pc < p*. Bayesian updating by specialists In the static model of price setting by a specialist or market maker just described, there is no room for updating the beliefs of the specialist or those of liquidity traders in light of the buying and selling behavior of insiders. Yet insider decisions provide information to the specialist about the insider's knowledge of the financial asset's value. The information about the asset's value revealed by purchasing patterns can be used to revise bid and ask prices. As a result, observed bid and ask prices convey information about the value of the asset. Glosten and Milgrom (1985) extend the Copeland and Galai (1983) model to show the dependence of the bid-ask spread on adverse selection. The Glosten-Milgrom model is dynamic, with Bayesian specialists updating their beliefs and revising bid and ask prices.1 As before, the market maker and the liquidity traders are less well informed than insiders. The specialist and the liquidity traders may have similar or different information, but are not systematically better or less informed than the other. For ease of presentation, I consider the special case in which the specialist and the liquidity traders both have only public information. Suppose that the market maker trades an asset whose true value v will be realized at a future date. The asset will take one of two possible values, zo or zi, where zo < z\. Insiders know the true value of the asset. 1

See also Easley and O'Hara (1987) for a model of price setting with Bayesian updating.

Adverse selection in financial markets

209

Market makers and liquidity traders revise their beliefs about the value of the asset at each date t. They believe that the value of the asset is z\ with probability fit and that the value is zo with probability (1 — fit). At each date t, the expected value of the asset for market makers and liquidity traders is defined by vt = Ptz\ + (1 - Pt)zo. The market maker and the liquidity traders update fr at each date in Bayesian fashion. The market maker chooses ask and bid prices pt and wt at each date such that zo <w>t
Ht{pu wt) = pt(zi - Pt) + (1 - Pt)(wt - zo).

Liquidity traders value the asset at pvt, where p represents the tradeoff between current and future consumption. Glosten and Milgrom interpret a high value of p as either a high desire for investment, imperfect access to capital markets, or a positive subjective assessment of the distribution of the asset's value, with the opposite for a low value of p. The preference parameter p is distributed randomly across liquidity traders. The preference parameter is an independent draw from a uniform distribution on the interval [0, 2], so that liquidity traders have a willingness to pay for the asset that can be above or below its expected value. A liquidity trader buys from the market maker at pt if pvt > pt and sells to the market maker at wt if pvt < wt. The market maker will not price above 2vt so as not to close out liquidity traders. The expected profit from dealing with a liquidity trader is (7)

Jt(pt, wt) = (pt - vt)[l - pt/(2vt)] + (vt -

wt)w2/(2vt).

In each period, the market maker trades with only one agent. Let a be the proportion of insiders in the population and let (1 — a) be the proportion of liquidity traders. Then, at any date t, the market maker's expected profit is (8)

n,(/?,, wt) = (1 - a)Jt(pt, wt) - ocHt(pt, wt).

The monopoly problem is difficult to solve because changing prices would help the market maker learn the true value of the asset sooner. The experimental value of changing prices would enter into the monopolist's pricing decision. Accordingly, following Glosten and Milgrom (1985), I consider only the competitive case.

210

Intermediation under asymmetric information

Suppose, as in Glosten and Milgrom, that the intermediary is not restricted to prices that balance expected supply and demand. As a result, Bertrand price competition drives the market maker's profit to zero, Ut(pt, wt) = 0, by separately setting the net gain from sales equal to zero and the net gain from purchases equal to zero. The competitive pricing conditions that result are (9) (10)

afrizi - Pt) - (1 - ot)iPt - vt)[l - pt/(2vt)] = 0 , a(l - pt)(wt - z0) - (1 - ot){vt - wt)wt/(2vt) = 0.

The prices that solve the quadratic equations (9) and (10) are obtained by taking the smaller of the two roots for pt and the larger of the two roots for wt. To interpret the competitive equilibrium pricing conditions, (9) and (10), rewrite them in the following manner: Pt

(12)

_ aptz\ + (1 - <x)vt[l - Pt/(2vt)] ~ apt + (l-a)[l-pt/(2vt)] '

wt = ^ - ~ ^

l-/3t) +

(l-a)[wt/(2vt)]

Therefore the ask price equals the expected value of the asset contingent on the trader's buying the asset from the market maker while the bid price equals the expected value of the asset contingent on the trader's selling the asset to the market maker. The ask and the bid prices reflect the market maker's revised expectation of the value of the asset. Thus the price spread is the difference between the revised expectations of the asset value contingent on a sale or a purchase, respectively. Expectations are revised upward in response to a sale made by the market maker and downward in response to a purchase made by the market maker. Consideration of pricing conditions (11) and (12) shows that the equilibrium ask and bid prices straddle the expected value of the asset at each date: wt < vt < Pt. This analysis shows how adverse selection creates a price spread. At any given date, the market maker may buy, sell, or not trade at all. Let bn represent the price at which the nth transaction occurs, where bn can be either the ask or the bid price. Then pricing conditions (11) and (12) can be summarized as (13)

bn = E[v\Snl

where Sn is the market maker's information given that a trade takes place. The sequence of trading prices forms a martingale relative to the

Adverse selection in financial markets

211

specialist's information:

(14)

= E[v\Sn] =bn.

This result is a stronger form of efficiency than the semistrong form, which is defined as the case in which the market prices of an asset reflect the information contained in past prices and other published information. An increase in the proportion of insiders in the population a will increase the ask price, and lower the bid price, with all other things equal. So an increase in a will result in an increase in the bid-ask spread for a given history of trades. The greater the proportion of insiders in the population, the more information will be conveyed by trades. This in turn may narrow future spreads by reducing the information differences between insiders and liquidity traders; see Glosten and Milgrom (1985). If the proportion of insider traders is too large, trade may break down, as in the classic market for lemons.

8.2

Competition between specialists

The models of Copeland and Galai (1983), Kyle (1985), and Glosten and Milgrom (1985) assume that perfect competition drives profits to zero for price-taking market makers. Dennert (1993) modifies these models to allow for Bertrand competition price by market makers. In this section, I summarize Dennert's model and discuss the properties of competitive equilibrium. Instead of allowing free entry, Dennert assumes that there are n registered market makers for a givenfinancialasset. Moreover, market makers are subject to a capacity constraint in the form of a (minimum) quantity up to which they have to quote prices. Each market maker i posts ask and bid prices (pi,wt),i = 1 , . . . , n. The market maker is committed to trade any quantity q < 1 at the posted ask and bid prices. The market maker does not know the true value of the financial asset v, which can be either v = l o r i ; = —1 with probabilities (1/2, 1/2). So the market maker's expected value of the asset equals zero. Informed traders know the true value of the asset. An informed trader can buy from or sell to all the market makers simultaneously. Informed traders are not subject to any limits on how much they buy or sell, unlike market makers. Thus an informed trader's demand for or supply of the asset presented to any given market maker i depends on only that market maker's prices.

212

Intermediation under asymmetric information

The insider buys from intermediary i if v = 1 and pi < 1, sells to intermediary i if v = —1 and wt > — 1, and does not trade with intermediary i otherwise. Thus the expected loss to a market maker from dealing with an insider is (15)

H(p, w) = (1/2)(1 - p) + (l/2)(w + 1),

if p < 1 and w > — 1. Only the market maker with the lowest ask price can make a sale, while only the market maker with the highest bid price can purchase the asset. A liquidity trader is either a buyer or a seller with equal probability. As a buyer, the liquidity trader has a reservation value of 1 and as a seller has a reservation value of — 1. The liquidity trader can trade exactly one unit of the asset or be inactive. The liquidity trader thus is a comparison shopper, looking across market makers for the best deal. If min* pi > 1, the liquidity trader will not buy, and if max* wi < — 1, the liquidity trader will not sell. The market maker's profit from dealing with a liquidity trader is (16)

J(p, w) = (l/2)p - (l/2)w,

where p < 1 and w > —1. As above, normalize the population of traders so that a is the proportion of insiders. Then the market maker's expected profit is again (17)

n(p, w) = (1 - a)J(p, w) - otH(p, w).

Following Dennert, the market maker does not face a stock constraint, so that the market maker has a sufficient amount of the asset on hand to cover any realized excess demand. So it is sufficient to consider only setting the ask price; setting the bid price is similar. If the market maker is the low-price leader, that is, if pi = min ; pj and pi < pj for all y # i, then the market maker sells to both types of traders: (18)

n,- = (a/2)(Pi - 1) + [(1 - a)/2]Pi = (Pi - a)/2.

If the market maker does not have the lowest price then he sells only to insiders: (19)

n* = (a/2)(Pi - 1).

Finally, if the market maker's price is a tie with m other firms for the lowest price (assuming that demand is shared equally), profit is (20)

n, = (a/2)(Pi - 1) + [(1 - a)/2]Pi/(m + 1).

Because market makers are capacity constrained, the equilibrium resembles that observed with Bertrand-Edgeworth competition. In particular, there exists no equilibrium in pure strategies. Suppose that p* is

Adverse selection in financial markets

213

the lowest price charged by other market makers, with a < p* < 1. Then, it is always profitable to undercut the price, so that /?* cannot be an equilibrium. Suppose that m > 1 market makers charge p = a. Then those market makers, tied at the low price, make a loss: n , = - ( l / 2 ) a ( l - a)m/(m + 1) < 0, so p = a cannot be an equilibrium. Finally, charging p = 1 guarantees zero profit. So a pure-strategy equilibrium cannot exist. There is a symmetric mixed-strategy equilibrium, with a price distribution i

(21)

-

-

.

<* 1 - a p with support [a, 1]. This is the only symmetric equilibrium and it is the only equilibrium in which all market makers are active.2 To show that this is an equilibrium, note that the probability that the market maker with price p charges the lowest price is [1 — F(p)]n~l = [a/(l — a)](l — p)/p. Therefore the market maker's expected profit, given that other firms are following the equilibrium strategy, is

(p - 1) + (1 - a)p[l (22)

-

=0.

So, since mixed strategies imply that the probability of a tie is zero, all market makers are indifferent between charging any prices on the interval [a, 1]. Thus F(p) is an equilibrium. It is evident from the form of the equilibrium distribution of prices that the probability that some price p is the lowest price in equilibrium is increasing in n. For n > 1, the probability of the event {min, pt > p} is given by l-a p which is increasing in n. Thus increased competition increases transaction costs for traders. For each market maker, the risk of trading with informed traders rises with the number of market makers, since uninformed traders buy from the lowest-priced market maker but informed 2

See Dennert (1993) for the proof of uniqueness of equilibrium.

214

Intermediation under asymmetric information

traders buy from each market maker. Market makers set higher ask prices on average to compensate for this risk. Since market makers make zero profit in equilibrium, the price spread must increase; thus competition creates transaction costs for traders. Dennett (1993) shows that equilibrium is robust to an enlargement of the strategy space. It is sufficient to consider only how the ask price is set, since setting the bid price is similar. Suppose that market makers can set price functions Pt(q). Insiders choose quantities X[ to maximize (23)

[v-Pi(xi)]Xi,

/= 1

/i.

Liquidity traders purchase from (or sell to) all market makers up to a total of one unit of the asset. The liquidity traders minimize purchase costs when buying the asset and maximize returns from sales when selling the asset. If the liquidity trader buys a unit, he chooses x\, X2,..., xn to minimize (24)

Y^ pi (xi )x*

subject to ^

i= l

xt = 1.

i= \

With competition in quantity schedules, there is still no equilibrium in pure strategies. Moreover, the equilibrium of the game with fixed quantities is a mixed-strategy equilibrium in the game with arbitrary price functions. Market makers randomize over functions of the form

Pi ifq = \ 1

*

otherwise

where the randomization occurs over Pt(l) with distribution function F defined by Eq. (21); see Dennert (1993). Therefore the equilibrium with price schedules is the same as in the Bertrand-Nash case. As a consequence of Bertrand-Nash price competition, duopoly is sufficient to drive profits to zero. Adverse selection creates risk for market makers, and an increase in the number of traders increases their risk exposure, thus increasing transaction costs for traders by raising price spreads. From this, Dennert concludes that "a Stock Exchange deciding to organize trading via market makers with the obligation to quote bid and ask prices at every time, should limit the number of market makers." The conclusion that exchanges need to limit the number of market makers should be tempered by considering the competitive framework. The assumptions of the model guarantee Bertrand-Nash competition. A number of competitive frictions would change the nature of competition and alter the equilibrium outcome. The market makers may offer differentiated services. They may have different transaction costs that are unobservable to other traders and market makers. There may be costly

Adverse selection in financial markets

215

matching between traders and intermediaries, as discussed in Chapter 5. There may be imperfect price information available to traders, resulting in search costs, as discussed in Chapter 6. Any of these factors would serve to give market makers some market power leading to positive profits, absent free entry. Increasing the number of market makers then could narrow or widen the price spread, depending on the relative effects of adverse selection and competition on pricing decisions. The conclusion that market makers should be limited also may depend on the assumption of risk-neutral market makers. Dennert (1993) points out that if market makers are risk averse, a greater number of market makers can lower spreads by sharing the asset's fundamental risk; see also Ho and Stoll (1983) and Grossman and Miller (1988).

8.3

Informed intermediaries

In the models considered in Section 8.2, specialists were at an information disadvantage compared with insiders, while being on a par with liquidity traders. Suppose instead that the intermediary is the informed trader and that all other traders are uninformed. Suppose further that the intermediary is an insider with market power and that all other traders lack market power. The question that arises is whether the market prices will reflect all available information or whether information asymmetries will remain after traders observe market prices. The efficient market hypothesis has been studied in perfect-competition models by Grossman (1976), Radner (1979), Allen (1981), and others. In contrast, Laffont and Maskin (1990) examine market efficiency when there is an informed trader with market power. They demonstrate that the informed trader strategically chooses the amount of information that will be conveyed by prices. They show that in a perfect Bayesian equilibrium, the large trader will induce a pooling equilibrium, thereby concealing private information rather than revealing it through the selection of prices. In this section, I review some elements of Laffont and Maskin's (1990) model. Kyle (1985) examines a related Bayesian model of insider trading by an intermediary. For a Stackleberg analysis of related issues, see Kihlstrom and Postlewaite (1983), Gould and Verrecchia (1985), Grinblatt and Ross (1985), and Cripps (1986). Suppose that there is a financial asset with return 9 + e. The variable 9 is realized before trade takes place, taking values 9\ or O2, where 9\ < 62. The shock e is a zero-mean random variable with distribution function F. The shock s is independent of 9. The intermediary knows the value of 0, which is unobservable to other agents before trade takes place. After trade takes place, the realizations of 9 and e become public knowledge.

216

Intermediation under asymmetric information

There is a risk-neutral intermediary who chooses bid and ask prices. For ease of presentation, it is sufficient to confine attention to the selection of a bid price w. The analysis is the same for the selection of an ask price. Each of the small traders has one unit of the risky asset. Each small trader supplies S(w) < 1 of the risky asset and retains 1 — S(w) of the risky asset. Since there is a continuum of small traders of measure one, the aggregate supply of the risky asset also equals S(w). The intermediary chooses the bid price w = w{6) to maximize profit: (26)

n(S, w, 0) = (0 - w)S(w).

The small trader has a prior probability on the two states {6\, 62} given by (/Jo, 1 — Po) that is revised based on the observed price. Let (fi(w), 1 — fi(w)) be the small trader's Bayesian posterior probability over the two states. Small traders are risk averse with von Neumann-Morgenstern utility function u? The representative small trader receives Sw for the sale of the risky asset and realizes income of (1 — S)(0 + s) on the retained share of the risky asset. Given the bid price w, the small trader chooses the amount of the risky asset to supply, S(w), that maximizes expected utility: (27)

U(0, w) = PEU(SW + (1 - 5)(0i

+ £))

+ (1 - P)Eu(Sw + (1 - S)(92 + e)). The perfect Bayesian equilibrium (PBE) for the model is the pair of strategies and the small traders' updated beliefs, w*(0), S*(w), P*(w). The equilibrium bid price w* maximizes profit in Eq. (26), and the small traders' asset supply 5* maximizes expected utility in Eq. (27). Laffont and Maskin (1990) show that there exist separating PBEs, that is, equilibria in which the large trader chooses a high or low price, depending on private information: w*(6\) < w*(02). They also show that for 9\ sufficiently close to O2, there exists a pooling PBE. At the pooling PBE, the bid price w° does not depend on the large trader's private information and the small trader does not draw any inferences from the bid price, so that the supply of the asset S°(w) does not reflect any Bayesian updating. At the pooling equilibrium the small trader chooses S°(w) = S°(w; 6\, 02) to maximize £/($), w). The large trader chooses the bid price w° to maximize expected profit given the small trader's prior beliefs Tlp: (28)

UP(S°, w, 0i, 02) = A)7r(S°, w, 0i) + (1 - A))7r(S°, w, 92).

Let u be increasing, u" < 0, and let u exhibit nonincreasing absolute risk aversion.

Adverse selection in financial markets

217

The pooling-equilibrium bid price w° solves a standard monopsony condition, (0 - w)S°'(w) - S°(w) = 0, where 0 = Mi + 0 - A>)02As a benchmark, consider the full-information case. The full-information supply of the small traders, SF(w, 0), solves max Eu(Sw + (1 - S)(0 + e)) s for any given 0. Given SF(w,0), wF{0) to solve (29)

the intermediary choose the price

max(6>-u;)S F(>,6>).

Let SF{6) = SF(wF(0), 0) be the equilibrium level of supply in the full-information case when the intermediary is of type 6. Laffont and Maskin (1990) show that for 6\ sufficiently close to 02, the large trader prefers the pooling equilibrium to any separating equilibrium. I give a sketch of their proof. They show that the large trader prefers the pooling equilibrium to the large trader's favorite separating equilibrium. The favorite separating equilibrium wi = w*(6t),i = 1,2, maximizes (30)

U(wu w2, 0i, 02) = [jSo(0i - wi)S

subject to the incentive-compatibility condition (31)

(92 - w2)SF(w2, 92) > (62 -

wOS^

The higher bid price W2 that solves the maximization problem of Eq. (30) and relation (31) satisfies W2 = wF(02). However, for the lower bid price w\, the incentive-compatibility constraint is strictly binding, so that w\ < wF(0\). The derivative of the large trader's pay-off with respect to 0\ is (32)

nei(wu

w2, 0i, 02) = foSF{wu 0i) + A)[(0i ~ u;i)^(u;i, 00 -5 F (u;i,0i)du;i/d0i].

The bracketed term in Eq. (32) equals zero because the incentive-compatibility constraint (31) is binding. Therefore (33)

n01(wi, w2, 0u0i)

F

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Intermediation under asymmetric information

Compare with the marginal value of 9\ in the pooling case evaluated at the pooling bid price w°:

(34)

nJ(S°, w°, 0i, 92) = A)SV°) + (0 - u

The small trader's problem in the pooling case shows that dS°/dO\ < 0. Now, supposing that 6\ = 02, Eqs. (33) and (34) imply that

n£ < PoS°(w°) = hsF(wi,0i)

= n0l.

So since the pay-offs Ylp and n are equal at 6\ = #2, lowering 6\ below O2 will have less impact on the pooling-equilibrium pay-off. Therefore, for 0i sufficiently close to 02 and 0i < #2, p

n >n.

Since n is the pay-off at the most-preferred separating equilibrium, the pooling equilibrium is the large trader's favorite equilibrium. Laffont and Maskin (1990, p. 71) explain the incentives of the large trader to set prices that conceal private information: Thus the important difference between separating and pooling equilibria lies not with prices but rather with quantities. In a pooling equilibrium, the large trader can buy all he wants at the market price (given the presumed linearity of the small traders' disutility). But this cannot be the case in a separating equilibrium because, in such an equilibrium, the price of the asset is low when the value of 6 is low. If the large trader could buy all he wanted at such a price, he would see to it that the price was always low, violating the hypothesized separating nature of equilibrium. Hence, the trader must be quantity-constrained at the low price. This incentive constraint implies that, on average, he cannot buy as much in a separating equilibrium as in a pooling equilibrium. Hence, he will favor the pooling equilibrium. When the small trader's preferences are nonlinear because of risk aversion, a similar argument applies. When 0\ is close to 62, the price in the unfavorable case w\ deviates less from the full-information price. The deviation is due to the binding incentive-compatibility constraint that is not present in the pooling case. Thus the rate of increase in the large trader's pay-off that is due to a change in 0i is lower in the pooling case. Hence reducing 0i below 62 has less effect in the pooling case, thus yielding a greater pay-off. Observe that the same analysis would apply to a large trader's setting an ask price. Therefore, in general, one would expect the bid-ask spread to be pooling, that is, it would be independent of the intermediary's

Adverse selection in financial markets

219

information if the parameters 6\ and 62 were confined to a narrow range. This analysis provides conditions under which markets fail the test of efficiency that requires prices to depend on all available information. This contrasts with the strong form of efficiency observed in perfect-competition model of intermediation, such as that of Glosten and Milgrom(1985).

8.4

Credit rationing by financial intermediaries

In credit markets, borrowers and lenders are asymmetrically informed. Borrowers generally have better information about the riskiness of the loan than lenders. Borrowers seeking to finance an investment project are likely to know more about the expected income stream that the project will generate. Financial intermediaries, such as banks, come between borrowers and lenders. Among the many market services banks provide is the design of loan contracts to address adverse selection. By screening potential loan applicants, banks can reduce the risks of loans. Banks use a variety of explicit screening devices such as loan applications, application fees, and reviews of proposed projects by loan officers. They also use implicit screening devices such as interest rates and other contract terms. In this section, I review the Stiglitz and Weiss (1981) model of adverse selection in credit markets. They show that the average riskiness of borrowers increases as the interest rate increases, because the worse-risk borrowers are willing to borrow at higher rates since their probability of repaying the loan is low. Therefore higher interest rates have a negative effect on the average quality of those borrowers applying for a loan. At the same time, higher interest rates serve to ration scarce credit among borrowers. This means that there is a trade-off for banks in setting prices for loans. Use of higher interest rates to ration credit raises the riskiness of borrowers. As a consequence of this trade-off, banks can have an incentive to set interest rates that are below market-clearing levels while using quantity rationing to allocate scarce credit. Suppose that a borrower wishes to finance a project whose expected return R is uniformly distributed on the interval [A — 0, A + 0], where A is a constant whose value is common knowledge and 6 is a parameter whose value is the borrower's private information. Given the distribution of returns, the expected return to the project is ER = A and the variance of the return to the project is var R = 02/3. Suppose that there is a continuum of borrowers, each with a different value of 6, and that the borrower types are uniformly distributed on the interval [0, A]. The distribution of returns with a higher 0 is riskier in the sense of a mean-preserving spread; see Rothschild and Stiglitz (1970).

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Intermediation under asymmetric information

V(R,r)

O+r)B Figure 8.1. The borrower's net return is a convex function.

Suppose that a risk-neutral borrower obtains a loan of size B at interest rate r. For ease of preservation, I normalize bankruptcy costs, collateral, and liability to zero. The borrower's net return V then is (35)

V(R, r) = max{/? - (1 + r)B, 0}.

A bank's net return from making a loan B at interest rate r is (36)

n(R, r) = min{/?, (1 + r)B}.

A bank pays its depositors an interest rate p so that its net profits are n(R, r) — (1 + p)B. Suppose that the market supply of funds from bank depositors is S(p). The borrower's net return V is a convex function of /?; see Figure 8.1. As a consequence, a riskier return increases the borrower's expected net returns; see Rothschild and Stiglitz (1970). To verify this for the specific form of the borrower's return, observe that, for a type 9 borrower, (37)

E0V(R, r) = [(A + 6) - (1 + r)B]2/46

for A - 9 < (1 + r)B < A + 9. Differentiating with respect to 9 yields dE0V(R,r) [A + 9 - (1 - r)B][(l + r)B - (A - 9)] (38) =

—w—

which is positive.

Adverse selection in financial markets

221

n(R,r)

Figure 8.2. The bank's profit is a concave function.

Consideration of the borrower's expected net return in Eq. (37) shows that the interest rate acts as a screening device. Borrowers will obtain a loan only if their expected net return is positive. The critical value of 6 such that the expected return is positive for higher values of 0 therefore is (39)

6* = (l+r)B-

A.

Clearly, as the interest rate increases, the critical value of 6 increases as well. Thus, with a higher interest rate, higher-risk applicants obtain loans. Note also that a higher loan amount B and a lower expected value of the project raise the average risk of applicants for a given interest rate. The bank's net return to lending n is a concave function of /?; see Figure 8.2. This implies that a riskier return decreases the bank's expected net return. To verify this general result, calculate the bank's expected net return: (40)

Een(R, r) = [2(A + 9)B{\ + r) - (1 + r)2B2 - (A - 9)2]/46

for A — 6 <(l + r)B < A+ 6. Differentiating with respect to 0 yields

, r)

(1 + r)2B2 + (A + 9)(A -6)-

2A(1 + r)B

which is negative. Note also that the expected return is increasing in the rate of interest.

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Intermediation under asymmetric information

The bank does not know the riskiness of individual loans, only the range of types that take loans, which equals [#*, A]. The expected return to the bank from lending at interest rate r is therefore (42)

nir)

-c

Ee7t{R,r)-

dd/A 1 - 9* IA

The expected-return function is likely to be nonmonotonic in the rate of interest. To see this, differentiate with respect to r: (43)

7t'(r) =

B

:[n(r)-A]

dE9n(R,r)

d9

A-6* The first term is negative since n(r) < A. The second term is positive since the bank's expected return is increasing in the rate of interest. The first term reflects the effect of the rate of interest on the pool of applicants while the second term reflects the additional interest earned on loans. Therefore the expected-return function can have one or more interior modes. Multiple interior modes can result in multiple equilibria. Suppose that the expected-return function has a single interior mode; see Figure 8.3. Let (r*, p*) be the equilibrium interest rates on loans and deposits,

A-e-

dr

Figure 8.3. The equilibrium interest rate on loans r* and the equilibrium interest rate on deposits p* with free-entry competition.

Adverse selection in financial markets

223 S(p)

S(p*)

D(r*)

Figure 8.4. Market equilibrium with credit rationing.

respectively. At a competitive equilibrium with free entry, firms earn zero expected profit on loans: (44)

n(r*) = (l + p*)B.

The equilibrium entry condition is depicted in Figure 8.3. An individual bank does not have an incentive to deviate from the interest rate r* that maximizes the expected return. Now consider the equilibrium bid-ask spread. The demand for loans is (45)

D(r) = [l-

9*(r)/A]B.

The market-equilibrium interest rate on loans r* and interest rate on deposits p* are shown in Figure 8.4 for the case of credit rationing. Given the assumptions of the Stiglitz and Weiss model, the market can just as easily get stuck with excess credit. The problem is the inflexible association of the two interest rates, given the free-entry equilibrium and the nonmonotonic expected return on loans. With n(r) either increasing or decreasing or the modes falling in the right place, banks could adjust rates to clear markets. The problem of credit markets' not clearing is not necessarily solved by elimination of the free-entry condition. The effects of adverse

224

Intermediation under asymmetric information

selection on the expected return to lending show up even when banks have market power. Suppose for example that a monopolistic firm was choosing the interest rates for loans and deposits.4 The form of the firm's expected return function could give it an incentive to quantity ration either borrowers or lenders. Stiglitz and Weiss (1981) also show that when borrowers can choose among projects with varying risks of bankruptcy, an increase in the interest rate on loans causes the borrower to choose projects with a higher probability of bankruptcy, thus possibly lowering the bank's expected return. They further show that imposing collateral effects on borrowers need not eliminate adverse selection effects. When borrowers are risk averse and when risk aversion decreases with the borrower's wealth, increasing collateral requirements will lower the bank's return. The higher collateral requirement restricts borrowing to wealthier individuals, who undertake riskier projects, raising the riskiness of the average (and marginal) borrower.

8.5

Conclusion

The models considered in this chapter show how financial intermediaries address problems of adverse selection. By centralizing trade, intermediaries can overcome some of the economic costs of adverse selection. By dealing with both insiders and uninformed liquidity traders, intermediaries offset losses incurred in dealing with insiders though profitable trades with liquidity traders. A greater number of insiders widen the bid-ask price spread. These results contrast with the case of an informed intermediary, who chooses to conceal information by pooling strategies, setting a bid-ask spread that does not depend on the intermediary's information. In credit markets, financial intermediaries have additional incentives to invest in observing the characteristics of borrowers. They can develop expertise in screening loans and in evaluating projects. Moreover, intermediaries can diversify the risks associated with making loans. Intermediaries can use instruments such as prices and collateral requirements to screen potential borrowers, recognizing the trade-offs inherent in such instruments. Thus intermediaries can provide lenders with reduced risk or greater returns in comparison with a decentralized credit market. The analysis in this chapter focused on the generation of information as part of the intermediary's buying and selling activities. The 4

The monopolist chooses r and p to maximize n(r) — (1 + p) B subject to loans equaling the minimum of D{r) and S(p).

Adverse selection in financial markets

225

intermediary generated information in the market in part through contracting with buyers and sellers. In general, an intermediary can sell information directly to consumers and suppliers as in the case of an investment newsletter. Alternatively, the intermediary can bundle the information, as with a mutual fund that sells shares. Additionally, the intermediary can charge for the use of information.5 Ramakrishnan and Thakor (1984) show that when intermediaries act as information providers, there are returns to mergers between intermediaries if they can monitor each other's efforts at gathering information within the organization. Risk sharing is not sufficient to create gains from mergers of intermediaries. If internal monitoring is costless, then as the number of information providers that constitute an intermediary becomes large, the expected costs of monitoring converge to a lower limit, indicating that there are benefits from monopoly intermediation. Adverse selection problems stem from the costs of observing the characteristics of buyers and sellers. Firms incur these costs in the production of transactions and the formation of contracts with their customers and suppliers. In Chapters 9 and 10,1 examine the importance of transaction costs in the theory of the firm. In Chapters 11 and 12,1 consider further the problem of adverse selection within the context of principal-agent models of the firm.

Admati and Pfleiderer (1990) examine both forms of information distribution.

Transaction costs and the contractual theory of the firm

Economists have long been aware of the costs of operating a market system. Friedrich A. Hayek spoke of "the unavoidable imperfection of man's knowledge and the consequent need for a process by which knowledge is constantly communicated and acquired."1 The decentralized nature of markets provides an efficient means of handling the vast amount of widely dispersed information. A central planner is incapable of acquiring such private information, and even if such information were available, making use of it would be prohibitively costly. The price system is a marvel because it offers what Hayek (1945, p. 527) termed "an economy of knowledge," even though its "adjustments are probably never 'perfect'." From a different perspective, Kenneth Arrow (1963) observed that "the failure of the market to insure against uncertainty has created many social institutions in which the usual assumptions of the market are to some extent contradicted." In his discourse on medical care, Arrow (1963) stressed the problems health insurers encounter that are due to moral hazard and adverse selection in the demand for medical care. He concluded that The logic and limitations of ideal competitive behavior under uncertainty force us to recognize the incomplete description of reality supplied by the impersonal price system. For example, he suggested that the relationship between doctor and patient provides some amelioration of the effects of moral hazard on health insurance companies. Concern over the economic effects of moral hazard and adverse selection inspired work on principal-agent models of the firm, which I turn to in Chapters 11 and 12. The seeming contradiction between the marvels of the market identified by Hayek and its failures detected by Arrow has a common source - transactions costs. It is the costs of transactions that make 1

See Hayek (1945 p. 530).

229

230

Intermediation and transaction-cost theory

government intervention in resource allocation necessarily inefficient. Those same transaction costs lead to the creation of market institutions that depart from the neoclassical ideal. The simplified picture of the firm in neoclassical economics is intended to illuminate the nature of markets. As I noted in Chapter 4, the firm is not so much a black box as it is some transparent technological process for producing outputs from inputs. Yet neoclassical economics can be faulted equally for treating markets as a black box. Given supply and demand functions, the market produces prices that exactly balance the quantity demanded and supplied through some unobservable mechanism. The precise way in which supply and demand schedules are transformed into market-clearing prices is missing. The Walrasian auctioneer remains an unsatisfactory and unrealistic justification. Yet the dual mystery of thefirmand the market are no coincidence, for the two are closely linked. If the market mechanism functions automatically, the firm's efforts are confined to production of output and reaction to price signals. The converse is also true: if the firm is a neoclassical price taker, the market mechanism must function independently of the activities of firms. Such an economic model assumes that economic transactions are frictionless and costless. As soon as one admits to the presence of costs in operating the system, everything changes. If there are costs to operating markets, then markets will not operate perfectly. It will be efficient for the economy to trade off some aspect of market performance, whether price adjustment or market clearing, against the costs of market activity. If there are costs to establishing markets, the set of markets will be incomplete, so that some products may not be traded. Moreover, as soon as there are costs to establishing and operating markets, the role of the firm changes significantly. Even those firms who appear to be purely producers of goods and services will modify their behavior to reduce the impact of market costs on their profit. Moreover, there exist opportunities for firms to enter into the business of market creation and management. Such specialized firms are the intermediaries that I have spoken of in the preceding chapters. Because transaction costs cause such a fundamental revision of the neoclassical theory of markets and the corresponding theory of the firm, it is highly worthwhile to investigate in greater detail just what these costs are. In this chapter, I consider the crucial role played by transaction-cost analysis in what I call the contractual theory of the firm. I review some of the definitions of transaction costs that have been advanced by the major contributors to the field.

Transaction costs and the contractual theory of the

firm

231

The transaction-cost literature seeks to explain "why are there firms?" by finding solutions to some type of presumed market failure. If it is costly to use market transactions to carry out some activity, the proposed solution is to bring that activity into thefirmthrough vertical integration. Thus the literature offers organizational solutions to the problem of reducing market costs. In this regard, the four issues addressed in this chapter are 1. transaction costs versus management costs, 2. transaction uncertainty versus the costs of allocation with the organization, 3. transactional opportunism versus organizational contracting costs, and 4. transactional opportunism versus the costs of ownership. I begin by considering the trade-off between transaction costs and management costs in Section 9.1. In his seminal article "The Nature of the Firm," Coase (1937) posited the avoidance of transaction costs as an explanation for the existence of firms. He viewed transaction costs as the costs of using the market. Firms expand their internal activities to the point where transaction costs and management costs are equalized at the margin. Second, in Section 9.2,1 consider the trade-off between uncertainty in the marketplace and the costs of internal coordination. Frank Knight (1921), in his pathbreaking book Risk, Uncertainty and Profit, posited the firm as a mechanism for dealing with uncertainty in the marketplace. The costs of market uncertainty are compounded by the bounded rationality of managers in processing market information. Firms are organizational responses for addressing and mitigating the costs of market uncertainty. Third, in Section 9.3,1 turn to the trade-off between opportunism in the marketplace and the cost of organizational solutions to reduce opportunism. I turn to the important work of Oliver Williamson, whose development of transaction-cost economics has three main elements: bounded rationality, asset specificity, and opportunism. He observes that firms "[o]rganize transactions so as to economize on bounded rationality while simultaneously safeguarding them against the hazards of opportunism."2 Firms substitute management of organizations for market transactions to address the problem of imperfect contractual commitments. Fourth, in Section 9.4,1 examine the trade-off between transactional opportunism and the costs of ownership. The work of Grossman and 2

See Williamson (1985, p. 32). The quoted sentence was italicized in the original.

232

Intermediation and transaction-cost theory

Hart (1986), Hart and Moore (1990), and Hart (1995) posits firm ownership of assets as a means of explaining the existence of firms. According to their approach, firms own assets to mitigate the effects of incomplete contracting and asset specificity. Ownership of productive assets improves incentives for investment in complementary transaction-specific capital, such as human capital. Accordingly, they explain the boundaries of the firm as determined by efficient allocation of asset ownership. In each case, I examine the implications of these transaction-cost trade-offs for the contractual theory of the firm. In Chapter 101 consider transaction costs and the contractual theory of the firm in the context of intermediation. I then evaluate these trade-offs from an intermediation perspective.

9.1

Transaction costs versus management costs

In only two paragraphs of his classic article, Ronald Coase (1937) provides a definition of transaction costs. He observes that "[t]he main reason why it is profitable to establish afirmwould seem to be that there is a cost of using the price mechanism." He also speaks of "marketing costs" and the "cost of carrying out the transaction in the open market." Transaction costs can take the form of variable costs, as Coase shows by emphasizing the cost of the marginal transaction. Coase distinguishes between market transactions and the allocation of resources within the firm. He lists a number of these costs. First, according to Coase, "[t]he most obvious cost of 'organizing' production through the price mechanism is that of discovering what the relevant prices are." Interestingly, Coase observes that such a cost "may be reduced but it will not be eliminated by the emergence of specialists who will sell this information." Thus specialists are a mechanism for improving the efficiency of information gathering. Coase further notes that "[t]he costs of negotiating and concluding a separate contract for each exchange transaction which takes place on a market must also be taken into account." Coase observes that, in certain markets, techniques are devised for minimizing but not eliminating these costs, such as exchanges for fresh produce. Thus Coase in a tentative way recognizes the presence of organized institutions of exchange. Finally, Coase adds to his list of costs, the "disadvantages" of using the price mechanism. He is referring to the opportunity cost of using the market, implicitly assuming that markets involve short-term contracts in comparison with contractual relations within the firm. Among the disadvantages of shorter term rather than longer-term contracts, Coase identifies the costs of making many short-term contracts in comparison with longer-term contracts. He compares such short-term contracting

Transaction costs and the contractual theory of the

firm

233

costs with the risk associated with long-term contracts that have fixed terms and the costs of writing long-term contracts with many contingencies. Any net benefits of longer-term contracts are thus an opportunity cost of using the market, according to Coase. Transactions for Coase include both spot trades as well as long-term contracts. Any usage of the market, whether for buying or selling, qualifies as a transaction. In contrast, Coase views the costs of management and the costs of the firm's contracts with its employees as organizational costs. Effectively, the firm must calculate its direct and indirect purchasing costs and compare there with the incremental costs of organizing production. The Coasian theory of the firm explains the existence of firms on the basis of contractual efficiency. The firm represents a set of contractual relations that are more efficient either in terms of contract formation or performance. The initial insight of Coase (1937, p. 390) is that "there is a cost of using the price mechanism" and that firms carry out various production tasks to reduce the costs of searching for prices, negotiating individual transactions, and specifying contingencies in long-term contracts. Thus, "by forming an organization and allowing some authority (an 'entrepreneur') to direct the resources, certain marketing costs are saved" (Coase 1937, p. 392). The relative costs of markets and organizations are viewed as the main determinants of the extent of the firm's activities. Thus transaction costs are of central importance in the contractual theory of the firm. The essential reasoning presented by Coase is an equilibrium condition: A firm will tend to expand until the costs of organizing an extra transaction within thefirmbecome equal to the costs of carrying out the same transaction by means of an exchange on the open market or the costs of organizing in another firm. This reasoning applies not only across products but over stages of production. Thus, in equilibrium, the vertical stages of production are divided among firms "in such a way that the cost of organizing an extra transaction in each firm is the same." Coase recognizes that the size of the firm is constrained by "diminishing returns to management" and by the effect of scale on the likelihood of the entrepreneur "making mistakes." He also notes that exchange transactions are far from homogeneous and that the costs of organizing differ across firms as well. The Coasian approach can be applied to practical issues such as vertical integration, often called the make-or-buy decision. A firm deciding on whether to make a part that it will use in manufacturing its final

234

Intermediation and transaction-cost theory

product or to purchase the part from another firm should compare not only the production cost of the part with its purchase price, but in addition the firm should consider the costs of organizing production and the costs of finding and bargaining with the parts supplier. If producing the part involves a nonstandard design, there may be costs of negotiation with suppliers that are high relative to the internal costs of organizing production. This may lead the firm to produce the part itself. This example illustrates the transaction costs that are incurred before contracts with suppliers are formed. Thus Coase's discussion of transaction costs provides an equilibrium theory of the firm based on the relative costs of transacting and organizing. The activities carried out by firms are those that are less costly to handle within an organization compared with market contracts. Harold Demsetz (1991, p. 162) provides one of the most telling criticisms of the Coasian approach: It is not so easy to distinguish purchase across a market from inhouse production because in-house production involves the use of inputs that are purchased. Purchasing inputs (across markets) is substituted for purchasing goods that are more nearly complete (across markets). Demsetz draws two conclusions from this: Hence, in-house production does not constitute a clear elimination of transaction costs. Similarly, purchasing goods from another firm, rather than producing these in house, involves an implicit purchase of the management services undertaken by the other firm, so management cost is not eliminated by purchasing more nearly complete goods across markets.3 Demsetz observes that the correct question is not whether the transaction cost of purchase is less than the management cost of production but rather whether the sum of management and transaction cost incurred through in-house production is more or less than the sum of management and transaction cost incurred through purchase across markets, since either option entails expenditures on both cost categories.4 Thus purchasing inputs entails transaction costs on the part of the buyer and the seller as well as management cost. 3 4

Demsetz (1991, p. 162). Ibid.

Transaction costs and the contractual theory of the firm

235

Therefore the make-or-buy dichotomy is not a clear-cut comparison of transaction costs with management costs. The decision revolves around what types of inputs to purchase and in what markets to purchase them. Purchasing an input entails the costs of using the market to the buying firm as well as the direct costs of purchase. The direct costs of the purchase in turn reflect the transaction, management, and other direct costs incurred by the supplier. Making an input oneself entails the transaction costs and direct purchase costs of the underlying inputs and the organizational costs of carrying out production. In fact, Demsetz notes, the cost of transacting is only one element of the difference between the cost of purchasing from others and the cost of making something oneself. That crucial difference also depends on technology and operating-cost differences betweenfirms.Otherwise, the analysis would carry the implicit assumption that allfirmshave the same technology. Thus, in the basic transaction-cost framework, technological "information remains full and free."5 Demsetz further identifies a conceptual measurement problem with distinguishing operationally between transaction and management costs: One person phones another and directs him to purchase specific assets by a certain time if they can be acquired for less than a stipulated price. Is this activity transacting or managing?... The inherent difficulty is that the same organizing activities often characterize exchange and management.6 The firm's transaction and management costs are not easily separable. Moreover, the firm incurs many other costs such as research and development, engineering, operations, marketing, and sales. It can be difficult to discern the incremental costs of procurement. Ultimately the make-or-buy decision has to do with vertical integration into the manufacture of inputs. The firm's choice of its vertical span reflects a number of factors including, but not limited to, the trade-off between transaction and management costs. There are technological costs or benefits from vertical integration. There also are advantages and disadvantages from vertical coordination compared with the independence of suppliers and distributors. The Coasian trade-off between transaction costs and management costs remains valuable because it alerted economists to the costs of using the market. However, the make-or-buy comparison that illustrates that trade-off remains rooted in the neoclassical cost-minimization approach. 5 6

Ibid, at p. 164. Ibid, at p. 165.

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Intermediation and transaction-cost theory

The firm pursues a given productive task, say making widgets. It then attempts to carry out that task in the least-cost manner, choosing whether to purchase or to manufacture key inputs, taking into account the direct and the indirect costs of the alternatives. Yet, how did the firm arrive at the decision to produce widgets? A theory of the firm should not presuppose that the firm's choices of what to produce and for whom are settled issues (let alone the question of who decides). The question of how to produce cannot be sufficient to determine the boundaries of the firm. This means that the make-orbuy decision, taken in isolation, has limited explanatory power as a theory of the firm. As I emphasize in Chapter 10, the optimizing choices made by firms extend beyond the task of production. The firm chooses a set of transactions depending on the economic value added of those transactions. The degree of vertical integration depends on the set of transactions chosen by the firm.

9.2

Transaction costs, uncertainty, and bounded rationality

Economic uncertainty is a common source of market transaction costs. Buyers and sellers face uncertainty about the characteristics of trading partners, the prices of goods and services, product quality, and product availability. Organizations can alleviate these costs through vertical integration and control over input production and output distribution by carrying out those activities in house. Reasoning in a manner that is similar to the make-or-buy trade-off, there is also a trade-off between the costs of dealing with market uncertainty and the costs of allocating goods and services within the organization. This suggests an explanation for firms as a means of minimizing the costs of dealing with uncertainty. Frank Knight (1921) stresses the importance of information and uncertainty as explanations for the organization of activities within the firm. Although this contrasts with the Coasian approach, these points of view can be reconciled in a general sense since problems stemming from incomplete information are an important source of transaction costs. However, Coase (1937) emphasizes his differences with Knight (1921), noting in particular that "it is possible to get a reward from better knowledge or judgment not by actively taking part in production but by making contracts with people who are producing." Coase continues, "It seems that nowhere does Professor Knight give a reason why the price mechanism should be superseded." The consequences of uncertainty are manifested within organizations because of the bounded rationality of firm managers. Economic agents,

Transaction costs and the contractual theory of the

firm

237

such as individual consumers and small producers, experience the consequences of bounded rationality in processing market information and attempting to make rational decisions based on that information. By combining the forces of many decision makers and taking advantage of specialization and division of labor, organizations can potentially improve information processing and the accuracy of decision making. The bounded rationality of economic actors and costly interaction within the organization create bureaucratic inertia and impose limits on the performance of organization in handling uncertainty. The trade-off between the benefits of market instruments for handling uncertainty and organizational instruments provides some explanation for what activities are carried out within organizations. For example, the net benefits of contingent contracts compared with the net benefits of organizational routines and relational contracts help to determine whether activities are performed through contracts or within the organization. Market uncertainty The Knightian view of the firm emphasizes economic uncertainty: "The problem of meeting uncertainty thus passes inevitably into the general problem of management, of economic control" (Knight, 1921, p. 259). The firm is organized as a means of mitigating the effects of uncertainty regarding production and final demand. This view finds its expression in models that represent the firm as the result of mergers designed to reduce uncertainty. Arrow (1975) presents a basic model of vertical integration in which upstream firms sell a randomly available resource to downstream firms. The upstream firm learns the amount of its resource stock one period before the market clears, thus providing an incentive for a vertical merger. Indeed, under some conditions, a single downstream firm will seek to acquire all the upstream firms, thereby eliminating all uncertainty about the total amount of the resource. Agency relationships in market contracts and those within the firm are subject to similar problems of moral hazard and adverse selection. A theory of the firm thus can be built around a comparison of the relative efficiencies of information processing in market relationships versus organizational relationships. Activities will take place within the firm when relationships within the organization handle information asymmetries more effectively than do market contracts. The economic analysis of the firm using an agency approach is taken up in Chapters 11 and 12. Consolidation of production and distribution can reduce the risk faced by the firm. If such risk can be diversified away in financial markets or

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through insurance contracts, then such risk reduction does not explain the organization of firms. However, given imperfect financial and insurance markets or imperfect information about the firm's costs and revenues, there may be risks that are not easily diversified. Therefore consolidation can be valuable as an alternative means of reducing the costs of risks to the firm. Horizontal consolidation can reduce the variance in the firm's demand and costs. Frank Knight (1921, pp. 251-252) observed that moral hazard problems associated with individual decision makers can prevent consolidation by an external agency or insurance company or association. Knight stated that, with centralization and unity of interest in an organization, the possibility of thus reducing uncertainty by transforming it into a measurable risk through grouping constitutes a strong incentive to extend the scale of operations of a business establishment. This fact must constitute one of the important causes of the phenomenal growth in the average size of industrial establishments which is a familiar characteristic of modern economic life. Knight stressed the importance of scale as a means of allowing managers to balance the risks of their errors in perception or judgment. The same diversification can be achieved through expansion of the firm's scope. Pooling productive capacity to serve markets in which demands are negatively correlated allows the firm to operate near full capacity for a greater amount of time, thus reducing average costs. Also, by pooling inventories, firms can smooth the pattern of demands across retail locations, reducing inventories and peak capacity requirements. Just as a retailer who supplies many seasonal products can operate more efficiently than specialized retailers, a firm can realize similar gains by providing diverse products. A diversified company can apply technical, marketing, and managerial expertise as needed across a variety of products. The managerial capacity of the firm is used effectively, despite random fluctuations in individual product sales. Vertical consolidation also yields returns from risk reduction if coordination can be achieved within the firm at lower cost than through contracts. A manufacturer can reduce the cost of risk that is due to fluctuations in the availability of productive inputs by manufacturing the parts. A retailer can ensure product availability by integration with a manufacturer, and conversely a manufacturer can seek to reduce demand risk by entering into distribution. Arrow (1975) presents a basic

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model of vertical integration in which upstream firms sell a randomly available resource to downstream firms. The upstream firm learns the amount of the resource stock one period before the market clears, thus providing an incentive for a vertical merger. In Arrow's model, under some conditions a single downstream firm will seek to acquire all the upstream firms, thus eliminating all uncertainty about the total amount of the resource. The cost, revenue, and risk advantages of consolidation of production are, of course, limited by organizational costs of a larger enterprise. The benefits of consolidation of production must be compared with contractual alternatives. Even taking account of organizational and contractual considerations, the gains from consolidation provide explanations for the determination of the firm's boundaries. The reduction of uncertainty from consolidation thus provides another ingredient to the theory of the firm. Bounded rationality The study of management is marked by a focus on how a manager makes decisions and how the manager's plans are implemented within the organization. In designing an organization, the manager begins with an examination of his own limitations as well as the limitations and the motivation of subordinates. Classical management was concerned with the mechanics of establishing a hierarchy and allocating responsibilities and authority within the hierarchy. Postwar management studies shifted attention to managerial decision making and the problem of inducing individuals within the hierarchy to respond to managerial directives and further the interests of the firm.7 If managerial capacity for processing information and making decisions were unbounded, strategy making could be viewed simply as an application of operations research and economic optimization. It is limits on managerial decision-making capacity and the possibility of bounded rationality that make the problem of formulating and implementing management strategy particularly interesting. Schoemaker (1990) argues that the rationality of managers can vary over time as the manager frames problems, gathers information, comes to conclusions, and then learns from experience. Differences in managerial capability leave room for 7

Many contributions to the study of management have been made in the field of organization behavior. Organization behavior applies approaches based on psychology and sociology to the study of individual activity and interaction within the firm. It is not possible to survey this large literature here, but many excellent reviews of the area can be found.

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improvement in a given company and create opportunities for competitors. Limitations of managerial capability also create roles for multiple decision makers within the organization. Oliver Williamson (1985, p. 45) observes that "[b]ounded rationality is the cognitive assumption on which transaction cost economics relies." Simon (1955, 1972, 1976) examines the implications of limited cognition for organizations. The notion of bounded rationality has had two principal influences on the management literature: individual motivation and organizational adaptation. One implication of bounded rationality is an emphasis on the limited capacity of managers and subordinates and the resulting need to delegate authority and share information within the organization. This implies that the decisions of managers and employees may involve "satisficing" rather than optimizing, and that careful attention must be paid to understanding individual motivation for performance. Another perspective based on bounded rationality emphasizes the limited cognition of the organization as a whole, leading the organization to behave in an adaptive manner. Consider first management boundaries and motivation. The motivational view of management has a number of important predecessors. Chester Barnard's (1938) contribution to management is justly celebrated. His work marks a significant departure from classical organization theory by defining a formal organization as "a system of consciously coordinated activities or forces of two or more persons" (p. 81). Barnard observes (p. 139) that "the individual is always the basic strategic factor in organization" and that therefore "the subject of incentives is fundamental in formal organizations." Barnard stresses the role of managerial leadership and concludes that "the most general strategic factor in human cooperation is executive capacity" (p. 282). His innovative discussion emphasizes the cooperative aspects of organizations, the distinction between the objectives of the organization and those of individuals in the organization, and the elaboration of the role of communication in organizations.8 Organizations involve vertical specialization, that is, differences in the tasks of managers and subordinates, in addition to horizontal specialization, that is, differences in functional specializations. As Simon (1976, p. 9, originally published in 1945) and others have observed, vertical specialization allows coordination across tasks, specialization of managers at making decisions, and accountability to superiors in the 8

Barnard's (1938, pp. 175-181) discussion of authority and communication is heavily influenced by the classical view, however, as it stresses the formal channels of communication within the organization.

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hierarchy. However, Simon (1976, pp. 81-84) cautions that there are limits to rationality: incomplete knowledge, imperfect anticipation of future events, and difficulty in identifying all possible alternatives. For Simon, the organization imposes a set of givens that influence the decisions of its members. The important role played by communication of information within the organization is due in part to limits on the cognition of individuals. Arrow (1974, p. 68) argues that since information is costly, it is more efficient to transmit the information centrally, that is, through the upper levels of the hierarchy. Knight (1921) finds that assignment of individuals to managerial positions may reflect greater capacity for decision making and information processing. Stinchcombe (1990) argues, from a sociology perspective, that the "social structure of organizations can be explained by the structure of the information problem they are confronted with" (p. 29). Limits on the rationality of individuals has important consequences for organizations. The classic text by March and Simon (1958) examines important early work on motivational constraints, conflict in organizations, and cognitive limits on rationality, and concludes that adaptive behavior is fundamental to an understanding of organizational structure. Because of limits on the knowledge, computation, and decision-making capacity of individuals, the organization breaks large tasks into smaller ones, assigning the means to achieve organizational goals as subgoals for different units of the organization (p. 168). Williamson (1975, p. 40) observes that organizations may facilitate "adaptive, sequential decision making, thereby to economize on bounded rationality." Ariel Rubinstein (1998) examines diverse attempts at economic modeling of bounded rationality. He considers models that address procedural decision making, defining knowledge, limited memory, choosing what to know, and limits on strategic decision making in games. Rubinstein examines the organizational implications of bounded rationality in terms of the complexity of group decision making. Groups have difficulties in making optimal decisions because of the cost of establishing channels of communication among members of the organization, the time costs of sequential communication, and the costs of aggregating preferences in group decision making. As is well known from the social choice literature, group decision making can fail to rank alternatives in a transitive manner. The costs of communication channels is highlighted by Marschak and Radner's (1972) classic model of communication in teams in which each member of a team imperfectly observes the current state of the world at some cost, with the decisions of the team depending on what

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(costly) channels of communication are established. In their framework (1972, p. 313), an organizer is faced with the problem of designing an organizational network that yields the highest expected pay-off "net of the costs of observation, communication and computation" incurred by members of the team. They further point out that the activities of the organizer also are likely to entail similar costs of decision making, as well as costs of resolving conflicts and allocating tasks. One approach to dealing with complexity in decision making is for organizations to react adaptively to changing states of the world. The view that organizations behave adaptively is reflected in the systems approach, which was particularly fashionable beginning in the 1960s and continues to influence management textbooks. Cyert and March (1963) present a behavioral theory of the firm based on a systems view of strategy making in the firm. They describe decision making by firms as a process of goal setting, feedback, adaptation, and search. The systems approach, which is due especially to the work of the biologist von Bertalanffy (1968), stresses an integrated view of various components of a larger set of interacting parts, with applications to automated feedback and control systems.9 The systems view has been applied widely in the sciences, mathematics, computer science, and the social sciences.10 Systems-theory studies of organizations often are based on a biological metaphor. For example, von Bertalanffy (1968, p. 47) states that "characteristic of organization, whether of a living organism or a society, are notions like those of wholeness, growth, differentiation, hierarchical order, dominance, control, competition, etc." Morgan (1986) highlights the organism metaphor for organizations and notes that the contributions of systems theory to the analysis of organizations include the concept of an open system, the stress on the organization's interaction with and adaptation to the environment, and the interaction among the subsystems of the organization. The adaptive systems view has been influential in the organizational literature. For example, Lawrence and Lorsch (1967) view the organization as an open system and stress the effect on the behavior of individual members of the organization of both interaction within the organization as well as the influence of the external environment. They suggest that the concern of classical organization theory with specialization and integration of functions within the organization should be 9 10

See also Bennis (1966) and Toffler (1970). von Bertalanffy (1968) claims a wide array of approaches as systems theories, including computer simulation, cybernetics, information theory, game theory, and decision theory.

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augmented by an examination of behavioral implications of the external environment.11 For example, the behavior of marketing managers is influenced strongly by their contact with customers and awareness of competitors. Lawrence and Lorsch find support for the traditional human relations theory of organizations.12 They propose a contingency theory of organizations to unite the classical and the human relations schools, which states essentially that organizational form is a product of the firm's strategic choices and the environment it subsequently encounters. The biological view of organizations is evident in a number of approaches. Hannan and Freeman (1977, 1989) and Aldrich (1979) study organizational ecology, viewing changes in the population of organizational forms as the result of changes in the social environment. Thus typical organizational forms change as individual firms with particular organizational forms are born or die off (enter or exit). There is then a reduced role of management strategy as a response to environmental change.13 An alternative but related biological view emphasizes organizational evolution and considers the effects of organizational characteristics on the adaptation of individual organizations to their environment. This literature emphasizes changes over time in the population of organizations (e.g., the number and size of firms).14 Economists also have studied the evolution of organizations.15 In contrast to standard economic models of firm optimization, Nelson and Winter (1982) emphasize the importance of organizational routines that serve as (1) organizational memory, (2) a means of coordination (truce), and (3) targets for purposes of control, replication, and imitation. They view corporate strategy as a set of heuristics for top managers. An economic model of selection and industry evolution, which is due to Jovanovic (1982), examines entry, exit, and survival of firms with random costs of production that differ across firms. The firm gradually learns about the probability distribution of its cost shocks and chooses to remain in the industry or to exit on the basis of the expected value of profits. 11

12

13 14 15

Lawrence and Lorsch (1967, p. 7) state that systems become differentiated as they grow and the separate parts must be integrated: "As an analogy the human body is differentiated into a number of vital organs, which are integrated through the nervous system and the brain. Second, an important function of any system is adaptation to what goes on in the world outside." Lawrence and Lorsch (1967, p. 182) find that "all the organizations in our sample seemed to function best when influence was located (either vertically in the hierarchy or laterally between functions) where the relevant knowledge was concentrated." See Hrebiniak and Joyce (1985) on this issue. Burgelman (1990) suggests that strategy in large organizations results from processes of organizational ecology within the organization. See, for example, the articles in Singh (1990). See Penrose (1952, 1959).

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Market uncertainty versus organizational costs The problems of market uncertainty and bounded rationality can be addressed by creating organizations. Internal production and allocation of goods and services allow for management controls that may not be replicated through market contracts. Further, the combined efforts of the organization's members allow for information processing that can alleviate the effects of market uncertainty and reduce the bounded rationality of individuals. In this way, organizational solutions to market uncertainty and bounded rationality contribute to the contractual theory of the firm. Yet, as Demsetz observed for the Coasian make-or-buy decision, the contrast between market and organizational alternatives is far from clear cut. Carrying out an activity in house does not necessarily eliminate uncertainty. Internal production and delivery can just as easily be subject to disruption and delay, and management controls can be imperfect. The firm's employees may go on strike. Moreover, in-house production is subject to market uncertainty because of the need to procure primary inputs. The firm will encounter the costs of searching for suppliers and negotiating prices for those primary inputs. Thus vertical integration entails market uncertainty. At the same time, outsourcing activities need not be fraught with uncertainty. There are contractual methods for guaranteeing timely delivery or quality of service. Technological innovations in interfirm transactions, such as just-in-time delivery and electronic data interchange, are comparable in efficiency with internal inventory controls. The firm's suppliers manage the uncertainty in their production and delivery processes. Thus outsourcing activities also entails the purchase of management services that reduce uncertainty. Thus vertical integration entails both organizational and market uncertainty as well as management costs. Similarly, reducing the span of the firm and relying on independent suppliers and distributors entail organizational and market uncertainty as well as management costs incurred by the supplier or distributor. Overcoming bounded rationality provides an explanation for building an organization as managers delegate authority and responsibility to subordinates to alleviate their limitations. The firm's internal routines and accumulated expertise help it to adapt to changes in its environment. Yet building an organization does not eliminate the problems associated with bounded rationality. Managers must still handle the problems of communicating with subordinates and coordinating their activities. Managing organizations is a difficult task that is at least as complex as administering the company's market relationships.

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Delegation of authority within the organization creates new problems attributable to the inherent differences in interests between principals and their agents. Employees' actions are costly to observe and employees' characteristics are costly to assess. It is costly for firms to design incentive contracts and to monitor performance. Contracts with employees are subject to moral hazard and adverse selection problems just as are contracts with external suppliers. As I have already emphasized, vertical integration merely moves procurement of inputs further upstream. Bounded rationality problems are likely to be present as the firm's managers deal with the uncertainties of those input markets. Moreover, the reduction of bounded rationality can be achieved through both market and organizational solutions. Managers can delegate authority to suppliers, distributors, and outside experts who can assist them with decision making and information processing. By simplifying contracts with trading partners, companies can reduce the costs of handling market transactions. As in the case of transaction costs, it is difficult to draw a clear distinction between market and organizational alternatives as a means of surmounting bounded rationality.

9.3

Transaction costs and opportunism

Oliver Williamson, the greatest advocate of transaction-cost economics, argues that the full range of organizational innovations that mark the development of the economic institutions of capitalism over the past 150 years warrant reassessment in transaction cost terms.16 According to Williamson, economizing on transaction costs applies to any issue that can be formulated as a contracting problem: "[e]very exchange relation qualifies."17 Williamson (1988) emphasizes what he terms the "process approach" to vertical integration. This approach has three main elements: (1) bounded rationality, (2) asset specificity, and (3) opportunism. Bounded rationality creates costs of writing contingent contracts. Asset specificity refers to irreversible, transaction-specific investment. Williamson (1985, p. 47) defines opportunism as "self-interest seeking with guile." Williamson (1988) contrasts the process approach, which emphasizes ex post decision rights, with the incentive approach, which focuses on ex ante investment decisions (see Grossman and Hart 1988). 16 17

Williamson (1985, p. 17). Ibid.

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For Williamson, transaction costs are those costs associated with the problem of contracting. Focusing on contracts rather than on spot transactions, Williamson distinguishes between ex ante and ex post transaction costs. Ex ante costs are those associated with contract formation; they are "the costs of drafting, negotiating, and safeguarding an agreement."18 These include the costs of including contingencies in the agreement. They also include the costs of such safeguards as common ownership or substituting internal organization for market agreements. Williamson identifies four main ex post costs of contracting: (1) the "maladaption costs" when contracts fail to respond to changing conditions, (2) the costs of renegotiating contracts in response to misalignments, (3) the setup and operating costs of governance structures for dispute resolution, and (4) the bonding costs of effecting secure commitments. As Alchian and Woodward (1988, p. 67) observe, Marshall in his Principles identified "composite quasi-rent" as the rent earned by an asset above its operating costs; this is the return to sunk investment and is the amount subject to appropriation if contracts are renegotiated. Marshall gives the example of a steel mill that makes an investment in facilities located near a power plant and contracts for power with the plant. The power plant seeks to extract the steel mill's quasi-rent, after the mill is established, by raising electricity rates. Extending and refining the ideas of Coase (1937) and Marshall, Williamson (1975, 1985) provides an extensive and important analysis of the role of transaction costs in the vertical integration decisions of firms. In comparing contracts with vertical integration, Williamson emphasizes costly contract contingencies, moral hazard in market contracts due to monitoring costs, and the possibility of technological spillovers in contracts. He states (1975, p. 83) that "were it possible to write and enforce a complex contingent claims contract between blast furnace and rolling mill stages, the integration of these activities, for thermal purposes would be unnecessary." Further, he identifies bounded rationality as a factor that makes complete contingent contracts prohibitively costly, noting that the ensurance of supplies argument for vertical integration is a special case of costly contract contingencies. Williamson (1975, 1985) stresses the importance of monitoring and enforcing performance after contracts have been formed. In law, irreversible investments specific to contractual relationships are referred to as reliance. Williamson identifies reliance, which he terms "asset specificity," as a key determinant in the organization of firms. A party 18

Ibid, at p. 20.

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investing in assets that are specific to a contractual relationship is subject to renegotiation or contractual holdup that takes advantage of the sunk investment.19 Williamson argues that transaction costs explain both the decision to shift a transaction from the market into the firm and the organizational form of the firm. In this regard, Williamson emphasizes that opportunistic behavior by contracting parties can occur if contracts are incomplete. Accordingly, he emphasizes the need for a complex hierarchy to manage vertically integrated companies so as to "harness opportunism" (1975, p. 98). Williamson (1975, Chapters 6 and 7) also introduces a number of factors that may limit the gains from vertical integration. Opportunism in market contracts may be limited by social norms of trust between transacting parties, so that incomplete contracts can be consistent with efficient performance. Furthermore, various factors may limit the size of the firm, including bounded rationality, bureaucratic opportunism, and limits on cooperation among employees. Riordan and Williamson (1985) address the effects of asset specificity on the trade-off between market transactions and vertical integration. Let A be the degree of asset specificity that is chosen by the firm. If A is small, the firm's assets can be redeployed to other markets, while if A is large the firm's assets have relatively little value outside their current application. The firm's production costs are C(Q, A), where Q represents output. An increase in asset specificity lowers total and marginal cost, CA < 0 and CQA < 0. The costs of asset specificity are zA, thus assuming that tailoring assets to a specific purpose is more costly than flexible, multipurpose technology. In the absence of other costs, the optimal degree of asset specificity would trade off the costreducing advantages with the costs of tailoring the asset, -CA(Q, A) = z, where the choice of asset specificity depends on the firm's output level. The problem is complicated by the transaction costs of market contracts versus the costs of managing an organization. A firm that relies more on outsourcing incurs market contracting costs M(A), which are increasing in asset specificity. A vertically integrated firm, in contrast, incurs additional management or governance costs G(A), which are also increasing in asset specificity. To represent limited adaptability of the market relative to the organization, they assume that the marginal costs of market contracting 19

The role of asset specificity in vertical contracting, as set out by Williamson (1971, 1975) is developed further by Klein, Crawford and Alchien (1978) and Riordan and Williamson (1985).

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exceed the costs of management: M'(A) > G\A). To represent the "high-powered incentives of markets" they assume that market costs to the firm are less than corporate governance costs when assets are not specific: M(0) < G(0). Then it follows that there is a critical level of asset specificity A* such that these costs are equal: M(A*) = G(A*). For asset specificity below the critical level A*, market transactions are less costly, while above the critical level, management is less costly. The firm chooses between two reduced-form cost functions. The cost of production plus market contracting costs from outsourcing is given by (1)

C\Q) = min[C(Q,A) + M(A) + zA]. A

The cost of production of the vertically integrated firm that relies more on internal management is given by (2)

C2(Q) = min[C(G, A) + G(A) + zA]. A

Since underlying asset specificity will differ for the two cost functions, marginal costs of production will differ.20 The profit-maximizing firm will equate marginal revenue to marginal cost so that the equilibrium output of the firm will differ depending on which cost function is used. The firm will choose its degree of vertical integration by choosing the highest profit alternative. The direct costs of opportunism occur through contract renegotiation. The firm will continue to operate as long as it earns revenues that cover its operating costs. Buyers or suppliers have an incentive to renegotiate contracts if they can obtain a greater share of the firm's quasi-rent. This gives the firm an incentive to reduce its transaction-specific investment below efficient levels. The reduction of investment leads to increased production costs or lower product benefits. Thus the efficiency losses from reduced investment are an indirect cost of opportunism. The effects of opportunism are addressed in a contractual model of Grout (1984) that explores the consequences of nonbinding contracts between capital and labor. In Grout's model, the shareholders of the firm and the workers' union bargain over the allocation of profit after capital has been invested in the firm. The firm's capital investment is irreversible and relation specific. The allocation of rents in the absence of binding contracts reflects only the firm's revenue and avoidable costs 20 jf M"(A) > 0, G"(A) > 0, and CAA > 0, then for any given output Q, the cost-minimizing level of asset specificity will be lower with greater reliance on outsourcing (cost function one) than with greater reliance on internal sourcing (cost function two).

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and the workers' opportunity costs. If contracts were binding and the payment to labor werefixedbefore capital was invested, the optimal level of investment would be chosen by the firm.21 Ex ante commitments lead to optimal investment since the two parties bargain over the division of a surplus whose size is yet to be determined by the level of investment. With the payment to labor fixed, thefirmchooses the investment level that equates marginal profit to the cost of capital. If contracts are not binding, the payment to labor is established by bargaining after capital is invested. The firm underinvests since sharing the total return lowers the firm's marginal return to capital. Limits on the ability to make binding contractual commitments in the marketplace may provide an explanation for contracts within the firm. Thus, Grout's model may be reinterpreted in the following way. Suppose that the firm and the workers are unable to make binding contracts for worker services on a temporary basis. Suppose further that when workers are employees of the firm, thefirmand the workers may enter into longer-term commitments to wage contracts. Then these contractual commitments will reduce the problem of holdup and create incentives for increased investment in relationship-specific capital. This provides a contractual explanation for the long-term employment arrangements of firms. Asset specificity and limited commitment ability can be used in a similar way to explain vertical integration of production activities within firms. Suppose that an upstream firm produces an input used by a downstream firm. Let x represent the quantity (or quality) of the input and let w be the payment made by the downstream firm to the upstream firm. The upstream firm's profit is equal to the payment minus production cost c(x): (3)

nu = w-c(x).

Let c(0) = 0. The downstream firm incurs an investment cost k that is assumed to be irreversible or sunk. The downstream firm's profit equals operating returns v9 which is a function of the input x and investment k minus the payment p and investment cost k: (4)

nD = v(x,k)-w-k.

Let v(0, k) = 0. 21

Hart and Holmstrom (1986) emphasize the general implications for the theory of contracts of this formalization of contractual holdup. Tirole (1986a) shows that underinvestment still occurs with asymmetric information in the bargaining stage. Besanko and Spulber (1992) show that the signaling value of investment will offset the incentives to underinvest that result from limited commitment.

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Suppose that a binding contract between the firms is feasible only through vertical integration. The integrated firm's profit will equal (5)

n =

V(JC, it)

-

C(JC)

- it.

The output and the investment that maximize profit will satisfy the optimality conditions: (6) (7)

vk(x*,k*)=l vx(x*,k*) = c'(x*).

The marginal value of investment equals marginal investment cost and the marginal value of the good equals marginal production cost. Suppose that the two firms agree to exchange the good but cannot reach a binding agreement on the price. After the downstreamfirmhas made its investment k, the upstream firm will wish to negotiate the price of the good, thus acting opportunistically. Suppose that the upstream and the downstream firms bargain over the payment and the input level. The downstream firm will continue to purchase the good as long as the price does not exceed current operating returns v. The sunk costs of investment are not considered in the decision whether or not to purchase the input. Therefore, at the Nash bargaining solution, the price and the input level that maximize the product of the two operating profits [v(x, k) — w][w — c(x)] solve the following conditions: (8) (9)

w = [v(x,k) + c(x)]/2, vx(x,k) = c'(x).

The equilibrium price and the input level are functions of the downstream firm's sunk cost, w(k), x(k). The downstream firm takes this dependence on the investment level into account. After substituting for w, the downstream firm's net profit is (10)

nD = [v(jc(it), k) - c(x(k))]/2 - k.

Thefirmchooses an investment to maximize net profit. Thus equilibrium investment is not optimal since the firm equates half the marginal return to capital to the marginal cost of capital: (11)

vk(x(k),k)/2=l.

The equilibrium outcome (Jc, k, w) solves Eqs. (8), (9), and (11). The distortion in investment also will yield a nonoptimal level of the input x in the second period. The problem is that the two firms do not enter into a contract that takes into account the initial investment level.

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The output and the investment of the vertically integrated firm differ from the equilibrium values in the case of market contracts with opportunism. Then, since control over k requires vertical integration by assumption, asset specificity and limited commitment create gains from expanding the firm. The gains equal the difference between the profit of the vertically integrated firm and the total profit of the firms operating independently. The model of opportunism suggests that the same firm will wish to control both the production of x and the production process that uses x as an input. The result is predicated on the assumption that market agreements are not binding. It also requires that the vertically integrated firm is not subject to other forms of opportunism, such as renegotiation of wages, as in Grout's analysis. The combination of input and output production determines the boundaries of the vertically integrated firm.

9.4

Transaction costs and ownership

Grossman and Hart (1986), Hart and Moore (1990), and Hart (1995) propose a property rights approach to the firm that seeks to extend Williamson's analysis of asset specificity and opportunism. The property rights approach tries to explain vertical integration based on the view that "ownership is a source of power when contracts are incomplete" (Hart, 1995, p. 29). This view suggests that because it is costly to write complete contingent contracts, there are transaction-cost savings and corresponding productivity benefits from joint ownership. Drawing on the standard example of vertical integration as an explanation for the General Motors' acquisition of Fisher Body, the property rights approach maintains that the merged company is able to exercise control rights so as to use the assets most productively in combination. The notion that contractual commitments within the firm may ameliorate problems of contractual holdup extends beyond the question of allocating gains from trade. Grossman and Hart (1986) suggest that there is an additional problem of controlling the activities of the firm. They present a model of integration of two firms in which each firm makes an investment decision in the first period and chooses the level of an additional activity in the second period. The second-period activity has a positive or negative external effect on the other firm's pay-off. For example, the firms may produce goods that are complements or substitutes in demand. Incentives for underinvestment are mitigated by joint control of the second-period activities, which can be interpreted as a merger of the two firms. In this setting, separate ownership is assumed to result in a reduction in the ability to make binding commitments while joint

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ownership allows binding commitments and unified control over the firm's activities. Such a model corresponds with a merger of two competitors or a merger of two firms whose activities create externalities for each other (corresponding to lateral integration). Hart and Moore (1990) extend the analysis of the firm to examine the effects of property rights on the efficiency of transaction-specific investment. They examine a multiagent setting in which each agent makes an investment in human capital. In the second period, joint ventures are formed in which rents are allocated cooperatively (by use of the Shapley value). They consider assets that are complements in production with the investment in transaction-specific capital. They show that inefficient investment occurs because of a separation in ownership of the complementary assets and control over the investment in transaction-specific capital. They show that if an agent's action is highly sensitive to ownership of an asset, then it is efficient for the agent to own that asset. They conclude that assets that are highly complementary should be jointly owned. Under some conditions, including economic independence of assets, joint ownership is likely to decrease overall efficiency. Hart and Moore (1990) point out that a key right provided by ownership is the ability to exclude others from use of the asset. They argue that ownership of productive assets, such as capital equipment or corporate goodwill, translates into authority over personnel. Personnel have some incentive to act in the interest of the owner because otherwise the owner will exclude them from access to the productive asset. Some of these issues can be illustrated with an example that adapts a model of Hart (1995). Suppose that a buyer purchases one unit of a good that is manufactured by a supplier. The buyer and the seller make relationship-specific investments, where A\ is the buyer's investment and A2 is the seller's investment. The buyer's value v(A\) is increasing in investment, and the seller's production cost c{A2) is decreasing in investment. The jointly optimal levels of investment maximize total surplus: (12)

W ( A U A2) = v(Ax) - A

x

- c{A2) - A 2 .

Therefore the jointly optimal investment levels solve v'(A*) = 1 and -c'(A*) = l. In addition, there are two productive assets, both of which are necessary for the production of the good. The assets are numbered 1 and 2. There are three possible ownership arrangement. The assets can be both owned by the seller, both owned by the buyer, or the buyer owns asset one and the seller owns asset two. The ownership arrangement of the assets is assumed to have no effect on the production of the good.

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However, the ownership arrangement does have an effect on the outcome of negotiations between the buyer and the seller. The reason for this is that whoever owns the asset can resell its services if the asset is not used in production. Moreover, the outside option value of the assets depend on the transaction-specific investment of the owner. Let S((Aj) represent the outside option value of asset / when it is owned by person j . Assume that the outside option value or scrap value of the asset is enhanced by the transaction-specific investment of its owner. The function st(Aj) is increasing in A ; . The outside option value thus determines the extent to which the investment A is fungible. Thus, while the investments Ai, A2 are transaction specific, owning the complementary asset allows a realization of returns if trade does not occur. The key assumption is that the buyer and the seller cannot make binding agreements on the value of their investment levels or the price of the good to be exchanged. After investment levels are chosen, the buyer and the seller negotiate over the price w. The negotiated price is determined by a Nash bargaining solution. The ownership of assets will affect each agent's reservation value and thus the allocation of surplus from the negotiation. There are three possibilities associated with the three ownership arrangements. First, suppose that the buyer owns asset one and the seller owns asset two. Then w solves (13)

max[u(Ai) -w - si(Ax)][w - c(A2) - s2(A2)l w

If the buyer owns both assets, then w solves (14)

max[u(Ai) -ww

s\(A{) - s2(Ax)][w

-

c(A2)].

If the seller owns both assets, then w solves (15)

max[u(Ai) - w][w - c(A2) - si(A2) - s2(A2)]. w

Clearly the surplus will differ in each case and the pricing formula will differ as well. In each case, the pricing formula will depend on the levels of the transaction-specific investment through the value and the cost functions and through the outside option value of the assets. The buyer will choose the transaction-specific investment A\ to maximize (16)

V = v(Ai)-Ax

-w.

The seller will choose the transaction-specific investment A 2 to maximize (17)

R=

w-c(A2)-A2.

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Intermediation and transaction-cost theory

The buyer and the seller will realize the effect of their investment on the outcome of the Nash bargain, as in the Grout model discussed above. In Eqs. (16) and (17), the price w = w{A\, A2) is given by the pricing formula based on Nash bargaining in the second period. As a result, the investment levels chosen by the buyer and the seller will depend on the arrangement of asset ownership. Clearly, in each case, asset-specific investment will depart from the efficient levels A* and A\. The total surplus W will differ under each of the three ownership allocations represented in maximization problems (13) to (15). Under different assumptions about the outside option and the effects of the transaction-specific investment on the buyer's value and the seller's cost, different ownership arrangements will be preferable to others. All three ownership arrangements are second best. Moreover, the surplus generated by the buyer and seller transaction is sensitive to the allocation of asset ownership. If only the most efficient firms operate at the market equilibrium, the analysis would suggest that the boundaries of firms are determined by the surplus-maximizing asset ownership arrangements. Thus the boundaries of firms depend on how transaction-specific investments affect productivity and outside options. The question is whether the allocation of asset ownership provides a compelling explanation for the how firms are organized. The crucial effects of ownership depend on the inability of buyers and sellers to enter into binding contracts. The ownership of assets is the only way for the buyer or the seller to capture even some share of the benefits derived from asset-specific investment. If opportunism is built into the relationship, through the assumption of inability to make commitments, and if ownership of assets is the only way to alleviate the problem, then having property rights inevitably becomes central to the purpose of firms. In Chapter 101 show that when intermediaries can address the problem of making price commitments, allocation of property rights no longer affects productive efficiency and therefore is not a sufficient explanation for the boundaries of the firm.

9.5

Conclusion

A common theme runs through the various approaches to the contractual theory of the firm: the trade-off between market costs and organizational costs. The firm chooses its extent of vertical integration by minimizing the sum of transaction costs and management costs. The firm also chooses whether to vertically integrate into input production and supply based on the trade-off between transaction uncertainty versus the costs of allocation with the organization. The firm further decides whether

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or not to enter into an activity requiring transaction-specific investment based on the relative costs of transactional opportunism and organizational contracting. Finally, the firm selects what assets to own based on a comparison of the costs of imperfect control over investment with the costs of asset ownership. In each case, the prescribed remedy for market transaction costs is expansion of the organization. The result is a theory of the firm that determines its boundaries on the basis of the relative costs of using the market and of internal allocation. Therefore cost minimization is the basis for the firm's choices of production and distribution activities, extent of vertical integration, types of investment, and asset ownership. Taken individually or in combination, these decisions determine the firm's activities, organizational structure, contracts, and assets. Thus the organizational solutions to costly markets provide a contractual theory of the firm. The firm solves a complex cost-minimization problem that mixes market and organizational alternatives. Although the firm is a sophisticated decision maker in terms of contracts and organizational design, transaction-cost analysis tends to neglect the firm's choice of what outputs to produce. The firm's output choices generally are taken as givens, much as they are in the derivation of the neoclassical cost function. Competition between firms does not play a central role in the analysis. As in the neoclassical model of perfect competition, firms presumably compete by minimizing costs. Those firms that operate at the market equilibrium are those with the least-cost combination of market transactions and organizational activities. Paradoxically, the transaction-cost literature, which so clearly identifies the costs of using markets, does not present a model of market microstructure. The focus is almost exclusively on organizational solutions to transaction costs. Yet some basic questions remain. What are the effects of transaction costs on the institutions of exchange? How are market prices determined when transactions are costly? How do transaction costs affect the firm's choices of what products and services to offer its customers? How do transaction costs affect competition between firms? I turn to some of these questions in Chapter 10.

10

Transaction costs and the intermediation theory of the firm

The analysis of intermediation and market microstructure in the preceding chapters lays the groundwork for a theory of the firm. That theory is distinct from the neoclassical, industrial-organization, and contractual theories discussed so far. The intermediation theory of the firm explains both why firms exist and what economic functions the firm carries out. The theory of the firm is based on a comparison between intermediated exchange and direct exchange. Economic agents createfirmsto intermediate transactions between buyers and sellers when net gains from trade exceed those obtained through direct exchange. The boundaries of the firm are determined by the set of complementary transactions that the firm assembles. Firms are formed to carry out innovative transactions, finding those that yield the greatest value added net of transaction costs. The intermediation theory of the firm also provides an explanation of how markets work and what institutions of exchange will prevail in competition. Intermediaries create and manage the institutions of exchange through their pricing and market-making activities. The most efficient market microstructure produces the greatest gains from trade net of transaction costs. Competition between intermediaries seeking to serve the market should enhance the efficiency of market microstructure. Intermediation theory is concerned with both the benefits and costs of transactions. In this sense the intermediation theory differs from the contractual theory of the firm, which concentrates on transaction-cost avoidance. By including the benefits of transactions in the analysis, the intermediation theory shows that firms are concerned with capturing gains from trade, the difference between consumer willingness to pay and supplier opportunity cost. In this chapter, I set out the basic outline of the intermediation theory of the firm. By drawing together the intermediation models that I have already discussed, I obtain a picture of the firm as a creator of innovative transactions. I extend the discussion to the question of what the determinants of the firm's boundaries are. The extent of vertical integration of market intermediaries is not necessarily determined by manufacturing technology 256

Transaction costs and the intermediation theory of the firm

257

since the firm can contract with suppliers and distributors for production and distribution services. As I emphasize, considerations of asset control to mitigate opportunism need not determine the extent of vertical integration. Moreover, ownership of productive assets that are complementary to productive investments need not govern the extent of vertical integration. Instead, the vertical boundaries of the firm are the result of innovation transactions that the firm is able to identify and accomplish. How do the implications of intermediation theory compare with those of contractual or transaction-cost theory that I discussed in Chapter 9? In contrast with the intermediation theory, the contractual theory of the firm focuses its attention on organizational solutions to the costs of market allocation. The firm arises to provide in-house production and distribution, allocation of goods and services within the organization itself, organizational contracts to control input usage, and ownership of critical, transaction-specific assets. According to the contractual theory of the firm, the boundaries of the firm are determined by one or more of the four trade-offs discussed in Chapter 9, namely transaction costs versus management costs, transaction uncertainty versus the costs of allocation with the organization, transactional opportunism versus organizational contracting costs, and transactional opportunism versus the costs of ownership. By its focus on organizational solutions to market costs, the transaction-cost literature begs the question: What is market allocation? Certainly not the neoclassical ideal of a frictionless auctioneer. The transaction-cost literature correctly emphasizes the presence of market search and contracting costs. However, rather than exploring the transaction costs of alternative market institutions, transaction costs are taken as a given, to be alleviated by the organizational alternative. The theory of the firm necessarily extends beyond the basic market versus organization trade-off because there are many ways to reduce market transaction costs other than allocating resources within an organization. Firms establish and manage alternative institutions of exchange, so that they can organize market exchange in a variety of ways. Firms can improve on market transactions by improving communication and writing better contracts with suppliers and customers. They can explore alternative ways to select prices and to match buyers and sellers. They can develop innovative transaction technology (such as electronic commerce). The point is that firms do not take markets as given when choosing between markets and organizational solutions. Rather, market institutions are endogenous; institutions of exchange are created by firms. If direct exchange is costly, there may be less costly intermediatedexchange alternatives.

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Intermediation and transaction-cost theory

Companies design market institutions to earn the returns to providing mechanisms of exchange. They earn some share of the gains from trade between buyers and sellers. The market institutions created by firms compete with organizational alternatives. Moreover, there is competition between alternative market institutions. For example, intermediated trade competes with decentralized exchange between buyers and sellers. Market microstructure varies considerably across industries, including formal auction markets, merchant sales at posted prices, and brokered exchange. The vertical integration decision is an essential building block for the theory of the firm but it is far from sufficient in and of itself. The provision of transaction services is at least as important to understanding the activities of the firm as is the make-or-buy decision. Suppose that a firm uses some input x to produce some output q. The question of whether to make x oneself or to buy x certainly will affect the boundaries of the firm. But why does the firm choose to produce q to begin with? Consider a firm that appears not to produce any goods and services in the traditional sense, but is simply a merchant. The make-or-buy decision is relevant only for determining why such a firm purchases the goods it sells instead of producing them. That decision does not answer the question of why the merchant exists at all. The merchant produces some services, but what are those services? The intermediation models discussed in Chapters 1-8 provide an answer to that question that is consistent with the transaction-cost approach and extends it at the same time. Individual consumers purchase final goods and services and sell labor services, resources, and other assets. Firms are not needed if economic agents acting as buyers or sellers can directly transact with each other. The gains from trade net of transaction costs may be greater when dealing through an intermediary than with decentralized, direct exchange between buyers and sellers. Thus, in a pure-exchange setting, the existence of firms is explained by the gains-from-trade benefits and transaction-cost savings of intermediated exchange. Production of goods is connected to but conceptually distinct from the creation of transactions. The production of goods and services could presumably be arranged through direct contracts between consumers as purchasers of outputs and sellers of inputs. The main determinants of firm boundaries are the benefits and costs of alternative transactions. The chapter is organized as follows. I begin in Section 10.1 by examining the implications of transaction costs for the intermediation theory of the firm. In Section 10.2, I examine some implications of the intermediation perspective for vertical integration and consider what the

Transaction costs and the intermediation theory of the

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appropriate unit of analysis is in microeconomics. Next, in Section 10.3, I reexamine the question of asset specificity and opportunism when intermediaries can make credible commitments and show that the need to control assets does not provide a convincing explanation for the boundaries of the firm. Then, in Section 10.4, I turn to the property rights approach to the theory of the firm and show that when intermediaries can make credible commitments, ownership of assets has a limited role in explaining the boundaries of the firm.

10.1

Transaction costs and market microstructure

Why dofirmsform? What are their economic functions? These questions are central to microeconomics. Economic models of markets are closely tied to underlying characterizations of firm behavior. For example, if the firm is a price-taking neoclassical firm, markets must clear through an unobservable Walrasian auctioneer. If firms are oligopoly price setters, as in industrial-organization models, markets clear through Bertrand price competition. If firms are transaction-cost minimizers, as in the contractual theory of the firm, the market institutions that emerge are those that are less costly than organizational alternatives, although the determinants of efficient market institutions remain unspecified. Intermediation theory provides an explanation for the formation of firms that is consistent with its description of how markets work. Firms form to carry out innovative transactions. There are returns to the formation of a firm when it can identify transactions such that the gains from trade exceed the total transaction costs for the firm and its trading partners. Firms profit by identifying ways to increase gains from trade or reduce transaction costs. Through these activities, firms establish and manage their markets. The formation of firms The intermediation theory of the firm does not rely on production. Consider a pure-exchange economy. With small numbers of consumers trading a limited selection of goods and services, one can imagine that firms are not needed. Consumers have little trouble meeting each other. They can bargain with each other over the terms of trade. If there are many consumers, life in the pure-exchange economy becomes more complicated. It may be difficult to locate suitable trading partners, creating search costs. There is uncertainty about the characteristics of trading partners. Bargaining with multiple partners can be time consuming. Achieving an efficient allocation of resources could require

260

Intermediation and transaction-cost theory

each consumer to trade with many other consumers, adding to the costs of trading. With many consumers, communication becomes increasingly difficult so that terms of trade can differ across transactions. Even without production, a pure-exchange economy can entail complex transactions. Transactions need not be limited to spot exchange. Even with the social contrivance of money, the problem of the double coincidence of wants emerges. Consumers may borrow or lend commodities to each other to smooth consumption patterns, particularly if endowments of goods are not all immediately available for consumption. They may wish to enter into state-contingent contracts, such as insurance, if consumer endowments or preferences are subject to exogenous shocks. Consumers may encounter time costs of negotiating contracts and monitoring performance. In the pure-exchange setting, the normal frictions associated with search, negotiation, communication, computation, contracting, and monitoring suggest that equilibrium exchange between consumers will not capture all potential gains from trade, however such an equilibrium might be defined. Put differently, the allocation of goods in an equilibrium with direct trade will not be Pareto optimal, at least in comparison with a frictionless environment. Marginal rates of substitution will not be equalized across consumers. Because of trade frictions, there may even be goods that fail to be traded. Therefore, as a result of transaction costs associated with direct exchange, there will exist allocations of goods that would make everyone better off. This creates profit opportunities for innovative transactions by intermediaries. These transactions can realize some of the gains from trade that were otherwise unattainable through direct trade. Firms are formed to centralize trade, intermediating multiple transactions between consumers acting as buyers and sellers of goods and services. Indeed, firms intermediate transactions between consumers and firms and between other firms. In the pure-exchange economy, firms carry out spot transactions and enter into contracts. It would be overly simplistic to view firms as producers of transactions, just as the neoclassical firm produces products with a given technology. The firm identifies arbitrage opportunities in the economy, choosing its transactions based on returns net of transaction costs. Firms negotiate or post prices and coordinate exchange. These are market activities that are distinct from traditional production. Firms are not bound by a priori restrictions on what technology they may employ or what products they may produce. Introducing production into the economy does not alter the intermediation framework in any fundamental way. Firms purchase the services of labor, capital

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equipment, resources, and other inputs through spot transactions or contracts. They can engage in complementary production and transaction activities when there are returns to vertical integration. Traders face the crucial question of whether to transact directly with other buyers or sellers or to transact through an intermediary. There are transaction costs in direct and intermediated exchanges. Suppose that a particular direct exchange yields the buyer value VD and entails opportunity cost CD for the seller, with a combined transaction cost TD. An intermediary produces a pair of exchanges that yields the buyer value V1 and entails opportunity cost C1 for the seller, with a total transaction cost for the buyer, seller, and intermediary equal to T1. Intermediated exchange occurs when it raises the net gains from trade: y£> _ cD - TD < V1 - C1 - T1. This analysis generalizes easily to multiple buyers and sellers. If the two types of transactions yield the same gains from trade, V1 — 1 C = VD — C D , then intermediated exchange occurs when it lowers transaction costs: These considerations determine when buyers and sellers will transact directly or through intermediaries. In markets with both direct and intermediated exchanges, transaction costs at the margin are equalized between the two forms of exchange for those transactions that yield the same gains from trade. If direct and intermediated exchanges entail the same transaction costs, T1 = TD, then intermediated exchange occurs when it raises the net gains from trade: VD_CD


_ci

Why would intermediaries create transactions that have higher net gains from trade? This can occur if the intermediary produces a better transaction for the same level of transaction cost, for example, by supplying price-setting or contract-writing services such that the good or service being exchanged increases buyer willingness to pay or lowers seller opportunity costs. The intermediary may improve communication between the buyer and the seller, thus alleviating information asymmetries. By superior commitment ability, the intermediary can allow buyers and sellers to make greater transaction-specific investments, as I show in Section 10.3. Because the intermediary participates in many transactions that allow it to gather market information, the intermediary can tailor the characteristics

262

Intermediation and transaction-cost theory

of the good or the service to better reflect buyer preferences or seller capabilities. Intermediaries seek out the best trades based on their expected share of net gains from trade. The firm's earnings are bounded by the difference between the buyer's willingness to pay and the seller's opportunity cost, net of the cost of transacting. As traders search for the best transactions, the effect will be to maximize gains from trade net of transaction costs. This results not only in the best organizational boundaries, but also in the most efficient market institutions, taking transaction costs into account. The formation of firms thus depends on there being advantages to intermediated exchange. In what follows, I discuss ways in which intermediaries can raise gains from trade or lower transaction costs. Coordinating exchange Firms coordinate transactions for their customers and suppliers. Firms incur the costs of carrying out transactions, which include record keeping, operating a system of payments, and provision of a central place of exchange. The costs of transactions include communication of price and product information with customers and suppliers. Allfirmscan be viewed as intermediaries between their customers and suppliers. Clearly, merchants, whether retailers or wholesalers, are intermediaries. Manufacturers carry out interrelated transactions that must accompany the productive transformation of inputs into outputs. Thus manufacturers are intermediaries between their customers and their suppliers of finance, labor, resources, parts and equipment, and technology. The finance literature has explored the intermediation role of financial firms, including banks, investment funds, stock brokerages, and insurance companies, as well as the operation of organized exchanges for securities, debt, futures, and other contracts. Finance distinguishes between the merchant function of dealers and the transformation of assets by intermediaries. Financial intermediaries create new assets based on their diversified portfolios, thus reducing risk or transferring income over time. The distinction between trading and transforming financial assets parallels that between merchant and manufacturer. Economic agents seeking to trade incur search costs. These are the time costs and transportation costs of finding a trading partner. Search costs also include the costs of gathering and processing information about the characteristics of trading partners, including their location, product quality, price offers, and contract terms. Intermediaries reduce

Transaction costs and the intermediation theory of the

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search costs by providing easily identifiable trading partners. Even if intermediaries were not distinguishable from other traders, their presence in the market increases the number of potential trading partners, thereby reducing search costs. Firms provide intermediation services by coordinating exchange for their customers and suppliers. Consumers need not go directly to suppliers and suppliers need not go directly to consumers, thus saving search and transportation costs for both sides of the market. Instead, consumers and suppliers can visit a central place of exchange provided by the intermediary. Central places of exchange provided byfirmsinclude a physical location, such as a store or central office, a catalog, a telephone number, a mailing address, or a computer network. In some cases, central places are provided by dealer associations such as the NASDAQ securities market. If there are fixed costs associated with setting up a central place of exchange, then there may be economies of scale in centralizing transactions. Moreover, there are also positive network externalities resulting from centralized exchange. The central place of exchange provides a hub-and-spoke system that saves the costs of marketing channels that would have to be established between the firm's customers and suppliers (see, for example, Alderson 1954). This is illustrated in Figure 10.1. Suppose that there are three consumers and three suppliers. Then, with decentralized exchange, nine marketing channels are required for linking all consumers and suppliers. With an intermediary, only six marketing channels are needed. Generally speaking, with N consumers and M suppliers and a cost K per marketing channel, the intermediary reduces transaction costs by [NM — (N + M)]K dollars. Townsend (1978), without distinguishing buyers and sellers, defines a market as "the smallest set of agents for which every agent of the set deals with other agents of the set and no agent outside the set." Let N be the number of agents in a market and Z be the number of bilateral transactions. Then the number of bilateral transactions is bounded by N -\
< N(N - l)/2,

with any of the agents acting as intermediaries. Townsend considers the core of an economy in which risk-averse agents have the same initial endowment of a capital good and the same stochastic technology. Each bilateral transaction has a cost. Economic agents reduce transaction costs cooperatively by trading through an intermediary. In the core allocation, the number of transactions reaches the lower bound N — 1, although, as Townsend points out, other configurations than the hub-and-spoke

264

Intermediation and transaction-cost theory

Consumer l ~ ^ ^

Z ^

Supplier l

Supplier 2

Consumer 2

w

Consumer 3~

Supplier 3

Decentralized Exchange

Consumer 1

Supplier 1

Consumer

Supplier 2

Consumer 3

Centralized Exchange

Supplier 3

Figure 10.1. Exchange without and with an intermediary.

form are possible. Agents may be lined up, with each agent trading with adjacent agents, or agents may be arranged in a pyramid, so that multiple intermediaries can exist. Thus different market structures can achieve the lower bound of the range of bilateral transactions. Discovering the terms of trade In addition to coordinating exchange, firms form to discover the terms of trade. They can design mechanisms for consumer or supplier bidding that reveal willingness to pay and opportunity costs, respectively. Firms set bid and ask prices to maximize profit and balance their purchases and sales. The ask price rations demand and the bid price stimulates supply. Selecting and adjusting prices are costly processes that involve gathering and processing information and evaluating the price responsiveness of customers and suppliers. Firms obtain demand information through customer surveys, statistical analysis of sales data,

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and marketing research. They gather supplier information through industry experience, trade shows, and market research. Firms must anticipate competitor prices and product offerings, so that pricing is a fundamental component of competitive strategy. Price information then must be communicated to trading partners through advertisements, catalogs and price lists. Posting and changing prices entails menu costs, just as a restaurant incurs the costs of printing its menus.1 Posting prices reduces transaction costs in comparison with decentralized exchange for some economic agents. If an agent's time costs of search are high, that agent will pay a premium to the intermediary to avoid search in a decentralized market. When there are uncertainties about the chances of finding a suitable trading partner, agents also will pay a premium to avoid the risks involved in finding a suitable trading partner. Similarly, when there is private information about willingness to pay and opportunity costs, the terms of trade that will emerge from decentralized bargaining are uncertain before bargaining begins. Economic agents may pay intermediaries a premium to avoid risky bargaining. Buyers experience transaction costs when they are rationed by suppliers. These costs include the time costs of delay in obtaining the goods and the services and the costs of further search to find an alternative supplier. Similarly, suppliers experience transaction costs when they are rationed by buyers. These costs include the storage and capital costs of holding inventories. Intermediaries can reduce these transaction costs by providing market-making services, standing ready to buy and sell. Provision of liquidity or immediacy to the market can reduce transaction costs relative to a decentralized market. Intermediaries can achieve these cost savings by pooling risks since they serve many buyers and sellers. Moreover, intermediaries can hold reserves of cash and stocks that would be too costly to be maintained by individual buyers and sellers. By reducing the risk of being rationed, intermediaries allow buyers and sellers to reduce precautionary buying and selling. Intermediaries help to clear markets by balancing their purchases and sales, which is closely related to their market-making role. Intermediaries allocate goods and services under uncertainty about supply and demand. By dealing with many buyers and sellers, intermediaries can use centralized warehouses, sophisticated inventory control, and 1

See Caplin and Spulber (1987) on the aggregate effects of price adjustment when firms have menu costs.

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Intermediation and transaction-cost theory

tracking of sales patterns to allocate goods and services. Moreover, intermediaries can adjust their pricing and advertising to reduce the effects of overabundance or scarcity. Mitigating adverse selection and moral hazard By mitigating the effects of adverse selection and moral hazard, firms enhance net gains from trade. Asymmetric information creates the potential for inefficient transactions. The intermediation theory shows that firms can improve the efficiency of transactions by improving contractual design and reducing the costs of forming and monitoring contracts. When observation of the characteristics of trading partners is costly, incentives to misrepresent information can exist and contracts will be subject to problems of adverse selection. There are various ways for intermediaries to improve matters, as the models in Chapter 9 showed. Intermediaries can use pricing and other contractual terms such as collateral requirements for loans to screen borrowers. By being involved in multiple transactions, the intermediary earns returns to investment in expertise or facilities to evaluate product quality and performance, thus reducing information asymmetries. Further, because intermediaries are long lived and are involved in multiple transactions, they have greater returns to building a reputation than do individual traders, so that the intermediary earns returns from certifying product quality. By providing information to buyers and sellers, intermediaries can reduce uncertainty and enhance the expected gains from trade. Intermediaries also earn returns from alleviating moral hazard problems. By monitoring the efforts of their suppliers, firms can improve product quality. Firms act as delegated monitors, designing contracts to control moral hazard on the part of borrowers; see Chapter 12. By acting as residual claimants, firms alleviate moral hazard in teams; see Holmstrom (1982) and the discussion in Chapter 11. Because intermediaries are long lived, and obtain returns to building a reputation, they have incentives to make credible commitments. As I show in Section 10.2, this allows intermediaries to alleviate opportunism by buyers and sellers. Commitment by intermediaries to price offers or other contract terms allows buyers and sellers to select more efficient levels of transactionspecific investments.

10.2

Intermediation and vertical integration

Section 10.1 identifies maximization of net gains from trade relative to decentralized trade as an explanation for the existence of firms. The

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existence question is distinct from that of the size, scope, and span of the firm. The vertical integration decision remains important as a determinant of the boundary of firms. There are many explanations for the firm's choice of its span, such as reducing operating costs, securing reliable supplies or ensuring reliable distribution, saving transaction costs, and competitive considerations such as avoidance of double marginalization. In this section, I suggest that the boundaries of the firm result from optimization over the set of available transactions. Chapter 9 showed that the transaction-cost literature, beginning with Coase (1937), identifies transaction costs as an explanation for vertical integration. Activities are located within the firm if an entrepreneur, by exercising authority, saves on the costs of using markets. For example, a firm decides to manufacture a part if its costs of doing so are less than the price charged by a supplier plus the costs of transacting with a supplier. Yet, as Demsetz observed, it is difficult to distinguish market transactions with a firm's internal allocation. Firms create and manage market transactions. Firms carry out intermediation tasks by buying from some economic agents and selling to others. They act as intermediaries when they can produce the greatest gains from trade net of transaction costs. Firms make the market or rely on the market-making activities of others. I do not conceive of markets as entities that exist separately from the buyers and the sellers, as in the Walrasian framework. The total transaction costs incurred by intermediaries, buyers, and sellers are the costs of operating markets. The intermediation theory of the firm suggests that the vertical decision represents a choice between transacting at different levels of the vertical production process. The firm is thus not defined simply by what production activities it chooses to carry out, but also by its choice of transactions. The boundaries of the firm are determined by revenue and cost complementarities in the transactions chosen by the firm. Schumpeter's entrepreneur In The Theory of Economic Development (1934), Joseph A. Schumpeter attributes an economic role to the entrepreneur as someone who carries out "new combinations." He tells the story of an entrepreneur who introduces technological change to the marketplace. The entrepreneur brings a power loom to a textile industry that had previously relied on manual labor. The entrepreneur earns a return to introducing the innovation. Even though the profit stream erodes eventually, the introduction results in positive profit. In discussing the returns to the innovation, Schumpeter reveals much about decision making by firms.

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Intermediation and transaction-cost theory

Schumpeter essentially dismisses the make-or-buy decision. Regarding the "entrepreneurial profit" earned from the innovation, he asks: Now to whom does it fall? Obviously to the individuals who introduced the looms into the circular flow, not to the mere inventors, but also not to the mere producers or users of them. Those who produce them to order will only receive their cost price, those who employ them according to instructions will buy them so dearly at first that they will hardly receive any profit. The profit will fall to those individuals whose achievement it is to introduce the looms, whether they produce and use them or whether they only produce or only use them. .. .The introduction is achieved by founding new businesses, whether for production or for employment or for both.2 He further asks What have the individuals under consideration contributed to this? Only the will and the action: not concrete goods, for they bought these - either from others or from themselves; not the purchasing power with which they bought, for they borrowed this - from others or, if we also take account of acquisition in earlier periods, from themselves. And what have they done? They have not accumulated any kind of goods, they have created no original means of production, but have employed existing means of production differently, more appropriately, more advantageously.3 This passage is telling, as Schumpeter's characterization of entrepreneurs implicitly dismisses a number of explanations for the formation and boundaries of the firm. Among the points that Schumpeter makes are the following: (1) The entrepreneur need not be a manufacturer, either of the capital equipment or of the final product, (2) the profit earned by the entrepreneur is not a return to ownership of capital equipment nor is it a return to ownership of the firm through the provision of finance, (3) the entrepreneur's profit is not a return to the research that produced the innovation, (4) avoiding uncertainty is not an explanation for the role of the entrepreneur as the "entrepreneur is never the risk bearer."4 Even if the entrepreneur selffinances, he bears the risk as an investor, not as an entrepreneur. 2 3 4

Schumpeter (1934, p. 132). Ibid. Ibid, at p. 137.

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In this sense, Schumpeter's competitive framework differs from that of the transaction-cost literature. The firm need not be a mechanism for avoiding market transaction costs, uncertainty, or opportunism. Ownership of assets to avoid opportunism by market-trading partners is ruled out. Instead, the entrepreneur can choose to avoid ownership entirely. The entrepreneur profits from creative market transactions rather than through the design of an organization to avoid transaction costs. Entrepreneurial profit is a return to those innovative transactions. The arrangements made for production, purchasing, finance, and innovation are incidental to carrying out the innovating combinations. Schumpeter emphasizes innovations in transactions that result in the firm's being able to "produce a unit of product with less expense and thus to create a discrepancy between their existing price and their new costs."5 In this he includes "innovations in business organization and all innovations in commercial combinations."6 As examples of this, he identifies finding new suppliers through "the choice of a new and cheaper source of supply for a means of production," or the provision of new products that allow "replacing one production or consumption good by another" that is cheaper or that satisfies needs more adequately.7 Finally, he includes as a source of entrepreneurial profit, the "search for new markets in which an article has not yet been made familiar and in which it is not produced."8 Schumpeter's theory of economic development encompasses nonentrepreneurial suppliers who simply copy the products and the technology of the entrepreneur. The followers generally earn just enough returns to cover the costs of the factors of production. This does not mean that markets have only one successful entrepreneur. In a dynamic economy, a succession of firms introduces entrepreneurial innovations, so that over time many different firms can be entrepreneurs in the same market. Schumpeter's notion of the entrepreneur who creates new combinations is closely related to intermediation. Intermediation yields economic profits as a return to innovative combinations of transactions. The intermediary maximizes profit through the creation of innovative transactions. The intermediation model is somewhat more general in that it encompasses all the institutions of exchange that are generated by firms. 5 6 7 8

Ibid, at p. 133. Ibid. iDia.

Ibid, at pp. 133-134. Ibid, at p. 135.

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The vertical integration decision The manufacturing function is conceptually separate from the transactions involved in buying and selling inputs and in buying and selling finished goods and services. Firms are needed to carry out those transactions just as other firms are needed to perform the manufacturing task. Firms buying inputs or selling outputs could contract out for production, as the make-or-buy discussion has clearly established. Common inputs in a series of production processes often are cited as reasons for vertical integration. For example, the need to reheat steel is avoided when the blast furnace and the rolling mill are combined in a single enterprise. I formally defined economies of sequence (Spulber 1989b) as the cost savings from combining stages in a production process within a single firm. Chandler (1990, p. 37) finds that cost savings from vertical integration were obtained in chemicals, metals, and machinery, but notes that vertical integration occurred in many companies for other reasons such as reliability of input supplies. Manufacturers that perform a variety of market-related and productive tasks do so because of economies associated with joint production of intermediation services and manufacturing. Such diversified firms intermediate between the sellers of inputs and the buyers of finished goods and services, supplying the transformation of inputs into outputs through production merely as a means to an end, the end being to carry out the purchase of inputs and their resale in the form of finished goods and services. As such, the production task is conceptually similar to the warehousing and transportation activities carried out by a retail or wholesale firm. The application of technology to the productive task, while valuable, is not an explanation for the workings of the economy. Rather, it is the organization of transactions byfirmsthat bears emphasis. As I noted in Chapter 9, the transaction-cost approach has tended to favor cost minimization as an objective. Taking the firm's output choices as given, the firm searched for the least-cost manner of delivering those outputs, choosing between purchase and in-house production of the necessary inputs. Thus firms were defined by the cost-minimizing combination of market transactions and organizational activities. Such an approach is predicated on exogenous specification of market institutions. Taking prices as given, the neoclassical firm derives its cost function by taking input prices as given and then choosing output to maximize profit, taking as given its output prices. For a firm that takes market institutions as given, one can imagine a similar process. For a given set of products to be sold, the firm can minimize costs, combining outsourcing

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and in-house activities to produce the output, thus deriving a general cost function that takes factor market institutions as given. Then the firm can choose the level of output to maximize profit by using the reduced-form cost function. However, even this general problem presents too restrictive a view of the firm. Suppose that the firm's products and services are not specified in advance. Then the general specification of the firm's profit-maximization problem is as follows. The firm contemplates a general set of available transactions (buying, selling, and contracting). The firm chooses those transactions that maximize profit. The buying and selling problems may not be easily separated. Thus a company may purchase widgets in location A and resell them in location B, depending on whether the anticipated price spread will exceed its transaction, transportation, and organization costs. The firm's vertical integration decision is a choice of what markets to transact in, rather than merely a production decision because production services are distinct from input and output purchases. The make-orbuy question implicitly assumes that the inputs with which to make are readily procured. Why should primary inputs be any easier to obtain than secondary ones? Consider the simple example in Figure 10.2. An upstream firm produces x by using input z. A downstream firm produces output q by using input x. A vertically integrated firm purchases z and sells x. The vertically integrated firm might contract with another firm for the production of x. It might also contract with another firm for the production of q. Thus the vertically integrated firm need produce neither x nor q and still buy z and sell q. The firm chooses whether to arbitrage between the market for z and that for q or between the market for x and that for q. Either choice entails costs of purchasing, transacting, and organizing. The firm compares the net return with the two sets of transactions. Arbitrage opportunities can arise in a variety of circumstances. Suppliers and customers can be separated by location, time, states of nature, information asymmetries, or differences in wants. Firms can bridge these gaps if the firm's transaction and other costs are less than the difference between consumer willingness to pay and supplier opportunity cost. Strategy and the theory of the firm Michael Jensen and William Meckling (1976, p. 310) suggest that goals and strategy making cannot be attributed to any firm, as one would to a person. They conclude that "[t]he 'behavior' of the firm is like the behavior of the market, i.e., the outcome of a complex equilibrium."

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Figure 10.2. Vertical relationships with suppliers and distributors.

In their view, the firm is a "nexus of contracts," a bundle of economic relationships, tied together by an invisible hand. Their suggestion that firms are lacking in strategies and that both firms and markets are just equilibrium sets of contracts mischaracterize both markets and firms. While I find the term "nexus of contracts" to be an apt snapshot description of firms, I believe that firms actively tie the knot. The many contracts entered into by the firm are the result of much more than a balance of market forces buffeting the organization. Competing firms make conscious strategic contracting decisions. They choose what spot transactions to carry out, what contracts to write, with whom to write them, and what terms to include in those agreements. The insight that it is easier for the firm's many customers, suppliers, employees, and investors to contract bilaterally with thefirmthan to form multilateral contracts with each other is certainly accurate. This insight is consistent with the view of the firm as a contractual intermediary. However, there is more to the formation of firms than economizing on multilateral contracts.

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The contracts written by the firm are those that the company has a comparative advantage in creating. The act of contracting itself is the firm's contribution. Firms that are better contractors have an economic advantage over other firms and over direct transactions between customers and suppliers. Contracting skills, as well as the relative costs of different types of contracts, explain the firm's collection of contracts, which in turn determines organizational structure. Contracting skills also include the choice of the firm's contract portfolio. Banks and other financial intermediaries assemble loan portfolios of varying maturities. Manufacturers contract with a host of suppliers. The combination of contracts is part of the firm's competitive advantage. Thefirmis more than a bundle of contracts, it is a center of transacting activity. I am emphasizing the transacting activity itself, the flow rather than the firm's stock of contracts. New contracts are continually being written, existing contracts are revised and renegotiated, and older contracts are fulfilled and terminated. The company chooses its economic relationships and assembles them through formal and informal contract negotiation. In choosing its transactions, the firm must discern arbitrage opportunities, that is, net gains from trade for customers and suppliers that exceed transaction costs. Arbitrage opportunities can be short lived, being sensitive to changes in consumer willingness to pay, supplier opportunity costs, and competitor imitation and preemption. Assembling a profitable set of contracts involves the continual creation of innovative transactions, Schumpeter's "new combinations." What should be the unit of analysis in microeconomics? In light of the preceding discussion, what should be the unit of analysis in empirical and theoretical microeconomics? Alternatives include the industry, the firm, the transaction, or the decision. Of course, different questions require different units of analysis. Competitive equilibrium analysis benefits from broad industry-level comparisons. Transaction-cost analysis must involve an analysis of specific transactions. Understanding the managerial decision process can be enhanced by studying particular decisions. The theory of intermediation and market microstructure requires an understanding of the institutions of exchange within a given market. This suggests that, for the intermediation theory at least, the firm is the proper unit of analysis. The firm is more than a nexus of contracts, it is a center of contracting activity.

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Industrial organization begins with the strategic decisions of individual firms but the objective is to examine industry equilibrium. Thus it is accurate to say that in industrial organization, the industry is the unit of analysis. For example, Weiss (1980) entitles his book Case Studies in American Industry and observes (p. 3) that "The term industry may cause some confusion. In theoretical discussions, it usually means all the firms selling on the same market but in empirical studies it often refers to all the firms using a similar technical process, whether or not they compete." In Weiss's cases and other industry studies, there is little if any detail about individual firms, with the focus being on industry-level data. Stigler (1968, Chapter 7) applies the survivor principle to the study of economies' scale of individual firms. He emphasizes the need for interindustry studies and states that "The intraindustry analysis has its chief role, one may conjecture, in providing a systematic framework for the analysis of the data commonly employed in industry studies" (1968, p. 88). However, by restricting attention to comparisons across industries, industrial organization may miss important aspects of firm activities. This can lead to serious oversights in those industries in which large companies play a major role in establishing and operating the market mechanism, as emphasized by Chandler (1977). Contractual theories of the firm of Coase (1937) and Williamson (1975), following Commons (1934), take individual transactions as the unit of analysis. Williamson studies organizations by building up from a careful understanding of individual transactions, emphasizing asset specificity, costly contractual contingencies, and frequency of recontracting. An evenfinerpartition is suggested by Herbert Simon (1957, p. xxxii), who asserted that in examining administrative behavior, the "decision premise i s . . . the appropriate unit for the study of human behavior." Williamson (1990, p. 187) argues that "The decision premise as a unit of analysis has never been operationalized in such a way as to give it broad and general application." Models of bounded rationality focus on the process of management decision making. Because of the central role of managers, the importance of managerial decisions should not be minimized, but it is often the characteristics of the firm and its markets that provide the context in which the decisions are made. Individual transactions may be toofinea partition for observing a firm's competitive strategy or its organizational design. Management case studies traditionally take an individual firm as the basic unit of analysis. The firm's organization, pricing, products, technologies, customers, competitors and suppliers play a central role. Case

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studies apply economic models to the study of an individual firmin a way that necessarily takes into account the firm's perspective. This need not be contradictory. Economic analysis of the firm must involve an objective analysis of the incentives that influence the firm's market activities and the incentives that motivate its managers. At the same time, the subjective viewpoint of the firm's managers is important for understanding how the employees of the firm perceive its organizational structure, how the firm's managers approach the firm's markets, and how the managers recognize regulatory and legal constraints on the firm's activities. 9 Taking the firm as the unit of analysis recognizes firm heterogeneity. It is apparent that firms differ in many ways. Beyond the obvious differences in firms across industries, firms differ greatly within industries. At a minimum, the individual characteristics of each firm's personnel, particularly managers and technical staff, certainly affect the firm's perspective, body of knowledge, and decisions. In addition, firms can have unique histories, which are preserved to some extent in the firm's organizational form, incentive programs, decision-making procedures, and company traditions. Moreover, firms acquire technical and market knowledge through production, purchasing, and sales activities. Companies develop reputations with customers and suppliers that are attached to the company itself or to its brands. Corporations differ in terms of their ownership structure, capital structure, and other legal aspects of incorporation. Companies can differ in terms of their assets, which can include land, natural resources, and patents. Moreover, firms differ in terms of their profitability and rate of growth. However, analysis of individual firms is of limited value if it is merely a superficial catalog of firm differences. To be useful, economic studies need to develop and apply general principles in examining individual firms. The institutional descriptions of the firm's organization and markets and of the firm's strategies serve as essential data that pose important questions. A theoretical framework is required for organizing and interpreting the data. 9

The activities of firms are often very complex, particularly in the case of large-scale corporations. A case study can be integrative- explaining the organizational design, marketing, operations, technology, investment, employment, and purchasing decisions of a singlefirm- to the extent that the theoretical framework of the case requires an overview of the firm's activities. Alternatively, a case study can focus on a very specific activity of the firm such as the design of an incentive scheme, the introduction of a new product, the decision to enter a new market, or the response to a regulatory change. The essential strategic question is to examine the sources of a firm's success or of its difficulties as a way of explaining why some firms are more successful than others. Identifying general determinants of success would certainly be of interest to researchers seeking to understand the organization and development of firms and would also be of interest to managers seeking to achieve success in their markets. Examining the determinants of success, which goes beyond Stigler's survivor principle, requires a understanding of the effects of firm heterogeneity.

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The intermediation theory of the firm provides such a framework by taking into account both the benefits and the costs of transactions. It raises questions about what determines the bundle of transactions that are assembled by the firm. How does the firm identify and develop Schumpeter's new combinations? What are the transactional alternatives for the firms set of suppliers and customers? Does the firm compete with diverse types of direct exchange? Does the firm face competing institutions of exchange? How do market transactions intermediated by the firm compete with vertically integrated firms that internalize the production and the distribution of intermediate goods and services? Examining how firms create innovative transactions is essential to developing further the theory of market microstructure. Taking the firm as a unit of analysis is useful for examining how firms create complementary transactions.

10.3

Intermediation and opportunism

The intermediation theory of the firm attempts to explain the formation and the boundaries of the firm based on transaction-cost savings from intermediated transactions. The implications of this analysis are substantially different from the theory of firm boundaries that is based on transaction-specific investment and opportunism, as summarized in Chapter 9. One significant way in which intermediaries can reduce transaction costs is to serve as market-commitment devices. Intermediaries that can make credible commitments can earn rents from the resulting reduction in contractual opportunism. Thus opportunism provides an explanation for the formation of firms. Firms are formed when they can improve on direct exchange by providing contractual commitment. The advantage of intermediaries over direct exchange also implies that intermediaries can improve outcomes relative to vertical integration as well. Thus, when intermediaries serve as commitment devices, they obviate the need to form organizations as a means of mitigating contractual opportunism by internalizing transactions. Rather than merge within a single company those productive activities that require transactionspecific investment, independent firms can carry out those activities and mitigate opportunism by transacting in the marketplace through intermediaries. Even when investments are irreversible, companies can resort to outsourcing and rely on third parties for procurement and distribution. Such an implication fits well with observed increases in outsourcing and vertical divestiture in many industries.

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There are a number of reasons why it is reasonable to assume that market intermediaries provide binding contractual commitments. By substituting their reputation for that of the parties to a contract, intermediaries can create contracts that indirectly bind a buyer and seller. Because intermediaries handle a greater volume of transactions than the individual buyers and sellers whom they deal with, their incentives to build a reputation for honoring agreements are increased. Moreover, as Biglaiser and Friedman (1997) suggest, intermediaries with a longer time horizon than buyers and sellers have enhanced incentives to preserve their reputation. Moreover, intermediaries can address bounded rationality by developing the required expertise and specializing in writing contingent contracts. Since they participate in multiple transactions, intermediaries earn returns to their contracting expertise. The explanation for the formation of firms based on their ability to make commitments differs fundamentally from the contractual theory of the firm that I reviewed in Chapter 9. Oliver Williamson finds that because bounded rationality results in incomplete contracts, market contracts result in opportunism. In other words, market-trading partners take advantage of transaction-specific investment to renegotiate agreements. Having made transaction-specific investments, a buyer or a seller is subject to renegotiation with a trading partner trying to capture their quasi-rent. In the contractual theory of the firm, the effects of opportunism are mitigated by the creation of organizations to allocation resources internally. Opportunism is alleviated by bringing certain contractual relationships within the firm. Optimal market contracts reflect a trade-off between the possibly prohibitive costs of writing binding complete contingent contracts in the market and the expected effects of opportunism. The firm's boundaries thus are determined by the costs of market opportunism versus the costs of managing and owning productive assets. Intermediation theory takes a different perspective. Why are market contracts assumed to be nonbinding while organizational relationships are more stable? Is this assumed asymmetry realistic or are there market institutions that favor contractual commitment? Are management of organizations and ownership of assets by firms the only mechanisms for overcoming the commitment asymmetry? Certainly there are legal institutions that address commitment. The asymmetry between lack of credible commitment in contracts and the irreversibility of investment is a fundamental concern of contract law. In particular, the law recognizes the need to protect the expectations of parties to contracts in the event

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of breach.10 I do not consider legal guaranties. Instead, I focus on the market-equilibrium outcome when a third party is able to make credible commitments. In markets, business reputations promote honoring of promises. Independent evaluations of contract performance, such as those performed by credit-rating agencies, also create incentives to honor contractual commitments. The formation of long-lived firms as bearers of reputation is a market response to opportunistic behavior by individual buyers and sellers. I consider a simple model that illustrates how an intermediary that can make binding contractual commitments generates efficient investment levels by a buyer and seller. Suppose that a buyer and a seller each make transaction-specific investments. Let A\ be the buyer's investment and A 2 the seller's investment. The buyer and the seller cannot contract over the investment levels. The buyer's value v(A\) is increasing and concave in the buyer's investment. The seller's production cost c(A2) is decreasing and convex in the seller's investment.11 The transaction-specific investments are assumed to be unobservable to other economic agents. Alternatively, they may be observable but they may still be noncontractable if they cannot be verified independently. It what follows, I show that this need not prevent buyers and sellers from making efficient investment decisions. The incentives provided by the intermediary's ability to commit to posted prices are sufficient to yield efficient investment. As in Chapter 9, the jointly optimal levels of investment are those that maximize total surplus: W(A\, A2) = v(A\) — A\ — c(A2) — A2. The jointly optimal investment levels solve (1)

i/(A?) = 1,

-c'(AZ) = 1.

Suppose that a buyer wishes to purchase and a supplier wishes to sell one unit of a good. They must choose individually whether to trade directly or through an intermediary. If the buyer and the seller decide to trade directly they can make side payments to each other before investing. The game proceeds as follows. Period 0. The intermediary makes a binding offer of an ask price p and a bid price w. Period 1. The buyer and the seller decide whether to try trade directly with the other agent or to accept the intermediary's offer. 10 11

Edlin and Reichelstein (1996) show that fixed-price contracts backed by legal protections for breach of contract can yield optimal investment levels. The game is deterministic. The model can be generalized to allow for uncertainty in the buyer's willingness to pay and the seller's opportunity cost.

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If they cannot agree to transact with each other, they both transact with the intermediary. Period 2. The buyer and the seller make their transaction-specific investments. Period 3. If the buyer and the seller both choose to transact with the intermediary, trade takes place at p and w. If the buyer and the seller both choose to transact with each other, they negotiate over the transfer price w°. Consider first the alternative outcomes in periods 2 and 3. If the buyer and the seller choose to transact with the intermediary in period 1 at prices p and w, then their investment levels satisfy the efficiency conditions (1), that is, investment levels are A* and A\. Suppose that the buyer and the seller agreed in period 1 to transact with each other. As assumed, they are not able to reach a binding agreement on the price of the good to be exchanged. After the buyer and the seller make their investments in period 2, they bargain over the terms of exchange in period 3. Assume that the gains are divided according to the Nash bargaining solution. The price of the good w° solves (2)

max[v(Ai) - w][w - c(A2)]. w

The gains from trade are divided evenly so that the transfer price in period 3 is (3)

w° = w°(Au A2) = [v(A{) + c(A2)]/2.

Anticipating this outcome, the buyer and the seller will choose Nash (noncooperative) investment levels A^, A5> in period 2. The buyer will choose the transaction-specific investment A\ to maximize (4)

V=

v(Al)-Al-w°(Al,A°2)

The seller will choose the transaction-specific investment A2 to maximize (5)

R=

w°(A°vA2)-c(A2)-A2.

The equilibrium price is w° = w°(A®, A^). The equilibrium levels of investment solve (6)

t/(A?)/2=l,

-c'(A»)/2 = l.

Thus both the buyer and the seller underinvest to counter the effects of opportunism. The intermediary cannot make the buyer or the seller worse off that they would be under direct trade. Further, even if the intermediary makes

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only the buyer or the seller better off than under direct trade, thus taking them out of the direct market, the intermediary cannot take advantage of that decision to extract all the surplus from the other trader, since the buyer and the seller can make side payments before making their investments. Both the buyer and the seller are at least as well off as they would be with direct trade. By profit maximization, the intermediary chooses prices /?*, w* such that the buyer and the seller are just indifferent between direct and intermediated trade:

(7)

p*

=

[v(A*l)-A*]-[v(Aol)-A°l-w0],

Therefore, in equilibrium, the buyer and the seller choose to deal with the intermediary rather than directly with each other. The intermediary's equilibrium profit /?* — u;* exactly equals the increased gains from trade due to efficient transaction-specific investments. The returns to intermediation are limited by the alternative of direct trade without contractual commitment. The intermediary's costs cannot exceed the increase in gains from trade relative to the direct-trade alternative. At the equilibrium of the game considered here, intermediated exchange ends up dominating direct exchange. This result suggests that vertical integration is not the only solution to the problem of opportunism. Market intermediaries earn returns to commitment that may not be present for smaller-scale buyers and sellers. By maintaining their reputation for honoring contracts, the intermediary allows buyers and sellers to invest efficiently. By posting prices for their customers and suppliers, intermediaries solve problems of commitment that may arise in direct exchange. By avoiding the problem of renegotiation, both buyers and sellers can earn the full marginal return to their investments, thus eliminating the incentive to underinvest that comes from sharing the marginal return. Accordingly, firms form as a means of solving the problem of opportunism. In the intermediation model, the firm does not solve the problem of opportunism by internal control over investment through vertical integration. Instead, the firm addresses the commitment problem itself by offering reliable prices to its customers and suppliers. By posting prices, intermediaries not only clear markets and allocate goods and services, they also allow efficient investment decisions.

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10.4

firm

281

Intermediation and ownership

The discussion in Section 10.3 shows that the problem of opportunism has a market solution. Commitment to prices by an intermediary is an alternative to vertical integration as a means of allocating the returns to transaction-specific investment. Investment levels are efficient without centralized control over transaction-specific investment. In this section, I show that price commitment by an intermediary also obviates the need for firms to consolidate ownership of productive assets. The property rights approach to the theory of the firm, which is due to Grossman and Hart (1986), Hart and Moore (1990), and Hart (1995), also is concerned with asset specificity and incomplete contracting. They emphasize the need for centralized ownership of assets by the firm as a means of receiving returns to the assets and exercising control over investment. The property rights approach thus emphasizes asset ownership as an explanation for the formation and the boundaries of the firm. This view contrasts with the irrelevance of ownership for entrepreneurs that Schumpeter emphasizes. The property rights view also contrasts with Coase's (1960) discussion in his article "The Problem of Social Cost." Coase observes that with private bargaining over externalities and an absence of transaction costs, the assignment of property rights is irrelevant because private bargaining always will reach the efficient outcome. Coase's argument has played a central role in the field of law and economics. Coase's assertion about the neutrality of property rights appears to break down when private bargaining fails to be efficient. If private bargaining yields inefficient outcomes, then varying the assignment of property rights generally will affect the allocation of resources generated by bargaining. However, there is an economic role for intermediaries precisely when private bargaining fails to be efficient. By reducing transaction costs, intermediation by firms mitigates the inefficiency of private bargaining. If intermediaries are present whenever agents encounter transaction costs, then it is necessary to examine the effect of property rights on the outcome of intermediated exchange. Among other reasons, private bargaining can fail to be efficient because noncontractable investment levels result in opportunism. The analysis in Section 10.3 showed that if intermediaries can credibly commit to buy and sell prices, then they can alleviate the problem of opportunism. In this section, I examine whether price commitment also is sufficient to restore the neutrality of property rights assignments.

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If property rights are neutral with intermediated exchange, then Coase's original insight is restored.12 If neutrality fails when there are transaction costs, but transaction costs create incentives for intermediaries to enter the market, then neutrality must be tested with intermediaries present. Recall the model of asset ownership presented in Chapter 9, In addition, there are two productive assets, numbered 1 and 2, both of which are necessary for the production of the good. Each owner makes a complementary transaction-specific investment, say in human capital, that is distinct from the productive asset. The transaction-specific investment of owner j , A ; , enhances the outside option value of the assets. As before, the function st(Aj) represents the outside option value of asset / when it is owned by person j . The investments A\, A2 are transaction specific because owning the complementary asset allows a realization of returns if trade does not occur. The ownership arrangement of the assets is assumed to have no effect on the production of the good. Recall that there are three possible ownership arrangements; the assets can be both owned by the seller, both owned by the buyer, or the buyer owns asset one and the seller owns asset two. The ownership arrangement affects the outcome of direct bargaining between the buyer and the seller. I consider here the latter case in which the buyer owns asset one and the seller owns asset two. The analysis for the other two cases is similar. I show that the assignment of asset ownership has a neutral effect on efficiency. In particular, intermediated exchange is efficient in all three cases. Consider again the multistage game in which an intermediary can commit credibly to an ask and a bid price. Period 0. The intermediary makes a binding offer of an ask price p and a bid price w. Period 1. The buyer and the seller decide whether to try to trade directly with the other agent or to accept the intermediary's offer. If they cannot agree to transact with each other, they both transact with the intermediary. Period 2. The buyer and the seller make their transaction-specific investments. Period 3. If the buyer and the seller both choose to transact with the intermediary, trade takes place at p and w. If the buyer and the 12

The presence of transaction costs due to asymmetric information about demand and supply also affects the optimality of private bargaining. In Chapters 7 and 8,1 showed how intermediaries can improve on private bargaining outcomes under asymmetric information. Therefore an examination of the effects of property rights assignment in a model with asymmetric information should also allow for intermediation.

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seller both choose to transact with each other, they negotiate over the transfer price w°. Suppose that the buyer and the seller choose to transact directly. Then, in period 3, the buyer and the seller bargain over the transfer price.13 For the case in which the buyer owns asset one and the seller owns asset two, the transfer price w° solves the Nash bargaining problem: (9)

max[v(Ai) - w - *i(Ai)][u; - c(A2) w

s2(A2)l

The equilibrium price is (10)

w° = w°(Au A2) = [v(Ai) -

JI(AI)

+ c(A2) + s2(A2)]/2.

Thus, if the buyer and the seller transact directly, the equilibrium levels of transaction-specific investment maximize V and /?, respectively: (11)

V = v(Ai) - Ax - w°.

(12)

R = w° - c(A2) - A2.

The equilibrium levels of transaction-specific investments solve

(13)

[v'(A°)+s[(

(14)

[-c'(A°)+s'2

Clearly the investment levels are not jointly efficient since they depend on the outside option value of the investment. Suppose instead that the buyer and the seller choose in period 1 to transact through the intermediary at prices p and w. Then the option value of investment plays no role in the investment decisions since ex post bargaining no longer occurs. As a consequence, their investment levels satisfy the efficiency conditions, (10

v'(A*) = 1,

-c'(A*2) = 1.

The same result is obtained regardless of the assignment of property rights since the outside option value of the assets does not affect the investment decision with intermediated exchange. By profit maximization, the intermediary chooses prices /?*, w* such that the buyer and the seller are just indifferent between direct and 13

Recall that if the buyer owns both assets then w° solves max[i;(Ai) - w - s\(Ai) - s2(A\)][w - c(A2)]. w

If the seller owns both assets then w° solves max[i;(Ai) - w][w - c(A2) - s\(A2) - s2(A2)].

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intermediated trade. The prices are the same as in Section 10.3:

=

[v(A*)-A*l]-[v(A°l)-Aol-w0],

(V)

p*

(8')

w* = [c(A*2) + A*2] + [w° - c(A°2) - A°2].

The outside option value of investment enters into the equilibrium prices though the direct-trade transfer price w°. Therefore the equilibrium prices chosen by the intermediary will depend on the assignment of property rights. In other words, the distribution of asset ownership does affect the distribution of rents. However, it does not affect the efficiency of investment with intermediated exchange. The intermediary's price spread equals the efficiency gains from intermediated exchange:

(15) p*-w* = [v(A*)-A*-c{A*2)-A*2] - [v(A?)-A?-c(A«)-A°]. The returns to intermediation are constrained by the direct-trade alternative. Since the three different assignments of property rights affect investment levels with direct exchange, each will result in different efficiency gains. Thus the profit of the intermediary will be different under the three ownership arrangements. The efficiency of intermediated exchange shows that consolidation of ownership is not the only explanation for the formation of firms. When intermediaries can make credible price commitments, buyers and sellers can own productive assets and make efficient investment choices. Price commitment by intermediaries restores the neutrality of property rights assignments observed by Coase in the context of private bargaining. The implication is that when firms can make binding commitments, avoiding opportunism is not sufficient as a determinant of the organizational boundaries of firms nor of the allocation of asset ownership. The neutrality of asset ownership is consistent with the heterogeneity of asset ownership arrangements that appear to exist within the same industry. Companies within the same industry choose between ownership, leasing, and contractual arrangements for the same services.14 The rise of outsourcing arrangements in the U.S. economy further suggests that firm decisions about market transactions need not be fully determined by a need to own productive assets. 14

Many companies outsource delivery services while others carry them out in house. For example, Wal-Mart owns its own delivery trucks, but K-Mart does not; see Stalk, Evans, and Shulman (1992).

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10.5

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285

Conclusion

Market economies are driven by a continual process of improvements in the technology and the structure of exchange. Transaction costs are the costs of establishing and operating markets. Incurring transaction costs is simply the means to an end, which is carrying out the highest value-added exchanges. Firms form to carry out those exchanges. The intermediation theory implies that the proper unit of analysis in microeconomics should be individual firms rather than individual transactions. An economic exchange often can be arranged through different sequences of transactions, including repeated spot transactions and longterm contracts. There are many ways of establishing prices, including posted take-it-or-leave-it prices, bargaining, and various types of auctions. There are multiple ways of providing a product or service, including selling the service, renting an asset used to create a service, or bundling goods and services together. Firms are formed when intermediated exchange creates greater net gains from trade than direct exchange. Moreover, the boundaries of the firm are determined by the innovative transactions that the firm believes will yield the highest economic returns. The focus on the firm as a creator of innovative transactions is consistent with Schumpeter's entrepreneur. The economic returns earned by the entrepreneur do not depend on operating technology, owning capital assets, providing finance, or carrying out research and development. The firm earns economic returns by intermediating transactions between buyers and sellers that improve on direct exchange between buyers and sellers. Moreover, firms acting as intermediaries provide alternatives to transactions within vertically integrated organizations. Intermediation theory suggests that exercising control over transaction-specific assets to mitigate opportunism is not a sufficient explanation for the boundaries of the firm. If a manufacturer and supplier cannot make credible commitments in direct exchange, there is an alternative to carrying out a merger. The manufacturer and the supplier can transact through third parties when intermediaries are able to make credible commitments to prices and contract terms. Intermediated exchange will occur when it produces net gains from trade that are greater than both the gains from direct exchange and those obtained by buyer-seller mergers. Intermediation theory further shows that consolidating ownership of productive assets within the firm to obtain the returns from complementary investments also is not a sufficient explanation for the formation of firms. If a manufacturer and a supplier must make complementary investments, such as human capital investments, that affect the outside

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option value of assets, the outside option value of the assets will affect the terms of trade from direct exchange. Again, however, merger of the manufacturer and the supplier is not the only solution to the complementary investment problem. The outside option effects will not be present in intermediated exchange. When an intermediary can credibly commit to prices and contract terms, the allocation of ownership rights between the buyer and the seller will not affect incentives to invest. The credibility of commitment by the intermediary will create incentives for the buyer and the seller to invest efficiently, thus raising the value of intermediated exchange relative to direct exchange. Moreover, consolidating asset ownership through mergers entails organizational costs as well as a loss of flexibility. What is more likely is that ownership arrangements will vary considerably within industries. There are many reasons to believe that specialized intermediaries can credibly commit to prices and contract terms. They earn returns to reputation by dealing with many buyers and sellers and by operating in many markets or in many time periods. Because they deal with many buyers and sellers, intermediaries are likely to operate through posted prices and generic contracts rather than opportunistic bargaining with individual buyers and sellers. The high costs of gathering information about individual buyers and sellers suggest that the intermediary will stick to general contract terms rather than adjusting those terms to capture quasi-rents from individual buyers or sellers. Moreover, the menu costs of changing prices will increase the intermediary's commitment ability. By centralizing and managing exchange, firms reduce transaction costs for buyers and sellers. By gathering information and building a reputation, they mitigate moral hazard and adverse selection. Through their commitment ability, firms as intermediaries alleviate market opportunism and reduce the need for consolidation to achieve ownership and control over productive assets. By establishing and operating the institutions of exchange, firms improve the efficiency of markets and thereby provide an alternative to allocation within organizations.

Part VI Intermediation and agency theory

11

Agency and the organizationalincentive theory of the firm

The organizational-incentive theory of the firm examines delegation and incentives in market contracts and within organizations. Based on economic principal-agent models, the organizational-incentive theory of the firm focuses on the relative costs of adverse selection and moral hazard in market contracts and within organizations. The theory extends the contractual theory of the firm, as discussed in Chapters 9 and 10, which emphasizes the advantages of organization as a means of avoiding market transaction costs. To understand the organizational-incentive theory of thefirmit is useful to begin by asking What is an agent? The question is important not only because of the centrality of principal-agent models in microeconomics. It is fundamental to how economic models characterize market contracts and organizational relationships. Because the notion of agency comes from law, it is worthwhile noting its legal implications. Agency in law is a fiduciary relationship, that is, one founded on trust. Black's Law Dictionary describes an agent as One who deals not only with things, as does a servant, but with persons, using his own discretion as to means, and frequently establishing contractual relations between his principal and third persons.1 1

As Steffen (1977) points out, the term "servant" is an anachronism although it is still used by the courts. He notes that while Blackstone in his commentaries used the term agent as a "fourth species of servants," more current usage, as in Restatement, Second, Agency §2 (1933), defines servant as a type of agent. Ronald Coase, writing in 1937, used the earlier terminology in defining what a firm is: We can best approach the question of what constitutes a firm in practice by considering the legal relationship normally called that of 'master and servant' or 'employer and employee.' In more modern terminology, Coase defines the firm as an agency relationship, in which the firm's employees acts under the direction of their employer.

289

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An agent, therefore, can be either one of the following: 1. A producer 2. An intermediary. A producer deals with things, devoting effort to completing tasks. An intermediary deals with other people, establishing contractual relationships. The traditional economic analysis of the principal-agent problem has tended to emphasize the master-servant relationship, that is, treating the agent as producer. The analysis has been extended to consider the agent as decision maker, choosing between alternatives that may not be observable to the principal. In this chapter, I examine the traditional agency framework and its implications for the theory of the firm. Then, in Chapter 12,1 consider an alternative view of the agency relationship, one that emphasizes the role of the agent as economic intermediary. This view has crucial implications for the analyzing the function offirmsand the elements of market microstructure. I do not propose to survey the vast literature on principal-agent models. Instead, I try to identify some key elements of agency models that provide insights about the formation of firms and their boundaries. In typical economic agency models, a person called a principal delegates authority to another, the agent, who chooses an action on behalf of the principal. The actions of the agent depend on the incentives provided by a contractual relationship with the principal. The agent as producer chooses a one-dimensional measure of effort, which represents work or expenditure.2 The agent, is variously, a manager devoting effort to cost minimization or enhancing productivity, a worker devoting effort to output production, a sharecropper devoting effort to farming, an insurance customer exercising care to avoid accidents, or a regulated firm choosing output or pollution levels. Agency relationships are subject to two basic inefficiencies. Moral hazard, or misdirected effort, occurs because of the costs of observing the effort that the agent devotes to a productive task. Similarly, adverse selection, or misrepresentation of information, occurs because of the costs of observing the agent's private information, such as the agent's productivity or cost of effort. Efficient incentive contracts do not fully overcome these monitoring problems. Moral hazard is not fully alleviated because contracts that induce efficient performance would involve costly shifting of risk to the agent. The principal would have to compensate the agent for the cost 2

See for example the important early works of Ross (1973), Spence and Zeckhauser (1971), Stiglitz (1974, 1975), Mirrlees (1976), Shavell (1979), and Holmstrom (1979).

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of bearing that risk. The efficient principal and agent contracts involve sharing the risk of uncertain outcomes and a departure from the effort levels that would be efficient under full information. Adverse selection is not fully alleviated under efficient contracts because contracts that induce efficient performance would require subsidies to the agent to induce both truthful revelation and efficient performance. The efficient contract tolerates a departure from effort levels that would be efficient under full information and correspondingly increase the principal's pay-off. According to the organizational-incentive view of thefirm,the costs of contingent contracting, monitoring effort, and observing employee characteristics create imperfect market contracts. These imperfections result in incomplete contracts, moral hazard, and adverse selection. The formation and the boundaries of the firm can be explained if these distortions in market contracts can be alleviated, but not necessarily eliminated, through the design of organizations. The idea is that actions or information that are hidden in market relationships may be observable inside the organization. Then delegation of authority and monitoring performance would be more effective within the firm. In addition, there may be greater flexibility in designing contractual relationships within the firm. This might allow more effective compensation schemes that provide enhanced incentives for effort or truthful revelation of information. Thus organizational relationships might improve the performance of agents. Agency models consider the effect of information on the boundaries of the firm. Information asymmetries that cause adverse selection and moral hazard in market contracts reappear within thefirm,placing limits on the growth of organizations. The chapter is organized as follows. In Section 11.1, I consider the implications of an agency for vertical integration and the boundaries of the firm. Next, in Section 11.2, I examine coordination of multiple employees within the organization. Then, in Section 11.3, I consider delegation of authority by the firm's owners to its managers. Finally, in Section 11.4,1 turn to delegation of authority by the firm's managers to its employees. I conclude the chapter in Section 11.5.

11.1

Vertical integration and the boundaries of the firm

The organizational-incentive approach views the firm as one organization among many, including markets and governments. Organizations are created where there are advantages from centralized control and coordination of individual activities. The firm, in this view, is understood

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to be an organization that does not rely primarily on market mechanisms for internal control and coordination. Arrow (1974, p. 33) observes that "organizations are a means of achieving the benefits of collective action in situations in which the price system fails." The benefits of centralized control stem from the hub-and-spoke view of the firm. It is less expensive for all information to be transmitted to the center and for important decisions to be sent from the center to the periphery of an organization than for all individuals to communicate with each other (Arrow, 1974, p. 68). The benefits of coordination are many. These include facilitating utilization of the benefits from specialization and division of labor noted by Adam Smith. To the extent that members of the organization provide complementary or substitute inputs to a common production process, joint optimization is required for achieving maximum profits.3 In the absence of coordination, not only would the joint profits not necessarily be maximized, but substantial reductions in total profits would result from the externalities associated with interrelated activities. The replacement of market-allocation methods by control and coordination procedures within thefirmnaturally raises questions of incentives and communication. What will motivate subordinates in the organization to carry out the objectives of management? Further, what will motivate subordinates in the organization to report information truthfully to management? Principal-agent models address the design of incentives to mitigate problems that are due to asymmetric information: unobservable effort (moral hazard) and unobservable information (adverse selection). These models provide a unifying framework within which to address the design of incentives within the firm. The principal-agent model has been applied to highlight specific external and internal agency relationships. In the case of external relationships, the firm itself, as represented by a manager, acts as a principal (with suppliers, customers, or retailers acting as agents), or as an agent (of investors, suppliers, or regulators). In the case of internal relationships, the focus is on the design of incentive contracts between managers and subordinates. The boundaries of the firm are determined by advantages of organizations in alleviating moral hazard or adverse selection problems that may arise in market contracts. For example, a manufacturer can choose between contracting with an upstream supplier or merging with the supplier, depending on the relative effectiveness of market contracts and organizational incentives. 3

See also Arrow (1974, p. 68) on this point.

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Incentives in market contracts and within the firm The organizational-incentive theory of the firm determines the firm's boundaries by comparing the net benefits to the principal from hiring the agent to perform services within the organization with net benefits from making market contracts with the agent. The comparison depends on presumed differences in the terms of organizational and market relationships. The trade-offs between the benefits and the costs of the two forms of contracting determine the make-or-buy choice. Vertical integration of two firms may be desirable if it provides one of the merging firms with access to information possessed by the other firm that might not otherwise be revealed through contracting. This information could include technology, demand data, or product characteristics. Then, in the absence of organization costs, the merger would eliminate those efficiency losses due to asymmetric information that existed in the vertical relationship between the twofirmsbefore the merger. Crocker (1983) draws this conclusion in a simple adverse selection version of the principal-agent model. The downstream retailer has private information about market demand. The upstream manufacturer prefers a merger to a principal-agent contract with the downstream firm. The merger is assumed to be costless and to realize all efficiency gains, whereas the contract with downstream firm is subject to the standard distortions associated with optimal revelation mechanisms. Of course, market contracts would be preferable if the merger were costly or if significant agency costs were present within the organization. Riordan (1990a) also compares market contracts with vertical integration.4 A manager chooses between hiring an agent, which will result in uncertain production cost, and making an offer to purchase an input, which may or may not be accepted. I consider a special case of his model to illustrate the basic issues. Consider a downstream firm, acting as a principal, that wishes to procure an input. The value of the input to the downstream firm is v, where 0 < v < 1. The downstream firm contemplates the standard Coasian make-or-buy choice. Suppose that the upstream technology requires a manager. The upstream technology is represented by a unit cost c. The production cost c is a draw from a distribution that depends on the upstream manager's effort, F(c \ e). Suppose that c is uniformly distributed on the interval [0, 1/(1 + e)], where e is the manager's effort level, so that F(c | e) — c{\ + e). The manager's effort cost is e2/2. The upstream 4

See also the related work by Riordan (1990b, 1991).

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manager's opportunity cost is normalized to zero. The upstream technology has a setup cost K. Consider first the case in which the downstream firm chooses vertical integration. This requires hiring the upstream manager at a fixed wage. As a consequence, the upstream manager does not devote any effort to cost reduction, so that e = 0. Thus the production cost is uniformly distributed on the unit interval. The downstream firm observes the realization of the random production cost and decides to produce the input if and only if v > c. The downstream firm's expected return from vertical integration is (1)

V1 = / (v - c)dc - K = v2/2 - K.

Jo

Next, consider the case in which the downstream firm purchases the input from an upstream firm at a price w. The upstream firm's owner/manager will supply the input only if the price offer exceeds the realization of costs, w > c. The upstream manager chooses effort to maximize the expected return. The downstream firm's price offer and the upstream manager's effort are chosen simultaneously. Let w* and e* be the Nash equilibrium values. Given w*, the manager chooses e to solve /*W*

(2)

B = max / e

(w* - c) dc(l + e) - e212.

Jo

The manager's choice of effort is e = (w*)2/2. The downstream firm chooses the price offer to maximize net benefit of the returns, given the equilibrium upstream manager's equilibrium effort e*: (3)

max(u — w)w{\ + e*).

The Nash equilibrium price and effort levels are W* = v/2 and e* = v2/S. The upstream firm incurs the setup cost K and receives a transfer T from the downstream firm. Competition in the market for managers implies that the upstream firm exactly breaks even: (4)

B + T - K = 0.

The net benefits to the downstream firm that purchases the input under contract Vc are thus (5)

Vc = (v - w*)w*(l + e*) - T.

Substituting w* = v/2 and e* = v2/S for the Nash equilibrium price and effort levels, B = v2/S and T = K - B, it follows that the net benefits

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of the downstream firm are (6)

Vc = (3/8)u2 + v 4 /32 - K.

The net benefits from vertical integration exceed those from buying under contract for this simple example: Vc < V1. Vertical integration is the preferred mode because the incentive distortion from afixedwage is less costly than the cost of paying an outside contractor. Riordan points out that vertical integration yields better information about upstream variable costs even if it reduces managerial incentives for cost reduction. More generally, he shows that the desired option is sensitive to the form of the cost distribution, F(c | e). Buying under contract is preferred to vertical integration if F(w* \ e*) > F(v | 0). The converse is a necessary condition for vertical integration to be the preferred mode of organization. It is easy to verify that this holds in the preceding example. It is useful to compare the outcome with the efficient solution. The efficient effort level solves

(7)

max / (v-c) dc(l + e) - e112.

* Jo

Thus the optimal effort level is e = v2/2, which exceeds the contractual level (as well as the lack of effort in the vertically integrated firm). Underproduction occurs in the contracting case because of the principal's monopsony power. Riordan and Sappington (1987) consider the effects of information on the choice between contracting and vertical integration. They examine a two-stage production process in which costs at each stage are observed only by the person carrying out that stage of production. The principal must decide whether to delegate to the agent either the first stage of production alone or both the first and the second stages of production. Both the principal and the agent are risk neutral so that attitudes toward risk do not affect their result. Moreover, neither has a technical advantage over the other. In Riordan and Sappington (1987), the upstreamfirmchooses a quality level x and the downstream produces an output level q. Let c be the unit cost of producing output, and let g be the cost of producing quality. The cost of quality g is the agent's private information. The production cost is statistically dependent on the cost of quality F(c | g), with the distribution function being common knowledge. There are two delegation modes: (1) partial delegation in which the principal makes the output choice, and (2) full delegation, in which the agent choose both quantity and quality. The partial-delegation option corresponds to market contracting.

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The principal can choose optimal agency contracts under both delegation modes. Riordan and Sappington show that when the cost realizations c and g are statistically independent, the principal is indifferent between organizational modes. When the two costs are positively correlated, the principal prefers partial delegation to complete delegation. Finally, when the two costs are negatively correlated but the degree of correlation is small, the principal prefers vertical integration to market contracting. Vertical integration and complementary incentives Holmstrom and Milgrom (1994) address vertical integration by using a multitask principal-agent model.5 They consider vertical integration in a complex framework that attempts to encompass three elements of the theory of the firm. First, their analysis includes the agency approach in which the firm offers pay for performance and engages in costly monitoring of employees, as in Alchian and Demsetz (1972) and Holmstrom (1982). Second, they address the asset ownership approach to the firm, as in Klein et al. (1978), Grossman and Hart (1986), and Williamson (1985). Third, they include the employer's discretion in designing tasks for agents and directing their activities, as suggested by Coase (1937) and Herbert Simon (1951). They argue that comparison of market contracts and organizations need not be one dimensional and suggest that there is covariation in these three aspects of vertical integration. Holmstrom and Milgrom (1994) propose that all three instruments (pay for performance, asset ownership, task design) are complementary, that is, using one of the instruments more intensively increases the marginal benefit of using the others more intensively. They then ask whether the three instruments will move in the same direction in response to a change in an exogenous parameter such as measurement costs. They identify conditions under which movements of the three instruments in the same direction result in statistical covariations in pooled data. Based on empirical studies of sales forces by Anderson (1985) and Anderson and Schmittlein (1984), Holmstrom and Milgrom (1994) consider an application of their model that groups the agent's responsibilities into four tasks: direct selling, investing in future sales to customers, nonselling activities, and selling the products of other manufacturers. They show that the returns to the principal of increasing the rewards to performance in any activity are enhanced by the increase in the rewards to performance of any other activity. For example, increasing commission 5

This model is developed in Holmstrom and Milgrom (1987).

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rates and sharing of transferable returns are complementary. Their result can be illustrated by means of a highly simplified example.6 Let e = (e\, ei,..., £#) be a vector of N effort levels, one for each of the agent's activities. The agent has effort costs C(e). Each of the effort levels is an input to a different production function that is subject to independent random shocks.7 The production function for each activity is q( =hi(ei)

+ 8i,

i = 1 , . . . , N.

Suppose that the shocks £; are normally distributed with zero expected value and variance af. Suppose that output is observable but contracts cannot be based on effort. The output levels are given linear rewards t = (t\, ^ • • •, *N) that correspond to commission rates, sharing of transferable returns, and so on. Therefore the agent's first-order conditions for effort satisfy (8)

t i h' i {e i ) = C i { e \

i=

l,...,N.

This defines effort supply functions e(t). Increasing the linear rewards shifts some risks of output fluctuations to the agent. This entails a cost of risk to the agent equal to where r is the agent's coefficient of absolute risk aversion.8 Holmstrom and Milgrom (1994) assume that the activities are substitutes in the agent's effort supply function, that is, an increase in the marginal reward for performance in any one activity decreases the supply of effort to every other activity: (9)

dei(t)/dtj<0

for a l l / / j .

Moreover, they assume that the rewards for performance activities are complementary in the agent's effort supply function, that is, (10)

d2ei(t)/dtjdtk

> 0 for all j / k and for all i.

The principal benefits from output production, with each output having a price p(. Let r] = (I/erf, I / o f , . . . , l/tfjy) represent precision of monitoring. Then the joint rewards are N

(11)

J(t, rj) = J2pihi(ei)

N

- C(e) -

Assume that the production functions are linear in effort. Then, given 6

7 8

Holmstrom and Milgrom (1994) allow greater complexity by assuming, for example, that some activities do not have direct rewards and by distinguishing among the four instruments in a detailed manner. Holmstrom and Milgrom (1994) assume that the shocks are jointly normally distributed. The agent is assumed to have constant absolute risk aversion.

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assumptions (9) and (10), the joint-rewards function / is supermodular in incentives t and precision of monitoring r\ on the domain where (pt — U) > 0, i = 1 , . . . , N. It is straightforward to check that all U and r)j are complementary, i, j = 1 , . . . , Af. In other words, if all the variables were increased simultaneously, the function value would increase by more than the sum of the increases in value obtained by increasing each of the variables. Although agency models are often focused on a single type of productive effort, the Holmstrom and Milgrom model is a reminder that agent efforts are multidimensional and the structure of rewards infirmsis likely to be multidimensional as well. These rewards have complementary effects. Under some conditions, rewarding agents for their performance of an activity has positive effects on their performance in other activities. Similarly, improved monitoring of an activity can have positive impacts on an agent's performance of other activities. Thus firms combine such things as asset ownership, sharing of rewards, bonuses and commission, and design of activities within thefirmto induce employees to undertake the right mix of effort levels in their many organization tasks. Overview The organizational-incentive theory of the firm determines the boundaries of the firm based on the relative effectiveness of market contracting compared with internal relationships. As in the transactioncost literature, this approach is based on the vertical integration decision. The conclusions are subject to the same type of questions that arise in the transaction cost approach to vertical integration, particularly those raised by Demsetz (1991). In particular, how do we distinguish purchases across markets from inhouse production? In-house production entails the use of inputs that are purchased, so that presumably thefirmwill need to form market contracts with suppliers of those inputs. Thus, whether the firm is purchasing primary inputs or goods that are more nearly complete, it will have to form market contracts with suppliers. Therefore external moral hazard and adverse selection problems appear in either case. Moreover, there are organizational activities involved in purchasing inputs or in manufacturing them. In either case, the firm will need to specify incentives for performance for members of its organization. As Demsetz observed, it is difficult to distinguish operationally between transaction and management costs. Internal moral hazard and adverse selection problems appear in either case. Thefirmcreates a combination of market contracts and organizational relationships whether it is making or buying a given input. Therefore it

Agency and the organizational-incentive theory of the firm

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must trade off mixtures of market and organizational incentives, rather than simply choose between them. Moreover, it is not apparent what distinguishes market relationships from organizational ones. Is effort more visible and easier to monitor in external or internal relationships? Is hidden information easier to obtain in external or internal contractual arrangements? Is there a greater range of contracting options in market or organizational relationships? The answers to these questions determine the outcome of the make-or-buy decision in a theoretical model, but are they realistic portrayals of the options available to companies? There are many types of vertical contracts between firms and their suppliers and distributors.9 Nonlinear pricing and incentive contracts can be used to induce revelation of information or additional productive effort from an upstream or downstream firm that is a trading partner. Other vertical contracts include resale price maintenance, exclusive dealing, tying, contingent contracts, licensing, and franchise agreements. The incentive effects and allocation of rents from these agreements can differ considerably. In choosing between whether to purchase primary inputs or more finished inputs, companies compare the performance of such vertical agreements between firms with the performance of internal expansion or vertical merger.10 As in the transaction-cost literature, the agency literature helps to explain the boundaries of the firm. It also attempts to explain the choice between market and organizational contracts. Agency models shed light on the structure of incentives in contracts and their consequences for efficiency of performance. While shedding light on these significant issues, the agency model leaves open the question of why firms are formed. Also, since the focus is on the design of incentives, broader issues of pricing and market clearing are external to the basic framework. Further, there remains the problem of designing market institutions to deal with moral hazard and adverse selection. As Chapter 12 suggests, however, the agency framework can be adapted to address these issues by considering the agent as a market intermediary.

11.2

Coordination of agents by the firm

Section 11.1 examined the choice of vertical integration as a means of improving monitoring and information gathering and as a way of improving the design of incentive contracts relative to market alternatives. 9 10

See Spulber (1989b, pp. 487-493), and Katz (1989). Companies also take into account antitrust law and other regulatory restrictions in choosing the form of vertical agreements.

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Intermediation and agency theory

The discussion in this section considers explanations for the formation and the boundaries of firms that are based on the need for a principal to coordinate the activities of multiple agents. The employees of afirmare input owners in that they own their human capital and labor services. A fundamental question is why these input owners do not contract directly with each other, instead of contracting with the firm. The hub-and-spoke description of the firm suggests that such indirect contracting saves on the number of contracting relationships. However, even in the absence of such costs, there is a need for firms if they are providing coordination that the agents could not achieve through direct contracting. Alchian and Demsetz (1972) identify the role of thefirmas a specialist who monitors team production efforts, designs incentives, and receives the residual rewards. They augment Coase's analysis by emphasizing the potential advantages of team production and organization, the difficulties in metering outputs, and the problem of shirking in teams. They argue that residual rewards are given to the firm's owners as a means of preventing shirking, as in standard principal-agent relationships. Based on this reasoning they differ with Knight's analysis of thefirmas a bearer of risk. They state (p. 793) that "the firm serves as a highly specialized surrogate market," since the firm collects and sells information to employees by organizing their production activities. Their analysis, while consistent with the present framework, is focused on internal monitoring rather than market making. Centralized control: plans versus markets Once the potential benefits of centralized control and coordination are identified, the question arises of how such benefits are to be achieved within thefirm.This question has been addressed first in regard to the problems of corporate planning and then by the classic debate regarding the advantages of markets versus planned economies. Without reviewing the details of this debate, it is worth noting that a great deal has been written on how to decentralize planning and control within the national economy. One approach, for linear programming models, applies the decomposition principle to solve the aggregate problem by solving a set of subproblems and iterating toward the optimal solution.11 This type of procedure can be interpreted as the decomposition of national plans into sectoral planning subproblems. The decomposition of 11

See Dantzig and Wolfe (I960).

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planning procedures into stages corresponding to national, sectoral, and regional plans is considered by Tinbergen (1967). Another approach to economic control uses centrally determined shadow prices in indicative planning (Lerner 1944 and Lange and Taylor 1964). Such planning procedures12 carry out central control but are said to be decentralized since each firm sends quantity signals to the central office and receives back prices. Alternatively, each firm signals its marginal rate of substitution and receives back a proposed vector of demands and supplies from the central office. Models of indicative planning consider firms as part of a single national enterprise that is decomposed into individual production units. Managers can choose a variety of mechanisms to allocate resources within the firm. According to Chandler (1977, p. 6), the modern multiunit business arose "when administrative coordination permitted greater productivity, lower cost and higher profits than coordination by market mechanisms" (see also Oliver Williamson, 1970). Companies applied the traditional planning models to derive prices for control and coordination of production activities within firms (see Arrow, 1964). Indeed, firms often referred to their systems of budgeting and accounting controls as corporate planning until the failures of centralized economic planning became manifest. The planning perspective is prominent in characterizations of the firm in traditional management science. There, the firm solves complex optimization problems by using various mathematical techniques (e.g., linear, nonlinear, and dynamic programming, and Bayesian decision analysis). The firm carries out various tasks such as serving queues, ordering inventory, determining the quickest way to complete a project at a given cost, or finding the least costly transport route. The organizational aspects and competitive strategies of the firm play a indirect role as sources of constraints and cost parameters. If prices can be used to carry out resource allocation within the firm, then how do organizations differ from markets? Certainly all activities within the firm are potentially subject to competition through outsourcing, divestiture, or exit from the activity. Allocation of resources within the organization responds to market incentives, but the general view among economists is that the mechanism for carrying out that allocation somehow differs from market alternatives. Thus mechanisms other 12

Indicative planning, as opposed to command-and-control or directive planning, refers to government attempts to influence the economy indirectly through announced targets, persuasion, and incentives. Indicative planning is considered in a multiperiod setting under uncertainty by Meade (1970). Arrow and Hurwicz (1960) and Malinvaud (1967) derive interactive procedures that require repeated exchanges of information between agents and a central planning office.

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than price adjustment may be responsible for coordination within the firm. Coordination and the residual claimant One explanation of the existence of firms is that they provide a mechanism for extracting residual returns from the joint productive efforts of employees. The firm, or equivalently the set of owners, not only designs incentives for the employees but serves as the residual claimant. Bengt Holmstrom (1982) points out that, with multiple agents, the principal's role is not essentially monitoring. Simply receiving the residual returns plays a crucial role in the design of incentives. He demonstrates that group incentives are not sufficient to solve the free-rider problem because group incentives that fully distribute rewards inevitably distort incentives. A group of input owners contracting with each other to carry out a project will distribute all the proceeds among themselves. The result is the classic budget-balancing problem: the sum of transfers exactly equals the total earnings attributable to the group. This creates a freerider problem because each member of the group receives only a share of the total return. As a result, each member receives only a share of the marginal product of that their effort creates. Individuals will equate their marginal cost of effort to the marginal return, anticipating that other members of the group will act in the same manner. The end result is that all members of the group shirk, and everyone in the group is made worse off in comparison with the joint optimum. What is needed to solve this problem is a principal who acts as a residual claimant by enforcing penalties or distributing bonuses. Thus the ownership of residual returns by the owners has positive incentive properties. To illustrate this, consider the basic model of Holmstrom (1982). Suppose that there are n members of the team, each of whom chooses effort ex•, i = 1 , . . . , n. The cost of devoting effort to the project for individual / equals e\. Letting e be the vector of effort levels, define x = h(e) as the group production function, where x is the monetary value of the output produced. Effort levels are unobservable so that team members cannot specify effort levels in their contracts with each other. Suppose that the opportunity cost of team members is normalized to equal zero. The optimal effort levels maximize total surplus:

1=1

Therefore the optimal effort levels solve ht(e°) = 1, / = 1 , . . . , n.

Agency and the organizational-incentive theory of the

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Each member of the team receives a share of the returns 57 (JC), where returns distribute total surplus: n

Y^ st(x) = x for all x. i=\

Given any sharing rule, the members of the team play a Nash noncooperative game that has equilibrium effort levels e*. Each member of the team will choose an effort level that maximizes their individual return, S( (x) — ei, taking the equilibrium effort levels of the other team members as given. If the sharing rule is differentiable, then the first-order conditions for the equilibrium effort levels are (12)

s'i(h(e*))hi(e*)

= l,

i = l,...,n.

Clearly, the effort levels are not optimal. If they were optimal, then hi would equal 1 for all i. Summing the first-order conditions in Eq. (12) would yield YTi=\ •*,' = w- This contradicts the definition of the sharing rule since YTi=\ s[ — 1 f° r anY X-U The inefficiency of any sharing rule results from free riding by the team members. The inefficiency of the sharing rule can be corrected by sharing rules that do not necessarily distribute the total surplus generated by the team. Suppose that an owner-manager is a residual claimant who obtains n =x — 1=1

The owner-manager selects a sharing rule defined by

ifx>x° if x < x° Given a forcing rule of this type, all the agents will select the optimal effort levels e°, i = 1 , . . . , n. Holmstrom (1982) suggests that the team may impose such a rule on itself without a third party. In that case, the bonus levels fully allocate the total surplus, that is, YTi=\ bi =x°. He observes that in a dynamic context, the punishment of zero payment could be viewed as a threat not to continue cooperation. However, he points out that it is not in the interest of the team members to discard any output ex post, since selfimposed penalties would not occur in a perfect equilibrium. Thus the enforcement problem requires a principal who acts as a residual claimant only, not as a member of the team. 13

The proof easily generalizes to include nondifferentiable sharing rules; see Holmstrom (1982).

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Hart and Moore (1988, pp. 774-5) suggest that the possibility of collusion by two of the agents against a third prevents the realization of efficiency gains from inclusion of a third party. They raise the possibility of side contracts between the buyer or seller with the intermediary and note that such contracts are equivalent to a merger between the buyer or seller and the intermediary. Since the contracts are equivalent to a merger, the situation of contracting through a third party would be reduced to bilateral contracting. Eswaran and Kotwal (1984) examine collusion between the owner-manager and one of the team members in Holmstrom's (1982) model of moral hazard in teams. They find that the owner-manager has an incentive to make a hidden side contract with one of the team members to induce shirking so that the sharing rule denies payment to all the other team members. Because the contract is hidden, all the other team members still invest the optimal level of effort but do not receive any payment since the total output fails to reach the critical threshold of the original forcing contract between the owner-manager and the team members. The objections to the use of third parties raised by Hart and Moore (1988) and Eswaran and Kotwal (1984) depend on the assumptions that side contracts cannot be observed by other parties and that they cannot be prohibited in the original contract. These assumptions are not realistic. Observability and verifiability of contracts is the more general situation. Contracts between a buyer or a seller and a third party are likely to be observable if such contracts amount to a merger. Also an intermediary that deals with many buyers and sellers would have a responsibility to disclose such contracts, particularly if the side contract affected the returns obtained by the parties to the original contract. Disclosure would be necessary if the terms of the side contract would lead parties observing the side contract to modify their actions under the original agreement. Moreover, if such hidden side contracts subvert earlier agreements made by the intermediary, they would jeopardize the intermediary's market reputation. Side contracts are likely to be verifiable by third parties since they cannot be enforceable unless they are subject to independent review. This implies that enforceable side contracts can be prohibited in the original agreements with the intermediary. What are the values of the bonus payments ft/?14 Suppose that the members of the team have the option of contracting with each other or with the firm. If they contract with each other as a team then each member / will obtain st(h(e*)) — e*, i = 1 , . . . , n. The owner-manager 14

Holmstrom (1982) does not address the principal's selection of the bonus amounts in competition with incentives chosen by the team.

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can make each of the members at least as well off as they would be as a team by offering them a bonus equal to their effort cost plus what they could obtain as a team: It should be emphasized that the firm is not contracting with the employees on the value of effort. The effort costs are used only in calculating the dollar value of the bonus. The employees will choose effort levels e° as an equilibrium response to the incentive scheme. The equilibrium profit of the firm will equal the returns to coordination:

*•('-§*)-(*-64 The firm's profit is positive because the efficient effort levels maximize net surplus and the noncooperative team equilibrium effort levels do not equal the efficient levels. The firm that earns the returns from coordination can be interpreted as performing an intermediary role for its employees. The firm earns a profit from coordinating their productive activities within the firm in a manner that resembles market coordination. This confirms the assertion of Alchian and Demsetz that a private market operates within firms. Coordination and residual control A related explanation for the existence of firms views them as mechanisms for exercising residual control over investments (in addition to claiming residual returns). By establishing internal markets for capital for example, thefirmmay alleviate moral hazard and incentive problems that arise in capital market transactions; see Williamson (1975). Alchian (1969) observes that The investment funds (capital) market within General Electric is fiercely competitive and operates with greater speed to clear the market and to make information more available to both lenders and borrowers than in the external "normal" markets. The implication is that internal allocation of capital, by combining elements of incentive contracts, competition, and the command and control powers of central management, is judged superior to capital markets. Gertner, Sharfstein, and Stein (1994) suggest that an important distinction between external finance, through bank debt in particular, as compared with centralized finance within the firm, is that the corporate

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headquarters owns the business units. They emphasize the residual control rights over the firm's assets, as in Grossman and Hart (1986). An internal capital market gives control rights to the capital supplier, that is, the corporate headquarters. Gertner et al. argue that centralizing control rights has several consequences. Because the corporate office has all the internal control rights, internal providers of capital have greater incentives to monitor the performance of the divisions, even if monitoring technology is equally efficient both within and outside the firm. Such enhanced monitoring incentives come at a cost, however. The reduced control experienced by division managers reduces their performance incentives. Finally, centralized allocation of capital offers the headquarters the advantage of combining assets that they own, for example, merging divisions to take advantage of production complementarities. The framework of Gertner et al. implicitly provides a theory of the firm as a means of establishing an internal market for capital. There is a trade-off between the monitoring and the control benefits of internal capital markets and the incentive benefits of external capital markets. Firms are formed when internal markets have advantages in allocating and managing capital investment. Overview Organizations serve as coordinating devices for productive agents. This subsection identifies the value of ownership in addressing problems of moral hazard and adverse selection. Ownership of the firm has two components: residual returns and residual control. By appropriating the residual returns from the joint efforts of the firm's employees, the firm breaks the budget-balancing constraint, thereby alleviating, but not eliminating, the problem of moral hazard in teams. By exercising residual control over the firm's investments, the firm improves monitoring of the performance of the firm's divisions, although incentives to perform may be reduced relative to external capital markets. Moreover, the firm can coordinate the activities of its divisions, separating or combining investment projects to take advantage of new information about performance or to realize complementarities.

11.3

Delegation of authority by owners to managers

Some incentive aspects of ownership having been identified, it is useful to recognize a closely related explanation for the formation of firms.

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Companies provide a means of separating ownership and control through delegation. Separation of ownership and control is desirable when managers have a comparative advantage over owners in running companies. From experience and training, managers develop expertise as competitors, leaders, supervisors, organizers, decision makers, and negotiators. There also are incentive effects from risk sharing between owners and managers. Owners, as principals, delegate authority to a manager who acts as the agent of the owners. The manager carries out productive activities or makes decisions about the operation of the firm. The manager of the firm is an agent with either hidden knowledge or hidden actions that are not observable to the firm's owners. The firm's owners design incentives for the manager and monitor the manager's performance. Within this framework, the firm is a vehicle for raising capital from investors and for hiring managers who will carry out investment projects. Comparison with classical finance Recognizing that managers make independent decisions represents a significant advance over traditional finance models of the firm. Classical finance views the firm as an investment project. An investment project is defined as a stream of (possibly uncertain) net returns over time. Net returns are the project's returns net of the cost of investment. The firm is charged with choosing only those projects with positive net present value. If the firm has to choose between mutually exclusive projects with positive net present value it should select the one with the highest net present value. Representing thefirmas an investment project is simply an application of the neoclassical model of thefirmas an operator of technology with all inputs except investment implicitly optimized. The returns to investment are the firm's profit as a function of investment with labor, manufactured inputs, and resources set at efficient levels for each level of investment. Once the firm is defined as an investment project, ownership of the firm by investors simply means ownership of a financial asset. Owning a financial asset gives the owner a stream of returns overtime. In this setting, the separation of ownership and control of the corporation is conceptually simple; the manager need maximize only the net present value of the company. The separation theorem of Irving Fisher (1965) demonstrates that shareholders are interested only in the firm's choosing a stream of returns that has the highest net present value. Investors are not concerned with the time pattern of the firm's net earnings. They can use perfect

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neoclassical capital markets to alter their time pattern of consumption and to vary the riskiness of their investment portfolio. Therefore shareholders unanimously wish for a manager to make decisions that maximize the net present value of the firm.15 Similarly, the Modigliani and Miller (1958) theorems about the irrelevance for the value of the firm of its capital structure and dividend policy depend on the conception of the firm as afinancialasset. If a more realistic picture of the firm is presented that recognizes the incentive effects of ownership and the role of information, the neutrality result may not hold in general. The Fisher separation theorem, the Modigliani and Miller irrelevance theorems, and other results from classical finance are founded on perfect market assumptions.16 Assuming that financial markets operate without friction is subject to the same criticisms as are assumptions that any other market operates perfectly. By what mechanisms are equilibrium prices determined? How does the market price adjust to changes in demand and supply? How do markets clear? The market mechanisms in financial markets are far from invisible. Indeed, the mechanisms of price adjustment and market clearing in financial markets are more evident than elsewhere. The existence of stock and futures exchanges, securities dealers, and brokerages are easily identified. These institutions and firms are not evidence of perfect markets in the neoclassical sense, as is often assumed, but rather testify to the costs of operating these markets.17 Market frictions create opportunities for firms to act as financial intermediaries, adjusting prices and coordinating transactions. These frictions also help to explain the ownership structure of firms and financial decisions. Separation of ownership and control The representation of the firm becomes more complex when the need for separation of ownership and control is recognized. The firm's owners play a specialized role as suppliers of capital. The firm's owners delegate authority to the manager because the firm's owners may have higher opportunity costs of carrying out the desired tasks than does the manager. The manager may have skills that the owners lack. Professional 15 16 17

See also Hirschleifer (1958) and Fama and Miller (1972). See for example Grossman and Stiglitz (1977) for an analysis of the goals of the firm based on shareholder voting. The markets function with increasing efficiency as a result of the innovative transactions created by financial intermediaries.

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managers have the usual advantages resulting from specialization and division of labor. As Fama (1980, p. 290) observes; Management is a type of labor but with a special role-coordinating the activities of inputs and carrying out the contracts agreed among the inputs, all of which can be characterized as "decision making." Risk allocation is another reason for the separation of ownership and control. Managers would not make efficient decisions if they bore all the firm's risk. Fama notes that the risk bearing function and ownership of capital are shared by both bondholders and stockholders. However, Fama notes (1980, p. 290) that ownership of capital should not be confused with ownership of the firm. Each factor in a firm is owned by somebody. The firm is just the set of contracts covering the way inputs are joined to create outputs and the way receipts from outputs are shared among inputs. In this "nexus of contracts" perspective, ownership of the firm is an irrelevant concept. Owners are simply investors who wish to reduce their risk by diversifying their portfolio, holding the securities of many firms. Fama concludes that (p. 291), "efficient allocation of risk bearing seems to imply a large degree of separation of security ownership from control of a firm." In contrast to classical finance, modern finance recognizes that ownership of the firm confers control rights in addition to residual returns. Diffuse ownership dilutes incentives for owners to devote effort to the firm's activities. Having multiple owner managers would inevitably lead to conflicts and free riding. Separation of ownership and management serves to unify control. The firm's owners delegate authority to a single manager who is responsible for controlling the firm's operations and coordinating its employees. Similarly, diffuse ownership dilutes incentives for owners to monitor management performance. Since each owner shares in the firm's returns, the owner does not obtain the full marginal return to effective monitoring effort. This leads to the possibility of free riding and thus deters owners from monitoring performance. This problem is addressed by delegation of the monitoring role to the corporate board. The board is charged with a variety of roles including hiring senior management, reviewing their performance, determining their compensation, and handling takeover bids. Jensen and Meckling (1976) present a positive theory of the private corporation as a "legal fiction," embracing contracting relationships for which divisible residual claims can be sold. They focus their analysis on

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the corporate form of organization with diffuse ownership, and stress the importance of minimizing agency costs as an explanation for corporate financing decisions.18 Since both outside equity and debt entail agency costs that are increasing in the proportion offinancingobtained from that source, the efficient capital structure of the firm is the one that equates the marginal agency costs of these two sources. The relative proportions of inside and outside financing reflect the familiar trade-off between the incentive effects of increasing the manager's ownership share and the increased risk borne by the manager. Jensen and Meckling (1976) propose a theory of corporate ownership structure to explain the relative shares of inside equity (held by managers), outside equity, and debt. Conflicts between debt holders and equity holders arise because equity holders are residual claimants. Because of limited liability and the implicit insurance provided by debt holders, equity holders have a greater preference for risky investments. Managers and equity holders have different interests arising because of the tendency of managers toward appropriating perquisites for the manager's consumption and devoting less than enough effort to creative activities. They suggest that the manager's incentive to cheat or shirk is increased as the manager's ownership share falls. The firm's capital structure is chosen on the basis of the incentives for performance associated with debt and equity.19 Because asset ownership confers control rights, in addition to residual returns, the capital structure of the firm is no longer neutral. By affecting incentives, changes in the firm's capital structure affect the value of the firm.20 Incentives for managers In managerial agency models, the manager devotes an unobservable effort to operating the firm or possesses some private information about the firm's productivity. Owners design incentives for the manager to perform duties or reveal information. Moral hazard problems arise because of the trade-off between shifting risk to the manager and providing incentives for performance. Adverse selection problems arise because the cost of providing incentives for revelation of private information. Managerial incentive models include compensation contracts and corporate takeovers. Compensation contracts are examined by Diamond and 18

19 20

Jensen and Meckling (1976, pp. 329-330) assert that agency costs within the firm will not depend on whether the firm is a monopolist or faces competition in its product or factor markets. See also Jensen (1986), Grossman and Hart (1982), and Harris and Raviv (1990). See also Grossman and Hart (1988), and Harris and Raviv (1989).

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Verrecchia (1982), Holmstrom and Weiss (1985), and Jensen and Murphy (1990) among others. Holmstrom and Tirole (1993) extend the model of managerial performance to examine the value of the firm's stock price in monitoring performance and structuring managerial incentives. Holmstrom and Weiss (1985) present a model of managerial moral hazard. Profit is a function of the investment, the manager's effort and an exogenous shock. The profit and the investment are observable to the principal but the effort and the shock are not observable to the principal. Because the firm's realized profit is observable, their model allows the owners to screen on the basis of both profit and investment. They obtain the standard result that the risk-averse manager bears only some of the risk and that owners tolerate some moral hazard in the manager's choice of effort. Holmstrom and Weiss demonstrate that the combination of asymmetric information and managerial risk aversion can amplify the variability in both observed profits and investment levels of the firm. Holmstrom and Weiss apply their managerial moral hazard model to show that there is greater cyclical variability in aggregate investment and profits. The state of the world is observable because the aggregate levels of investment and output in the economy can be used to infer the firms' productivity. They assume that managers observe a signal about productivity, and the fraction of managers that observe a high versus a low signal is random. Indexation is valuable for the optimal contract since relative performance provides useful information. In addition, if the manager chooses investment before observing the aggregate shock, fluctuations in aggregate output and investment are higher than with symmetric information. If the manager chooses investment after observing the aggregate shock, aggregate fluctuations can be either greater or less than in the symmetric information economy. The possibility of takeovers affects managerial incentives in decision making and revelation of information. They exercise a disciplinary effect on management according to Grossman and Hart (1980), Easterbrook and Fischel (1981), and Scharfstein (1988b). Stein (1988) suggests that takeovers can result in managers choosing underinvestment. Laffont and Tirole (1988) find that the threat of takeovers can lead managers to behave myopically. Product market competition and management incentives Market competition provides incentives for managerial performance. This literature includes the problem of incentives in contests

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and tournaments.21 This approach is applied by Hart (1983), Scharfstein (1988a), and Hermalin (1992) to examine market incentives for managerial performance. They examine a market in which there are two types of firms: entrepreneurial firms, which are managed by their owners, and managerial firms, in which owners delegate authority to managers. Their analysis shows that the proportion of entrepreneurial firms will affect managerial performance although they disagree on the direction of the effect. Hart shows that with infinitely risk-averse managers, with no utility of income above a critical level, competition reduces managerial shirking. Scharfstein shows that competition can increase shirking when the manager's marginal utility of income is positive. Hermalin shows that the informational effects of competition can go either way. More work remains to be done to clarify these issues.22 Abstracting from the informational effects of competition, Schmidt (1997) identifies a threat-of-liquidation effect that stimulates managerial effort to avoid the disutility of liquidation. In addition, there is a value-of-a-cost-reduction effect that creates a disincentive for managerial effort. The latter effect is analogous to the reduced incentives to innovate that are due to the lower returns under increased competition. If the market for managers clears, only the first effect is observed and competition increases managerial performance. With an excess supply of managers and employed managers earning efficiency wages, both effects are observed, and the net effect of competition on managerial effort remain ambiguous. As Chapter 12 emphasizes, the agency problem has greater generality than the choice of effort. Some studies have extended the management decision problem. Holmstrom and Ricart i Costa (1986) observe "[i]t is likely that many executives believe their managers are industrious enough; what they worry about more is how effective these managers are at making decisions." They suggest that because managers are concerned about the impact of decisions on their careers, there will be a divergence between the financial value of current performance and the reputation value. The manager is directly concerned with the human capital impact of decisions and only indirectly concerned with the financial impact through incentives. The manager's incentives consist of contracts with the current employer and outside wage offers. The manager's ability is unobservable but can only be inferred through realizations of investment projects. The optimal (second-best) contract involves offering a fixed 21 22

See Lazear and Rosen (1981), Green and Stokey (1983), Nalebuff and Stiglitz (1983), and the references therein. See also Bull and Ordover (1987).

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wage and then matching outside offers, which essentially has a option structure. A number of studies point out that the selection of a one-dimensional effort level does not capture the manager's decision problem, which is a question of selecting the right project, not simply of working hard. Lambert (1986) examines the choice by risk-averse managers between a project with a certain outcome and one with a risky outcome. The manager does devote effort to generating a signal about the project. Although the risk-neutral principal should absorb all the risk, the contract with unobservable effort involves some risk sharing and thus distortion of the manager's investment decisions. Sah and Stiglitz (1986) depart from the agency framework by assuming that the individuals within organizations act as project evaluators. Within a hierarchy, a project must pass a series of screens as it moves up the organization. In a polyarchy, such as a market, competing decision makers can undertake projects independently of each other. All decision makers are prone to errors, but polyarchies tend to accept more projects than hierarchies. Managers and signaling private information If the firm's managers have private information about the value of the firm that is not available to its investors, the capital structure of the firm may act as a signal that conveys information to investors. By observing the firm's capital structure, investors can draw inferences about the manager's private information.23 These inferences in turn affect the market value of the firm's equity, so that capital structure or dividends are no longer neutral. A large class of models, beginning with that of Ross (1977), examines a variety of financial actions that act as signals to financial markets. Capital structure and dividends are signals of private information about the firm's performance in Ross (1977) and other studies.24 In Grinblatt and Hwang (1989), the fraction of the new issue retained by the firm and its initial offer price convey information to investors. In Ambarish, John, and Williams (1987), firms signal with dividends and the level of investment (equivalently the net new issues of stock). Spiegel and Spulber (1997) show that regulated firms encounter countervailing incentives in signaling to two audiences. They have incentives to signal higher costs to regulators and lower costs to capital markets. 23 24

See Harris and Raviv (1991) for a literature survey. See, for example, Bhattacharya (1979), Miller and Rock (1985), John and Williams (1985), and Blazenko (1987).

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Their model shows that in such cases, the capital structure of firms is uncorrelated with their expected values, reflecting the pooling of diverse firm types. This result suggests that countervailing incentives should be taken into account in future empirical studies of capital structure and cost of capital of regulated firms. Moreover, this result can explain why Miller and Modigliani (1966), in their classic study of the electric utility industry, found "no evidence of sizeable leverage or dividend effect [on firm value] of the kind assumed in much of the traditional finance literature." While this empirical result supports the Modigliani and Miller (1958) irrelevance theorem, it conflicts with later financial signaling models in which capital structure conveys the firm's private information about its value. The countervailing incentives identified by Spiegel and Spulber (1997) serve to reconcile these two approaches in the case of regulated industries. Financial signaling is affected by product market interaction.25 Gertner, Gibbons, and Scharfstein (1988) consider a model of signaling to two audiences. In their model, a firm uses its capital structure to signal private information to both the product and the capital markets. The equilibrium may be either pooling or separating. Poitevin (1989) considers an entry model in which the entrant has private information about the entrant's marginal cost. The low-cost entrant issues debt and equity to signal efficiency, while the high-cost entrant issues only equity to avoid the risk of bankruptcy when competing with the incumbent.

11.4

Delegation of authority by managers to employees

The agency theory of the firm also draws on the advantages of managers' delegating authority to the firm's employees. This delegation again achieves returns from the specialization of function and division of labor and overcomes limits on managerial time, effort, capacity, and capabilities. The agency model of the firm includes a production relationship as in the neoclassical firm (this is implicit in the probability density over outcomes in the above formulation). The production relationship differs from the neoclassical firm in that the productive input is unobservable to the firm's manager and therefore is not subject to direct control. This crucial difference requires a redefinition of the firm's problem to 25

Brander and Lewis (1986) consider the effects of debt as a commitment device in duopoly competition in a full-information setting. Their analysis does not consider the incentive effects of capital structure on managers.

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include all the personal characteristics of the agent: utility of the reward, disutility of effort, and reservation utility. Moreover, while the neoclassical framework can easily handle uncertainty in the production process, unobservability is another matter, requiring that signals (if any) about the production process be incorporated into the compensation scheme. Thus the characteristics of the agent and the information structure become part of the incentive model of the firm. In hidden-knowledge models, the description of thefirmincludes the allocation of information between the principal and the agent. Each may have information that is unavailable to the other.26 More generally, the order of moves and other institutional features of the strategic relationships within organizations need to be specified as part of the incentive theories of the firm. Agency models have great flexibility, particularly when applied to study compensation schemes for managers and employees (see, especially, Milgrom and Roberts, 1992). Milgrom and Roberts (1988,1990) develop a theory of influence activities that examines costly political rent seeking within the firm. They assert that "efficient organization is not simply a matter of minimizing transaction costs" (1990, p. 58). They compare the costs of bargaining over short-term market contracts with the influence costs resulting from centralized control of organizations. Agency models have proved to be of great practical value in understanding incentives for action and communication within hierarchies. Moreover, agency models are useful in guiding the design of incentive schemes to motivate subordinates. Agency models have been used to make important advances in the fields of accounting, finance, and marketing, especially in those studies that take an organizational incentive view of the firm. Agency theory is applied in a variety of accounting models.27 These accounting models are primarily concerned with incentives to gather information and to communicate the information accurately. Information gathering and reporting can be carried out by a subordinate within the firm, by an independent auditor, or by the firm itself reporting to outside monitors. Consider first managerial accounting models that examine reporting within the firm. The agency approach can be used to examine the types of information that should be gathered. For example, Demski and Sappington (1986) show that costly disaggregation of information required by line-item reporting provides useful 26 27

See, for example, Baron and Myerson (1982) on mechanism design by an uninformed principal and Myerson (1983) on the design of incentives by an informed principal. See Baiman (1982, 1989) for surveys of work in this area.

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information about agent activities. This can be useful in designing incentives for performance and in controlling subcontracting activities. The agency approach highlights the connection between incentives for productive effort and for obtaining information. Demski and Sappington (1987) extend the agency model to study delegation of authority to an expert, in which the expert's actions include both productive effort and costly gathering of information about a decision problem.28 The expert is not able to communicate the information to the principal, so there is a trade-off between incentives for information gathering and incentives for the productive activity. Baiman and Demski (1980) provide sufficient conditions for the principal and the agent to prefer that an agent acquire superior information before the productive activity. In a multiperiod setting, they also show that the choice of information production will affect productive actions. Agency models also can be applied in an accounting context to examine organizational design. In this way, Melumad and Reichelstein (1987) compare centralized control and delegation of authority in firms, taking account of the possibility of communication by agents. Accounting research also applies agency models to external reporting of information by the firm through financial statements. The principalsupervisor-agent model applies to the relationships among shareholders, auditors, and the firm's management, or among government authorities, auditors, and management. Agency models have been widely used to study the auditing problem. Dye (1986) presents an auditing model in which the principal devises an investigation strategy. Antle and Nalebuff (1991) examine bargaining between auditors and their clients over reported income under asymmetric information. Another class of accounting models examines incentives for voluntary disclosure of information. Verrecchia (1990) extends these analyses to examine the effect of the quality of internal information received by a manager on the manager's incentive to disclose that information to interested parties outside the firm. Wagenhofer (1990) allows for the possibility that information disclosed to investors may also be used strategically by a competitor and gives conditions for full and partial disclosure to occur. Marketing models apply agency models to describe the internal organization of the firm, focusing, for example, on incentives for sales effort in sales force compensation plans (see Basu et al. 1985 and Coughlan and Sen 1989). Lai (1986) examines the delegation of pricing authority 28

This corresponds, for example, to a firm that delegates authority to perform a task to a subcontractor, such as product design, parts manufacturing, or marketing.

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to the sales force. Rao (1990) considers compensation of multiple sales personnel. These studies and others in marketing, while focusing on the marketing function, provide important insights into the firm's internal structure. Another area of marketing with important implications for the theory of the firm is the study of marketing channels. Stern and El-Ansary (1988, p. 3) define marketing channels as "sets of interdependent organizations involved in the process of making a product or service available for use or consumption." Marketing channels involve not only the physical distribution of goods and services but also the series of exchanges and contractual relationships among manufacturers, wholesalers, and retailers that comprise the vertical distribution process.

11.5

Conclusion

Organizational-incentive theories of the firm focus on the control and the coordination of activities within the firm, often to the exclusion of external market forces. This contrasts with the neoclassical, industrialorganization and contractual theories of the firm. The neoclassical firm, represented by its technology, primarily buys and sells goods in the market. The firm in industrial-organization models, also represented by costs, pursues competitive strategies in the market. The firm in contractual models compares the relative transaction costs or informational efficiencies of carrying out activities in the market or inside the firm. Organizational-incentive theories of the firm raise a different set of questions regarding authority and communication within the firm, rather than considering market allocation of goods and services, competitive interaction between firms, or trade-offs between market and in-house production. Organizational-incentive models of the firm have great value in addressing the design of rewards within the hierarchy. These models of the firm have important applications in finance, accounting, and marketing. The organizational-incentive theory of the firm is a major complement to neoclassical and industrial-organization theories of the firm that often neglect organizational issues. Despite these significant contributions, the organizational-incentive theory of the firm generally does not address the firm's role as a market actor. The incentives for the principal as a manager of the firm are exogenous and often unspecified. The agent must be motivated to perform a task of interest to the principal, but the principal's objective is not always explicitly connected to market competition. The agent acts within the organization rather than in the market so that market benchmarks for the agent's performance often are absent.

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The comparison between incentives in organizations and markets requires a more complete treatment that explicitly compares the two types of relationships and that takes into account the effects of competition on incentives for performance. Such a comparison also involves considering how moral hazard or adverse selection problems differ in market and organizational settings. Evaluating the economic performance of incentives and organizational design requires understanding why principals retain agents. The intermediation theory of the firm provides some insights into these difficult issues. I turn in Chapter 12 to models that view the agent as market intermediary.

12

Agency and the intermediation theory of the firm

In Chapter 11,1 reviewed models of delegation in which agents are producers and decision makers. In this chapter, I emphasize that the agency relationship frequently involves agents acting as market intermediaries. Agents enter into economic transactions with third parties on behalf of their principal. Acting for their principal, agents negotiate contract terms, carry out competitive strategies, and monitor performance. Thus agency provides a framework that helps to unite the divergent views of the firm as producer and as intermediary.1 The distinction between the theory of agents as producers and agents as intermediaries is roughly analogous to the difference between decision theory and game theory. Decision theory is a game against nature while game theory takes strategic interaction between players into account. Similarly, agents as producers choose effort levels or make decisions, while agents as intermediaries interact with other principals or other agents. Strategic interaction provides a more complicated and perhaps a more accurate picture of what agents do. Viewing agents as market intermediaries has important implications for the intermediation theory of thefirm,both in terms of the organization of firms and the economic role of firms. As I mentioned in Chapter 11, the organizational-incentive view centers on agency relationships within the firm, emphasizing the design of incentives for effort and revelation of information. Viewing agents as intermediaries, in contrast, focuses attention on how the firm acts in the market through its employees (and independent agents). Thus directors act for the firm in the market for corporate control and in the labor market for executives. Managers are active in mergers and acquisitions and in the employee labor market. Managers and employees engage in purchasing and sales activities in 1

Not all agents are intermediaries and not all intermediaries are agents. All employees of the firm are agents, but some employees may be purely operations personnel. Some market intermediaries act strictly in their own interest without contracting with a principal.

319

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markets for goods and services. They search for trading partners, bargain over prices, and negotiate contract terms. Agency models have additional implications for the intermediation theory of the firm. The advantages of using agents in markets helps to explain both delegated intermediaries within the firm as well the firm's role as a market intermediary. The intermediation theory of the firm emphasizes that the economic role of firms derives from advantages of intermediation over direct exchange between buyers and sellers. If there are economic benefits from strategic delegation, buyers and sellers will employ firms to act as their representatives. This helps to explain why firms enter into formal or informal agreements with buyers or sellers to carry out search, contracting and monitoring functions. Viewing agents as intermediaries raises substantial issues that do not arise in models that are focused on the choice of effort levels. Negotiating contracts and handling business transactions appear fundamentally different from choosing effort levels in production. This raises a number of questions about incentive contracts. Do incentive contracts with agents acting as intermediaries differ significantly from incentive schedules studied by economists in models of moral hazard and adverse selection? What types of incentives for agents are important in negotiating and monitoring contracts? The intermediation relationship is not well understood. When do principals rely on agents for business transactions and when do they prefer to act for themselves? What are the advantages and disadvantages of transacting and contracting through agents? Are contracts negotiated through agents different from contracts negotiated by the principal? How does bargaining with an agent differ from bargaining with the principal? This chapter addresses some of these questions in a very preliminary way. I begin, in Section 12.1, by reviewing definitions of agents in law, business, and political science. I observe that in these practical areas, agents generally handle relationships with third parties, representing the interests of their principal. Thus agents that are employees of firms act as market intermediaries. In Section 12.2, I review models of delegated bargaining. One advantage of using agents in negotiation is as a commitment device, as recognized by Schelling (1956). Principals employ agents to influence the outcome of bargaining through incentives or rules governing the agent's actions. Moreover, agents can be a means of disguising the principal's preferences. By choosing an agent whose preferences differ from those of the principal, the principal can attempt to influence the terms of exchange. By strategic contracting or by choosing an agent that differs from the principal in terms of patience, risk aversion, willingness to pay,

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or opportunity costs, the principal may obtain more favorable contract terms. This suggests that the firm's employees, by acting as market intermediaries, provide the firm with a commitment device in negotiating prices and contracts with third parties. In Section 12.3,1 consider the value of agents as commitment devices in competition. Models of Vickers (1984), Fershtman and Judd (1987), Sklivas (1987), Fershtman, Judd, and Kalai (1991), Salas Fumas (1992), and others demonstrate that delegation can be used to influence competitive outcomes. See the survey of multiprincipal-agency relationships in Gal-Or (1997). The discussion suggests that delegation of competitive strategy to the firm's managers serves as a commitment device. In Section 12.4,1 examine models of agents acting as delegated monitors. Agents negotiate contracts for the principal and monitor their performance. Melumad, Mookerjee, and Reichelstein (1997) show the advantages of delegated contracting when contract contingencies are costly. The analyses of Douglas Diamond (1984), Ramakrishnan and Thakor (1984), Stephen Williamson (1986), Krasa and Villamil (1992), and others establish that delegated monitoring is superior because of diversification by intermediaries. The analysis shows that there are efficiency gains to buyers and sellers that result from delegation of monitoring to third parties. Firms earn returns by consolidating the monitoring function, whether they are monitoring their own employees or third parties with whom they have contracts. I present my conclusions in Section 12.5.

12.1

What is an agent?

The answer to the question "What is an agent?" often is "an intermediary." Thinking of agents as intermediaries is consistent with descriptions of agents in law, business, and political science. The law of agency is concerned with the principal's relationships with third parties when the principal is acting though an agent. In business, there are many applications of agency including contracting and the organization of companies. In politics, voters delegate authority to elected representatives to act on their behalf in negotiation with other representatives. Agents in law Agents in legal usage are closely tied with third-party business transactions. There is an important distinction between contractual relationships between the principal and the agent and relations that the principal and agent have with third parties. The role of the agent is to

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represent the principal in business dealings. For example, Black's Law Dictionary (1983) defines an agency relationship as "[a]n employment for purpose of representation in establishing legal relations between principal and third persons." As Steffen (1977, p. 26) observes, "the essentials of 'agency' are few": First, the relation is a consensual one; an agent agrees or at least consents to act under the direction or control of the principal. Second, the relation is a.fiduciaryone, an agent agrees to act for and on behalf of the principal.2 Steffen adds that the agent "is in no sense a proprietor entitled to the gains of the enterprise - nor is he expected to carry the risks." Economic models of agency, by concentrating on the agent as producer, necessarily focus attention on the principal-agent relationship itself. Thus economists devote considerable attention to the nature of contracts between the principal and the agent, for example, incentives for performance, incentives for disclosure, and risk sharing. It appears necessary to extend the basic framework when the purpose of the agency relationship is interaction with third parties. The agent's activities in dealing with the third party may not lend themselves to standard incentive contracts. Moreover, there will be an interplay between the terms of the principal-agent contract and the terms of the contract with the third party. The principal-agent relationship taken in isolation closely resembles standard contractual relationships, which is perhaps why research on agency is commonly referred to by economists as the theory of contracts. Forming an agency relationship requires an offer by one party and acceptance by the other party. The contract can be express or implied. As with any voluntary contract, there must be gains from trade for both parties, referred to in law as consideration. There are general rules that handle rights and remedies associated with breach of the principalagent contract. In law, the contractual relationship between the principal and the agent is referred to as the relation inter se. Steffen (1977, p. 15) observes that, in law, the issues that make up the relation inter se, those of consent, control, fiduciary, and allocation of gains or risk, "present housekeeping questions." In contrast to the inter se relationship between the principal and the agent, traditional agency law focuses most of its attention on interaction with third parties. Thus, agency "is concerned with transactions between 2

Emphasis in original. See also American Law Institute (1958).

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the enterprise - whether in the form of partnership, individual proprietorship, joint venture, corporation, business trust, or some other - and third persons."3 Oliver Wendell Holmes (1891) noted the long history in law of the maxim quifacitper alium facit per se. Black's Law Dictionary (1983) defines an agent in terms of business representation: A person authorized by another to act for him, one intrusted with another's business. One who represents and acts for another under the contract or relation of agency A business representative, whose function is to bring about, modify, affect, accept performance of, or terminate contractual obligations between principal and third persons. One who undertakes to transact some business, or to manage some affair, for another, by the authority and on account of the latter, and to render an account of it. One who acts for or in place of another by authority from him; a substitute, a deputy, appointed by principal with power to do the things which principal may do. There are many subspecies of agent identified by Black's Law Dictionary, most of which involve business representation.4 A principal employs a special agent to conduct a particular transaction and a general agent to conduct multiple transactions over time. An exclusive agent represents the principal in an exclusive territory, although the principal may sell there directly. A managing agent supervises and controls a department of a corporation and a high managerial agent is an officer of a corporation charged with formulating company policy or managing subordinates. An independent agent is a contractor. A mercantile agent includes brokers and factors, with a factor also called a commission agent or a commission merchant. A transfer agent acts on behalf of the issuers of securities. In common usage, an agent in a particular industry is an intermediary: an insurance agent sells insurance, a real estate agent brings together buyers and sellers, and a travel agent arranges transportation and lodging for other companies. Traditional agency law can be divided into the areas of contracts and torts. Concerning torts, the principal generally is liable for actions of the agent that harm third parties. Agents may cause harm to third parties when acting under the principal's delegated authority. The legal issues that arise are similar to those that arise with contract liability. When a third party is harmed, there is a need to determine the overall liability 3 4

Steffen(1977,p. 2). The definitions in this paragraph are drawn from Black's Law Dictionary (1983).

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of the principal and agent, as well as the allocation of liability between them. In particular, if the agent acts within the scope of his authority, the principal is liable for his actions under the doctrine of respondeat superior (let the employer respond).5 Contractual relationships with third parties that are created by the agent usually are binding on the principal. I now consider some of the issues relating to contracting through agents. Contracting through agents The main purpose of agents is contracting for the principal.6 Although the agent negotiates the contract, the contractual relationship is between the principal and the third party. The principal wishes to make sure that the terms of the contract are those that would have emerged from direct negotiation. The contract between the principal and the agent thus must contain incentive provisions aimed at creating this outcome. Legal rules bearing on contracting through agents are intended to result in efficient contracts not only between the principal and the agent, but also between the principal and the third party. This explains why legal characterizations of the principal-agent relationship primarily target issues that arise in the process of contracting with third parties. The question of whether contracts made by agents are binding depends on a number of factors, including the agent's authority. The agent derives delegated authority by a grant from the principal, although the grant of authority can be express or implicit. Implicit authority can be implied by the general task that the principal assigns the agent, it can be apparent from standard practice for the type of business, or it can be on an emergency basis, if the principal's interest requires that the agent must exercise judgment beyond the normal scope of authority.7 The duties of an agent to the principal illustrate the agent's contracting role. These duties include the following: being loyal, protecting confidential information, obeying instructions, informing the principal, taking care, and accounting accurately.8 Loyalty means that the agent does not act as the other contracting party, the agent does not take transaction benefits that were intended from the principal, the agent does not enter into competition with the principal, and the agent does not represent two principals with conflicting interests.9 5 6 7 8 9

Corley, Shedd, and Holmes (1986, pp. 342). See, for example, Clark and Kinder (1986, p. 339). Clark and Kinder (1986, pp. 323-327). See Corley et al. (1986, pp. 298-308). Ibid.

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The duties of a principal to the agent include the duty to pay compensation for services rendered and for reasonable expenses. Conflicts typically arise in determining the rights real estate agents and sales representatives have to obtain commissions.10 Also, the principal has a duty to indemnify the agent against liability.11 Agency law spells out contractual liability between the principal, the agent, and third parties through numerous precedents and provisions. There are six possible combinations of liability between the principal, the agent and the third party. Many of the rules depend on whether the principal is disclosed to the third party. The principal is said to be disclosed if the third party knows the existence and identity of the principal. If the principal is disclosed, the principal is legally bound to the third party as long as the agent that negotiated and entered into the contract for the principal does not exceed his or her authority.12 Rasmusen (1996) considers delegated contracting by assuming that having an agent introduces error relative to direct bargaining but saves on transaction costs. While the agent plays a passive role in the model, he assumes that the principal and the third party can devote effort to reducing errors made by the agent. Different assignments of liability affect whether the effort levels of the principal and third party are socially optimal. Delegated contracting generally has not been addressed in economic models of agency. The substantial body of rules and precedents pertaining to contracting through agents suggests the need for economic models of contracting through agents. There are a number of questions to be addressed. What are the types of incentives needed to give agents incentives to negotiate contracts whose terms are similar to direct negotiation? How will contracts negotiated by agents differ from those negotiated directly between the interested parties? How do moral hazard and adverse selection problems (associated with the actions of principals, agents as well as third parties) affect contract terms? How do principals reduce mistakes and deviation from their interests in contract negotiation? Agents and organization of the firm Viewing agents as intermediaries sheds light on the organization of firms. The employer-employee relationship is a principalagent relationship. Thus all the firm's employees, including workers, 10 11 12

Ibid., pp. 305-306. Ibid. Corley et al. (1986, pp. 315-331).

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managers, and even directors, are its agents.13 Certainly many employees are assigned to standard productive tasks, manufacturing, maintenance, engineering, clerical, and so on. However, many employees carry out transacting and contracting tasks for the firm. As I emphasized above, firms are a center of contracting. Employees are charged with establishing and maintaining relationships with third parties. As agents of the firm, employees in the purchasing department contract with suppliers, those in personnel contract with prospective employees, those in finance contract with banks, lenders, and investors, and employees in sales contract with wholesalers, retailers, and final customers. Management also plays a significant contracting role, making contracts with companies that provide services and inputs to thefirmand with joint-venture partners. Directors handle mergers, acquisitions, and divestitures, contracting in the market for corporate control. Such tasks as mergers and acquisitions require effort in the form of due diligence, but also entail representing shareholder interests in handling takeover bids and reviewing management strategy. Directors also handle personnel contracts with top management. Of course, it is often difficult to distinguish operationally between transacting and producing. Purchasing an input is both procurement and production. The firm's activities serve its purpose of intermediating between its suppliers and customers, as I have emphasized. The firm's employees, acting as its agents, carry out the tasks necessary to accomplish the firm's intermediation activities. Thus viewing the firm as a whole as a market intermediary is consistent with the view that its employees carry out intermediation activities. The firm's employees create transactions and contracts with third parties. Whether it is established as a partnership, sole proprietorship, joint venture, corporation, or trust, the organization of the firm is a collection of internal principal-agent relationships. Many, if not most of, these relationships are outward directed, that is, they are designed to achieve efficient relationships between the firm and third parties. To take the example of a corporation, Easterbrook and Fischel point out that the corporate venture has many real contracts, including the articles of incorporation, issues of securities, and debt agreements: Everything to do with the relation between the firm and the suppliers of labor (employees), goods and services (suppliers and contractors) is contractual.14 13 14

Stefan (1977, pp. 19-20) notes that directors are agents because they are paid by and owe a fiduciary duty to the corporation. Emphasis in original: Easterbrook and Fischel (1991, p. 16).

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The corporation chooses a set of contracts and a "governance structure that is most beneficial to investors, net of the costs of maintaining the structure."15 The corporation's cost of capital depends on the terms of its contracts. As Easterbrook and Fischel (1991, p. 5) observe, "[t]hose who promise the highest returns - and make the promises binding, hence believable - will obtain the largest investments." The fiduciary relationship of investors with the firm's managers bears emphasis. Easterbrook and Fischel (1991, p. 92) stress that delegating authority to managers based on trust has the advantage of flexibility to deal with contingencies as they arise and offers the advantage of deterrence over continual monitoring. As a result, courts defer to managers under the business judgment rule. Performance can vary over time, but long-run performance is monitored both by the capital markets and managerial labor markets. In addition to delegating authority to employees, firms contract through independent agents. These include independent sales representatives, labor-market search firms, and outside legal counsel. An interesting question is, what are the determinants of the firm's choice between inside and outside agents? Firms not only act through agents, whether employees or independent agents, they also deal with the agents of others. Easterbrook and Fischel (1991, p. 16) observe that the companies negotiate with representatives: "Indenture trustees negotiate on behalf of bondholders, unions on behalf of employees, and investment banks on behalf of equity investors." The company taken as a whole acts as an agent for others, whether its customers or suppliers. In a general sense, the company acts as an agent of its owners, investing capital and choosing competitive strategy. The company is an agent of its customers, producing goods and services and contracting with suppliers. In some contractual relationships, companies also can be viewed as agents of its suppliers, carrying out marketing and distribution tasks. In general, delegation of authority by the firm to its agents requires granting discretion to find trading partners and form contracts. Thus, although agents are under the control of the principal, their usefulness to the principal lies in their exercise of some degree of autonomy in search and bargaining. As market intermediaries, agents must apply their judgment to the choice of transactions, the negotiation of contract terms, and the monitoring of contractual performance. It is here that the fiduciary aspects of agency play an important role because the agent must be prepared to react not only to economic shocks but also to strategic behavior of third parties. 15

Easterbrook and Fischel (1991, p. 4)

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Incentives for agents are needed to align their interests with those of the principal so that contract terms are close to those that would have emerged with direct negotiation between the principal and the third party. Incentives are needed for the agent to devote effort to the search process, to avoid errors in relaying the principal's directions, and to report accurately to the principal. As I show in Sections 12.2 and 12.3, there are many situations in which delegation of contracting to agents creates strategic advantages for the principal. Political agents In understanding agents as market intermediaries, it is useful to observe that political agents also are charged with intermediation tasks. Elected officials, acting as agents of their constituents, are not charged simply with carrying out political tasks, such as providing public services. Legislators must bargain with other legislators to produce legislation. The legislature's members and the president bargain with each other. Moreover, the president negotiates treaties and trade deals with the heads of other countries. Public policy makers delegate authority to the heads of administrative agencies. As emphasized by Spulber (1989b), practically all types of economic regulation are formed through a process of bargaining with consumers and firms in regulated markets. The administrative agencies act as intermediaries between consumers and firms in setting regulated rates for utilities, in determining environmental standards, and in choosing rules for financial markets. The heads of administrative agencies in the executive branch act as agents of elected officials. The timing of policy-making actions will affect the ability of the policy maker to make credible commitments. The limits on the commitment ability of policy makers plays a role in the strategic contest for political control over the agency between the legislative and the executive branches. Delegation allows the government to respond flexibly to changing economic conditions while letting public officials make commitments to policy directions. The instruments of control represented by appointments, statutes, and oversight illustrate the main timing issues. The administrative agency is established before economic parameters that affect regulatory outcomes are observed. Administrative appointments and statutes are chosen before uncertainty about these economic parameters is resolved, while oversight can take place after policy makers have the opportunity to acquire information from the agency. Furthermore, appointments and statutes precede agency actions, while oversight involves interaction

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between policy makers and the agency that is contemporaneous with agency actions. Appointments of the agency director and the senior staff guide the future direction of the agency. Spulber and Besanko (1992) show how the president makes credible commitments to future agency actions by choosing an agency director whose preferences over consumer and firm interests differ from his or her own. The divergence between the president's preferences and those of the desired agency director are shown to depend on the agency's ability to make credible commitments and on whether the agency's regulatory action and the action of the regulated firm are profit substitutes or complements. Furthermore, the president initiates an appointment action subject to the advice and consent of the U.S. Senate. This creates an additional source of divergence between the preferences of the policy makers and those of the agency over consumer and firm interests. The theoretical analysis is applied to a case study of an environmental standard setting by the U.S. Environmental Protection Agency. In political choice models, agents provide a means of disguising the preferences of policy makers. Rogoff (1985) examines a model in which the president delegates monetary policy to a more conservative central banker who places greater weight on controlling inflation versus reducing unemployment than does the president.16 Besanko and Spulber (1993) analyze the enforcement of merger policy through the approval process for horizontal mergers. They demonstrate that the policy maker will prefer to appoint an enforcer who gives greater relative weight to consumer surplus versus producer surplus than does the policy maker. In Calvert, McCubbins, and Weingast (1989), the legislative and the executive branches choose an agent on the basis of the agent's most preferred point in the policy space. They introduce uncertainty regarding agent preferences as well as agent choices and discuss the problem of political control of agencies.

12.2

Delegated bargaining

Schelling (1956) points out that bargaining power is more than simply skill in debate, obstinacy, misrepresentation or bluffing. Rather, he observes, it is the ability to make credible commitments, that is, to bind oneself in a way that convinces the other party to the negotiation.17 Threats are not credible if they cause the party making the threat to be 16 17

See Melumad and Mookherjee (1989) on delegation as commitment in income tax audits. See also Schelling (1960).

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worse off if it is carried out. The promise to transfer money to a third party unless a desired outcome is achieved also is not credible if the third party can be brought into the negotiation. Statements made in bargaining can be credible if they are backed by the need to preserve reputation.18 Schelling states that if the buyer can make an observable credible commitment to an agent who represents the buyer in the negotiation with a seller, then that commitment will bind the buyer in a manner that is convincing to the seller.19 A buyer and a seller are negotiating over the price of an object. Suppose that the buyer's value is i; = $10, the seller's opportunity cost is c = $0, and the price can be in only $1 increments. Suppose further that the buyer and the seller will transact only if they achieve positive gains from trade. If the seller makes a take-it-or-leave it offer to the buyer, any offer less than or equal to $9 will be accepted, allowing the seller to capture most of the surplus. Assume that (1) the buyer can credibly commit to negotiating only through an agent, (2) the buyer charges the agent with offering exactly $x, compensating the agent only a price at or below $x, (3) the buyer can credibly commit not to change the instructions given to the agent, and (4) the contract with the agent is known to the seller. Then the (unique subgame-perfect) outcome is for the buyer to commit to a price of $1 so that the bargaining between the seller and the buyer's agent will result in a price of $1. The four requirements needed for the buyer to make credible commitments through the use of an agent seem needlessly complicated. If the buyer can make such a complicated commitment through an agent, would it not be simpler to assume that the buyer is making a credible commitment to a price offer? What makes the use of an intermediary credible is that the buyer can enter into an enforceable contract with the agent. The enforcement is carried out by an external legal system, for example. Also, the buyer can carry out the commitment to negotiate only through the agent and not to change the agent's instructions simply by being unavailable during the negotiation process; see Schelling (1956, p. 285). Suppose that the buyer can renegotiate the contract with the agent. Then the commitment is not credible, since the seller understands that it would be profitable for the buyer and the agent to renegotiate the contract to avoid outcomes that make them both worse off. In the example given above, suppose that the buyer promises the agent to purchase only through that agent and to pay the agent $1 if the agent purchases the 18 19

Schelling (1956, p. 284). Schelling (1956, p. 284).

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good for $1 and zero otherwise. The seller makes an offer of $8. It is in the interest of the buyer and the agent to renegotiate the contract in a way that splits the buyer's surplus of $2 between the buyer and the agent. Dewatripont (1988) recognizes the possibility that Pareto-improving renegotiation limits the commitment value of contracts. In the context of an incumbent firm's signing labor contracts to commit to a high output that deters entry, he investigates whether contracts that are renegotiation proof can be a commitment device. Dewatripont shows that when contracts are Pareto efficient, given the information available at the time of renegotiation, they can serve as the basis for strategic commitment. While the initial contract is observable, the use of renegotiation-proof contracts allows for secret renegotiations, which will never occur in equilibrium. Revealing the content of the contract poses some difficulty. Katz (1991) observes that with unobservable contracts, principals will give agents incentives to match their principal's preferences, which eliminates the commitment value of delegation. Fershtman and Kalai (1997) distinguish between instructive delegation, in which the agent must follow a set of instructions, and incentive delegation, in which the outcome of bargaining determines the agent's pay-off. In the case of instructive delegation, they show that the buyer cannot benefit from commitment through delegation.20 However, if the instructions are observable with a small but positive probability, there is a perfect equilibrium with the buyer's receiving a price of $1. Consider the case of incentive delegation. Suppose that the incentive contract must be in dollar increments. The agent incurs a positive effort cost e < 1. Then, in the case of incentive delegation, Fershtman and Kalai show that a price of $ 1 can be an outcome even with an unobserved contract. The buyer's equilibrium contract gives the agent $1 if the price is $1 and zero for any higher price. The seller offers a price of $1 in equilibrium. Another way of using agents in bargaining is as a distortion of the principal's preferences. The preferences of the agents need to be observable. The value of distorting preferences for strategic purposes is widely recognized; see Kurz (1977,1980), Crawford and Varian (1979), Kihlstrom, Roth, and Schmeidler (1981), and Sobel (1981). Kihlstrom et al. (1981) show that with the Nash bargaining solution, risk-averse bargainers have an incentive to understate their level of risk aversion, so that in equilibrium both report linear utilities. This suggests that 20

Fershtman and Kalai (1997) consider trembling-hand perfect equilibria.

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principals will prefer to delegate bargaining to agents who are less risk averse than the principals. Misrepresenting patience also has strategic value. At the perfect equilibrium of a bargaining game of alternating offers, Rubinstein (1982) shows that the outcome depends on the relative impatience of the buyer and the seller. Suppose that the buyer has value v and positive discount factor S\. The seller has value c and positive discount factor 82. If the buyer makes the first offer, the equilibrium allocation of surplus gives the buyer a share of surplus equal to (v ~ c)(l - « 2 )/(l - 8x82). An increase in the buyer's patience, that is, an increase in 8\, raises the buyer's share. An increase in the seller's patience, that is, an increase in
12.3

Delegated competition

The use of agents as commitment devices extends to delegated competition. The firm can design managerial incentives to influence the firm's competitive strategy. The design of management incentives influences the outcome of the strategic game played by the managers. The principal can be the firm's owner, its directors, or upper-level management.

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The competitive strategy in question can be at the corporate level, at the division level, or at the level of individual businesses. Vickers (1984) introduces an example of a two-stage game in which firm managers in the second stage set outputs to maximize a weighted sum of profits and output. Owners choose the incentives for managers in the first stage. The owners base the reward for managers in part on output as a means of influencing the outcome of the second-stage competitive equilibrium. This analysis is extended further by Fershtman and Judd (1987) and Sklivas (1987), who allow either Cournot or Bertrand-Nash competition in the second-stage game. They restrict attention to rewards for managers based on a linear weight on costs: R-yC, where R denotes revenues, C denotes costs, and y is a weight that can be greater than, equal to, or less than one. Each firm's owners choose the value of the weight in stage one and managers choose competitive strategies in stage two. The values of the weights are publicly observable. In the model of differentiated oligopoly with price competition, Fershtman and Judd (1987) show that owners penalize costs at the margin more than they reward revenues, setting the weight to be greater than one. This leads to conservative competitive behavior that raises prices toward the monopolistic price in the second-period subgame. Profits are higher than in the noncooperative game without delegation but below the fully collusive outcome. In the Cournot case, owners reward sales by setting the weight to be less than one. This leads to aggressive behavior in the subgame, increasing outputs of the firms relative to the standard Cournot outcome. In the Cournot case, profits are lower than in the noncooperative game without delegation. Fershtman et al. (1991) allow for general contracts between owners and managers that are fully observable in the second-stage game. They obtain a folk theorem for delegation games showing that strict Paretooptimal outcomes can be implemented by target compensation functions. Suppose that the collusive outcome in the second-period duopoly pricing subgame is p®, p\, which yields profits equal to n? = Tli(p®, p®), for each firm / = 1,2. Suppose that the noncooperative outcome yields profits n* = Il|(/7*, /?p, / = 1,2. Then the collusive outcome p j , p^ can be implemented uniquely if II? — n* > s by the target compensation function: otherwise ' Each firm's owners offer their manager the compensation function T,

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which flattens the agent's returns relative to that of the principal. In contrast to the case of linear incentives, the more general compensation function allows the firms to achieve the collusive outcome. Salas Fumas (1992) considers delegated competition in which owners weight the relative performance of the competing firms. Thus compensation for the manager of firm / is based on // = n / - / z / n ; ,

i ^j,i;j

= 1,2.

where /x,- is a linear weight that can be positive or negative. Profits are subject to shocks and managers are risk averse. Therefore increasing the weight on the competitor's profit increases the manager's risk. Because owners must compensate managers for their costs of bearing risk, owners have an incentive to reduce the weight on the other firm's profit. In the case of Cournot output competition, the delegation effect and the risk effect reinforce each other and the owners choose negative weights in equilibrium. In the case of Bertrand price competition with differentiated products, the delegation effect and the risk effect counteract each other, and the sign of the weight is indeterminate. Gal-Or (1993) extends the duopoly analysis to examine managerial specialization resulting from dividing the firm into departments. She shows that the equilibrium with competition may result in there being one centralized firm and one decentralized firm with separately managed sales and production departments, with managerial compensation in each firm varying accordingly. Different organizational strategies are pursued by the firms since departmentalization by one firm lowers the rival's incentive to departmentalize. This provides an interesting endogenous explanation for diversity. Caillaud, Jullien, and Picard (1995) examine competing agencies with hidden knowledge. Agency with moral hazard generally results in underproduction by the agent relative to the action that is ex post efficient. They show that the level of underproduction is maximal among the set of efficient contracts. Thus principals can make credible commitments through publicly observable contracts only if it is desirable to commit to actions that are costlier to the agent than those that would result from secret contracting. If agents engage in Cournot competition, then precommitment effects of publicly announced contracts are desirable, as in the standard analyses of this problem However, if agents engage in Bertrand price competition with differentiated products, no precommitment effects from disclosing the contract arise if the contract can be secretly renegotiated. Integrating market competition and organizational structure leads to a richer description of firms by introducing some of the organizational

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issues missing from the neoclassical and industrial-organization theories of the firm. At the same time, a clearer understanding of incentives and delegation of authority emerges from the introduction of competitive forces into a multiple-organization framework.

12.4

Delegated monitoring

The costs of writing contingent contracts and monitoring performance can create advantages for delegated contracting. Under delegated contracting, a principal contracts with an intermediary, who then writes a contract and supervises the performance of an agent. The delegated monitoring framework lends itself to various organizational and contractual interpretations. Hierarchical contracting applies whether the agent is a member of the organization or an outside supplier. Within organizations, supervisors or middle managers act as intermediaries between the principal and the agent. If the agent is outside the organization, the intermediary can be a sales or a purchasing employee. The intermediary can be outside the organization if the principal hires an individual (or firm) outside the organization to contract with a third party. In addition to writing contracts, there are advantages to delegated monitoring. Financial intermediation can provide economic advantages over direct lending.21 Lenders delegate monitoring of borrowers to financial intermediaries who diversify risks. The diversification of risks by delegated monitors provides another important example of the benefits of intermediated exchange in comparison with direct exchange. This helps to explain the existence of firms such as banks that carry out financial intermediation. The implications extend beyond the financial sector to firms that act as delegated monitors of suppliers and distributors. Delegated contracting In hierarchies, principals delegate some types of contractual design and monitoring to subordinates, creating principal-supervisoragent relationships, with supervisors acting as middle principals; see, for example, Geanakoplos and Milgrom (1991), Qian (1994), and McAfee and McMillan (1995). In McAfee and McMillan (1995), only the agent has private information, with the supervisor designing the contract. The supervisor extracts information rents in return for reporting the agent's information to the principal. As a result, adding layers to the organization causes information rents to increase exponentially with the length of the 21

See also Leland and Pyle (1977) and Chan (1983).

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hierarchy. Moreover, because of the costs of incentives, the principal's marginal cost of producing output also increases with the length of the hierarchy, thus reducing the organization's chosen output.22 Melumad, Mookerjee, and Reichelstein (1995) point out that delegated contracting can be a means of distributing information processing among members of the organization. The advantages of overcoming bounded rationality come at the cost of loss of control. They consider a model of a principal and two agents and compare a centralized arrangement, in which the principal contracts directly with both agents, with a decentralized arrangement, in which the principal contracts with only one agent who in turn contracts with the other agent. They derive a delegation mechanism that eliminates the incentive problems inherent in delegated contracting. The result relies on the principal's being able to monitor the contribution of the intermediary to the joint product and to design the sequence of contracts. Melumad et al. (1995) show that if the principal cannot monitor the intermediate agent's contribution, the intermediary takes advantage of his or her monopoly power, creating a problem that resembles that of double marginalization in a successive monopoly. The intermediary will bias the assignment of production task by shifting production away from the final agent. Melumad et al. (1997) also consider a model with a principal and two agents and show the advantages of delegated contracting when contract contingencies are costly. They point out that in models for which the revelation principle applies, centralization of decision making dominates delegation arrangements. However, when the costs of incorporating contract contingencies is prohibitive, the number of contingencies will not be sufficient for the revelation principle to hold. In such a setting, it is advantageous for the principal to forego some control over agent decisions as a means of obtaining greater flexibility. Melumad et al. (1997) consider centralized contracting in which the principal offers a contract to both agents. The agents report information to the principal. They show that with centralized contracting, the principal is better off when the agents act sequentially rather than simultaneously. They compare centralized contracting with decentralized contracting, as represented by a three-tier hierarchy in which one of the agents acts as an intermediary. Under delegated contracting, the principal offers a contract to the intermediary. The intermediary commits to the contract with the principal before designing a contract for the agent. 22

See also Tirole (1986b), Demski and Sappington (1987), Laffont (1990), Baron and Besanko (1992), and Gilbert and Riordan (1995) on incentives in multilevel hierarchies.

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The intermediary reports to the principal before the agent. However, the intermediary chooses productive effort only after the agent. In this setting with limited communication, delegated contracting dominates centralized contracting. Monitoring by financial intermediaries Why delegate monitoring of performance to others? The standard explanations for the use of agents apply to monitoring. Agents may bring skills to the monitoring task and they may have a lower opportunity cost of time and effort relative to the principal. However, there are additional explanations for delegated monitoring. If multiple principals delegate monitoring to a single agent, the agent may achieve economies of monitoring by producing information more efficiently. An agent that monitors multiple investment projects can derive advantages over monitors of individual projects by reducing the variance of average returns by the statistical properties of large samples. This is not sufficient to give an advantage to monitoring by agents. In addition, the costs of monitoring the delegated monitor must be low as well. Delegated monitoring lowers the total cost of monitoring if monitoring costs in the direct-exchange case exceeds the sum of (1) the total costs to the principal of monitoring the agent's performance and (2) the cost of monitoring by the agent. If the total costs of monitoring are lowered by delegation, intermediated exchange has a transaction-cost advantage over direct exchange. Douglas Diamond (1984), Ramakrishnan and Thakor (1984), Stephen Williamson (1986), and Krasa and Villamil (1992) consider agents who act as financial intermediaries. Intermediaries incur debts from lenders and in return make loans to borrowers. They derive optimal incentive contracts for borrowers and intermediaries. In these three models, borrowers observe the realization of returns to an investment project but intermediaries and lenders do not. The intermediaries' role is created by the costs of monitoring. These studies show that optimal contracts between lenders and the firm, and between the firm and borrowers, take the form of simple debt contracts with bankruptcy costs. The structure of the debt contracts results in more effective monitoring by intermediaries. Krasa and Villamil (1992) show that with a sufficient number of entrepreneurs, two-sided debt contracts are more efficient than direct exchange. Two-sided debt contracts refer to the intermediary's contracts with lenders and entrepreneurs, who are the final borrowers. They show that two-sided simple debt contracts strictly dominate all other types of contracts.

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Boyd and Prescott (1985) allow intermediation by multiagent coalitions. Following Townsend (1979, 1983), they consider the core of a game in which agents form financial intermediary coalitions that could be interpreted as firms. They assume that there are both ex ante and ex post informational asymmetries. Before contracting, there is asymmetric information about entrepreneurs that results in adverse selection problems. Also, intermediaries can produce information by costly evaluation of the outcome of investment projects. Financial intermediaries in equilibrium produce costly information on final borrowers and issue claims whose state-contingent pay-offs are different from the claims issued by final borrowers. Boyd and Prescott conclude that such firms are required because securities markets are not sufficient to address both adverse selection problems and information production. Lacker (1989) considers financial intermediation in an overlapping generations framework. Optimal contracts take the form of simple debt contracts. Each agent lives for two periods and has a commonly observable investment technology with a privately observable random return. The productivity of investment differs across agents, so that agents with more productive investment technologies become lenders. Agents trade with only those of the same generation. Because of informational asymmetries, some agents will become intermediaries between agents of their generation. Delegated monitoring of borrowers To illustrate the basic issues, I examine an example based on the model of Douglas Diamond (1984). Consider an economy with entrepreneurs who need capital to invest in projects and lenders with capital available for making investments. The market equilibrium in which entrepreneurs borrow directly from lenders is compared with the market equilibrium with a monopoly financial intermediary. Consider first the market equilibrium without an intermediary. Suppose that there are N entrepreneurs in the economy and mN lenders. An entrepreneur requires one unit of investment and each lender has available 1/m units of investment capital.23 For the direct-exchange case, it is sufficient to examine the decision of a single entrepreneur. The entrepreneur undertakes an investment with an uncertain pay-off y, which is uniformly distributed on the unit interval, so that Ey = 1/2. 23

The investment is normalized to one and the competitive return is less than one without loss of generality. The assumption could be interpreted as an assumption that investment is the only store of value, with money depreciating at a faster rate. Alternatively, the required investment level could be normalized to equal some number less than the competitive return.

Agency and the intermediation theory of the

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After making the investment, the entrepreneur observes the realized value of y. The value of y is the entrepreneur's private information so that it is not observable by lenders. After observing y, the entrepreneur makes a payment z to his lenders, where z < y. Because the entrepreneur has an incentive to understate the outcome of the investment project so as to reduce the payment to lenders, the debt contract includes a nonpecuniary penalty function H(z). The penalty function can represent a loss of reputation for the entrepreneur. The entrepreneur chooses an optimal penalty function that maximizes the entrepreneur's net benefits, subject to two constraints. First, the entrepreneur's payment strategy must be incentive compatible. The entrepreneur's strategy z(y) maximizes the entrepreneur's expected net benefit,

E[y-z-H(z)] subject to z < y. Second, the expected payment by the entrepreneur must be greater than or equal to the competitive interest rate available to lenders r:

Ez(y) > r. Given the incentive compatible strategy z(y), which depends on H, the optimal penalty function for the entrepreneur H maximizes expected profit:

E[y-z(y)-H(z(y))l subject to the lender's individual-rationality constraint. The optimal contract between the entrepreneur and the lenders has the form of a debt contract with face value h and a penalty function H*(z) equal to the shortfall from h: where h = 1 - (1 - 2r) 1 / 2 . To see why the penalty function is optimal, observe first that, given //*, the entrepreneur's optimal strategy is zKy)

~ \h

otherwise *

Given this strategy, the lender's individual rationality constraint is satisfied exactly, that is,

Ez(y) = r. The penalty function maximizes the entrepreneur's net benefits. This

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Intermediation and agency theory

is because H* gives the smallest penalties such that the entrepreneur's incentive-compatible strategy satisfies the lender's individual-rationality constraint.24 Under direct exchange, entrepreneurs earn the expected profit n = E[y - z(y) - H*(z(y))] = E[y - h] = 1/2 - h. For entrepreneurs to be profitable requires that h
s(y) = jgy

otherwise The intermediary lends to all N entrepreneurs and earns a total return equal to G = J ] g(j/)- Assume that the returns to projects are independently distributed. Although the intermediary can observe the outcome of the project, lenders cannot observe the intermediary's income. It follows that the optimal contract with lenders must include a deadweight nonpecuniary penalty function, which is the same as the optimal penalty function derived in the case of direct exchange. Suppose that the intermediary pays Z to lenders. The intermediary's objective is expected returns net of the investment costs of monitoring:

n = E[G - Z - H(Z)] - Nk. 24

Observe that, by construction, h is the smallest number such that if the constraints z < y and z < h are satisfied, then Ez(y) > y. So there must exist some payment h+ > h that is incentive compatible. If z = h+ is incentive compatible given contract H(z) then y - h+ - H(z) >

max [y - z -

H(z%

Thus, for all z' e [0, h+], it follows that

H(z) >h+ + H(h+) - z'. Since h+ > h and H(z) > 0 for all z, it follows that H(z') >h-zf

=

H\z').

Note that H*(z) = 0 for z > h. Thus H* gives the smallest penalties such that the entrepreneur's incentive-compatible strategy satisfies the lender's individual-rationality constraint. So H* is the optimal penalty function.

Agency and the intermediation theory of the

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341

By the same reasoning as in the case of direct monitoring, the optimal penalty function for the intermediary is of the form

H(Z) = max{fN - Z, 0}, where fN depends on the number of loan contracts N. The intermediary's payment strategy Z(G) is a function of total receipts and depends on the penalty function (

}

{G

~\f

N

if G
The expected payment made by the intermediary to lenders must at least equal their opportunity cost of capital. Thus the optimal contract for the intermediary exactly satisfies the lender's individual-rationality constraint:

EZ(G) = Nr. This equation determines the value of the critical parameter fN. The entrepreneurs must earn at least what they could earn with direct exchange. With intermediation, an entrepreneur earns

E[y-g(y)] = 1/2- g + g2/2. The intermediary increases the face value g until the entrepreneur is exactly indifferent between direct exchange and intermediated exchange: so that g = 1 — (1 — 2/i) 1/2 . The face value exceeds the penalty in the direct-exchange case, which in turn exceeds the competitive rate of return: g > h > r. Substitute for the repayment policy Z(G) and the optimal nonpecuniary penalty function H(Z) in the intermediary's expected net return of the investment costs of monitoring:

n = E[G - fN] - Nk. Since the outcomes of the entrepreneur's investment projects are independently distributed, EG = N(g — g2/2) = Nh. So the intermediary's expected net return equals the number of loan contracts times the difference between the penalty parameter in the direct-exchange case and the cost of monitoring by the intermediary, minus the penalty parameter in the delegated-monitoring case:

Tl = N[h-k-

fN/N]

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Intermediation and agency theory

Therefore the intermediary is economically viable if and only if

h-k-

fN/N

>0.

If the intermediary makes only one loan to a single entrepreneur, then fl=h and the intermediary is not profitable since II = — k. By the (weak) law of large numbers, it can be shown for large N that the penalty parameter divided by N falls below h and tends toward the interest rate r.25 Thus, given h > r + k, the intermediary is profitable for sufficiently large N.26 The intermediary is able to compete against direct exchange by economies from monitoring many different loans. The intermediary observes a sample of realizations of loan projects rather than a single project. By the central limit theorem, the variance of the average payment received from entrepreneurs falls as the number of loans increases. As a result, the cost to lenders of monitoring the intermediary is lower the more loans the intermediary makes. The intermediary with more loans then earns a spread that is sufficient to cover the costs of observing entrepreneur performance.

12.5

Conclusion

Agents often are market intermediaries. Principals delegate authority to agents to bargain with third parties, to carry out competition with third parties, and to monitor the performance of third parties. Principals employ agents if the effectiveness of the agent outweighs the costs of monitoring and providing incentives to the agent. Many of the advantages of agents are well known. Principals turn to agents to alleviate the principal's bounded rationality and limited capacity. The opportunity cost of the agent may be lower than that of the principal. The agent may have greater expertise, abilities that complement those of the principal, or a comparative advantage relative to the principal. Some of the benefits of agents are related to the separation of function and division of labor. In addition to these benefits of employing agents are those strategic advantages that stem from market interaction with third parties. This 25

Using the form of Z(G), rewrite the individual-rationality constraint EZ(G) = Nr in terms of the distribution of the sample mean G/N on [0, g]:

PNE[G/N | G/N < fN/N] + (1 - PN)fN/N N

26

= r,

where P = Prob{G/N < f N / N } . By the weak law of large numbers there exists N* < oo such that PN < 8 for all 8 > 0, because EG/N = h> f N / N for N > 1; see Diamond (1984, p. 401). Thus, for large N, f N / N approaches r. Since h = 1 - (1 - 2 r ) ' / 2 , this means that 1 - r - (1 - 2 r ) ] / 2 > k.

Agency and the intermediation theory of the

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343

chapter identified a number of advantages. Principals negotiate through agents because the principal can make binding commitments to the agent, so that the principal that receives the benefits of commitment in the negotiation with third parties. Principals compete through agents because the principal can commit to incentives for a manager that translate into commitments to competitive strategies. Principals contract through agents not only for purposes of commitment but to reduce the costs of contingent contracting. Principals monitor through agents because of efficiencies from consolidating the monitoring function. Understanding that agents are intermediaries has important implications for the design of incentives and organizational structure. The firm's employees do not simply carry out productive tasks within company walls. Rather, employees are the firm's representatives in the market place. The firm relies on its employees to carry out transactions and negotiate contract terms with customers and suppliers. Employees must be given incentives to represent the firm's interests to third parties. The basic economic model of agency can be extended to address intermediation activities. This analysis shows that delegation within the firm is firmly grounded in the firm's market relationships. The agency framework adds another dimension to the intermediation theory of the firm. Firms are formed to establish agency relationships within organizations. The firm's employees carry out the firm's buying and selling activities. Moreover, firms are formed because those outside the firm - owners, customers, and suppliers - derive economic benefits from intermediated transactions. Firms themselves act as the agents of consumers or other firms in many ways. Firms act as the agents of their customers when they negotiate contract terms with suppliers of products and services and with investors. Firms provide commitment devices for buyers who may obtain more favorable contract terms from a firm than they could through direct bargaining with an individual supplier. Recall the discussion in Chapter 10 of the incentives for firms to make credible commitments. Firms provide delegated monitoring services by monitoring their own employees and the performance of independent contractors. Firms earn returns as intermediaries by consolidating contracting and monitoring functions.

Conclusion

Money may be the oil of commerce, but intermediaries are its engine. Financial, wholesale, and retail intermediaries and marketing, sales, and purchasing units of vertically integrated manufacturers carry out a wide variety of intermediation activities that are essential to the functioning of market economies. The preceding chapters define an intermediation theory of the firm that explains why firms are formed and how their boundaries are determined. The analysis also provides an intermediation theory of market microstructure that helps to explain how prices are determined and how supply and demand are brought into balance in a market equilibrium. The intermediation approach extends and unifies in a consistent way the four main classes of theories of the firm: neoclassical, industrial organization, contractual, and organization incentive. Of course, any unifying view emphasizes some features of models at the expense of others, treating some settings as special cases or ideal conditions. The intermediation theory of the firm provides sufficient generality that it retains some of the fundamental features of existing theories of the firm. The intermediation theory of the firm retains the input-output perspective of neoclassical economics, focusing on not only the firm's role as a producer but also on an additional set of activities. Like the neoclassical firm, coordination of the purchase of inputs and sale of outputs is stressed. Unlike the neoclassical setting, firms do not necessarily take all prices as given. Firms, rather than the Walrasian auctioneer, operate markets, coordinate the activities of buyers and sellers, select prices, and balance supply and demand. The intermediation theory of the firm encompasses industrialorganization models in which firms with market power set prices competitively. Imperfect competition models can be viewed as a special case of intermediation in which the firm takes factor prices as given. The intermediation setting allows for the exercise of market power in both product and factor markets. Interaction with suppliers and customers reemphasizes the industrial organization concern with vertical 344

Conclusion

345

integration. Competition between intermediaries broadens the range of competitive strategies as firms interact in both factor and product markets. The intermediation theory of the firm and the resulting market models recognize the importance of transaction costs emphasized by contractual theories of the firm. The intermediation theory stresses the costs of alternative market microstructures, including direct exchange and various forms of intermediated exchange. It also recognizes the role of opportunism and the returns to commitment ability. By stressing the role of market intermediaries, the theory opens up a set of market alternatives to expansion of organizations and allocation of goods and services within vertically integrated firms. Moreover, the intermediation theory of the firm draws upon the principal-agent model in a manner consistent with organizationalincentive theories of the firm. Recognizing that agents are often intermediaries, the firm delegates transacting and contracting to employees and to agents outside the firm. The firm designs incentives to align the agents' interests with those of the firm in contract negotiation and performance monitoring. Moreover, the firm itself often acts as an agent or intermediary for its customers or suppliers. In this conclusion, I briefly review the intermediation theory of the firm. I stress some of the implications for economic analysis of an intermediation approach to market microstructure. I consider some of the implications of the discussion for the economics of management strategy. I conclude with a few public policy observations.

The intermediation theory of the firm The intermediation theory of the firm shows that firms are formed when they increase net gains from trade relative to direct exchange. The intermediation framework identifies the economic incentives for firms to coordinate trade between buyers and sellers. Companies earn economic rents by increasing the gains from trade for buyers and sellers or by reducing total transaction costs. The intermediation theory of the firm explains the formation of firms in a way that does not depend on production technology but rather compares the net benefits of alternative forms of economic exchange. The intermediation theory of the firm establishes a common framework for examining a wide variety of economic activities undertaken by firms. Firms acting as intermediaries can compete effectively with the decentralized-exchange alternative. Firms reduce costs relative to decentralized trade when they provide focal points that reduce the delays

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Intermediation and agency theory

and the search costs that finding a suitable trading partner entails. Firms posting prices offer advantages over matching and search markets when there are delays and asymmetric information associated with bargaining over the terms of trade, as shown in Chapters 5 and 6. Firms earn returns to intermediation in markets with asymmetric information. By intermediating between buyers and sellers, firms break the budget-balancing constraint of direct exchange. By standing between buyers and sellers in negotiations, firms can design pricing and contract mechanisms to induce revelation of demand and cost information. By dealing with many buyers and many sellers, firms can replace complicated allocation mechanisms with simpler nonlinear pricing or even linear posted prices. As the number of buyers and sellers becomes large, these simpler pricing mechanisms are approximately efficient, as shown in Chapter 7. Firms alleviate information asymmetries in many other ways. They produce and distribute information about supply and demand and product characteristics, thus reducing adverse selection problems. In product markets, firms test products and certify quality, reducing the inefficiencies that accompany unobservable product characteristics. In financial markets, firms address adverse selection by offsetting the costs of dealing with informed traders against the returns from providing service to uninformed liquidity traders. Firms act as market makers, providing liquidity and immediacy to markets by standing ready to buy and sell. They adjust prices to reflect the information revealed by trades, as discussed in Chapter 8. In credit markets, firms perform credit allocation and screening functions by setting interest rates and evaluating applications for loans. The intermediation theory of the firm addresses the role of transaction costs by clarifying the role of firms in the creation and operation of markets. Intermediation analysis shows that the dichotomy between markets and organizations is perhaps too simplistic. There are many alternative forms of market exchange with differing gains from trade and transaction costs. There are of course many different forms of organization. The point is that the solution to costly market exchange is not necessarily the creation of larger, vertically integrated organizations, as discussed in Chapter 9. Instead, companies can interpose themselves between buyers and sellers to alleviate problems that arise from direct exchange, without mergers between buyers and sellers, as Chapter 10 emphasizes. The intermediation theory of the firm extends contractual theories of the firm. In the works of Coase (1937) and Williamson (1975), the existence of firms as intermediaries is due to the creation of organizational

Conclusion

347

forms that minimize transaction costs. In intermediation theory, firms do not necessarily allocate resources within the organization. Instead, they produce more efficient market transactions as a means of avoiding the costs of searching for a trading partner and of negotiating contracts. The notion that an individual firm decides between using the market and forming organizations on the basis of transaction costs is consistent with intermediation. However, intermediaries do more than use markets; they create innovative transactions that take advantage of technological change and market opportunities, becoming centers of contracting activity. Firms interpose their reputations for those of their trading partners. By virtue of longer lives and a greater volume of transactions, firms are able to make credible contractual commitments that might not be possible in direct exchange. These contractual commitments allow intermediaries to offset opportunism in bilateral contracts, thus providing a market alternative to vertical integration. The make-or-buy choice is supplemented by the option of pursuing third-party transactions through intermediaries. By offering fixed prices to buyers and sellers, firms create incentives for those buyers and sellers to make more efficient investment decisions, thus enhancing the gains from trade, creating rents to intermediation. Similarly, the ability of intermediaries to make contractual commitments can reduce the need to control complementary transaction-specific assets, thus providing an alternative to ownership of assets by the firm. Asset ownership is costly. Ownership of assets can create inflexibility by restricting companies to particular types of manufacturing technology, particular outputs, or specific locations. Firms can retain flexibility by leasing and other transactions that do not require asset ownership. By offering commitment to prices and contract terms, intermediaries create transaction alternatives to vertical integration designed to consolidate asset ownership. The intermediation theory of the firm sheds light on the principalagent aspects of organizations, as discussed in Chapters 11 and 12. The organizational-incentive theory of the firm examines moral hazard and adverse selection problems stemming from delegation of authority and design of incentives within organizations. However, as I have emphasized, agency relationships within companies are formed in the context of external market relationships. In practice, the principal-agent relationship generally involves the agent dealing with third parties on behalf of the principal. In short, agents often act as intermediaries for their principal. Principals derive a number of economic returns by transacting through agents. Agents acting as intermediaries provide commitment opportunities that

348

Intermediation and agency theory

have value in negotiation. If the principal can make credible commitments to agents that would not be feasible in direct negotiation, the principal has an incentive to deal through agents in bargaining over prices and other contract terms. The firm's employees act as agents in dealing with customers, suppliers, investors, and other trading partners. Dealing through intermediaries also has value in competitive strategy. Firms can commit to competitive strategies by selecting incentives for managers, thus influencing the outcome of competition. The intermediation theory thus helps to clarify the role of employees, who serve as agents of the firm not only in carrying out routine production and operations tasks but also as market agents of the firm. Firms are formed to carry out the task of delegating authority to employees and monitoring that performance to achieve the benefits of strategic delegation. Moreover, delegated contracting and monitoring can have advantages of direct exchange. When contingent contracting is costly, delegated contracting can save on the costs of writing contracts. The intermediation theory of the firm also recognizes that in addition to employees acting as agents of the firm, the firm itself acts as an agent of its customers or suppliers. Lenders delegate authority to financial intermediaries who supervise contracts with borrowers. When observing performance is costly, delegated monitoring can reduce costs when intermediaries pool and diversify risks. Customers rely on retail and wholesale intermediaries to act as their agents in negotiating contracts with suppliers. The intermediation theory of the firm thus identifies many situations in which firms enhance gains from trade net of transaction costs in comparison with direct exchange. In addition, firms create institutions of exchange that bring buyers and sellers together in ways that yield greater net returns than vertical integration.

Market microstructure and intermediation The preceding analysis contains a theory of market microstructure in which firms acting as intermediaries establish the microstructure of markets. In competition with other intermediaries as well as direct exchange, firms establish the bid-ask spread. The spread fluctuates in response to demand and supply shocks and changes in transaction costs. The bidask spread depends on the market power of intermediaries, with such underlying determinants as search costs, product differentiation, and uncertainties about competitor costs. Additional determinants of the spread are the extent of risk, adverse selection, and moral hazard in market transactions.

Conclusion

349

The notion of intermediation as an essential component of market microstructure applies to the institutions of exchange in markets for all types of goods and services. The analysis applies to markets for products and services, including but not limited to financial transactions such as banking, insurance, or securities. Economic andfinancialmodels of market microstructure provide a rich set of tools for examining the economy. Market microstructure in all types of markets is undergoing substantial change. With the rise of the Internet and electronic data interchange, retail and wholesale transactions for all types of goods and services are becoming increasingly automated. Financial trading is becoming increasingly automated including computerization of trade execution.1 The result is an increase in the volume and the rate of transactions and evolution of the institutions of exchange. Models of market microstructure are useful for understanding these developments. The central role of firms in adjusting prices and balancing supply and demand suggests some changes in the way that basic economics is presented to students. Students first meet economics in the form of the supply and demand graph with the equilibrium price and quantity denoted clearly. Much to the dismay of the typical student, the question of how the equilibrium is attained often is bypassed. The price is merely said to adjust presumably by itself in response to shifts in the demand and supply curves. The course moves on to the derivation of the underlying demand and supply curves from consumer preference and production technology assumptions. The intermediation analysis presented in Chapters 1-4 suggests that careful attention can be paid to how the price adjusts in a manner that is consistent with traditional analysis. The bid-ask spread can be exhibited at the outset of the discussion with the spread attributed to transaction costs and economic rents earned by intermediaries. Intermediaries adjust prices upward or downward as a means of balancing purchases and sales in response to shifts in supply and demand. The traditional Walrasian market-clearing price is the limiting case of a frictionless economy in which intermediaries have no transaction costs and engage in Bertrand-Nash competition. The efficiency of competitive markets continues to hold with the important qualification that transaction costs are low. Market performance relative to the frictionless ideal depends on the time costs of search, the costs of bargaining, and the extent of information asymmetries experienced by buyers and sellers. Market efficiency will depend on the costs and the effectiveness of competing intermediaries and the institutions of exchange they create. 1

See Domowitz (1992, 1993).

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Intermediation and agency theory

Management implications The centrality of thefirmas a creator and operator of markets emphasizes the importance of managers. The intermediation framework highlights the complexity of the decision problems faced by managers by recognizing the firm's central role in pricing and market clearing. To carry out the tasks envisioned by intermediation models, managers require substantial information about customers and suppliers. Moreover, they must coordinate their activities in upstream and downstream markets. Understanding market microstructure models suggests modifying analysis of competition strategy. Elsewhere (Spulber 1998a), I examine how managers formulate competitive strategies by recognizing their role as economic intermediaries. The intermediation theory of the firm suggests a set of innovative competitive strategies. Carrying out transactions, such as recording orders, sending bills, and acknowledging receipt of payments appear secondary to the more glamorous activities of innovation and manufacturing. Yet transaction costs can be substantial. By performing such tasks rapidly, accurately, and inexpensively, companies can gain a comparative advantage. Information gathering and distribution by companies is valuable for both its customers and suppliers. This implies that managers must give priority to the company's information systems and transactions processing. Inventory management by companies clears markets. Managers have found that they can earn economic rents by quickly adjusting inventories to meet customers demands. The use of new techniques such as just-in-time inventories allow the pattern of orders and production to track customer requirements closely, thus performing the functions resembling the idealized spot market. Such market responsiveness requires alert managers who can identify market trends while making sure that the company is sufficiently flexible to respond. The intermediation framework draws on financial market techniques. It is essential for managers to recognize that their purchasing and selling activities represent arbitrage across input and output markets. The profit of the firm reflects the firm's bid-ask spreads. Just as financial intermediaries adjust their positions to reflect changes in the spreads, so market makers in commodity markets need to improve the rapidity of their response. It is estimated that 100,000 airline fares change every day. Major airlines practice yield management, which involves changing the relative amounts of seats offered at full and discount fares in real time in response to changing demand patterns. Continuing innovations in computer and communications technologies enhance the ability of

Conclusion

351

companies to adjust prices, production, and inventories to changes in supply and demand. The study of intermediation and market microstructure is of increasing significance for management strategy. Technological and market changes are continually creating new types of intermediaries and fundamentally altering market microstructure. Some speak of disintermediation to indicate the decline of traditional banking.2 However, this simply means that the functions of traditional banking are taken over by a host of new financial intermediaries, including discount brokers and mutual fund families, not to mention the reconfiguration of banks themselves as supermarkets for financial services. Others identify the rise of electronic commerce as a source of disintermediation. However, the popularity of the Internet is giving rise many new types of intermediaries who provide services on line or help consumers sort through the plethora of goods and services.

Public policy implications The market microstructure framework raises fundamental public policy questions. Among these questions is whether or not the market power of intermediaries represents market failure. It is clear that the centrality of intermediation activity in the market microstructure setting stands in contrast with the exogenous market clearing assumed in traditional economics. While market power of firms is a feature of models of industrial organization, it sometimes is interpreted as imperfect competition. However, price setting does not provide prima facie evidence of market failure. Price setting by firms is the way in which the market mechanism normally functions. Price setting by firms is not only consistent with competition, it is the means by which markets clear. The equilibrium bid-ask spread, which separates buyer willingness to pay and supplier costs is a consequence of transaction costs, asymmetric information, and the returns to intermediation activities. Establishing the existence of market failure would still require a showing of insurmountable barriers to entry or some demonstration of improper behavior such as collusion. Moreover, the departure of output and prices from the Walrasian equilibrium does not necessarily imply that there is a role for government in improving the allocation of goods and services. Recognizing the importance and the complexity of the market intermediation by firms shows 2

See, for example, Edwards (1996).

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Intermediation and agency theory

just how difficult and costly this task can be. Experience indicates that governments will encounter substantially higher transaction costs when they undertake those tasks. Elsewhere I emphasize that many types of regulation involve the government's acting as an intermediary between buyers and sellers.3 For example, in traditional rate-of-return regulation, state regulatory agencies oversee bargaining between consumers and a regulated utility, approving rate proposals and reviewing cost and demand projections. The Federal Communications Commission operated the auctions to allocate licenses to use spectrum for personal communications services.4 These activities involve government agencies in intermediation roles that may be performed more efficiently by private companies. Models of market microstructure suggest that establishing and adjusting prices to clear markets is not due to an exogenous mechanism but rather is an intrinsic part of the economic activities offirms.Market microstructure analysis suggests that public policy should not be designed to favor production of goods over market-allocation activities. Since intermediation contributes significantly to the economy's value added, there should not be taxes and other incentives that promote investment in manufacturing facilities over expenditures for creating and operating markets. Regulators should refrain from price controls and other restrictions that impair or attempt to supplant the functioning of private intermediaries. Policy makers should avoid the presumption that, whenfirmsundertake market making and price setting, insufficient competition exists. Instead, these activities are the ways that firms intermediate economic transactions and make markets work.

3 4

See Spulber (1988, 1989b). See the special issue of the Journal of Economics & Management Strategy, Vol. 6, Fall, 1997, on Market Design and the Spectrum Auctions.

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Index

Adverse selection agency relationships and, 290-291 alleviation of, xxii-xxv in financial markets, 203-225 mitigation of, 266 in product markets, 171-202 Agency law, 321-324 Agency theory of the firm, 14,19-20, 289-352 Agents advantages of, 342-343 contracting by, 324-325 coordination by the firm, 299-306 definitions of, 289-290 economic, as producers or intermediaries, 134-137 intermediation theory and, 289-318 legal, 321-324 organization of the firm and, 325-328 organizational-incentive theory and, 289-318 political, 328-329 types of, 131, 193 what are they? 321-329 Akerlof, G., xxviii, 173, 193, 194 Alchian, A., xxviii, 246, 296, 300, 305 Alderson, W., 263 Aldrich, H., 243 Allocation of output, 183-193 over time and under uncertainty, 34-40 Ambarish, R., 313 Amihud, Y., 13 Anderson, E., 296 Arrow, K., 229, 237-239, 241, 292, 301 Ask-bid spread. See Bid-ask spread Asymmetric information adverse selection and, 171-225 in financial markets, 203-225 in product markets, 171-202 Auction techniques, 76-79 Bagehot, W., 205 Baiman, S., 316 Banks. See Financial intermediaries Bargaining, delegated, 329-332

Bargaining process, 119-120, 171-172 Barnard, C , 240 Barro,R., 11 Basu,A., 316 Bayesian specialists, 208-211 Bayes-Nash equilibrium, 75-76 Bayes-Nash mechanisms, 174,178 Benabou, R., 142, 160 Bertrand competition, 61-80 when costs differ, 74-79 with differentiated products and purchases, 68-71, 334 with homogeneous products, 64-68 between intermediaries, xv-xvi by market makers, 211-214 with rivals' costs unknown, 75-79 with switching costs, 71-74 and theory of the firm, 16-17 Bertrand-Edgeworth competition, 212 Bertrand-Nash competition, 214, 333 Bertrand-Nash equilibrium, 68, 70-71, 76-79 Besanko, D., 329 Bhattacharya, S., 118, 134, 138-139, 144 Bid-ask spread in financial markets, 143-145, 203-211 overview, xviii, xx, xxv and price setting, 27, 30-32, 34-35, 40-48 supply and demand and, 11-12 Bidding process of intermediary firm, 75-79 Biglaiser, G., xxiii, 173, 193, 196, 197, 277 Blinder, A., 44 Borrowers monitoring of, 338-342 and rationing, 219-224 Borrowing, and price setting, 36—40 Boundaries of the firm, 291-299 Bounded rationality, 236-245 Boyd, J., 338 Broker's commission rate, 50-51 Business services, as intermediation, 21, 23-24 Caillaud, B., 334 Calvert, R., 329 Carlton,D., 11,44,56,57

369

370

Index

Centralized control, 300-302 Centralized exchange, 263-264 Chamberlin, E., 29 Chandler, A., 7, 270, 274, 301 Circular flow of economic activity, 7-13 Clower, R., xviii Coase, R., xxvi, 18-19, 231-234, 236, 246, 267, 274, 281, 296, 300, 346 Commons, J., 274 Competition delegated, 332-335 between intermediaries, 61-80 and market equilibrium, 81-107 monopolistic, 104-105 between specialists, 211-215 see also Bertrand competition Consumers continual entry of, 159-161 role in market equilibria, 146-164 with willingness to pay, xxi Contracting by agents, 324-325 delegated, 335-337 Contractual theory of the firm vs. intermediation theory, 257 overview, 18-19 transaction costs and, 229-255 Coordination of agents by the firm, 299-306 Coordination of exchange, 262-264 Copeland, T., xxv, 143, 206, 211 Cost difference, and competition, 74-79 Cost function of firm, 109-112 Costly intermediation, 126-139 Coughlan, A., 316 Cournot competition, 29, 333-334 Crawford, V., 331 Credit rationing, 219-224 Cripps, M , 215 Crocker, K., 293 Customers, switching by, 63, 71-79 Cyert, R., 242 D'Aspremont, C , 174 Debreu, G., 113 Decentralized trade vs. intermediation, 117-168 overview, xiv Decision making by firms, 4-7 and rationality, 239-245 Decision theory, 319 Delegated bargaining, 329-332 Delegated competition, 332-335 Delegated monitoring, 335-342 Delegation to intermediaries, overview, xxvii-xxix by managers to employees, 314-317 by owners to managers, 306-314 Demand. See Supply and demand Demand shifts, and price adjustment, 40-48

Demsetz, H., xvii, xxviii, 234-235, 244, 267, 296-300, 305 Demski,J.,315,316 Dennert, J., 144, 204, 211-215 Dewatripont, M., 331 Diamond, P., xxviii, 134,138, 142, 144, 310, 321, 337, 338 Differentiated products, 68-71 Direct exchange vs. intermediation, ix, xiii transaction costs, xvi Discount rate, xxii, 141, 144, 158-163 Dye, R., 316 Easterbrook, R, 311, 326-327 Economic theories of the firm, 13-21 Edgeworth, E, 29 Edlefson, L., 57 El-Ansary, A., 317 Employees as agents, xxviii, 325-326 delegation to, 314-317 Entrepreneur, Schumpeter's, 267-269 Equilibrium general, 81-105 monopoly, 157-162 pooling, 216-218 see also Walrasian equilibrium Equilibrium price distribution, 150-154 Eswaran, M., 304 Excess inventories, 49-51 Exchange coordination, 262-264 Experts, guarantees by, 193-196 Ex post efficiency, 174 Fama, E., 309 Fershtman,C, 321,331,333 Financial intermediaries advantages of, xxviii adverse selection effects, 203-225 credit rationing by, 219-224 monitoring by, 337-338 role in U.S. economy, 21, 23 Financial markets, adverse selection, 203-225 Firms boundaries of, 291-298 contractual theory, 18-19, 229-255 coordination of agents by, 299-305 cost function, 1009-112 decision making by, 4-7 economic efficiency of, 87-88 economic theories of, 13-21 formation of, 259-266 industrial-organization theories, 16-18 as intermediaries, overview, 1-13 intermediation theory of, 1-21, 256-286 as market makers, 8-13 matching and intermediation by, 117-137 as microeconomic unit of analysis, 273-276

Index neoclassical theory, 15-16, 83-93 organization of, 325-328 organizational-incentive theories, 19-200 price setting by, 27-58 production function, 108-109 search by, 140-162 strategy for, 271-273 as technology operator, 85-86 Fischel,D., 311, 326-327 Fisher, L, 307-308 Formation of firms, 259-262 Freeman, J., 243 Friedman, J., 29, 197, 277 Galai,D., xxv, 143,203-211 Gal-Or,E., 321,334 Game theory, 319 Garman, H., xviii, 31-32, 143 Geanakoplos, J., 335 Gehrig,T., 117, 118, 123, 125, 131, 133, 137, 142-143 General equilibrium, 81-105 Gerard-Varet, L., 174 Gertner,R., 305-306, 314 Gibbons, R., 314 Glosten, L., xxv, 143, 203, 208-211 Gould, J., 215 Grinblatt,M.,215,313 Grossman, S., xxvi, 19, 215, 231, 245, 251, 281,295,306,311 Grout, R, 248-251, 254 Guarantees by experts, 193-197 Gul, F , 160 Hagerty, K., 118, 134, 138-139, 144 Hannan, M., 242 Hart, O., xxvi, 19, 232, 245, 251, 252, 281, 296,304,306,311 Hayek, E, 229 Hermalin, B., 312 Ho, T., xviii Hogan, S., 142 Holmes, O., 323 Holmstrom, B., 263, 296-298, 302-304, 311, 312 Holt, C , 74 Homogeneous products, and competition, 64-68 Hotelling, H., 29, 63, 69 Hwang, C , 313 Incentives managerial, 310-313 vertical integration and, 293-298 Indicative planning, 301 Industrial-organization competition in, 61-80 price setting in, 29-30 Industrial-organization theory of the firm, 14, 16-18

371

Inflation, and pricing, 4 3 ^ 8 Information asymmetry. See Asymmetric information Informed insiders, 205-211 Informed intermediaries, 215-219 Insiders, 205-211 Insurance pricing, 34-35 Interest rate, 219-224 Intermediaries competition between, 61-80 defined, 3 economic functions of, 10-13 as experts, 193-197 financial, 203-225 informed, 215-218 main function of, 3 ^ market clearing by, 182-193 price setting by, 148-150 as traders in financial markets, 203-225 Intermediated exchange advantages of, ix, xiii, xx vs. matching and searching, xix-xxi see also Intermediation Intermediation advantages of, xiii under asymmetric information, 171-225 basic model, 30-32 costly, 126-139 vs. decentralized trade, 117-168 and general equilibrium, 81-108 and market microstructure, 3-26 matching and, 117-139 vs. a matching market, 118-126 and matching with production, 134—137 ownership and, 281-284 price setting and, 27-58 with production, 179-182 with random matching, 130-134 review, 348-349 search and, 140-168 between single buyer and seller, 173-179 transaction-cost theory and, 229-282 in U.S. economy, 21-26 vertical integration and, 266-276 Intermediation theory agency and, 319-343 example of, xiii-xvi market microstructure and, 3-26 review, 344-348 summarized, ix, xiii transaction costs and, 256-282 Intermediation theory of the firm, 1-21, 256-286 Inventories management of, 350 market microstructure and, xvii-xviii market pricing and, 48-55, 350 Jaffe, J., 205 Jensen, M., 271, 309-311

372

Index

John, K., 313 Judd, K., 321, 333 Jullien, B., 334 Kalai,E.,321,331 Katz,M.,331 Keynes, J., 43 Kihlstrom, R., 215, 331 Klein, B., 296 Klemperer,P.,71,72 Knight, K, 231, 236-238, 241, 300 Kotwal, A., 304 Krasa, S., 321,337 Kurz,M, 331 Kyle, A., 204, 215 Lacker, J., 338 Laffont, J., 204, 215-218, 311 Lai, R., 316 Lambert, R., 313 Lange, O., 301 Law, agents in, 321-324 Lawrence, R, 242-243 Leijonhufvud, A., xviii Lenders, and rationing, 219-223 Lerner, A., 301 Lim, C , xviii Liquidity traders, 205-211 Loans, pricing of, 36-^0 Logue, D., 205 Lorsch, J., 242-243 MacMinn, R., 142 Make-or-buy decision, 233-235; see also Vertical integration Management costs, vs. transaction costs, 232-236 Management strategy, 350-351 Managers delegation to employees, 314-317 importance of, 350-351 incentives for, 310-313 owners delegation to, 306-314 rationality and, 239-245 signaling private information, 313314 Mankiw, N., 44 Manufacturers intermediation by, 24-25 price setting by, 32-34 March, G., 241, 242 Market clearing by intermediaries, 182-193 inventories and, 48-57 prices and, 10-12,51-57 Market contracts, vertical integration and, 293-296 Market equilibrium competition and, 61-81

with continual entry of consumers and suppliers, 159-162 defined, 121 and matching market, 121 -126 in neoclassic analysis, 15 with one-time entry of consumers and suppliers, 150-154 in search model, 140-168 Walras's law and, 112-113 Market for lemons, xxiii-xxiv, 173, 193 Market intermediaries. See Intermediaries Market makers in financial markets, 205-225 functions of, 8-13 Market microstructure defined, ix, 3 and intermediation, 3-26 and intermediation theory, 3-57 review, 348-349 theory, xvii-xix and transaction costs, 259-266 Market model, basic, 144-150 Marschak, J., 241 Marshall, A., 246 Maskin, E., 76, 189, 144-150 Matching vs. intermediated exchange, xix-xxii and intermediation, 117-139 with production, 134-137 random, 130-134 Matching market, xx, 118-126 McAfee, R.P., 335 McCubbins, M., 329 McMillan, J., 335 Means, G., 43-44 Meckling, W., 271, 309-310 Melumad,N., 316,321,336 Mendelson, H., 13 Milgrom, P., xxv, 143, 203, 208-211, 296-298,315,335 Miller, M., 308, 314 Modigliani, R, 308, 314 Monitoring, delegated, 335-342 Monopolistic competition, 104 Monopoly equilibria, 157-162 Monopoly, vs. intermediation, 154-158 Monopoly intermediation and general equilibrium, 96-103 price setting by, 27-58 Monopoly pricing, 187-188 Mookherjee, D., 179, 321, 336 Moore, J., xxvi, 19, 232, 251, 252, 281, 304 Moral hazard in agency model, 290-291 mitigation of, xxv-xxvii, 266 Morgan, G., 242 Murphy, K., 311 Mussa,M., 188 Myerson,R., 171, 174, 179

Index Nalebuff,B., 316 Nash equilibrium, 65-66 Nelson, R., 243 Neoclassical economics price setting in, 28-30 Neoclassical theory of the firm, 14-16, 83-93 "Nexus of contracts," 272, 273 Nonlinear pricing, 188-193 Opportunism intermediation and, 276-280 mitigation of, xxv-xxvii transaction costs and, 245-251 Organization of the firm, and agents, 325-328 Organizational-incentive theory of the firm, 14,19-20,289-318 see also agency theory Output allocation vs. nonlinear pricing, 190-193 vs. price discrimination, 187-188 profit-maximizing, 183-187 Ownership delegation to management, 306-314 incentive aspects, 302-306 intermediation and, 281-284 separation of control, 307-310 transaction costs and, 251-254 PBE (perfect Bayesian equilibrium), 216 Picard, P., 334 Planning, corporate, 300-302 Poitevin, M., 314 Political agents, 328-329 Pooling equilibrium, 216-218 Postlewaite, A., 215 Prescott, E., 338 Price discrimination, vs. output allocation, 187-188 Price setting and allocation, 34-40 by firms, 7-13, 27-58 intermediation and, 27-58 monopoly, 187-188 in neoclassical economics, 28-30 nonlinear, 188-193 and public policy, 351-352 Principal-agent model, 14, 19-20, 290, 292 Principal-agent relationship, 321-324 Product differentiation, 62-63, 68-71 Product markets, adverse selection, 171-202 Product quality, 193-197 Production function of firm, 108-109 intermediated trade with, 179-182 intermediation and matching with, 134-137 technological efficiency, 85-86 Profit-maximizing broker, 174-179

373

Profit-maximizing output allocation, 183-187, 190-193 Property rights, xxvi, 281-284, 251-254; see also Ownership Public policy, 351-352 Pure-exchange economy, 96-100 Qian, Y., 335 Quantity rationing, 4 8 ^ 9 , 56-57 Radner, R., 215, 241 Ramakrishnan, R., 225, 321, 337 Random matching, 130-134 Rao, R., 317 Rasmusen, E., 325 Rationing of credit, 219-224 excess inventories, 49-55 of quantity, 48-49 Reichelstein, S., 179, 316, 321, 336 Residual control, 305-306 Residual returns, 302-305 Retail trade, 21-22 Revenue function of firm, 109-112 Revenue-maximizing price, 65-68, 78 Ricart i Costa, J., 312 Riley,J.,76, 189 Riordan, M., 247, 293-296 Risk allocation, 34-40 Roberts, J., 315 Rogoff, 329 Romer, D., 44 Rosen, S., 188, 215 Ross, S., 313 Roth, A., 331 Rothschild, M , 219-220 Rubinstein, A., 117, 118, 126-134, 137, 143, 241,332 Rumelt, R., 17 San, R., 311 SalasFumas,V.,321,334 Samuelson, P., 4 Sappington, D., 295-296, 315, 316 Satterwaite, M., 171, 174, 179 Scharfstein, D., 305-306, 311-314 Schelling, T., 320, 330 Schmeidler, D., 331 Schmidt, K., 312 Schmittlein, D., 296 Schoemaker, P., 239 Schumpeter, J., 267-269, 273 Search model, 140-168 Searching and bargaining process, 119-120 vs. intermediated exchange, xix-xxii Sen, S., 316 Sheshinski, E., 45 Signaling, financial, 313-314 Simon, H., 240-241, 274, 296

374

Index

Sklivas, S., 321, 333 Smith, A., 7-8, 292 Sobel,J.,331 Sonnenschein, H., 160 Specialists adverse selection, 205-210 competition between, 211-214 Spence, A., 188 Spiegel, Y, 313, 314 Spulber, D., xviii, xxii, 140, 179, 188, 270, 313,314,328-329,350 Stahl, D., 62, 64, 67 Steffen, R., 322 Stein,!, 305-306, 311 Stern, L., 317 Stigler, G., 142, 274 Stiglitz, J., 5, 10, 205, 219-224, 313 Stinchcombe, A., 241 Stockouts, 49-51 Stoll, H., xviii Strategy, for firm, 271-273 Suppliers continual entry of, 159-161 with low-opportunity costs, xxi role in market equilibria, 147-164 Supply and demand, and price adjustment, 11-12,32,40-48 Switching costs, 63, 71-74 Taylor, R, 301 Technological efficiency, 85-86 Terms of trade, 264-266 Thakor, A., 225, 321,337 Time, as transaction cost, 141 Tinbergen, J., 301 Tirole,J.,311 Townsend, R., 263, 338 Traders, in financial markets, 203-225 Transaction costs bounded rationality and, 236-245 defined, 232 firm's role in setting, 9-13 vs. management costs, 232-236 market microstructure and, 259-266 opportunism and, 245-251 overview, xiv-xv ownership and, 251-254 uncertainty and, 236-245 and Walrasian equilibrium, 94-96 zero-monopoly-rent bid and, 75-76

Transaction-cost theory contractual theory and, 229-255 intermediation and, 229-282 intermediation theory and, 256-282 overview, 14, 18-19 Uncertainty, and transaction costs, 236-245 Unit of analysis, microeconomic, 273-276 U.S. economy, intermediation in, 21-26 Varian,H.,331 Verrecchia,R.,215,311,316 Vertical differentiation, 66-67 Vertical integration boundaries of the firm and, 291-299 complementary incentives and, 296-298 decision about, 270-272 intermediation and, 266-276 make-or-buy decision and, 233-235 Vickers,J.,321,333 Vickrey, W., 174 Villamil,A.,321,337 von Bertalanffy, L., 242 Wagenhofer,A.,316 Walrasian equilibrium vs. market equilibrium, 154-157 price setting, 28-29 transaction costs and, 94 Walrasian price, 31, 55, 65-68 Walras's law, 112-113 Weingast, B., 329 Weiss, A., 205, 219-224, 274 Weiss, L., 311 Weiss, Y., 45 Wholesalers, in U.S. economy, 21-23 Williams, J., 313 Williamson, O., xxvi, 18, 231, 240, 241, 245-247, 251, 274, 277, 296, 301, 305 Williamson, S., 321, 337, 345 Wilson, R., 160, 189 Winkler, R., 206 Winter, S., 243 Wolinsky, A., 117, 118, 130-134, 137, 143 Woodward, S., 246 Yanelle, M , 144 Zarnowitz, V, 57 Zero-monopoly-rent bid, 75-76