Competition, Innovation, and Antitrust: A Theory of Market Leaders and Its Policy Implications

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Competition, Innovation, and Antitrust

Federico Etro

Competition, Innovation, and Antitrust A Theory of Market Leaders and Its Policy Implications

123

Professor Federico Etro Università degli Studi di Milano Bicocca Dipartimento di Economia Politica Piazza dell‘Ateneo 1 Milano 20126 Italy [email protected]

Front cover picture: The Astronomer by Johannes Vermeer Courtesy of the Louvre Museum ©

Library of Congress Control Number: 2007933809

ISBN 978-3-540-49600-7 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com © Springer-Verlag Berlin Heidelberg 2007 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Production: LE-TEX Jelonek, Schmidt & V¨ ockler GbR, Leipzig Cover-design: WMX Design GmbH, Heidelberg SPIN 11938798

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Printed on acid-free paper

A Francesca, Riccardo e Leonardo

Preface

In 1934 Springer published a book by Heinrich von Stackelberg, “Market and Equilibrium”, which contained pathbreaking studies on oligopolistic markets. In particular, it analyzed the behavior of a firm acting as a leader with a first mover advantage in the choice of its production level over another firm acting as a follower. That analysis became the foundation of the economic theory of market leaders and is the starting point of my book. In the following pages I develop a generalization of Stackelberg’s idea, with a focus on the understanding of the behavior of market leaders under diﬀerent entry conditions, particularly when entry in the market is endogenous. Rather than limiting the analysis to the eﬀects of the market structure on the behavior of the market leaders, I also study the eﬀects of the behavior of market leaders on the market structure. In other words, this book can be seen as an attempt to describe endogenous market structures where the strategies, the expectations on the strategies of the others, and also the entry decisions are the fruit of rational behavior. In the last few decades, economic theory has put a lot of emphasis on the rational behavior in the choice of actions and strategies and on the rational expectations on these choices. Most fields of economic theory have embraced both these elements adopting the rational expectations approach in models with perfect competition first and imperfect competition later. The theory of industrial organization has embraced these elements with the adoption of game theory as the standard tool of analysis of the interactions between firms. Meanwhile, economists have often neglected the rational behavior of the firms in their entry decisions, both in partial equilibrium and general equilibrium models. For this reason, microeconomic and macroeconomic analyses of markets with imperfect competition have been often limited to situations in which the number of firms was exogenously given. The main scope of this book is to provide a general microeconomic analysis of markets where entry decisions are rational decisions, and to understand the eﬀects of endogenous entry on the equilibrium behavior of the firms and on the welfare properties of the equilibrium market structure. A great deal of this work is inspired by and based on the revolutionary contributions of game theoretic analysis to industrial economics and antitrust policy in the last three decades. The pathbreaking works of Avinash Dixit,

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Michael Spence, Joseph Stiglitz, Paul Milgrom, John Roberts, Drew Fudenberg, Jean Tirole, Michael Whinston and others during the 80s made it clear how one could study the rational behavior of market leaders and draw welfare implications in a solid game theoretic framework. On the policy front, the main consequence of these studies was the development of the so-called post-Chicago approach to antitrust, which emphasized a number of situations in which an incumbent could engage in anti-competitive practices such as predatory pricing, bundling, vertical restraints, price discrimination, anticompetitive mergers and so on. The game theoretic approach was able to emphasize that these practices could harm consumers by excluding other entrants or by facilitating collusion. This approach challenged the former school of thought associated with the Chicago school and represented by Richard Posner, Robert Bork and others who were (and still are) skeptical toward antitrust intervention against exclusionary strategies and mergers. The classic book by Jean Tirole “The Theory of Industrial Organization” (1988) today remains the best exposition of the game theoretic foundations of the modern industrial organization, of the strategic interactions between firms, and of the policy implications of the post-Chicago approach. In the Introduction to the second part of that book, entitled “Strategic Interaction” and entirely dedicated to the strategic behavior of firms, Tirole points out a fundamental distinction for the behavior of a market leader facing an entrant: this leader will be aggressive under strategic substitutability and accommodating under strategic complementarity,1 unless it tries to foreclose entry. Since competition in quantities is associated with strategic substitutability and competition in prices with strategic complementarity, Tirole’s taxonomy of business strategies based on this distinction became a classic result of the modern industrial organization and aﬀected most of its subsequent evolution. The natural consequence for markets where firms compete in prices is indeed a simple one: incumbents adopting aggressive pricing strategies or equivalent strategies must have a predatory intent, otherwise they would adopt accommodating strategies. Since then, most of the antitrust analysis of exclusionary practices was based on related arguments. This book develops a general characterization of the strategic interactions between firms taking into account alternative entry conditions. The traditional analysis of incumbents and entrants that I sketched above has a main problem: it largely neglects the role of the endogenous entry of competitors in constraining the behavior of the incumbents. Entry in a market is endogenous when in equilibrium there are no profitable opportunities to 1

The strategic variables of two firms interacting in a market are defined strategic substitutes when an increase in the variable chosen by one firm induces the other firm to adjust its own strategic variable in the opposite direction. They are strategic complements when an increase in the strategy of one firm induces the other one to adjust its own strategy in the same direction. The terminology is due to Bulow et al. (1985).

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be exploited by potential entrants. A simple situation in which this occurs is when entry is simply free. A more general situation emerges when firms or entrepreneurs are active in diﬀerent markets and the rate of profit must be equalized across these markets. Another and more realistic situation in which entry can be regarded as endogenous is when there are large fixed costs of entry or limited sunk costs (traditionally considered barriers to entry) that constrain endogenously the entry decision of the firms. Overall, we do believe that endogenous entry should be regarded as the standard situation in most markets, while exogenous entry only emerges in extreme situations where entry is not a decision taken by the firms, but it is determined by other institutional or regulatory authorities. When entry is endogenous market leaders are always aggressive under both strategic substitutability and complementarity, under both competition in quantities and in prices, and even under other forms of competition. This has radical implications for the pricing strategies, for the choice of strategic investments in cost reductions, quality improvements and advertising, for the choice of the financial structure, for the decisions to bundle goods or price discriminate, for the production decisions in the presence of network externalities, two-sided markets and learning by doing, for the adoption of vertical restraints, for the decision to merger or collude with a rival, and for many other important issues in industrial organization. Evidently, the endogenous entry approach has crucial consequences on concrete antitrust policy for the analysis of the behavior of market leaders and also for merger and collusion issues. When entry is endogenous, incumbents are always aggressive, typically without exclusionary purposes, and their strategies hardly harm consumers; mergers in markets where entry is endogenous take place if and only if they create enough cost eﬃciencies; and cartels between a limited number of firms facing endogenous entry are ineffective. The flavor of these results goes back to the Chicago view, but our game theoretic analysis is derived from the standard post-Chicago approach, which is augmented with endogenous entry. The literature on industrial organization is quite fragmented because separate analysis is usually undertaken for models of competition in quantities, models of competition in prices and models of competition for the market. A possible advantage of the approach I adopt in this book is the provision of a unified framework for the analysis of market structures. This framework encompasses most models of competition in quantities, prices and models of competition for the market, and can be used to analyze and compare diﬀerent market structures in a simpler manner. The book contains a large amount of unpublished material, especially in the theoretical analysis of Chapters 2 to 4. The applied analysis in Chapters 5 to 7 is based on policy oriented work, some of which was realized as the chief economist of the Task Force on Competition established by the International Chamber of Commerce of Paris in 2006.

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In Chapter 1, I introduce the basic theoretical tools of industrial organization and describe the simplest examples of competition and innovation. The starting point is a market in which a firm decides how much to produce on the basis of demand and cost conditions. In such a context, I describe the behavior of a monopolist and compare it with the behavior of two firms in a Cournot duopoly; on this basis I introduce the discussion of the fundamental subjects of antitrust analysis as mergers, foreclosure and collusion. Then, I employ the same model to describe competition between multiple firms within the four main market structures analyzed in this book. In the first (Nash competition), firms take decisions independently and their number is exogenous. In the second (Marshall competition), the number of firms is endogenized assuming that firms enter in the market if and only if they expect positive profits. In the third (Stackelberg competition), there is again an exogenous number of firms but one of them, the leader, takes its decision before the others. In the fourth (Stackelberg competition with endogenous entry), there is still a leader with a first mover advantage, but the number of firms is endogenous and again derived assuming that firms enter in the market if and only if they expect positive profits. The same analysis can be extended to a model where firms sell diﬀerentiated products and choose their prices. I analyze such a model adopting the simplest demand and cost conditions, and characterizing the same four diﬀerent forms of competition as before: with price competition, however, I show that the behavior of the leader is radically diﬀerent according to whether entry is endogenous or not. Finally, I provide a simple example of competition for the market where firms invest to increase their relative chances to innovate, I analyze the four diﬀerent equilibria, and apply the result to discuss the incentives of an incumbent monopolist to invest in R&D. In Chapter 2, I present a general model of competition and I show that most models used in industrial organization are nested in this general model. Applications include virtually all symmetric models of competition in quantities with homogenous and diﬀerentiated goods, models of price competition with Logit or isoelastic demand, and standard contests or patent races. I discuss in some detail how to characterize the Nash equilibrium and the Marshall equilibrium for the general model and for its main applications. Then, I extend these equilibria with a firm, the leader, which undertakes a preliminary investment aﬀecting competition ex post, as in the literature on strategic investments started with the contributions of Avinash Dixit and others. This general approach allows one to verify what the strategic incentives of the leader are to engage in a number of commitments or investments and to be aggressive or accommodating in the market.2 I perform this analysis in the presence of an exogenous number of competitors and of an endogenous number, and derive the general principle for which market leaders facing en2

A more aggressive strategy reduces the profits of the other firms, a more accommodating strategy increases them.

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dogenous entry always take those strategic decisions that induce them to be aggressive in the market. Then, I apply these results to specific decisions of a leader: 1) investments in cost reductions; 2) persuasive advertising (and other demand enhancing investments); 3) decisions on the financial structure and the optimal equity-debt ratio; 4) preliminary production levels in the presence of network externalities and two-sided markets; 5) bundling of goods; 6) price discrimination; 7) delegation of pricing decisions to downstream distributors for interbrand competition; and 8) horizontal mergers. In Chapter 3, I generalize the analysis of the forms of competition in which a leader has a first mover advantage and followers decide their strategies independently in a subsequent stage. I characterize the Stackelberg equilibrium and the Stackelberg equilibrium with endogenous entry within the general framework and for alternative forms of competition in quantities and in prices. In particular, I derive the general principle for which market leaders facing endogenous entry are always aggressive under both strategic complementarity and strategic substitutability: they produce more than the rivals when competing in quantities and they set lower prices when competing in prices. I also derive the conditions under which a market leader is so aggressive to adopt an entry-deterring strategy. This happens under constant or decreasing marginal costs of production and homogenous goods, independently from the size of the fixed costs of production and of the shape of the demand function, and it provides a game theoretic foundation for some of the insights of the limit-pricing framework associated with Joe Bain, Paolo Sylos Labini and Franco Modigliani and of the contestability approach associated with William Baumol, John Panzar and Robert Willig. The latter approach could be re-interpreted in terms of Stackelberg competition in prices with endogenous entry and homogenous goods, but our framework allows us to extend its spirit to the more general case of product diﬀerentiation. In such a case (as when marginal costs are increasing), market leaders prefer to allow entry while still adopting aggressive strategies under both quantity and price competition. Finally, I show that, when entry is endogenous, the allocation of resources is improved by the presence of the leader. The spirit of these results extends to the more complex cases with asymmetries between firms, multiple leaders or endogenous leadership, and to the case of multiple strategic variables. In conclusion, I illustrate how one can apply these results to diﬀerent policy questions: 1) I reconsider the role of a collusive cartel in the presence of endogenous entry, and argue that this is ineﬀective unless it has a leadership role (in which case the cartel coordinates aggressive strategies between its members); 2) I review the problem of the optimal state aids and trade policy for firms exporting in a foreign country, and I show that the traditional results break down when the domestic firms are engaged in competition in a market where entry is endogenous (in such a realistic case, state aids inducing aggressive export strategies, and in particular export subsidies,

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are always optimal); and 3) I analyze the role of privatizations and liberalizations in markets for private goods. In Chapter 4, I exploit the results of the previous chapters and apply them specifically to models of competition for the market. My starting point is a simple model in which all firms choose an initial investment that delivers drastic innovations according to a stochastic process. Analyzing the usual four forms of competition, I show the general principle for which incumbent monopolists that are leaders and face endogenous entry in the competition for the market, invest in R&D more than any other firm. This outcome overturns a standard result of the theory of innovation, due to Kenneth Arrow, for which incumbent monopolists would have lower incentives to invest in R&D and replace their own technological leadership. The same result on innovation by leaders is confirmed in a more realistic version of the model in which firms invest over time, when innovations are non drastic, and especially when they are sequential. The investment of the technological leaders in the presence of sequential innovations leads automatically to an explanation for the persistence of monopolistic positions, which is associated (somewhat paradoxically) with free entry in the competition for the market. On this basis, I develop a theory of technological progress driven by market leaders which is closely related to the original ideas of Joseph Schumpeter on the role of monopolies in enhancing growth - ideas that are hardly consistent with the recent literature on endogenous technological progress, in which leaders do not invest in R&D because of the Arrow eﬀect. Finally, I discuss the relationship between competition in the market on one side and competition for the market on the other side. In Chapter 5, I apply my theoretical analysis to antitrust policy, particularly to issues concerning abuse of dominance. First, I review the traditional approaches to antitrust policy and emphasize the strengths and the limits of the Chicago school and of the post-Chicago approach. Subsequently, I provide a first attempt to derive policy implications from the theoretical analysis on the behavior of market leaders in the presence of exogenous entry and endogenous entry. I emphasize that any inference on the market power of a leader from its market share can be highly misleading. Moreover, when entry of firms is endogenous, one should be extremely careful in associating aggressive pricing strategies by market leaders (or related strategies as bundling) with exclusionary purposes. I also note that when firms compete to obtain sequential innovations protected by intellectual property rights (IPRs), persistence of technological leadership can derive from endogenous entry in the competition for the market rather than market power in the competition in the market. Therefore, antitrust policy should be careful in evaluating dominant positions in dynamic high-tech sectors, and should avoid interfering with the protection of IPRs which is the source of investments in R&D and technological progress. In conclusion, I apply these ideas to current antitrust policy with particular reference to the eﬃciency defense for dominant firms,

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to the determination or predatory pricing, to bundling as an exclusionary strategy, and to issues of IPRs protection. In Chapter 6, I apply my theoretical analysis to the markets of the New Economy, in particular to the software sector, which is characterized by a number of peculiar features analyzed in the book as network externalities, two-sided markets, high investments in R&D and a pre-eminent role of the leader in both the competition in the market and for the market. This leader has been also the subject of antitrust investigations in US and EU, therefore I analyze these famous antitrust cases from an economic point of view, and try to focus on its main aspects: 1) whether Microsoft is a monopolist; 2) whether its bundling strategies are predatory and harm consumers; and 3) whether antitrust authorities should force the disclosure of its IPRs to promote competition in the software market. I can briefly summarize the results of my investigation as follows: 1) evidence from the competition in and for software markets witnesses the lack of monopolistic power by Microsoft and better defines its role as that of a Stackelberg leader in a market with endogenous entry; 2) bundling strategies by Microsoft appear as natural aggressive, or pro-competitive, strategies which may harm competitors but create benefits to all consumers; and 3) forced disclosure of the IPRs of Microsoft for interoperability purposes may severely jeopardize investment in R&D rather than promoting it, with negative consequences for the consumers in the long run. In Chapter 7, I conclude this book by suggesting ways to investigate the empirical predictions of the theory of market leaders concerning the pricing policy of the leaders, and their decisions on quality, advertising, distribution, financing and R&D investments as functions of the entry conditions. I also re-interpret my results on the behavior of market leaders from the point of view of business administration recommendations for marketing and strategy. Finally, I suggest avenues for future theoretical research on market leadership and on endogenous entry. My initial interest in the role of market leaders and endogenous entry, especially in the market for innovations, was inspired by discussions with Michele Boldrin at U.C.L.A. While our later research eﬀorts have taken radically diﬀerent directions, I am grateful to him for inspiring motivations. At U.C.L.A., between 1998 and 2000, I also benefited from interaction with Harold Demsetz, Jack Hirshleifer, David Levine, John Riley, Bill Zame and, most of all, with Karina Firme whose wisdom and intelligence has enlightened many of my thoughts on these issues (and others as well). I presented a prototype model on the behavior of leaders in markets with endogenous entry for the first time in a seminar at M.I.T. in November 2000. In that occasion, comments by Robert Barro and Daron Acemoglu shaped a lot of my subsequent theoretical investigations. I developed the first ideas of this book at N.B.E.R. and Harvard University: the rigorous logic and the depth of the suggestions of Robert Barro have been crucial for my understanding of

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many topics, and my way of thinking about economic issues is largely shaped around his free market ideals. At the time, I also benefited from interesting discussions with Philippe Aghion, Oliver Hart, David Laibson, Gregory Mankiw, Ricardo Reis, Silvana Tenreyro and Joseph Zeira. Since then, I have presented parts of this book at diﬀerent conferences, seminars and lectures in many places around the world, including U.C.L.A., Harvard University, University of Milan, Bicocca, CERGE and Charles University (Prague), European University Institute (Florence), University of Vienna, University of Virginia (Charlottesville), the Finnish Competition Authority and ETLA (Helsinki), the Roundtable on The Lisbon Agenda and the future of Information Technology IPRs (Brussels), the Telecom Conference on the Economics of the Information and Communication Technology (Paris), the Conference on Competition and Regulation of the Athens University of Economics and Business (Corfù), the DIW Roundtable on Competition and IPRs (Berlin), the Conference on EU and Greek Competition Policy (Athens) and others. I am grateful to many participants for important comments, and especially to Jacques Bourgeois, Guglielmo Cancelli, David de Meza, Vincenzo Denicolò, David Encoua, Maxim Engers, David Evans, Leonardo Felli, Hans Jarle Kind, Joseph Harrington, Massimo Motta, Meir Pugatch, Jennifer Reinganum, Patrick Rey, David Ulph and Martti Virtanen. Between 2002 and 2003, while I was economist for the Ministry of Economy of my country and teaching at Luiss University (Rome), I also benefited from interesting conversations with Riccardo Faini and Domenico Siniscalco on related policy issues. A large part of the antitrust implications of my theories is derived from my professional experience as a consultant on antitrust issues for international organizations and private companies. I am thankful to many brilliant people from these organizations and companies with whom I have collaborated since 2004, especially for providing a unique opportunity to apply, discuss and test many of the ideas presented in this book. However, the responsibility for what follows is only mine and should not involve any of the institutions I have been and am aﬃliated with. Since 2004, I have contributed to organize INTERTIC, the International Think-tank on Innovation and Competition (website www.intertic.org), and ˇ c: I am extremely grateful to its co-founder and vice-president, Krešimir Zigi´ interacting with him has been fundamental for many of the ideas presented in this book. Simon Anderson, also vice-president of Intertic, has been a continuous source of inspiration during the last years: I am extremely grateful for many of his precious comments. Similarly, I need to thank all the other members of Intertic, and especially Avinash Dixit, Yannis Katsoulacos, Vincenzo Denicolò, Barbara Spencer, Stephen Martin and Dennis Mueller for their valuable comments. The 2007 Intertic Conference, held at the University of Milan, Bicocca (“International Conference on Innovation and Competition in the New Economy”, May 4-5, 2007) put together some of the best

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international economists working on issues of competition, innovation and industrial policy and has been a source of deep inspiration; I am thankful to all the participants, and especially to the members of Intertic and to Kris Aerts, Rabah Amir, Carlo Cambini, Guido Cozzi, Raymond De Bondt, Giovanni Dosi, Nisvan Erkal, Katerina Goldfain, Heli Koski, Kornelius Kraft, Eugen Kováˇc, Daniel Piccinin, Jan Vandekerckhove and Viatcheslav Vinogradov for stimulating debate. I completed this book at the University of Milan, Bicocca, one of the most modern and advanced challenges of graduate and postgraduate education in Italy. At its Department of Economics I found the ideal environment to write these pages. I am very grateful to all of my colleagues, especially Luigino Bruni, Floriana Cerniglia, Emilio Colombo, Mario Gilli, Giovanna Iannantuoni, Jean Jacques Lambin, Silvia Marchesi, Graziella Marzi, Mariapia Mendola, Ahmad Naimzada, Piergiovanna Natale, Pier Luigi Porta, Luca Stanca and Patrizio Tirelli, for many comments and suggestions on preliminary versions of the book. A special thanks to Flavia Ambrosanio, Massimo Bordignon, Umberto Galmarini and Piero Giarda from the Catholic University of Milan, who directed me toward the study of economic issues more than ten years ago, and helped me with generosity and precious suggestions since then. I would also like to thank the Editor of Springer, Niels Peter Thomas, who has been extremely kind in supporting this project from the beginning and improving it in many ways, and Irene Barrios-Kezic for outstanding editorial assistance. Finally, I am extremely grateful to Indira Pottebaum who read the manuscript many times and gave me a lot of precious comments. While preparing this book, I was teaching industrial organization and competition policy to advanced undergraduates and I am thankful to my students at the University of Milan, Bicocca, for many questions and comments on Chapter 1. This chapter is extremely simplified and can be used for a short undergraduate course on oligopoly theory; an updated version for teaching purposes can be found at www.intertic.org (where other material related to this book can be found as well). Also Chapters 5, 6 and 7, which are entirely verbal, should be accessible to anyone who has no formal background in economic theory, but is interested in antitrust issues and in the evolution of the New Economy, the software market and the Microsoft case. Chapters 2, 3 and 4, however, are more advanced at a technical level and could be used for a postgraduate course on industrial organization or on the theory of innovation. Finally, I tried to write each chapter as a self contained treatment of a particular topic, therefore the reader may also look at a chapter of his or her interest without having to read the previous parts. My approach to industrial organization issues is largely aﬀected by studies in other fields as macroeconomics, international economics and business administration, and it probably reflects the fact that I have never taken a course in industrial organization. Also for these reasons, this book should be

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seen as a complement of other graduate textbooks in the field, and not as a substitute. Tirole (1988) is the “first-mover” and still the leader in the market for game theoretic textbooks in industrial organization, but of course it does not include two decades of literature (especially on the theory of innovation and on the evolution of the post-Chicago approach to antitrust). Many other good and diversified textbooks have appeared (or endogenously entered) in this market in the following years. Shy (1995) oﬀers a wide review of basic models at an advanced undergraduate level. Anderson et al. (1992) and Vives (1999) provide more sophisticated analysis respectively of the models with product diﬀerentiation and of the leading models of oligopolistic interaction, but they largely ignore the role of market leaders in their frameworks. Martin (2002) provides an excellent guide to many theoretical and empirical issues, but (as the other cited books) it contains a limited treatment of many aspects that are relevant to the markets of the New Economy, as network externalities, multi-sided markets, Schumpeterian theories of innovation and the related antitrust issues. Scotchmer (2004) provides a nice overview of the theory of innovation, but her analysis does not include the most recent progress in the theory of innovation by leaders and of its consequences for endogenous technological progress and for R&D policy. Motta (2004) is a useful survey of the theoretical and applied literature on antitrust policy before the advent of the endogenous entry approach and of the related policy implications. Finally, the classic books by Bork (1993) and Posner (2001) on the major achievements of the Chicago school could be also used in parallel to our treatment, which is largely aimed at formalizing some of the informal results of the Chicago view on antitrust policy. A last word on the cover of this book, for which I have chosen a painting by the Dutch artist Jan Vermeer, The Astronomer, now visible at the Louvre Museum in Paris. This masterpiece, painted in 1668, depicts a researcher engrossed in scientific investigation, and directing his attention toward a celestial globe,3 metaphor of the sphere of knowledge at a time when a radical change of paradigm was taking place in science. The Astronomer seems to be pondering about the mysteries of the universe, and is working indoors without looking through the window at the heavens, but the penetrating light coming from the window is enlightening him, the globe, the astrolabe and the focus of his work. Doing scientific research is a bit like touching a piece of the sphere of knowledge; the rest, as always, is left for future research. I hope you will have as much fun reading this book as I did in writing it. Federico Etro Department of Economics, University of Milan, Bicocca Milan, July 2007

3

See James A. Welu, 1975, “Vermeer: His Cartographic Sources”, The Art Bulletin, Vol. 57 (4), pp. 529-47.

Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii 1.

Competition, Leadership and Entry . . . . . . . . . . . . . . . . . . . . . . . 1.1 A Simple Model of Competition in Quantities . . . . . . . . . . . . . . 1.1.1 Monopoly and Antitrust Issues . . . . . . . . . . . . . . . . . . . . . 1.1.2 Nash Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.3 Marshall Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.4 Stackelberg Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.5 Stackelberg Equilibrium with Endogenous Entry . . . . . 1.2 Increasing Marginal Costs and Product Diﬀerentiation . . . . . . 1.2.1 U-shaped Cost Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 Product Diﬀerentiation . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 A Simple Model of Competition in Prices . . . . . . . . . . . . . . . . . . 1.4 A Simple Model of Competition for the Market . . . . . . . . . . . . 1.4.1 The Arrow’s Paradox . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.2 Innovation by Leaders . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 4 5 8 9 10 12 15 16 18 20 25 27 31 34 36

2.

Strategic Commitments and Endogenous Entry . . . . . . . . . . . 2.1 Market Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Nash Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Marshall Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Competition in Quantities, in Prices and for the Market . . . . . 2.4.1 Competition in Quantities . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Competition in Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.3 Competition for the Market . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Strategic Investments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1 The Fudenberg-Tirole Taxonomy of Business Strategies 2.5.2 Strategic Commitments with Endogenous Entry . . . . . . 2.6 Cost Reductions and Signaling . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Advertising and Demand Enhancing Investments . . . . . . . . . . . 2.8 Debt and the Optimal Financial Structure . . . . . . . . . . . . . . . . . 2.9 Network Externalities and Two-Sided Markets . . . . . . . . . . . . .

41 44 48 49 50 50 54 58 59 61 63 66 70 72 76

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2.10 2.11 2.12 2.13 2.14

Bundling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vertical Restraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Price Discrimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Antitrust and Horizontal Mergers . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

79 82 84 87 89

3.

Stackelberg Competition and Endogenous Entry . . . . . . . . . . 3.1 Stackelberg Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Stackelberg Equilibrium with Endogenous Entry . . . . . . . . . . . . 3.3 Competition in Quantities, in Prices and for the Market . . . . . 3.3.1 Competition in Quantities . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Competition in Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3 Competition for the Market . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Asymmetries, Multiple Leaders and Multiple Strategies . . . . . 3.4.1 Asymmetries Between Leader and Followers . . . . . . . . . 3.4.2 Multiple Leaders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.3 Endogenous Leadership . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.4 Multiple Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.5 General Profit Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Antitrust and Collusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 State-Aids and Strategic Export Promotion . . . . . . . . . . . . . . . . 3.7 Privatizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91 94 97 100 100 106 108 109 109 110 113 114 116 118 120 123 124 125

4.

Dynamic Competition and Endogenous Entry . . . . . . . . . . . . 4.1 A Simple Patent Race with Contractual Costs of R&D . . . . . . 4.1.1 Endogenous Entry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Welfare Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Dynamic Competition for the Market . . . . . . . . . . . . . . . . . . . . . 4.2.1 Nash Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Marshall Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Stackelberg Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4 Stackelberg Equilibrium with Endogenous Entry . . . . . 4.2.5 Non-drastic Innovations . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.6 Strategic Commitments . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Sequential Innovations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Endogenous Value of Innovations . . . . . . . . . . . . . . . . . . . 4.3.2 Endogenous Technological Progress . . . . . . . . . . . . . . . . . 4.4 Competition in the Market and Competition for the Market . 4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

131 135 138 141 142 143 144 144 146 148 150 151 152 155 159 162 165

Contents

xix

5.

Antitrust and Abuse of Dominance . . . . . . . . . . . . . . . . . . . . . . . 5.1 The Traditional Approaches to Abuse of Dominance . . . . . . . . 5.1.1 The Chicago School . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.2 The Post-Chicago Approach . . . . . . . . . . . . . . . . . . . . . . . 5.2 The Theory of Market Leaders and Endogenous Entry . . . . . . 5.2.1 Competition in the Market and Policy Implications . . . 5.2.2 Competition for the Market and Policy Implications . . 5.3 A Digression on IPRs Protection . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Patents in Dynamic Sectors and Innovations . . . . . . . . . 5.3.2 Open-Source Innovations . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.3 Conclusions on IPRs Protection . . . . . . . . . . . . . . . . . . . . 5.4 Reforming Antitrust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.1 Eﬃciency Defense . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 Predatory Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.3 Bundling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.4 Intellectual Property Rights . . . . . . . . . . . . . . . . . . . . . . . 5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

171 174 174 176 178 179 186 189 190 191 194 195 196 197 201 203 204

6.

Microsoft Economics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 The Software Market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.1 Network Eﬀects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.2 Multi-sided Platforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.3 Microsoft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 The Antitrust Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 The US Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 The EU Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Is Microsoft a Monopolist? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Why Is the Price of Windows so Low? . . . . . . . . . . . . . . 6.3.2 Does Microsoft Stifle Innovation? . . . . . . . . . . . . . . . . . . . 6.4 Bundling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.1 Strategic Bundling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.2 Technological Bundling . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Intellectual Property Rights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.1 Patents, Trade Secrets and Interoperability . . . . . . . . . . 6.5.2 Licenses and Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

207 208 210 212 215 218 218 221 223 225 228 230 232 234 235 236 238 240

7.

Epilogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Empirical Predictions of the Theory of Market Leaders . . . . . . 7.2 Implications for Business Administration . . . . . . . . . . . . . . . . . . 7.3 Implications for Economic Theory . . . . . . . . . . . . . . . . . . . . . . . . 7.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

243 243 252 252 255

8.

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257

xx

Contents

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275

2. Strategic Commitments and Endogenous Entry

In this chapter we will study a general model of market structure and characterize the incentives of a firm to adopt diﬀerent strategic commitments to gain a competitive advantage over the rivals. We will develop a unified general framework in which standard models of competition in the market and for the market are nested, including those analyzed in Chapter 1 and others analyzed and extended in Chapters 3 and 4. Virtually all models of competition in quantities with homogenous or imperfectly substitute goods and with general shapes of the cost function are nested in our general model. Also encompassed are a wide class of models of competition in prices (as long as the demand function satisfies some regularity conditions), including models with a constant expenditure demand function or isoelastic demand functions (derived from quasilinear utilities or homotethic utilities à la Dixit and Stiglitz), and a wide class of models of competition for the market, whose detailed analysis will be postponed to Chapter 4. The initial focus of this chapter will be on Nash equilibria and on Marshall equilibria, that is on market structures characterized by symmetry between an exogenous number of firms in the former case and an endogenous number of firms in the latter case. Nash competition can be interpreted as a form of competition with an exogenously limited number of firms, whose equilibrium can be seen as a short term equilibrium of a given market or even as a general equilibrium for a market where entry is exogenously constrained (for instance by legal or regulatory barriers to entry). A symmetric Nash equilibrium can be easily characterized through a single equilibrium profit maximizing condition that takes into account symmetry between the firms, for instance a mark up rule for the Cournot model of competition in quantities or for the Bertrand model of competition in prices. Such a characterization allows one to study the comparative statics of the equilibrium variables and hence it is at the basis of the analysis of the interaction between exogenous variables (as costs, taxes, demand parameters, or even the number of firms in the market) and endogenous variables (output, prices, profits). Marshallian competition can be interpreted in terms of a medium or long run equilibrium in which there are not exogenous barriers to entry. In such a context entry is endogenously determined by the presence of profitable opportunities to be exploited. When these opportunities are exhausted, the entry

42

2. Strategic Commitments and Endogenous Entry

process stops. In the Marshall equilibrium, the strategies of the firms and the number of firms are jointly determined by a profit maximizing condition and by an endogenous entry condition (typically a zero profit condition or a no arbitrage condition between entry in diﬀerent sectors), both taking into account symmetry between firms. Also in such a case, we can easily verify the impact of changes in demand and supply conditions and other exogenous policy parameters on the equilibrium variables, namely output, prices and the number of firms. Building on this general framework and on this standard characterization of equilibria, we will introduce the analysis of market leaders verifying their incentives to adopt alternative strategic investments that can create a competitive advantage in the subsequent competition with the other firms.1 As we will see, the behavior of the leaders changes when they face an exogenous number of competitors or an endogenous number. The first case has been characterized at least since the work of Fudenberg and Tirole (1984) and Bulow et al. (1985) on duopolies. Suppose that firm i has the gross profits Π(xi , X−i , k), which depend on its strategy xi , the aggregate statistics X−i summarizing the strategies of the other firms, and the preliminary investment k. Then, the strategic incentives to invest for this firm depend on the impact of the investment on the marginal profitability (Π13 ),2 and on the nature of the strategic interaction between firms (Π12 ). Therefore, they are typically diﬀerent in models of competition in quantities, where output choices are often strategic substitutes (Π12 < 0), and in models of competition in prices, where strategic complementarity usually holds (Π12 > 0). On this basis, Tirole (1988) has built a taxonomy of business strategies that implies four diﬀerent strategies for the leader: a firm may overinvest or underinvest initially to be more accommodating or aggressive subsequently. As shown in Etro (2006, a), things simplify drastically when entry of firms is endogenous, because in such a case the strategic incentives to invest are independent from the strategic interaction between firms: the optimal investment of a firm depends only on whether the investment increases or not the marginal profitability, which leads to results that do not dependent on whether prices or quantities are the strategic variables. More precisely, when entry is endogenous, a firm invests always in the direction that leads to an aggressive behavior in the market. Of course, our interest in this outcome relies on the belief that in most situations entry in the markets is indeed endogenous, and the proper way to analyze the behavior of firms should take this element into account. The abstract and general rules we just pointed out have a lot of applications to industrial organization and related fields, and this chapter will analyze a few of them. Fundamental strategic investments are those aﬀect1

2

See Singh et al. (1998) on the empirical relevance of strategic investments by leaders. Subscripts denote derivatives with respect to the arguments.

2. Strategic Commitments and Endogenous Entry

43

ing supply, as cost reducing investments or overproduction in the presence of learning by doing, and those aﬀecting demand, as investments in quality improvements, in advertising, in product diﬀerentiation. We will show that when entry in the market is endogenous, a market leader has always a strategic incentive to overinvest in the first typology of investments because this leads to aggressive behavior, while the role of demand enhancing investments is more complex. Another application concerns the theory of corporate finance: starting from the literature on the relation between the optimal financial structure and product market competition (Brander and Lewis, 1986) we will examine the incentives to adopt strategic debt financing for markets with free entry. It turns out that under quantity competition there is always a strategic bias toward debt financing, while under price competition there is only when uncertainty aﬀects costs, but not when it aﬀects demand. In general, departing from the standard Modigliani-Miller neutrality result, a financial tool like debt is useful when it constrains equity holders to adopt more aggressive strategies in the market, and this is the case when positive shocks increase marginal profits. Other new applications developed in detail here concern discrete commitments. We will examine the case of bundling strategies. In an influential paper, Whinston (1990) has studied bundling in a market for two goods. The primary good is monopolized by one firm, which competes with a single rival in the market for the secondary good. Under price competition in the secondary market, the monopolist becomes more aggressive in its price choice in the case of bundling of its two goods. Since a more aggressive strategy leads to lower prices for both firms as long as both are producing, the only reason why the monopolist may want to bundle its two goods is to deter entry of the rival in the secondary market. This conclusion can be highly misleading because it neglects the possibility of further entry in the market. We show that, if the secondary market is characterized by endogenous entry, the monopolist would always like to be aggressive in this market and bundling may be the right way to commit to an aggressive strategy: bundling would not necessarily exclude entry, but may increase competition in the secondary market and reduce prices. Many other implications are relevant for antitrust policy. For instance, we will consider the theory of vertical restraints for interbrand competition (Rey and Stiglitz, 1988; Bonanno and Vickers, 1988), and show that a market leader facing endogenous entry would want to delegate distribution to a downstream retailer through wholesale prices below marginal cost: in such a case we have an example of a pro-competitive vertical restraint. Other results that are relevant for antitrust purposes concern the incentives to adopt limited interoperability, third degree price discrimination, and aggressive pricing in the presence of network externalities or multi-sided markets. Finally, we will apply our result to horizontal mergers and show that

44

2. Strategic Commitments and Endogenous Entry

they create a strategic disadvantage for firms facing endogenous entry: therefore, in markets where entry is endogenous, mergers can only emerge when they create large eﬃciency gains, a point which is largely in line with the informal results of the Chicago school. The chapter is organized as follows. Sections 2.1 describes our general framework and Sections 2.2-2.3 characterize the Nash equilibrium and the Marshall equilibrium. Section 2.4 clarifies which models of competition in quantities, in prices and for the market are nested in the general framework, and derives some properties of these models. Section 2.5 analyzes general strategic investments in Nash and Marshall equilibria. Section 2.6-2.13 apply the results to a number of industrial organization issues. Section 2.14 concludes.

2.1 Market Structure A market structure is characterized by a number of firms, their strategies, a relationship that links all the strategies with the profit of each firm and an equilibrium concept, which requires consistency between all the optimal strategies. In general, firms can choose many diﬀerent strategies, for instance they can choose the price of their products, their quality, the investment in advertising and so on, and they can also choose these and other strategies for diﬀerent products or diﬀerent periods. However, in this chapter we will refer to the case of a single strategy. Imagine that in the market there are n firms and that the vector of their strategies is x = [x1 , x2 , ..., xn ] where xi is the strategy of firm i. We may think that diﬀerent firms have diﬀerent features and diﬀerent technological options, and there can be diﬀerent profit functions, say πi (x) for each firm i. A market structure is a set of strategies x for n firms with profit functions π i (x), such that xi = arg max π i (x) for each i. A large portion of this book will deal with models of competition in the market where firms choose their output or their prices to maximize revenues net of the production cost c(·), which is increasing in the level of production, and net of a fixed cost F ≥ 0. In particular, we will deal with models of quantity competition, as those studied in Chapter 1, where the strategy qi represents the level of production of firm i, and profits are given by: πi (q1 , .., qi , .., qn ) = qi pi (q1 , q2 , .., qn ) − c(qi ) − F where pi (·) is the inverse demand, decreasing in the output of every firm. Interesting applications that will be described in detail include models with linear demand, as those adopted in Sections 1.1-2, models with isoelastic demands and homogenous goods, and models with imperfectly substitutable goods.

2.1 Market Structure

45

Another wide class of models is based on price competition and imperfect substitution between goods, where the strategy pi represents the price of firm i and profits are given by: πi (p1 , .., pi , .., pn ) = pi Di (p1 , .., pi , .., pn ) − c [Di (p1 , .., pi , .., pn )] − F with a direct demand function Di (p1, .., pi , .., pn ) that decreases in the price of firm i and increases in the price of the other firms. Applications that will be investigated later on include models with the Logit demand (as those studied in the example of Section 1.3), models with isoelastic demand functions, constant expenditure demand functions and others. We will also study forms of competition for the market in which firms choose a strategy zi that allows to conquer a market whose value is V with a probability that depends also on the choices of the other firms, Pri (z1 , .., zi , .., zn ). In such a case, expected profits are: E [πi (z1 , .., zi , .., zn )] = Pr i (z1 , .., zi , .., zn )V − c (z1 , .., zi , .., zn ) − F where the cost function c(·) can depend on the investment of each firm. Examples include the simple contest we studied in Section 1.4, more complicated patent races where firms invest over time and innovate according to complex stochastic processes, and also models of rent seeking where the probability that an agent obtains a generic rent is the ratio between the agent’s investment and total investment by all other agents. These market structures are general enough to include most of the realistic competitive frameworks analyzed in the theory of oligopoly. However, since a main topic of this book is the eﬀect of entry on the strategic interaction between firms that have the same production technologies available and that face the same demand structure, we need to impose some further restrictions on the functional forms to be used. In particular, in the main analysis we will focus on models in which all firms have the same cost technology and there are not exogenous diﬀerences or asymmetries between them. Accordingly, we will not deal with spatial models of horizontal or vertical diﬀerentiation like the Hotelling (1929) duopoly with spatial diﬀerentiation.3 3

Imagine two firms choosing their prices p1 and p2 with the profit functions πi (pi , pj ) = pi D(pi , pj ) where demands are: D(p1 , p2 ) =

(p2 − p1 ) (k1 + k2 ) + , 2 2(k2 − k1 )

D(p2 , p1 ) =

(p2 − p1 ) (2 − k1 + k2 ) − 2 2(k2 − k1 )

Such an apparently complicated structure can be derived from a very simple situation. Imagine that consumers of a single unit of product are uniformly distributed along a market of unitary length, that is on [0, 1]. On this market two firms are located at distances k1 and k2 > k1 from the origin, produce homogenous goods at no cost and sell them at prices p1 and p2 . Each consumer at distance d from the origin will buy the good that minimizes the price plus a cost

46

2. Strategic Commitments and Endogenous Entry

Clearly in such a model, the equilibrium prices and profits depend on the initial locations of the two firms/products.4 In other words, profit functions and equilibrium outcomes depend on exogenous and firm specific parameters which introduce a substantial asymmetry between the firms. Moreover, if we were going to evaluate the entry opportunities in such a market, the result would be completely dependent on the location of the new entrants compared to the location of the incumbents.5 The reason is that every new firm would compete just with its two closest rivals (for the consumers between them) and therefore each firm would have a diﬀerent profit function depending on its particular competitors and their features.6 Such a situation can depict markets where geographical location or, in a metaphorical sense, horizontal diﬀerentiation are a crucial element. However, it badly characterizes many other markets where each firm has to compete with all the other firms at once since all products in the market are potentially substitutes (which, in the applied analysis, is what defines a market). For this reason, our focus in this book, in line with the tradition associated with Chamberlin (1933), will be on models that allow for competition between symmetric firms. Finally, since we are interested in characterizing endogenous entry of firms, we will limit our attention to markets where equilibrium profits decrease when entry occurs, a realistic feature that is not always verified in standard models.7

4

5

6

7

which is quadratic in the distance from the location of the corresponding firm, that is good i such that pi + (ki − d)2 is smallest. This framework allows division of consumers between those buying good 1 and those buying good 2, delivering the demands above. Indeed, maximizing the two profit functions with respect to the prices and solving for them, one can find the equilibrium with p1 = (2 + k1 + k2 )(k2 − k1 )/3 and p2 = (4 − k1 − k2 )(k2 − k1 )/3. Clearly one could endogenize the location decision (for instance, with two firms, they would choose maximum diﬀerentiation, placing themselves at the borders of the market with k1 = 0 and k2 = 1). See the fundamental contribution of D’Aspremont et al. (1979) for a formal and general treatment, and Anderson et al. (1992) for further discussion. We could easily extend the model to n firms symmetrically distributed along a circle where consmers are also distributed uniformly and choose between products as before (Vickrey, 1964). The Nash equilibrium would generate the price √ Marshall equilibrium would imply n = 1/ 3 F p = 1/n2 for each firm, and the √ 3 firms selling at the price p = F 2 . For instance, we will exclude from our main analysis the basic model of price competition with linear demand (associated with Bowley, 1924) as Di = a − pi + b j6=i pj . In the Nash-Bertrand equilibrium, this model implies that the profits of each firm increase in the number of firms. Something that makes no sense in real markets. See Section 3.4.5 on this point.

2.1 Market Structure

47

More formally, in this book we will focus on a class of market structures with profit functions that are symmetric, additively separable and decreasing in the strategies of the other firms. For consistency, we will drop separate notations for diﬀerent strategies and adopt a generic strategic variable xi ≥ 0 for any firm i. Given the strategies xj for all j = 1, 2, ..., n, each firm i has a net profit function: πi = Π (xi , β i ) − F

(2.1)

which depends on two main factors: the strategy of the same firm xi and a factor which summarizes the strategies of the other firms β i . We assume that: Π1 (xi , β i ) R 0 for xi S x(β i ) for some turning point x(β i ), and Π11 (x, β) < 0, or more generally that Π (x, β) is quasiconcave in x. Therefore, it is an inverted U curve in x for any β. The eﬀects (or spillovers) induced by the strategies of the other firms on firm i’s profits are summarized by: βi =

n X

h(xk )

(2.2)

k=1,k6=i

for some function of the strategies of each other firm h(x) that is assumed continuous, diﬀerentiable, non-negative and increasing in x. The gross profits are assumed to decrease in the strategies of the other firms and in their summary statistics β, that is Π2 (x, β) < 0.8 In general, it could be that Π12 is positive, so that we have strategic complementarity (since this implies ∂Π1 (xi , β i ) /∂xj > 0), from now on denoted with SC, or negative so that we have strategic substitutability (since this implies ∂Π1 (xi , β i ) /∂xj < 0), denoted with SS from now on. In the former case x0 (β i ) > 0, which implies that the reaction functions are upward sloping (∂x(β i )/∂xj > 0 for all firms), in the latter x0 (β i ) < 0, which implies that the reaction functions are downward sloping (∂x(β i )/∂xj < 0 for all firms). Of course, intermediate cases with non monotone reaction functions can emerge as well. An important outcome of the following analysis will concern the characterization of the firms strategies under diﬀerent conditions. For this purpose, let us introduce a behavioral definition: a strategy x is aggressive compared to another strategy x0 if x > x0 , and is accommodating in the opposite case; a firm adopting a strategy x > x0 is more aggressive than a firm adopting a strategy x0 . 8

For models of competition in prices an axiomatic foundation for a similar profit function can be derived by a demand system that satisfies the Independence from Irrelevant Alternatives property (the ratio of quantities demanded of any two goods is independent of the existence or price of a third good).

48

2. Strategic Commitments and Endogenous Entry

2.2 Nash Equilibrium Our first analysis is about competition between n firms. This number is kept exogenous and no other firms can enter in the market even if there are profitable opportunities to be exploited. This could happen because there are legal or institutional constraints on the number of actors in the market, or because the underlying technology is only available for a restricted number of firms. In a Nash equilibrium every firm chooses its strategy to maximize its own profits given the strategies of the other firms and the equilibrium strategies must be consistent with each other. In this kind of game, a pure-strategy Nash equilibrium exists if the reaction functions are continuous or do not have downward jumps. While in general this may not hold, weak conditions for existence have been studied for many applications,9 and in this general framework we will just assume the existence of a unique and symmetric equilibrium. More precisely, we can define the following concept of symmetric equilibrium: Definition 2.1. A Nash Equilibrium between n firms is such that: 1) each firm chooses its strategy x to maximize its profits given the spillovers β from the other firms; 2) β = (n − 1)h(x). Notice that the last condition guarantees consistency between the fact that all firms choose the same strategy x and that the spillovers for each firm are at the same level β. We will assume that in equilibrium all firms make positive profits, or in other words, that the fixed cost is small enough to allow each firm to gain from being in the market. To characterize the equilibrium, notice that, given the strategy of each other firm, firm i chooses its own strategy to satisfy the first order condition Π1 (xi , β i ) = 0. Imposing symmetry in equilibrium between the followers we have: Π1 [x, (n − 1)h(x)] = 0

(2.3)

which completely defines the equilibrium strategy x. We require Π11 + (n − 1)Π12 h0 (x) < 0 to assume local stability.10 To investigate the comparative properties of the Nash equilibrium with respect to the number of firms n, which is the only exogenous variable, let us totally diﬀerentiate the equilibrium condition to obtain: dx Π12 h(x) = T 0 if Π12 T 0 dn {−[Π11 + (n − 1)Π12 h0 (x)]}

(2.4)

The related eﬀects on profits are: 9 10

See Vives (1999). In this book we will not deal with dynamic concepts of stability and evolutionary learning. On this issue see Fudenberg and Levine (1998).

2.3 Marshall Equilibrium

Π2 h(x)Π11 dΠ =− <0 dn {−[Π11 + (n − 1)Π12 h0 (x)]}

49

(2.5)

An increase in the number of firms increases the strategic choice of each firm if SC holds, and decreases it under SS,11 while we always have a negative impact of entry on the profits of each firm as long as Π2 < 0.

2.3 Marshall Equilibrium Now we will drop the assumption that the number of firms is exogenous and look at the more realistic situation in which firms can actually enter in the market if there are profitable opportunities to be exploited. If entry is free, it occurs until the gross profits are equal to the fixed costs of production. Nevertheless, one could also think of the profits in other sectors as constraining entry: according to this “general equilibrium” interpretation, a no arbitrage condition between sectors would make sure that net profits are equal in all sectors and it would endogenizes entry. As we noticed above, the profits for each firm in the Nash equilibrium are always decreasing in the number of firms. This implies that when there are positive profits in equilibrium with n firms, there is an incentive for outsiders to enter in the market. Then we can define a symmetric Nash equilibrium with endogenous entry as follows: Definition 2.2. A Marshall equilibrium is such that 1) each firm chooses its strategy x to maximize its profits given the spillovers β from the other firms; 2) the number of firms n is such that all firms make non negative profits and entry of one more firm would induce negative profits for all of them; 3) β = (n − 1)h(x). To characterize the equilibrium, we still have the first order equilibrium condition: Π1 [x, (n − 1)h(x)] = 0

(2.6)

Moreover, we can impose the endogenous entry requirement as a zero profit condition. We will neglect the integer constraint on the number of firms: this is a good approximation when there are many firms - in general, the exact equilibrium number of firms would be the higher integer that is smaller than our equilibrium number. The endogenous entry condition becomes: 11

It can be equivalently shown that the eﬀect of any other exogenous parameter depends on its impact on the marginal eﬀect of the strategic variable.

50

2. Strategic Commitments and Endogenous Entry

Π [x, (n − 1)h(x)] = F

(2.7)

These two equations define the strategy of each firm and the number of firms as functions of the fixed cost. Local stability requires now Π2 h(x) + Π11 + (n − 1)Π12 h0 (x) < 0. To study the comparative statics of the system, we totally diﬀerentiate it with respect to F to obtain: Π12 dx R 0 if Π12 Q 0 = dF −Π11 Π2

dn Π11 + (n − 1)Π12 h0 (x) = < 0 (2.8) dF Π11 Π2 h(x)

as long as Π11 + (n − 1)Π12 h0 (x) < 0. Hence, a Marshall equilibrium implies strategies decreasing (increasing) in the fixed cost under SC (SS) and a number of firms decreasing in the fixed cost. An interesting interpretation of these comparative statics eﬀects emerges if we think of a general equilibrium model where an increase in F corresponds to a positive shock on the profitability of the other sectors. Such a shock would make firms more aggressive in a market with SS and more accommodating in a market with SC, but it would always reduce the number of firms. For instance, if we think of markets with competition in prices in general equilibrium, a positive shock in one sector has the eﬀect of increasing prices and reducing entry in the other sectors, an implication rarely matched by macroeconomic models with imperfect competition (since these models typically neglect the endogeneity of entry).12

2.4 Competition in Quantities, in Prices and for the Market In this section we will show that general models of competition in quantities and in prices and models of competition for the market are nested in our general framework, and we will analyze the Nash equilibrium and the Marshall equilibrium in these models. 2.4.1 Competition in Quantities In Chapter 1 we examined some simple cases of competition in quantities. Here we will examine more general models of this kind. Consider a general demand function:   n X pi = p  xi , h(xj ) j6=i

12

Introducing another exogenous parameter, say k, aﬀecting each profit function Π(xi , β i , k) with Π3 > 0, the strategies are decreasing in k whenever Π13 Π2 > Π3 Π12 , while the eﬀect on the number of firms is ambiguous.

2.4 Competition in Quantities, in Prices and for the Market

51

decreasing in both arguments, and a cost function c(xi ) for firm i, with c0 (·) > 0, where xi is the quantity produced by firm i. Profits are then:   n X πi = xi p  xi , h(xj ) − c(xi ) − F (2.9) j6=i

Using our definitions, the gross profit function can be written as: Π (xi , β i ) = xi p (xi , β i ) − c(xi )

(2.10)

and it can be easily verified that it is nested in our class of market structures (2.1) under weak conditions. This model is general enough to take into account diﬀerent shapes of the cost function and imperfect substitutability between goods. In general, it can be characterized by SS or SC since we have Π12 = px + xi pxβ , whose first element is negative and whose second element, proportional to the impact of a change of production of other firms on the slope of inverse demand, has an ambiguous sign. Pn Here, for simplicity, we will focus on the case where β i = k=1,k6=i xk , that is h(xi ) = xi . For instance, assuming linear demand functions as those studied in Chapter 1, we would have: pi = a − xi − bβ i ,

b ∈ (0, 1]

where Π12 (xi , β i ) = −b < 0 implies SS. This frequently used demand function can be derived from the maximization of a quadratic utility function as:   n n X X X X 1 U =a Ci −  Ci2 + b Ci Cj  + C0 (2.11) 2 i=1 i=1 i j6=i

where Ci is consumption of good i and C0 is the numeraire. Goods are homogenous when b = 1 and they are imperfectly substitutable otherwise. Another interesting case is associated with the following non linear demand: p = (a + xi + β i )

−γ

,

a ≥ 0, γ > 0 −γ−2

whose sign is positive where Π12 (xi , β i ) = −γ [a + β i − γxi ] (xi + β i ) for xi low enough and negative for xi high enough: consequently, the reaction functions have an inverse U shape. This demand can be derived from a standard constant elasticity utility function: P 1−γ (a + nJ=1 Cj ) U= (2.12) + C0 1−γ for γ > 0.

52

2. Strategic Commitments and Endogenous Entry

It is also possible to have situations in which SC holds always. For instance, Stackelberg (1934) presented an example with exponential demand p = exp [−(xi + β i )υ ] which generates SC for υ ∈ (0, 1). Nevertheless, we should keep in mind that output strategies are complements only in the extreme cases in which demand is highly convex. A general characterization of Cournot models is beyond our scope, therefore, in the rest of this section, we will focus on some particular cases. Homogenous goods. In the case of homogenous goods, the Nash-Cournot equilibrium condition under symmetry becomes:13 p(X) + xp0 (X) = c0 (x) where total output is X = nx (under the second order condition 2p0 + xp00 < 0). This is the usual rule equating marginal revenue and marginal cost, and can be rewritten as a mark-up rule (p − c0 ) /p = −xp0 /p, whose right hand side is the inverse of the elasticity of direct demand = −(dx/dp)(p/x). Therefore, we obtain the following expression for the equilibrium price: p(X) =

c0 (x) 1 − 1/

(2.13)

Focusing on the linear costs case with a constant marginal cost c, the comparative statics with respect to the number of firms provide: x(E − 1) dx = dn 1 + n − nE

dp [n − E(n − 1)]xp0 = <0 dn 1 + n(1 − E)

where E ≡ −xp00 (nx)/p0 (nx) is the elasticity of the slope of the inverse demand with respect to the individual output of a firm, which is an index of the convexity of the demand function (E = 0 under linear demand). Notice that the second order condition requires E < 2 while the assumption of local stability requires E < 1 + 1/n. It follows that an increase in the number of firms reduces their individual production unless E ∈ [1, 1 + 1/n] (which can hold only under SC), while total production always increases (and the eﬀect on profits is always negative). As a matter of fact, when the number of firms increases, the price converges to the marginal cost and the competitive result can be achieved as a limit if the fixed costs of production vanish (Novshek, 1980). Comparative statics with respect to the marginal cost provides: dx p0−1 = <0 dc 1 + n(1 − E) 13

dp n = >0 dc 1 + n(1 − E)

dΠ x(nE − 2) = dc [1 + n(1 − E)]

On the existence, uniqueness and other properties of such an equilibrium see Vives (1999), Amir and Lambson (2000). For a general analysis of the Cournot model with increasing returns to scale see the important work of Amir (2005).

2.4 Competition in Quantities, in Prices and for the Market

53

The price increases less (more) than proportionally if E < (>)1/n, while profits decrease in the marginal cost unless E ∈ (2/n, 1 + 1/n). Notice that this general Cournot model with n firms boils down to the monopoly model after imposing n = 1, and we can verify that these comparative statics results match those emerging in the classic case of a monopoly for n = 1. For instance, under linear demand (E = 0), a unitary increase of the marginal cost increases by half the monopolistic price, but by two thirds the duopolistic price, and so on until full shifting of the marginal cost on the price under perfect competition (for n → ∞): a more convex demand function leads to a larger shift of the cost change on the price. Generally, these results are quite useful since they can be used to evaluate the complex impact on the equilibrium prices and profits of an increase in costs due to diﬀerent factors as a change in the costs of the inputs of production or in the indirect taxes.14 Let us move to the Marshall equilibrium. The two equilibrium conditions are now the optimality condition for a representative firm and the zero profit condition: p(X) + xp0 (X) = c0 (x), xp(X) = c(x) + F

(2.14)

Totally diﬀerentiating the system we can derive the comparative statics of a change in the constant marginal cost. The new eﬀects are: dx p0 x2 = <0 dc n∆

dp 2x2 p02 = >0 dc ∆

dn p0 x = (2 − nE) dc ∆

Since ∆ ≡ x2 p02 (2p0 + xp00 ) > 0 by the second order condition, we can easily obtain that the cost increase raises the price less (more) than proportionally if E < (>)0. The number of firms is decreasing in the marginal cost except in the case of a highly convex demand function. Hyperbolic demand. As an example, let us look at the hyperbolic demand: p = Pn

1

J=1

(2.15)

xj

which can be derived from a standard logarithmic utility: ! Ã n X U = log Cj + C0

(2.16)

J=1

14

For instance, in the linear case with a specific tax ts and an ad valorem tax tv we have: p=

n a + n+1 n+1

c + ts 1 − tv

which shows that the price is decreasing in the number of firms and in both the taxes. For more results on tax incidence in oligopoly see Delipalla and Keen (1992), Myles (1995), and in presence of tax evasion Etro (1997, 1998a,b), Cowell (2004) and Marchese (2006).

54

2. Strategic Commitments and Endogenous Entry

where Cj is consumption of good j and good 0 is the numeraire.15 It can be easily verified that the Nash equilibrium is characterized by a production for each firm equal to x = (n − 1)/n2 c, and by the following price and gross profits: p=

c 1 − 1/n

Π=

1 n2

(2.17)

Notice that profits are now independent from the marginal cost, which is in line with our general result (since E = 2/n implies dΠ/dc = 0), while they decrease in the number of firms. In a Marshall equilibrium (assuming F < 1), √ we have the equilibrium output x = ( F − F )/c and: p=

c √ 1− F

1 n= √ F

(2.18)

where the mark up is increasing in the fixed cost of production and the number of firms is decreasing in it, but independently from the marginal cost. 2.4.2 Competition in Prices The model of price competition with homogeneous goods, due to Bertrand (1883) is quite trivial since only the firm with the lowest price serves the market. Things become more interesting when goods are not perfectly homogeneous. This is the case we will now deal with. In our analysis (and through out the rest of the book), we will focus on a large class of models of price competition with substitute goods where the direct demand can be written as:   n X Di = D pi , g(pj ) (2.19) j=1,j6=i

with D1 < 0, D2 < 0, g(p) > 0 and g 0 (p) < 0: the first assumption implies that the demand of firm i decreases in the price of firm i, and the remaining assumptions make sure that it increases with the prices of the other firms. Focusing on the case of a constant marginal cost, we then have the gross profits:   n X πi = (pi − c)D pi , g(pj ) − F (2.20) j=1,j6=i

In Chapter 1 we developed an example based on the Logit demand:

15

Notice that the hyperbolic demand is nested in the non linear one cited above for a = 0 and γ = 1.

2.4 Competition in Quantities, in Prices and for the Market

N e−λpi Di = Pn −λpj j=1 e

55

(2.21)

which belongs to our class of demand functions after setting g(p) = exp(−λp), that satisfies g 0 (p) < 0. Anderson et al. (1988) have shown that this demand is consistent with a representative agent maximizing the utility: µ ¶X µ ¶ n 1 Cj Cj ln U = C0 − (2.22) λ j=1 N

Pn for the when when j=1 Cj = N and −∞ otherwise (total consumption Pn n goods is exogenous), under the budget constraint C0 + j=1 pj Cj = Y , with C0 as the numeraire. This interpretation allows one to think of 1/λ as a measure of the variety-seeking behavior of the representative consumer. Other important cases derive from the class of demand functions introduced by Spence (1976) and Dixit and Stiglitz (1977) and derived from the of a utility function of a representative agent as U = h maximization ³P ´i P n θ u C0 , V under the budget constraint C0 + nj=1 pj Cj = Y , j=1 Cj where C0 is the numeraire, u(·) is quasilinear or homothetic, V (·) is increasing and concave, and θ ∈ (0, 1] parametrizes the substitutability between goods. Consider the utility function:   θ1 n X U = C0α  Cjθ 

(2.23)

j=1

with θ ∈ (0, 1) and α > 0. In this case the constant elasticity of substitution between goods is 1/(1 − θ) and increases in θ: for this reason this model is often referred to as the CES (constant elasticity of substitution) model. Demand for each good i = 1, ..., n can be derived as: −

1

Y pi 1−θ Di = Pn − θ (1 + α) j=1 pj 1−θ

(2.24) θ

which belongs to our general class after setting g(p) = p− 1−θ , which of course satisfies g 0 (p) < 0. Similar demand functions and related models of price competition have been widely employed in many fields where imperfect competition plays a crucial role, including the new trade theory, the newkeynesian macroeconomics, the new open macroeconomy, the endogenous growth theory and the new economic geography.16 We now have to verify that the profit functions derived from this class of demand functions are actually nested in our general model with gross 16

Anderson et al. (1992) have provided a detailed analysis of the foundations for the Logit and CES demand functions through three diﬀerent approaches (rep-

56

2. Strategic Commitments and Endogenous Entry

profits Π (xi , β i ). For this purpose, we will adopt a simple trick changing the strategic variable for each firm i from the price pi to its inverse xi ≡ 1/pi .17 Of course, choosing a price or its inverse is just a matter of mathematical definition, however it allows us to greatly simplify our discussion. First of all, increasing xi = 1/pi is now equivalent to reducing the price of firm i in both models of competition in quantities and in prices. Moreover, under our specification of the demand functions, we can now define: µ ¶ 1 h(xi ) = g with h0 (xi ) = −(1/x2i )g 0 (1/xi ) > 0 xi and rewrite gross profits as: µ ¶ µ ¶ 1 1 Π (xi , β i ) = −c D , βi xi xi

(2.25)

The model belongs to our class of consistent market structures (2.1) under weak regularity conditions. Moreover SC holds as long as DD12 < D1 D2 , since, after rearranging, we have Π12 = (D1 D2 − DD12 ) /x2i . It can be easily verified that SC holds in both the Logit model and the Dixit-Stiglitz model. Therefore, in the rest of the book, we will implicitly assume that SC holds in models of competition in prices. Being aware of our re-interpretation of these models through the change of variables, we can now analyze our symmetric equilibria focusing on prices. The general case. The Nash-Bertrand symmetric equilibrium with n firms is characterized by the first order condition: D [p, (n − 1)g(p)] + (p − c) D1 [p, (n − 1)g(p)] = 0 as long as the second order condition 2D1 + (p − c)D11 < 0 is satisfied. The optimality condition can be rewritten as a mark-up rule: p=

c 1 − 1/

(2.26)

where ≡ −pD1 /D > 0 is the elasticity of the direct demand. Assuming that SC holds, we have the comparative statics results: dp ∝ p2 g(p) [D2 + (p − c)D12 ] < 0 dn

17

dp ∝ −p2 D1 > 0 dc

resentative consumers models as those emphasized here, discrete choice models with stochastic utility and a multidimensional generalization of the Hotelling model) and of the existence of the related equilibria. For the case of an exponential subutility in the Dixit-Stiglitz preferences see Behrens and Murata (2007). I am thankful to Avinash Dixit to point this out. We borrowed this device from Mas-Colell et al. (1995, Ch. 12).

2.4 Competition in Quantities, in Prices and for the Market

57

while the eﬀect of a change in the marginal cost on the profits is ambiguous. The Marshall equilibrium requires that all firms choose their prices optimally and that profits are driven to zero by endogenous entry: D [p, (n − 1)g(p)] + (p − c) D1 [p, (n − 1)g(p)] = 0

(2.27)

D [p, (n − 1)g(p)] (p − c) = F

(2.28)

Total diﬀerentiation of this equilibrium system generates the following comparative statics result: dp ∝ −g(p)D [2D2 + (p − c)D12 ] > 0 dc while the eﬀect of the marginal cost on the number of firms is ambiguous. Some examples. As we have seen in Chapter 1, in the case of a Logit demand (2.21) under exogenous entry we have: p=c+

n (n − 1)λ

Π=

N −F λ(n − 1)

(2.29)

while the endogenous entry equilibrium implies:18 p=c+

F 1 + N λ

n=1+

N λF

(2.30)

In the case of a CES demand (2.24), the Nash equilibrium generates the following price and profits:19 p=

c(n − θ) θ(n − 1)

Π=

Y (1 − θ) γ(n − θ)

(2.31)

This clearly implies a price decreasing in the number of firms and increasing more than proportionally in the marginal cost (dp/dc > 1). Gross profits for each firm are independent from the marginal cost, decreasing in the number of firms and converging to zero when this number grows. Finally, in the Marshall equilibrium of the Dixit-Stiglitz model we have:20 18

19

The first best would require one firm less than in the Marshall equilibrium. The second best under the zero profit constraint would require a price p = c + 1/λ with N/F λ firms. In this case under specific and ad valorem taxation we have: p=

20

(c + ts )(n − θ) (1 − tv )θ(n − 1)

which implies overshifting of both taxes. The first best would require price equal to the marginal cost with Y (1−θ)/F (1+ θα) firms. The second best under the zero profit constraint would require a price p = c/θ with Y (1 − θ)/F (1 + α) firms.

58

2. Strategic Commitments and Endogenous Entry

p=

cY θ [Y − F (1 + α)]

n=

(1 − θ)Y +θ (1 + α)F

(2.32)

Notice that these equilibria can be compared with those that would emerge with the same isoelastic demand function if firms were competing in quantities rather than in prices.21 In that case one could solve for the Cournot equilibrium with an exogenous number of firms and obtain a price p = cn/θ(n − 1). This is higher than the price obtained above: competition in prices reduces the mark up and the profits of the firms compared to competition in quantities (this result holds in a more general set up than this). Finally, in all these cases the equilibrium price does not converge to the marginal cost when the number of firms increases (it converges to c+1/λ with the Logit demand and to c/θ with the isoelastic demand). This is possible because of product diﬀerentiation, which allows firms to maintain a certain degree of market power even if there are many competitors in the market; for this reason these kinds of models are often referred to as models of monopolistic competition - and in general equilibrium applications they are often employed neglecting the strategic interactions (so that the number of firms does not aﬀect equilibrium prices and profits, and endogeneity of entry is irrelevant). 2.4.3 Competition for the Market A large class of models of investment in innovation or competition for the market can be studied within our general framework. For instance, in Chapter 1 we studied a simple contest where every firm could obtain an innovation with probability xi ∈ [0, 1] after investing x2i /2. The expected profits were: n Y

πi = xi

j=1,j6=i

(1 − xj ) V −

x2i −F 2

(2.33)

That model was nested in our general framework, even if in such a case we would need a few steps to realize it: x2i −F = 2 S 1 x2 − n j=1,j6=i log 1−xj V − i −F = xi e 2 Sn

πi = xi e

21

j=1,j6=i

log(1−xj )

V −

Maximizing the utility (2.23) one obtains the inverse demand: pi =

−(1−θ)

Y xi (1 + α)

n j=1

xθj

and therefore a profit function which is nested in our general specification (2.1).

2.5 Strategic Investments

59

Now, setting h(x) = log [1/(1 − x)] which implies h0 (x) = 1/(1 − x) > 0, we can rewrite gross profits as: Π (xi , β i ) =

xi V x2 − i β e i 2

(2.34)

which is clearly nested in our model (2.1) and implies SS since Π12 = −V /eβ i < 0.22 As we have seen in Chapter 1, and as one can easily verify from the first order condition under symmetry, the Nash equilibrium is characterized by an investment in innovation implicitly given by: x = (1 − x)n−1 V

(2.35)

while in the Marshall equilibrium, where the number of firms reduces expected profits to zero, the investment is: √ x = 2F (2.36) Another related contest which is nested in our framework is a rent seeking contest in which agents invest to obtain rents with a probability given by their investment relative to the total one (Tullock, 1967). In Chapter 4 we will study more realistic forms of competition for the market where firms invest over time and innovations arrive according to a stochastic process depending on the investment of each firm (Loury, 1979). While that framework will allow us to consider further issues, many basic insights from the simple contest outlined here will be conserved.

2.5 Strategic Investments A main leitmotif of this book is about the behavior of market leaders in different forms of competitive environments. In the rest of this chapter we will approach this issue extending the framework analyzed until now to strategic investments or commitments by the leading firm. With strategic commitments we refer to any kind of preliminary decisions that aﬀect the strategic condition of the leaders compared to the other firms. In the jargon of marketing, we may refer to all those commitments that aﬀect the marketing mix, the so-called 4 P’s of marketing: product, price, place and promotion, here meaning quality of the good, costs, distribution and advertising (see Kotler, 1999). In the jargon of strategy, we may refer to all those commitments that aﬀect the competitive strategy and provide a competitive advantage to the leader (see Porter, 1985). 22

This model can also be used as a foundation of a simple principle-agent model (for an introduction see Milgrom and Roberts, 1992) with which one can study hyerarchies within teams (see Goldfain, 2007).

60

2. Strategic Commitments and Endogenous Entry

More formally, in what follows we will study markets in which all firms compete simultaneously as before, but one of them, the leader, will have a chance to undertake a preliminary investment which will aﬀect competition ex post. The purpose, of course, is to understand what kind of decisions are taken by market leaders, whether they are going to induce an aggressive or an accommodating behavior, and how they aﬀect equilibria. The pioneering analysis in this field is due to Dixit (1980) and Fudenberg and Tirole (1984), who focused on duopolies, while here we will consider the situation in which there is an exogenous number of firms n, possibly larger than two. Consider the following sequence of moves: 1) in the first stage a leader, firm L, makes a strategic commitment on a variable k (we will often refer to this as to a strategic investment); 2) in the second stage each follower chooses its own strategy xi and the leader chooses its own strategy xL after knowing the commitment of the leader. Therefore, all firms, the leader and the followers, play in Nash strategies in the second stage. In the second stage the profit of the leader is defined by: πL = Π L (xL , β L , k) − F

(2.37)

where, without loss of generality, we will assume that Π3L ≡ ∂Π L /∂k > 0: the variable k increases the profitability of the leader. The profit of each other firm remains: π = Π (x, β) − F For a given strategic commitment, the second stage is characterized by the first order conditions for a Nash equilibrium. For the sake of simplicity, we follow Fudenberg and Tirole (1984) assuming that a unique equilibrium exists with symmetric strategies for all the firms except the leader and that there is entry of some followers for any feasible k. Therefore, we have the equilibrium conditions: Π1L (xL , β L , k) = 0

Π1 (x, β) = 0

(2.38)

In general, we will say that the investment makes the leader tough when L > 0, that is a higher strategic investment k makes the leader more agΠ13 gressive (increases xL ), and makes the followers less (more) aggressive under L SS (SC). The investment makes the leader soft when Π13 < 0. In what follows we will analyze many diﬀerent kinds of investments, and in each application, there will be a cost for these investments. The leader will choose its investment by comparing its impact on the profit and its impact on the cost. Our interest, however, will be on the strategic eﬀect, that is the eﬀect of the investment of the leader on the behavior of the followers, defined as: SI(k) = Π2L (xL , β L , k)

∂β L ∂k

(2.39)

2.5 Strategic Investments

61

If the cost of the strategic investment is given by some positive and increasing function f (k), the net profit of the leader will be: πL (k) = Π L (xL , β L , k) − f (k) − F and the optimality condition will be: Π3L (xL , β L , k) + SI(k) = f 0 (k) It is clear that the strategic incentive is the interesting part for our purposes, since it tells us how the leader can exploit its commitment capacity in a strategic way to aﬀect the equilibrium of the market and obtain more profits. To realize this, imagine what would happen if the leader could not choose k before competing with the other firms, but had to choose it simultaneously with the choice of the market strategies of all firms: then, the strategic incentive would not play any role in the choice of the investment (only the direct eﬀect would remain). The importance of the commitment capacity relies exactly on the possibility of using the investment in a strategic way to aﬀect the behavior of the other firms. When SI is positive we will say that there is a strategic incentive to overinvest, while when it is negative we will say that there is a strategic incentive to underinvest. Of course, overinvestment and underinvestment should be thought relative to the direct incentive to invest. 2.5.1 The Fudenberg-Tirole Taxonomy of Business Strategies Let us generalize the standard results of Fudenberg and Tirole (1984) on the strategic investment of a leader in duopoly to the case with an exogenous number of firms n. The two equilibrium first order conditions (2.38) can be easily diﬀerentiated to obtain ∂β L /∂k, and hence the strategic incentive: SI(k) =

L Π12 h0 (xL )Π2L Π13 Ω

(2.40)

where Ω is positive by assumption of stability of the system.23 The sign of L this incentive is the same as that of −Π12 Π13 , and we have the following traditional result: Proposition 2.1. In a Nash equilibrium: L 1) when the strategic investment makes the leader tough (Π13 > 0), there is a strategic incentive to over- (under-) invest under strategic substitutability (complementarity); 23

Here: Ω=

L Π11 L Π11 + (n − 2) h0 (x)Π12 + Π12 Π12 > 0 (n − 1)h0 (x)

62

2. Strategic Commitments and Endogenous Entry

L 2) when the strategic investment makes the leader soft (Π13 < 0), there is a strategic incentive to under- (over-) invest under strategic substitutability (complementarity).

Now, imagine that in the absence of a strategic incentive to¢ invest, the ¡ leader was going to choose an investment k¯ such that Π L x, β, k¯ = Π (x, β) for any x and β.24 This is a neutrality assumption that allows to derive simple and interesting conclusions in a number of applications. It clearly implies that only the strategic incentive is going to induce the leader to behave in a diﬀerent way from the other firms. In other words, only the strategic commitment can provide the leader with an advantage in the market and in the second stage we have: xL R x if and only if k R (Q)k¯

L when Π13 > (<)0

Under this neutrality assumption, the implications for the strategy in the second stage are quite simple: Corollary 2.2. In a Nash equilibrium with strategic investment, the leader is always aggressive under strategic substitutability and always accommodating under strategic complementarity. The intuition for these results is well known. The strategic decision of the leader depends on the impact on the strategic interaction with the other firms. Imagine first that the strategic investment makes the leader tough, L that is more aggressive (Π13 > 0). In such a case overinvestment is optimal when an aggressive behavior in the market induces a less aggressive behavior of the other firms (which requires SS: Π12 < 0): this outcome corresponds to what has been called a “top dog” strategy in which the leading firm is aggressive to obtain non aggressive strategies of the other firms, a typical outcome of models of competition in quantities. However, when an aggressive behavior of a firm induces the other firms to be aggressive as well (which requires SC: Π12 > 0), as in models of competition in prices, it is optimal to underinvest strategically: this corresponds to a “puppy dog” strategy where, in the words of Fudenberg and Tirole (1984), underinvestment “accommodates entry by turning the incumbent into a small, friendly, nonaggressive puppy dog.” The spirit of puppy dog strategies emerges in most models of competition in prices with product differentiation25 . As an example, Laﬀont et al. (1998) have shown that a puppy 24

25

Within our specification of the cost function for the strategic investment, this ¯ = f 0 (k). ¯ requires Π3L x, β, k As noticed by Tirole (1988), puppy dog strategies emerge in the Hotelling duopoly as well. Considering the location k1 < k2 as the strategic choice of two firms on the unit segment, one can verify that ∂ 2 πi /∂pi ∂pj > 0 and ∂ 2 π i /∂pi ∂ki is positive for firm 1 and negative for firm 2. Hence both firms have a strategic incentive to diﬀerentiate products.

2.5 Strategic Investments

63

dog strategy emerges in (unregulated) markets for interconnected networks (for example the telecommunications industry) where an entrant chooses to invest strategically in geographical coverage before competing with the incumbent: then, the optimal strategy of the entrant is to underinvest to soften price competition.26 A puppy dog behavior can emerge also in an indirect way. A typical example is a price protection policy implemented through a “mostfavored-customer clause”. This guarantees a firm’s customers that they will be reimbursed the price diﬀerence with the lowest price oﬀered by other firms: as shown by Tirole (1988) this policy softens price competition and increases profits. L When the strategic investment makes the leader soft (Π13 < 0), the incentives take other directions: in the words of Fudenberg and Tirole (1984), the “fat cat strategy is overinvestment that accommodates entry by committing the incumbent to play less aggressively post entry. The lean and hungry strategy is underinvestment to be tougher.” A “lean and hungry look ” emerges in case of SS (Π12 < 0). As an example, consider our simple model of Chapter 1 with competition for the market between an incumbent monopolist and an outsider. Because of the Arrow eﬀect, the monopolist with positive profits from its leading technology had lower incentives to invest in innovation than the outsider, and higher current profits were inducing less investment by the incumbent and more by the outsider. In such a case, the incumbent would have liked to underinvest in profit enhancing strategies to have a strategic incentive to invest more in R&D. The “fat cat” strategy emerges in models of price competition (Π12 > 0) with a strategic investment that reduces the incentives to be aggressive, for instance, as we will see later on, with an investment in nonprice (or persuasive) advertising, which typically allows a firm to set high prices after having developed a goodwill.27 For further discussion on the taxonomy of strategic investment in duopolies, see the extensive treatment of Tirole (1988, Part II). 2.5.2 Strategic Commitments with Endogenous Entry We will now follow Etro (2006,a) and assume that the number of potential entrants is great enough that a zero profit condition pins down the eﬀective number of firms, n. To be precise, we will look at the subgame perfect equilibrium of the game with the following sequence of moves: 1) in the first stage, firm L enters, pays the fixed cost F and chooses an investment k; 26 27

See also Cambini and Valletti (2007). The quotation of Shakespeare from Julius Caesar (Act. 1, Sc. 2) introducing Fudenberg and Tirole (1984) is quite suggestive: “Let me have about me men that are fat.”

64

2. Strategic Commitments and Endogenous Entry

2) in the second stage, after knowing the investment of the leader, all potential entrants simultaneously decide “in” or “out”: if a firm decides “in”, it pays the fixed cost F ; 3) in the third stage all the firms that have entered choose their own strategy xi simultaneously. The equilibrium conditions are the two previous first order conditions (2.38), and the zero profit condition binding on the followers: Π (x, β) = F

(2.41)

We can now prove that a change in the strategic commitment by the leader does not aﬀect the equilibrium strategies of all other firms, but reduces their equilibrium number. Let us use the definition β L ≡ (n − 1)h(x) to rewrite the equilibrium system (2.38)-(2.41) in terms of the three unknown variables x, xL and β L : Π1 [x, h(xL ) − h(x) + β L ] = 0 Π1L [xL , β L , k] = 0 Π [x, h(xL ) − h(x) + β L ] = F The second equation provides an implicit relationship xL = xL (β L , k) with L L L L ∂xL /∂β L = −Π12 /Π11 and ∂xL /∂k = −Π13 /Π11 > 0. Substituting this expression we obtain a system of two equations in two unknowns, x and β L : Π1 [x, h(xL (β L , k)) − h(x) + β L ] = 0,

Π [x, h(xL (β L , k)) − h(x) + β L ] = F

Totally diﬀerentiating the system and imposing stability, which requires L L − h0 (xL )Π12 < 0, it follows that x = x(k), β L = β L (k) and xL = Π11 xL (β L (k), k) are the equilibrium functions with: dx =0 dk

L dβ L h0 (xL )Π13 = L L dk Π11 − h0 (xL )Π12

L Π13 dxL =− L L dk Π11 − h0 (xL )Π12

and dn/dk = (dβ L /dk) /h(x). This shows that in a Marshall equilibrium, an increase in the strategic investment does not aﬀect the equilibrium strategy of all the other firms but reduces their equilibrium number. In the initial stage, the strategic incentive becomes: SI(k) =

L h0 (xL )Π2L Π13 L − h0 (s)Π L Π11 12

(2.42)

L whose sign is just the sign of Π13 . This delivers our main result:

Proposition 2.3. In a Marshall equilibrium, when the strategic investment makes the leader tough (soft), there is a strategic incentive to over- (under-) invest; moreover, the leader is always aggressive compared to the followers.

2.5 Strategic Investments

65

L Basically, whenever investment makes the leader tough (Π13 > 0) and entry is endogenous, it is always optimal for the leader to adopt a “top dog” strategy with overinvestment in the first stage so as to be aggressive in the final stage. On the other side, when investment makes the leader soft L (Π13 < 0), we always have a “lean and hungry” look with underinvestment, but also in this case, the outcome in the final stage is an aggressive behavior of the leader. To understand the intuition of this simple but general result, let us focus on the first case, in which investment makes the leader tough. Let us suppose that SC holds: this is the most interesting case because endogenous entry overturns the traditional results (but a similar mechanism works under SS as well). Under our assumptions a leader may accept the cost of underinvesting strategically (compared to the optimal direct investment) to become more accommodating, and this would be the optimal thing to do when the number of competitors is exogenous. Now, let us consider the consequences of an accommodating strategy when entry is endogenous. Since strategies are assumed to be complements, accommodation by the leader would induce accommodating strategies by the followers as well. The associated increase in expected profits would attract entry of other firms, which will also behave in an accommodating way. Since entry occurs as long as there are profitable opportunities to exploit, the followers must obtain zero profits in equilibrium. Therefore, the entry process induced by an accommodating strategy exhausts all possible gains for the followers. What about the leader? Its attempt to induce accommodation has the cost of distorting its strategy from the optimal direct level. Moreover, it wastes all the potential benefits from accommodation because it increases entry. Accordingly, underinvestment cannot increase the profits of the leader. Consider now an aggressive strategy induced by an initial overinvestment of the leader. Such a strategy may induce the rivals to be more aggressive as well, and this would reduce entry in the market. Therefore, the leader distorts its investment strategy from the directly optimal level but succeeds in reducing the negative externalities derived from the strategies of the rivals because of the reduction in their number. The optimal level of overinvestment trades oﬀ the costs of the distortion in the investment level and the benefits of the reduction of the number of entrants. Finally, notice that the same argument would go through in the case the investment made the leader soft, but in that case underinvestment would induce the optimal aggressive strategy. We will now apply the above results to some basic forms of strategic commitments as investments in cost reductions, advertising, financial decisions, bundling or price discrimination strategies, strategic contracts, strategic mergers and so on. There are many other applications that are not discussed in this chapter. Our focus will be limited to the applications with substantial relevance for the understanding of the behavior of market leaders

66

2. Strategic Commitments and Endogenous Entry

and for our future discussions of antitrust issues. We will emphasize how the results can drastically change according to whether we assume that entry is exogenous or endogenous, but we will mainly pay attention to the case of endogenous entry. After all, we do believe that entry of firms is an endogenous choice in most markets, and not an exogenous fact.

2.6 Cost Reductions and Signaling Our first application is to a situation where a firm can adopt preliminary investments to improve its production technology and hence reduce its costs. Traditional results on the opportunity of these investments for market leaders are ambiguous when the number of firms is exogenous, but, as we will show, they are not when entry is endogenous. From now on, we will assume for simplicity that marginal costs are constant. Here, the leader can invest k and reduce its marginal cost to c(k) > 0 with c0 (k) < 0, while the marginal cost cannot be changed for all the other firms. One could think of the cost reducing investment as an investment in R&D to improve the production technology, but also in terms of learning by doing: past production reduces future costs.28 Consider first a model of quantity competition. The gross profit of the leader becomes: Π L (xL , β L , k) = xL p (xL , β L ) − c(k)xL

(2.43)

L Notice that in such a model, Π12 has an ambiguous sign, but we have: L Π13 = −c0 (k) > 0

consequently the leader will overinvest in cost reductions when facing a fixed number of competitors (as long as SS holds), and will always overinvest and produce more than the other firms when entry is endogenous. For instance,√assume an inverse demand p = a − X, a constant marginal cost c(k) = c − gk for the leader investing k, and c for the entrants, where g measures the productivity of the R&D investment, whose cost is f (k) = k. A Nash equilibrium with n firms would imply: xL =

a − nc(k) + (n − 1)c , n+1

x=

a + c(k) − 2c n+1

The optimal investment by the leader can be derived as: 28

This is the typical case of the aircraft industry (Boeing, Airbus), the production of chips (Intel) and many other sectors with a fast technological progress. See Sutton (Ch. 14) for an analysis of these markets.

2.6 Cost Reductions and Signaling

k=

67

(a − c)2 g

[(n + 1)2 − ng]2

which clearly generates an equilibrium output for the leader that is higher than the one of the entrants (notice that SS holds in this example). The optimal investment is increasing in the productivity of the R&D technology, that is in g. Moreover, if this productivity is high enough, it is optimal to induce entry deterrence. The bias toward overinvestment in cost reducing technology aimed at an aggressive behavior in the market holds also when entry is endogenous, in which case the equilibrium production of the leader and of the entrants are: √ √ F xL = , x= F 1−g and the leader induces such an equilibrium through the preliminary investment: k=

gF 2

(1 − g)

in cost reductions. This implies the following rule for the optimal ratio between R&D spending k and sales of the leader pxL : √ R&D g F √ (2.44) = Sales (1 − g) (c + F ) Of course, this result requires g to be small enough, otherwise entry deterrence ³ √ ´2 would be optimal, and it would require an investment k = a − c − 3 F /g. In this framework, the chance to undertake a strategic investment in a cost reducing technology leads to the same outcome we obtained in Section 1.2.1, when the leader could simply choose its output before the other firms and marginal costs were increasing: the leader is aggressive to produce more than the other firms, but the cost of an aggressive strategy (increasing marginal costs of production there, costs of R&D investment here) limits the production of the leader. A lot of research has extended this model to the realistic case of spillovers of the R&D activity of the incumbent on the entrants (for ˇ c et al., 2006 and Vandekerckhove and De Bondt, 2007), instance, see Zigi´ and the tendency toward overinvestment under endogenous entry holds also in that case.29 29

Assuming that investment k by the leader induces a marginal cost for the entrants √ c−χ gk, where χ ∈ [0, 1) is a measure of the degree of spillovers, the equilibrium with endogenous entry implies an investment: k=

(1 − χ)2 gF [1 − g(1 − χ)2 ]2

68

2. Strategic Commitments and Endogenous Entry

Consider now the model of price competition where the leader can invest to reduce its marginal costs in the same way and its profit function becomes: Π L (xL , β L , k) = [pL − c(k)] D (pL , β L )

with pL = 1/xL

(2.45)

Now we have: L = c0 (k)D1 p2L > 0 Π13

Accordingly, underinvestment in cost reductions emerges when entry is exogenous (since SC holds), but overinvestment is optimal when there is endogenous entry. Whenever this is the case, the leader wants to improve its cost function to be more aggressive in the market and sell its good at a lower price. Summarizing, we have:30 Proposition 2.4. Under both quantity and price competition with endogenous entry, a firm always has an incentive to overinvest in cost reductions and to be more aggressive than the others in the market. This theory of cost reducing investments aimed at inducing aggressive behavior toward the competitors and ultimately at decreasing prices, has been extended in a genuinely dynamic framework in an important work by ˇ c et al. (2006). They depart from the static model of quantity competiZigi´ tion analyzed above and study a dynamic duopoly in which the leader can invest over time to reduce the marginal cost gradually. The optimal accommodating strategy generates an increasing investment associated with a decreasing price. The optimal entry deterring strategy requires a heavy initial investment able to deter entry as soon as possible, and a lower investment in the subsequent monopolistic phase, which generates a decreasing price in the predatory phase and an increasing price in the monopolistic phase. The predatory strategy is optimal when the investment is productive enough (g is high enough) and the speed of adjustment of the marginal cost (namely of its reduction with the investment) is high enough. However, the surprising

30

that is decreasing in the spillovers, which dissipate R&D eﬀort from the perspective of the leader. Only when spillovers are small enough (χ < 1/2), it can be √ 2 optimal to deter entry with the investment k = a − c − 3 F /g(1 − 2χ)2 as long as the cost reducing technology is productive enough. A related application is available in the case of multimarket competition, where cost reductions can be obtained indirectly through production in other markets. For instance, if k is production in a separate market and there are economies of scope, in the sense that the marginal cost in one market is decreasing in the production in the other market, the leader will always overproduce in both markets to reduce its marginal costs. Contrary to the outcome in a duopoly, analyzed by Bulow et al. (1985), this does not depend on whether SS or SC holds.

2.6 Cost Reductions and Signaling

69

result is that the sharp decrease in the equilibrium price due to the predatory investment in R&D leads to permanent gains for the consumers also in the monopolistic phase after predation (when potential entry still constrains the R&D activity). Our results can also be used to re-interpret models of predatory pricing through cost signaling. In a classic work of the modern industrial organization (and of the post-Chicago approach to antitrust), Milgrom and Roberts (1982) have studied the entry decision of an entrant in a duopoly with an incumbent that is already active in the market, and have introduced incomplete information: since the study of informational asymmetries is beyond the scope of this book, we will just sketch their idea to emphasize the similarities with our approach. Imagine that the entrant does not know the cost of the leader, which can be a high cost or a low cost, but would like to enter only when facing a high cost leader. Milgrom and Roberts study under which conditions preliminary strategies of the leader induce entry deterrence. For instance, a low cost leader can signal its own eﬃciency through initial over-production or under-pricing (associated with a sacrifice of profits) as long as this is relatively cheaper for the low cost leader compared to the high cost one. This sorting or single crossing condition, first pointed out by Spence (1974) in a diﬀerent context,31 is respected here exactly because the marginal profitability of production decreases with the marginal cost. In our terminology, this L corresponds exactly to our condition Π13 > 0: when the marginal cost is lower (c(k) is lower because the investment k is higher), the marginal benefits of an aggressive strategy is higher. This means that the marginal cost of an aggressive strategy is lower for a low cost firm. Then, in a separating equilibrium, a low cost leader is initially aggressive overproducing enough to signal its eﬃciency and induce the follower not to enter, while a high cost leader does not imitate such a strategy because it is more profitable to behave monopolistically initially and accommodate entry subsequently. This result shows that cost reductions can have a strategic role also in the presence of incomplete information about costs.32 Notice that even without exclusionary purposes, a leader may like to signal its own type to aﬀect post-entry competition with incomplete information on costs. Under competition in quantities (and SS), a low cost leader may signal its eﬃciency to reduce the equilibrium output of the entrant and increase its own, but under price competition it is a high cost leader that wants to signal its ineﬃciency to induce high prices by the entrant and obtain high 31

32

The initial application was to the signaling of productivity through higher education (which requires a lower relative eﬀort for more productive agents). For an introduction to the economics of asymmetric information see Tirole (1988, Ch. 9), Hirshleifer and Riley (1992) and Laﬀont and Tirole (1993). When the probability that the leader is low cost is high enough a pooling equilibrium occurs. In such a case, the high cost leader produces the same monopolistic output of the low cost leader, and the entrant does not enter anyway.

70

2. Strategic Commitments and Endogenous Entry

profits for both, a point first made by Fudenberg and Tirole (1984). Without developing the argument in technical details, we can point out that when entry is endogenous there can only be a gain from signaling eﬃciency for a low cost incumbent, since signaling a high cost would not soften price competition, but just induce further entry. In the spirit of our model, we can conclude by suggesting that also under incomplete information about costs, there is a role for a positive strategic investment in cost reductions (for signaling purposes) whenever entry in the market is endogenous. And this does not necessarily imply exclusionary aims.

2.7 Advertising and Demand Enhancing Investments We will now consider investments which aﬀect the demand function of a firm, such as nonprice advertising (aimed at brand positioning and at enhancing the goodwill), and investments for quality improvements or product diﬀerentiation. These investments tend to increase demand and also reduce the substitutability between goods.33 Under endogenous entry, the aim of the leader is always to be aggressive in the market, but diﬀerent strategies emerge under quantity and price competition. Consider a model of quantity competition characterized by the inverse demand p (xL , β L , k) for the leader. The marginal eﬀect of investment on inverse demand is positive (p3 > 0), while the one on its slope is negative (p13 < 0), which implies that a higher investment not only increases demand, but it also makes it more rigid.34 In this case, its gross profit becomes: Π L (xL , β L , k) = xL [p (xL , β L , k) − c]

(2.46)

Consequently, we have: L = p3 (1 − η) Π13

where η ≡ −xL p31 /p3 is the elasticity of the marginal eﬀect of investment on price with respect to production. As long as this elasticity is less than unitary, L which means that investment does not make demand too rigid, we have Π13 > 33

34

See Tirole (1988, Ch. 2 and Ch. 7) on product selection, quality and advertising, and on product diﬀerentiation. This may not be the case for informative advertising (which informs consumers abour product price and availability) or other forms of investment that attract marginal consumers. Since these consumers are by definition more sensitive to price changes, the investment may increase both demand and its elasticity (Becker and Murphy, 1993). In general, marketing studies suggest that investments in advertising make demand more rigid for a price increase and more elastic for a price decrease (Kotler, 1999). A classic work in the field is Lambin (1970).

2.7 Advertising and Demand Enhancing Investments

71

0. While under exogenous entry the investment choice of the leader depends on many factors, under endogenous entry overinvestment takes place if and only if η < 1.35 Whether this is the case or not, the leader ends up selling more than any other firm. Consider the case of homogenous goods and a unit cost of advertising given by pA . Then, we can easily verify that the impact of advertising on L the output of the leader is ∂xL /∂k = Π13 / (∂p/∂x), and the optimal ratio between expenditure in advertising, pA k, and sales, pxL , must satisfy the following condition which generalizes the classic one by Dorfman and Steiner (1954): Advertising = εpk (2 − η) Sales

(2.47)

Here εpk ≡ (k/p)(∂p/∂k) is the elasticity of price with respect to advertising. According to the standard Dorfman-Steiner condition the optimal advertising-sales ratio should equal this elasticity, but when a leader can advertise for strategic purposes and faces endogenous entry, the optimal advertising-sales ratio would be larger than that as long as advertising does not make demand too rigid. Let us move to the case of competition in prices. Under this form of competition we have a demand for the leader D(1/xL , β L , k) with D3 > 0 and D13 > 0 and the gross profit becomes: Π L (xL , β L , k) = (pL − c) D (pL , β L , k)

with pL = 1/xL

(2.48)

where the crucial cross eﬀect is: L Π13 = − [D3 + (pL − c)D13 ] p2L < 0

In this case with an exogenous number of firms the leader would overinvest to increase its price and exploit the induced increase in the price of the competitors. However, under endogenous entry the behavior of the leader radically changes and there is always underinvestment so as to reduce the price below the price of the followers.36 35

36

The model can also be reinterpreted in terms of product diﬀerentiation. It is well known that, from the 1950s to the 1970s in US, established firms in the readyto-eat breakfast cereal industry rapidly increased the number of the brands they oﬀered with aggressive purposes against further entry in the market. Vertical diﬀerentiation is another way to interpret our model. For instance, if deˆ L /k, β L ) mand depends on the price-quality ratio, according to some function D(p L where k is quality, it is easy to derive Π13 < 0: committing to a high quality leads to choose high prices. Nevertheless, in Section 3.4.4 we will study a more realistic situation in which committing to high quality is the best strategy for a leader facing endogenous entry.

72

2. Strategic Commitments and Endogenous Entry

Fudenberg and Tirole (1984) have introduced another simple example of investment in advertising that is nested in our framework and is derived from Schmalensee (1982). Imagine that firms compete in prices on the same customers, but the leader, through a costly investment in advertising k, can obtain an extra demand D(k) from new customers, with D0 (k) > 0. This simple stylized set up delivers a profit function for the leader: Π L (xL , β L , k) = (pL − c) D(k) + (pL − c) D (pL , β L )

with pL = 1/xL

while the profits for the other firms are the same as before. The cross eﬀect L is now Π13 = −D0 (k)p2L < 0. Hence, as Fudenberg and Tirole (1984) noticed in the case of two firms, “if the established firm chooses to allow entry, it will advertise heavily and become a fat cat in order to soften the entrant’s pricing behavior”, but, we add, when entry of firms is endogenous, the leader will underinvest in advertising to keep low prices while allowing some firms to enter in the market. Summarizing our results for nonprice advertising, we have: Proposition 2.5. Under quantity competition with endogenous entry, a firm has an incentive to overinvest in nonprice advertising as long as this does not make demand too rigid; under price competition with endogenous entry the leader has always an incentive to underinvest in nonprice advertising. Once again this result overturns common wisdom obtained by duopoly models, especially under price competition.

2.8 Debt and the Optimal Financial Structure We can also apply our results to the theory of corporate finance to study the strategic role of the financial structure. As shown by Brander and Lewis (1986, 1988) and Showalter (1995, 1999) in models of duopolies with uncertainty, when product decisions are managed by the equity holders, debt can aﬀect the marginal profitability, and hence there can be a role for a bias in the optimal financial structure, departing from the standard neutrality results of Modigliani and Miller (1958).37 The outcome depends on the kind of competition, but also on the kind of uncertainty. For finance to play a role in product market competition, we need to introduce uncertainty on profits. Imagine that the total financing requirement 37

See Tirole (2006, Ch. 7) for a survey on the relation between corporate finance and product market competition, and Brealey and Myers (2002) for a general introduction to the theory of the optimal financial structure. Between many empirical analysis on alternative financing tools in diﬀerent contexts, see the recent work of Cenciarini et al. (2006).

2.8 Debt and the Optimal Financial Structure

73

for each firm is fixed and each firm has enough cash to finance production entirely without issuing debt. Furthermore, suppose that the credit market is perfectly competitive, so that lenders break even. In such a context, the Modigliani-Miller neutrality result holds only if the financial structure does not aﬀect product market competition. For simplicity, we will assume that the financial structure of the outsiders implies no debt. The leader, however, can adopt a diﬀerent financial structure by issuing positive debt at a preliminary stage. Afterward, the equity holders of all firms choose their market strategies, uncertainty is resolved and payoﬀs for equity holders and debt holders are assigned. Assume that the profit functions are disturbed by a random shock z ∈ [z, z¯] independently and iden¯ tically distributed according to the cumulative function G(z) with density g(z). The initial ownership of the leading firm can decide its debt level k to be repaid out of gross profits, if these are suﬃcient. Once this choice is taken, competition takes place, uncertainty is solved and each firm obtains its own profits net of the debt or goes bankrupt. If the gross profits of the leader can be written as R(xL , β L , z) with the usual notation, the value of equity, corresponding to the expected profits net of debt repayment can be written as: L

E(k) = Π (xL , β L , k) − F =

Zz¯

[R(xL , β L , z) − F − k] g(z)dz

(2.49)

zˆ

where the lower bound zˆ is such that gross profits are zero: R(xL , β L , zˆ) − F = k Notice that dˆ z /dk = 1/Rz (xL , β L , zˆ). We assume usual properties for the profit function (Rxx (xL , β L , z) < 0), and we also assume, without loss of generality, that the random variable is chosen so that Rz (xi , β i , z) > 0: this implies that the cut-oﬀ level of the positive shock zˆ below which bankruptcy occurs is increasing in the debt level (dˆ z /dk > 0). We could think of a model of competition in quantities where: R(xi , β i , z) = xi p(xi , β i , z) − c(xi , z) with pz (xi , β i , z) > 0 and cz (xi , z) < 0: a positive shock increases demand or reduces costs. In Xcase of demand uncertainty with the stochastic linear demand p = z − xj and zero marginal costs, we would have zˆ = (k + X F )/xL + xj , which is of course increasing in the debt level. In this example and generally under weak conditions, a positive shock increases the marginal profitability of production (Rxz (xL , β L , z) > 0). We can also have a model of competition in prices with: R(xi , β i , z) = [pi − c(z)] D (pi , β i , z)

with pL = 1/xL

74

2. Strategic Commitments and Endogenous Entry

and we allow explicitly for an impact of uncertainty on both demand and costs. Our assumptions are compatible with Dz (1/xi , β i , z) > 0 and cz (z) < 0: a positive shock increases demand and/or reduces costs. Moreover, under mild conditions assumed in what follows, a positive demand shock increases the marginal profitability of a price increase (Rxz (xL , β L , z) < 0), while a positive cost shock always decreases it (Rxz (xL , β L , z) > 0). In general we have: Π1L (xL , β L , k) =

Zz¯

Rx (xL , β L , z)g(z)dz − [R(xL , β L , zˆ) − k]

dˆ z dk

zˆ

whose last term is zero by the definition of zˆ. In any equilibrium, the optimal behavior of each firm would require that the expectation of its marginal profit is set equal to zero. But notice that what is relevant for a firm with a positive debt are the expected profits conditional on these being positive after debt repayment, and this aﬀects substantially the marginal profits as well. When Rxz (xL , β L , z) is positive, marginal profit increases in zˆ and hence in the debt level, and the opposite happens when Rxz (xL , β L , z) is negative. As always, it is crucial to derive the sign of the cross eﬀect:38 dˆ z = dk −Rx (xL , β L , zˆ) = R 0 if Rxz (xL , β L , z) R 0 Rz (xL , β L , zˆ)

L Π13 (xL , β L , k) = −Rx (xL , β L , zˆ)

This implies that when the number of firms is exogenous and the leader accommodates entry, under SS there is a strategic incentive to issue debt when a positive shock increases marginal profits (Rxz (xL , β L , z) > 0) and under SC in the opposite case (Rxz (xL , β L , z) < 0). For instance, under competition in quantities there is typically a strategic role for debt financing (Brander and Lewis, 1986), while under competition in prices there is a role for debt financing only in the presence of demand uncertainty, but not in case of cost uncertainty (Showalter, 1995).39 Things are diﬀerent, however, when entry takes place endogenously until expected profits are zero. In this case we can apply Prop. 2.3 and conclude with: Proposition 2.6. Under endogenous entry, a firm has an incentive to adopt debt financing to be more aggressive in the competition whenever a positive shock increases marginal profits. 38

39

The sign of the marginal profit at its bounds zˆ and z¯ depends on the sign of Rxz (xL , β L , z). In particular Rx (xL , β L , zˆ) Q 0 if Rxz (xL , β L , z) R 0. For further details see Etro (2006e). Notice that a bias toward debt financing is equivalent to a bias toward risk-taking behavior, a well known consequence of debt contracts (at least since Stiglitz and Weiss, 1981). Debt financing to deter entry can emerge with quantity competition and SS or with price competition and cost uncertainty (Showalter, 1999).

2.8 Debt and the Optimal Financial Structure

75

In general, under quantity competition there is always a strategic bias toward debt financing, while under price competition the same bias emerges only when uncertainty aﬀects costs, but not when it aﬀects demand. The intuition is again related with the role of debt financing in inducing a more aggressive behavior in the market, which is always desirable for the leader facing endogenous entry. Under quantity competition, debt induces the management to care only about the good states of the world (high demand and low costs) and therefore to choose aggressive strategies. Similarly, under price competition and demand uncertainty a higher debt increases the marginal profitability of a higher price strategy. Accordingly, it helps implementing a more accommodating strategy in the market: just what a leader would like to do when facing exogenous entry, but the opposite of what would be desirable in front of endogenous entry. However, under cost uncertainty, the management decides the price to maximize profits conditional on a good state of the world, meaning low costs, which leads to a bias toward low prices: this is a suboptimal strategy with exogenous entry, but an optimal one with endogenous entry.40 To complete our analysis, notice that the initial ownership would actually choose debt to maximize the overall value of the firm, which corresponds to the equity value E (k) plus the debt value:

D(k) =

Zzˆ z ¯

[R(xL , β L , z) − F ] g(z)dz + k[1 − G(ˆ z )]

where the first term represents the expected repayment in the case of bankruptcy and the second one the expected repayment in case of successful outcome for the firm. Taking into account the dependence of the equilibrium on debt k, the value of the firm is then: V(k) = E(k) + D(k) =

Zz¯ z ¯

R [xL (k), β L (k), z] g(z)dz − F

(2.50)

which corresponds to the expected profits of the firm. When a positive shock increases the marginal profitability of an aggressive strategy, the optimal financial structure requires an amount of debt k∗ that induces the management to behave as a Stackelberg leader in front of the other firms - as we will see 40

Chevalier (1995) examines changes in supermarket prices in local markets after “leverage buyouts” and finds that prices decrease following an LBO in front of rival firms which are not highly leveraged, while they increase when the LBO firm’s rivals are also highly leveraged. She associates the former result to predatory strategies and the latter to a softening of price competition, but she does not control for the endogeneity of entry in these local markets, which makes hard to evaluate the results.

76

2. Strategic Commitments and Endogenous Entry

in the next chapter, this is the best equilibrium the leader can aim for; more debt would induce an excessively aggressive strategy. When a positive shock decreases the marginal profitability of an aggressive strategy, the financial structure cannot improve the performance of the firm: in this case, for instance with price competition and demand uncertainty, the optimal financial structure requires no debt. Summing up, the optimal ratio between the value of debt and the value of equity can be defined as: · ¸ Debt D(k ∗ ) = max 0, (2.51) Equity E(k∗ ) Notice that this rule has been derived assuming a perfectly competitive credit market, free entry in the product market, no taxes and no bankruptcy costs, exactly as for the Modigliani-Miller theorem; further generalizatins could be considered.41

2.9 Network Externalities and Two-Sided Markets Many markets are characterized by network externalities, in the sense that demand is enhanced by past production and the consequent diﬀusion of the product across customers. This may happen for cultural or social reasons, for instance because goods become fashionable when they have been already chosen by other customers, or because of technological reasons, for instance because the willingness to pay for a good by each consumer depends on how many other consumers have the same good. The last situation is typical of advanced technological markets: in principle we may attach a high value to video phone communication, but until many of our friends will have a video phone, we are unlikely to attach a high value to owning one as well. The classic study of competition in this kind of markets is due to Katz and Shapiro (1985).42 Here we will focus on a more stylized model of the behavior of market leaders in the presence of network externalities. We will adopt the simplest model of quantity competition with homogeneous goods and introduce a time dimension. Imagine that in a first period the leader is alone in the market and produces k facing the inverse demand p(k) and a marginal cost c. In the second period other firms compete in quantities and the leader faces the inverse demand p(X)φ(k), where X is total 41

42

The model could be extended introducing bankruptcy costs and adding multiple periods to examine dynamic strategies for entry deterrence: as shown by a wide literature on the so-called “long purse” or “deep pocket” theory of predation, when initial aggressive strategies by the incumbent reduce the financing opportunities of the entrants, financial predation can indeed be optimal (see Holmstrom and Tirole 1997, Hart, 1995, and Tirole, 2006). See also Amir and Lazzati (2007).

2.9 Network Externalities and Two-Sided Markets

77

production and φ(k) is some increasing function of past production, which is a measure of the diﬀusion of the good between consumers, and induces network externalities. The gross profit function for the leader becomes: Π L (xL , β L , k) = p(k)k − ck + δ [p (X)φ(k) xL − cxL ]

(2.52)

where δ ≤ 1 is the discount factor, while the net profit of the other firms is simply π i = xi p(X) − cxi − F . Since the other firms do not enjoy network eﬀects, one can easily show that in a free entry equilibrium the future production xL (k) of the leader will be increasing in its initial production with ∂xL /∂k = −cφ0 (k)/φ(k)2 p0 (X) > 0.43 Moreover, in equilibrium we have the cross eﬀect: L Π13 =

δcφ0 (k) >0 φ(k)

which, according to our general principle, shows that the leader will always engage in initial overproduction to be more aggressive when the market opens up to endogenous entry. We can also derive a simple expression for the optimal initial production: ¡ ¢ cφ0 (k)xL (k) p(k) + kp0 (k) = c − δp X)φ0 (k xL (k) − δ φ(k)

(2.53)

This rule equates the marginal revenue of initial production to its eﬀective marginal cost, which includes the myopic marginal cost c, a second term that represents the direct benefit due to the network eﬀects on future demand (determining what is sometimes called a penetration price), and a last term representing the indirect (strategic) benefits due to the commitment to the adoption of a more aggressive strategy in the future. Notice that in the presence of network externalities, an incumbent expecting strong competition in the market may want to price well below marginal cost not with the purpose of excluding any other firm to enter in the market, but to be able to compete aggressively in the future: this is more likely when the marginal costs of production are low and the discount factor is high. Summarizing we have: Proposition 2.7. In markets with network externalities an incumbent has an incentive to overproduce initially so as to be more aggressive when endogenous entry takes place in the future. The model above, can be re-interpreted in an interesting way when we assume that the externality function is simply φ(k) = k. This implies that net 43

We focus on an interior equilibrium, but it is clear that a corner solution can emerge: such a tipping equilibrium is actually typical in markets with network eﬀects (see Cremer et al., 2000).

78

2. Strategic Commitments and Endogenous Entry

profits in the competitive market are proportional to kxL . To fix ideas, imagine that the firms under consideration produce local newspapers. The leader decides a capacity production for k copies of its local newspaper, but also sells advertising space on the newspaper in quantity xL and in competition with other newspapers (located elsewhere and with their own local readers). Of course, advertising is more valuable when a newspaper has more readers, and more precisely what matters is exactly the number of interactions between readers and advertisement, which is simply k · xL . This is the simplest example of a two-sided market because newspapers sell two products (news and advertising) to diﬀerent customers, and there are network eﬀects between them (actually only in one direction in this example, since we assumed that readers are indiﬀerent to the size of advertisement space on the newspapers). As first pointed out by Rochet and Tirole (2003) and Armstrong (2006), in such a two-sided market firms charge the diﬀerent sides in diﬀerent ways with the aim of enhancing network eﬀects: in general the aim is to get on board many agents from the side whose size creates more value for the other side. In our example, for instance, the direct eﬀect of the sales of newspapers (and maybe related bundled gadgets) on the profits from advertising induces a production beyond the myopic monopolistic output level. However, here we want to point out a new strategic element: a leader facing competition on one side (advertising), will have an additional indirect incentive to overproduce on the other side (newspapers), to enhance the value of the platform and to be aggressive in the competition with other firms (for the advertising).44 Similar situations emerge in many multi-sided markets where platforms compete on the volume of transactions between diﬀerent groups of buyers and sellers (think of credit cards, operating systems)45 and multiple factors can 44

45

One can verify that the same happens under price competition, which is the usual assumption in models of two-sided markets. However, under SC, overproduction by the leader is strictly related with the endogeneity of entry. When the number of competitors is exogenous, a leader would like to commit to (relatively) high prices for the newspapers so as to be accommodating in the competition for advertising space against other newspapers: only when entry is endogenous the need of being aggressive in the advertising market induces to price newspapers at a (relatively) low price. See Section 6.1.2 for further discussion. For instance, consider a variant of the previous example where both sides are now charged for each interaction, and c is the marginal cost of an interaction, so that: Π L (xL , β L , k) = [p(k) + p(X) − c] · k · xL In case the leader is just a monopolist, k and x would be chosen to satisfy the Rochet-Tirole (2003) optimality condition: p(k) + p(x) − c =

p(k) p(x) p(k) + p(x) = = (k) + (x) (k) (x)

2.10 Bundling

79

induce diﬀerent strategic behavior toward diﬀerent sides. Market relations easily become complex when network eﬀects act in both directions (in the case of informative advertising, readers may have positive externalities from more advertising in the newspapers), and especially when one or both sides engage in multi-homing (in case of national newspapers, readers may read more than one of them). In Chapter 6 we will discuss some of these issues within concrete applications.

2.10 Bundling There has been a lot of attention in the economic literature on the rationale for bundling products rather than selling them separately.46 A fundamental reason for this is that many antitrust cases have focused on such a practice as an anti-competitive one. Therefore, in this section we will try to understand when market leaders adopt bundling as a strategic device for exclusionary purposes. According to the traditional leverage theory of tied good sales, monopolists would bundle their products with others for competitive or partially competitive markets to extend their monopolistic power. Such a view as been criticized by the Chicago school (Bork, 1993, Posner, 2001) because it would erroneously claim that a firm can artificially increase monopolistic profits from a competitive market. Bundling should have diﬀerent motivations, as price discrimination or creation of joint economies, whose welfare consequences are ambiguous and sometimes even positive. Whinston (1990) has changed the terms of the discussion trying to verify how a monopolist can aﬀect the strategic interaction with its competitors in a secondary market by bundling. His main finding is that bundling tends to strengthen price competition against these competitors, therefore the only reason why a monopolist could bundle is to deter entry in the secondary market. However, here we will show that, when entry is endogenous, bundling may become the optimal “top dog” (aggressive) strategy.

46

where (x) = −p(x)/xp0 (x) is the elasticity of demand: the side whose demand is more elastic should be charged relatively more because this keeps demand on both sides balanced and maximizes the volume of interactions for a given total price. Now, imagine that the leading platform competes on one side, but L = p0 (k)k < 0, there is can commit to output k on the other side. Since Π13 a strategic incentive to commit to underproduction to be more aggressive on the competitive side. Leaders may alter the Rochet-Tirole rule leading to charge more one side to create strategic eﬀects on the competitors on the other side. Notice that tying refers to selling one product (the tying product) conditional on the purchase of another one (the tied product), but there will not be any substantial diﬀerence between the two for our purposes. This section follows Etro (2006e).

80

2. Strategic Commitments and Endogenous Entry

Imagine that a monopolistic market is characterized by zero costs of production and unitary demand at price v, which corresponds to the valuation of the good alone. Another market is characterized by standard price competition, a fixed cost F and a constant marginal cost c. Gross profits for the monopolist without bundling are: πM = v + (pM − c) D (pM , β M ) − F

(2.54)

while profits for the other firms are πi = (pi − c) D (pi , β i ) − F . In Bertrand equilibrium with endogenous entry the monopolist enjoys the profits π M = v. Under bundling, demand for the monopolist is constrained by demand for the other good, which is assumed less than unitary. The bundle price corresponds to PM = v 0 + pM , where v 0 ≥ v is the valuation of the primary good when bundled with a secondary good of the same firm: this maybe higher for eﬃciency reasons, complementarities or network externalities of diﬀerent kind. In such a case, the profits for the monopolist become: πMB = (PM − c) D(PM − v 0 , β M ) − F 0 = (pM + v 0 − c) D (pM , β M ) − F 0 where F 0 ≤ F is the fixed cost of production in case of bundling: this may also be lower than before because of cost eﬃciencies. The other firms have the same objective function as before. In Bertrand equilibrium the monopolist chooses the price PM = pM + v 0 satisfying: (PM − c)D1 [pM , (n − 1)g(p)] + D [pM , (n − 1)g(p)] = 0

(2.55)

while each one of the other firms chooses p satisfying: (p − c)D1 [p, g(pM ) + (n − 2)g(p)] + D [p, g(pM ) + (n − 2)g(p)] = 0 (2.56) If endogenous entry holds, the number of firms satisfies also: (p − c)D [p, g(pM ) + (n − 2)g(p)] = F

(2.57)

so that the profit of the monopolist bundling the two goods becomes π MB = (PM − c) D [pM , (n − 1)g(p)]. Notice that if we define β = g(pM )+(n−2)g(p) the equilibrium spillovers received by the entrants as a consequence of the price chosen by their competitors, the equilibrium conditions (2.56)-(2.57) jointly determine p and β independently from the price of the monopolist. Using β M = β + g(p) − g(pM ) we can rewrite the equilibrium first order condition of the monopolist as an implicit expression for pM = pM (v 0 ), and immediately derive that the equilibrium price of the secondary good decided by the monopolist has to be decreasing in v 0 .47 47

In particular we have: −D1 [pM , β + g(p) − g(pM )] dpM = <0 dv 0 ∆

2.10 Bundling

81

Clearly, bundling is optimal if πM B > π M . We need to verify under which conditions this happens. Before doing that, let us look at the way in which bundling changes the strategy of the monopolist. Since ∂π MB /∂pM − ∂π M /∂pM = v 0 D1 < 0, bundling makes the monopolist tough. This implies that the monopolist is led to reduce the eﬀective price in the secondary market by choosing a low price of the bundle. Since SC holds, a price decrease by the monopolist induces the other firms to reduce their prices. Under exogenous entry, as in the Whinston (1990) model with two firms, this reduces profits of all firms in the secondary market, hence bundling is never optimal unless it manages to deter entry. Under endogenous entry, however, this result can change: bundling can now be an eﬀective device to outplace some of the other firms without fully deterring entry in the secondary market, but creating some profits for the monopolist in this market through an aggressive strategy. In particular, bundling is optimal if the low price of the bundle increases profits in the competitive market more than it reduces them in the monopolistic one. It is easy to verify that bundling is optimal if: [pM (v 0 ) − c] D [pM (v 0 ), β M ] − F 0 > v − v 0 D [pM (v 0 ), β M ] whose left hand side is the gain in profits in the competitive market and whose right hand side is the loss in profits in the monopolistic market: Proposition 2.8. Under price competition with endogenous entry in a secondary market, a monopolist in a primary market can have an incentive to bundle both goods to be aggressive. It is important to remark that, in this case, bundling does not need to have an exclusionary purpose as assumed by the leverage theory of tied good sales. The reduction in the price of the two bundled goods together can also benefit consumers. This is even more likely when they are complements, when there are network externalities between products, or when bundling creates eﬃciency eﬀects. Bundling is an example of a discrete strategy: a firm either bundles two goods or not. A similar story can be used to evaluate a related discrete strategy, the choice of product compatibility and system compatibility, or interoperability: as Tirole (1988, p. 335) has correctly noticed, “a manufacturer that makes its system incompatible with other systems imposes a de facto tie-in.” Typically, product compatibility softens price competition because consumers can mix and match products of diﬀerent firms: these products endogenously become complements, while they would be substitutes in case of incompatibility. Since price cuts are more profitable when competing products are substitutes rather than complements, interoperability softens price competition. where ∆ ≡ 2D1 +(pM +v 0 −c)[D11 −g 0 (pM )D12 ] −g 0 (pM )D2 < 0 by the stability of the equilibrium system. In other words, the price of the bundle increases less than proportionally with v 0 or the monopolist oﬀers the bundle with a discount on the secondary good compared to its competitors.

82

2. Strategic Commitments and Endogenous Entry

Therefore, according to the standard outcome under price competition with an exogenous number of competitors, the only reason why a leader would choose a low level of interoperability would be to induce their exit from the market. On the contrary, our results suggest that, when entry in the market is endogenous, a leader may favour a limited level of interoperability for a diﬀerent purpose than entry deterrence: just because this strategy would strengthen price competition and enhance the gains from a low pricing strategy in the system competition, that is the competition between alternative systems.

2.11 Vertical Restraints Vertical restraints are agreements or contracts between vertically related firms. They include franchise fees, that specify a non-linear payment of the downstream firm for the inputs provided by the upstream firm with a fixed fee and a variable part (so that the average price is decreasing in the number of units bought), quantity discounts and various forms of rebates, that often play a similar role to the one of the francise fees, exclusivity clauses and other minor restraints. When these restraints improve the coordination of a vertical chain, they are typically welfare improving, however, when they aﬀect interbrand competition, that is competition between diﬀerent products and diﬀerent vertical chains, they can induce adverse consequences on consumers: namely they can be used to keep prices high and, therefore, they should be punished by the antitrust authorities. This is the standard result of the theory of strategic vertical restraints in interbrand competition (Bonanno and Vickers, 1988; Rey and Stiglitz, 1988), which suggests that, as long as firms compete in prices, a firm has incentives to choose vertical separation and charge his retailer a francise fee together with a wholesale price above marginal cost to induce an accommodating behavior. Consider an upstream firm that produces a good at marginal cost c and fixed cost F , and delegates its distribution on the market to a downstream firm through a contract implying a fixed fee Υ and a wholesale price w for the good. The downstream firm sells this same good at the price pD to maximize net profits: πD = (pD − w)D(pD , β D ) − Υ

(2.58)

while the other firms, that are vertically integrated and face the same cost structure, have the standard profit function πi = (pi − c)D(pi , β i ) − F . The upstream firm can preliminarily choose the optimal contract, meaning the wholesale price w and the fee Υ that maximize net profits: πU = (w − c)D(pD , β D ) + Υ − F

(2.59)

2.11 Vertical Restraints

83

It is always optimal to choose w such that the profits of the downstream firm are maximized, and the fee that fully expropriates these profits. Of course, a choice w = c would be neutral for the market outcome. However, Bonanno and Vickers (1988) have shown that, if competition is between an exogenous number of firms, it is optimal to choose a high wholesale price w > c to soften price competition, and increase prices compared to the outcome in which the firm is vertically integrated. This is the classic example of an anti-competitive vertical restraint adopted by a market leader through strategic delegation of accommodating pricing.48 When entry in the market is endogenous, the market leader cannot operate as above, because high wholesale prices would put the downstream firm out of the market. A market leader can still gain from delegating pricing decisions, but the optimal contract is now radically diﬀerent. In particular, we know from our general results, that competition in prices with endogenous entry between the downstream firm and the other firms would lead to a price pD (w) increasing in the wholesale price for the downstream firm, a price for the other firms p = pD (c) and an endogenous value for β; moreover, both p and β would be independent from w, and β D (w) = β + g(p) − g(pD (w)). One can verify that the optimal contract solves the problem: max πU = (w − c)D [pD (w), β D (w)] + Υ − F

{w,Υ }

s.v. : πD = [pD (w) − w] D [pD (w), β D (w)] − Υ ≥ 0 and requires a wholesale price for the retailer smaller than the marginal cost and implicitly given by:49 w∗ = c +

(pD − c)D2 g 0 (pD )
(2.60)

This wholesale price generates a lower equilibrium price and higher output for the downstream retailer than for the other firms, but generates positive profits. Summing up: Proposition 2.9. Under price competition with endogenous entry, it is optimal to delegate distribution to a downstream retailer with a francise fee contract involving a wholesale price below marginal cost so as to induce an aggressive pricing. 48

49

As well known in the literature, analogous results can be obtained removing intrabrand competition through exclusive territories for downstream retailers (these would feel free to set higher prices softening competition) or facilitating collusive outcomes through resale price maintenance. On vertical restraints see the survey by Tirole (1988, Ch. 4). On vertical mergers see also Motta (2004, Ch. 6). On exclusive dealing see Whinston (2006). One can verify that in the case of our Logit demand function (2.21), the optimal contract requires w∗ = c − F/N .

84

2. Strategic Commitments and Endogenous Entry

In such a case, the vertical restraint leads to a lower price for the consumers and there is no ground for conjecturing any anti-competitive behavior.50 Therefore, also in the case of vertical restraints aﬀecting interbrand competition, entry conditions are crucial to derive proper conclusions.

2.12 Price Discrimination When firms sell the same good at diﬀerent prices for diﬀerent consumers, they are adopting a policy of price discrimination, which is often regarded as an anti-competitive practice by antitrust authorities dealing with exclusionary or exploitative abuses by dominant firms: for this reason, in this sction we will try to understand the motivations for the adoption of price discrimination.51 Typically, this increases profitability, but it also allows to diﬀerentiate prices between consumers with a diﬀerent willingness to pay. Moreover, notice that price discrimination requires a certain commitment, because similar goods must be sold not only at diﬀerent prices for diﬀerent consumers, but also in diﬀerent packages and with diﬀerent advertising. In theory, when firms enjoy perfect information on the preferences of the consumers and can set a price equal to the maximum willingness to pay of each consumer, they can fully extract the consumer surplus, something known as first degree price discrimination. However, the usual forms of discrimination are much more limited. A large literature has focused on the more realistic case of incomplete information, in which firms oﬀer diﬀerent deals and customers choose their favorite: a typical example of this second degree price discrimination involves price-quantity bundles, often involving quantity discounts. A market often analyzed in the literature is the insurance market, where high risk types demand more insurance and low risk types demand less insurance (but firms do not know who is who). In such a market, simple price competition with free entry leads to a market failure because high risk types drive out low risk types and the market collapses (Akerlof, 1970). In such a case, diﬀerent prices for diﬀerent quantities naturally emerge in a competitive framework. Rothschild and Stiglitz (1976) have shown that a free entry equilibrium of this kind is characterized by low risk types accepting limited insurance associated with a low price and high risk types accepting full insurance at a higher price. Such a separating equilibrium works because high risk types prefer their contract rather than imitating the low risk types and obtain cheaper but limited in50

51

A similar result emerges also in models of competition in quantities, but this is less surprising since it confirms the outcome of delegation games with an exogenous number of competitors. See Tirole (1988, Ch. 3) for an introduction to price discrimination.

2.12 Price Discrimination

85

surance.52 On the contrary, a pooling equilibrium cannot exist because a firm may deviate by oﬀering a contract which is profitable if accepted just by the low risk types. The relevance of this theory of competitive price discrimination due to asymmetric information has been challenged on empirical ground because we rarely observe a positive correlation between risk and insurance, even in the automobile insurance market (Chiappori and Salanie’, 2000). However, this should not surprise because this (as many other insurance markets) is not a one shot market, but is characterized by short term contracts which are periodically updated. In a dynamic version of the Rothschild-Stiglitz model, pooling equilibria with experience rating naturally emerge (Etro, 2000), and they exactly mimic the bonus-malus policy that characterizes this market everywhere: initial contracts are standard for anybody, but future contracts are updated in a Bayesian fashion according to the performance of the drivers (which is public knowledge).53 Notice that also this form of dynamic price diﬀerentiation based on observable features (the accident record) is a form of price discrimination, still emerging in an equilibrium with endogenous entry. When firms discriminate on the basis of observable characteristics, we talk about third degree price discrimination. We can provide a simple example of the role of this form of price discrimination within our framework. For simplicity, imagine that all firms compete simultaneously for a common set of consumers, whose demand is DA (pi , β i ) for each firm i, and the leader also serves a local market with demand DB (pi ) (we assume that has to serve 52

53

While Rothschild and Stiglitz (1976) limited their analysis to two types of consumers, the model can be extended to multiple types: in such a case the equilibrium price function is nonlinear and can involve quantity discounts (Etro, 1999, 2000). Hence, the empirical literature started with Cawley and Philipson (1999), who tested (and rejected) the convexity of the price function in insurance markets is highly misleading: contrary to their erroneous claim, bulk discounts can perfectly characterize the equilibrium price of competitive insurance markets with asymmetric information (exacly as they can characterize the optimal monopolistic price discrimination; see Maskin and Riley, 1984). To gain insights on the nature of the pooling equilibrium in a two period Rothschild-Stiglitz model (Etro, 2000), let us suppose that a pooling contract is oﬀered in the first period by all firms. The usual problem is that a new firm may deviate by oﬀering a contract which is profitable if accepted just by the low risk types. In the one period model this kind of contract always exists. In the two period model, however, the high risk types have a new incentive to accept a similar deviation (and make it unprofitable), since by doing that, they would gain a reputation as low risk types and the associated second period contract with cheap full insurance. If agents are patient enough, any deviation is accepted by both types and so it is not profitable: hence the pooling contract is an equilibrium. Of course, also separating equilibria with immediate revelation of the risk types exist for low discounting.

86

2. Strategic Commitments and Endogenous Entry

both markets simultaneously). The leader can commit to a policy of price B discrimination, and then choose two separate prices pA L and pL for the same good sold at diﬀerent kinds of customers. The marginal cost of production is c for all firms. The profits of the leader are then: A A B B B B B A A π L = pA L D (pL , β L ) + pL D (pL ) − c[D (pL ) + D (pL , β L )] − F (2.61)

while the profits of the other firms are simply: ¡ ¢ A A π i = pA i − c D (pi , β i ) − F

Otherwise the leader can adopt a uniform pricing policy and choose a unique price pL for both kinds of customers, with the same profit function as above. The idea behind the commitment to discriminate is that price discrimination requires a small preliminary investment in package diversification and separate advertising for the products sold for the diﬀerent kind of customers. Consider the case of an exogenous number of firms. Choosing price disB crimination, the leader sets the two prices, say pA L > pL , and obtains monopolistic profits in the local market and (given symmetry) the same profits as the other firms in the symmetric Bertrand equilibrium for the common market. Choosing uniform pricing, the leader chooses an intermediate price A pL ∈ (pB L , pL ) in Bertrand equilibrium, and SC implies that also the other firms will reduce their equilibrium prices. Ultimately, the leader reduces its profits in the local market and strengthens competition in the common market. Clearly, in this case, price discrimination is the optimal choice, since it allows the leader to maximize profits in the local market and to soften competition in the common one. Consider endogenous entry now. Under price discrimination, all firms choose the same price pA L in the common market and entry drives profits to zero in this market, while the leader enjoys only its monopolistic profits in the local market setting the optimal price pB L . Assume again that the deB mand conditions are such that pA > p . In this case, by adopting uniform L L A pricing, the leader will choose an intermediate price between pB L and pL , and will obtain two results: on one side, profits in the local market will decrease because pricing is above monopolistic pricing, on the other side, profits in the common market will increase because the leader is endogenously committed to aggressive pricing, which is always optimal in a market where entry is endogenous. If the former loss is smaller than the latter gain, it is optimal to adopt uniform pricing rather than committing to price discrimination.54 This simple example is just aimed a suggesting that price discrimination can have a role in softening price competition (compared to uniform pricing) inducing negative consequences for consumers: this eﬀect, however, is less 54

Notice that this can happen because the loss from a small deviation from monopolistic pricing is a second order loss, while the gain in the common market is a first order gain.

2.13 Antitrust and Horizontal Mergers

87

likely to emerge in markets where entry is endogenous, since in these markets an aggressive uniform pricing strategy can be optimal. In conclusion, we may have a possible new case for the association of price discrimination by market leaders with anti-competitive purposes.55

2.13 Antitrust and Horizontal Mergers We have seen that even when they face endogenous entry of competitors, market leaders can obtain positive profits by adopting certain strategic commitments. One may think that a preliminary merger with other firms and a subsequent cooperation in the strategic decisions may serve a similar role. When the number of firms in the market is given, this is typically the case. Moreover, a merger induces a more accommodating behavior which exerts an indirect eﬀect on the other firms. When SS holds the other firms become more aggressive, when SC holds they become more accommodating as well:56 for this reason, loosely speaking, mergers tend to be more profitable under competition in prices. However, once again, the situation changes when entry is endogenous. In such a case the merger can aﬀect entry, which creates a new eﬀect, often taken into account in antitrust policy considerations, but not in the theory of mergers until now.57 In our context, a merger induces accommodation by the merged firm, which attracts entry and reduces the profits of the merged firm: consequently, there is no any strategic rationale for mergers when entry in the market is endogenous.58 Consider a merger between two firms, say firms k and j. The net profits of the merged firms become: ¡ ¢ πM erger = Π (xk , β k ) + Π xj , β j − F˜

55

56 57

58

Notice that a diﬀerent situation emerges if the demand conditions are such that B under price discrimination we have pA L < pL . Then, with exogenous entry, a uniform price by the leader increases prices and profits in market A and reduces them in market B, with ambiguous consequences, while with endogenous entry price discrimination is always optimal (and if it is not allowed, the leader is better oﬀ not serving market A). See Salant et al. (1983) and Deneckere and Davidson (1985). See also the work of Davidson and Mukherjee (2007) that extends the endogenous entry model of Etro (2002) to the case of mergers between firms producing homogenous goods, and especially Erkal and Piccinin (2007,a), who extend the analysis to the case of product diﬀerentiation. See Motta (2004, Ch. 5) for a survey of the literature on horizontal mergers. He points out that “the firms’ ability to raise prices after a merger is also limited by the existence of potential entrants. Firms which would find it unprofitable to enter the industry at pre-merger prices might decide to enter if the merger brings about higher prices or lower quantities. By anticipating this eﬀect, post-merger prices might not rise at all” (p. 236).

88

2. Strategic Commitments and Endogenous Entry

where F˜ is the new fixed cost of production. Using the fact that β j = β k + h(xk ) − h(xj ) for k, j = 1, 2, we have the first order conditions: Π1 (xk , β k ) + Π2 (xj , β j )h0 (xk ) = 0 k, j = 1, 2

(2.62)

which clearly shows an accommodating behavior for both strategies. As we know, such a behavior creates a strategic disadvantage when entry in the market is endogenous. The equilibrium after the merger is characterized by two identical strategies for the merged firm, xk = xj = xM , a strategy for the followers x, and respective spillovers β M and β such that: Π1 (xM , β M ) + Π2 (xM , β M )h0 (xM ) = Π1 (x, β) = 0, Π(x, β) = F This implies xM < x and β M > β: the equilibrium strategy of the other firms is always the same after the merger, but the accommodating behavior of the merged entity induces further entry so as to decrease its gross profits below those of each independent firm. Nevertheless, the merger can still be profitable if π Merger > 0, which requires F˜ < 2Π(xM , β M ). In a market where entry is endogenous, the only way a merger can be profitable is by creating cost eﬃciencies.59 This conclusion exactly matches the informal insights of the Chicago school on horizontal mergers (Bork, 1993, Posner, 2001), and can be summarized as follows: Proposition 2.10. In a market with endogenous entry, a horizontal merger induces accommodating behavior of the merged firm and attracts entry of other firms: the merger is profitable if and only if it creates enough cost eﬃciencies to compensate for the strategic disadvantage of the merged firm. Notice that in models of competition in quantities and prices, as long as the merged firm does not deter entry, the equilibrium after the merger implies the same total production or the same price indexes as before (see also Chapter 3). Therefore, consumer surplus is not aﬀected by the merger. Since the latter takes place only when there are significant cost eﬃciencies, it follows that horizontal mergers in markets where entry is endogenous are welfare improving.60 59

60

For instance, in the linear model of competition in quantities of Section 1.1, the merged firm would produce the same as the two separate firms, therefore the merger could be profitable only if F˜ < F . In the model with imperfect substitutability of Section 1.2.2, a merger between two firms would lead them to produce 2 − b times as before and to reach the joint profits π Merger = (2 − b)(2 + b − b2 )F/2 − F˜ which are positive if product diﬀerentiation is strong enough (b or F˜ small). The Erkal-Piccinin model extends the analysis to more complex demand functions: under competition in prices with a demand system derived from the quadratic utility function (2.11), a merger increases the prices of the merged

2.14 Conclusions

89

2.14 Conclusions This chapter has examined Nash and Marshallian competition within a general framework, and it has studied the strategic incentives of market leaders to undertake preliminary investments that can aﬀect competition. A main result of this investigation has been that the behavior of market leaders facing endogenous entry is always biased toward the implementation of aggressive strategies. As we noticed in the examples of Chapter 1, this result confirms what we found in models of Stackelberg competition with endogenous entry, that is in models where the leader does not undertake full fledged investments to constraint subsequent decisions, but simply commits to strategies before the other firms. Since the ultimate results are analogous, we can safely look at models of Stackelberg competition with endogenous entry as reduced forms of the more general models of Marshallian competition with strategic investments analyzed in this chapter. The advantages of the first kind of models are that they are simpler, they allow to derive clear welfare comparisons with the corresponding models of Marshallian competition, and they allow further extensions. For this reason, in the next chapter we will move on to the study of general models of Stackelberg competition in the market with and without endogenous entry. In Chapter 4 we will do the same for general models of Stackelberg competition for the market with and without endogenous entry.

firms and reduces the prices of the other firms while increasing entry (nevertheless, in the absence of cost eﬃciencies, the impact on consumer surplus is typically negative).

3. Stackelberg Competition and Endogenous Entry

In the 1930s, Stackelberg (1934) pioneered the study of a market structure where a firm has a leadership over the rivals. Market leaders obtain a stable advantage on the followers when they are first movers in the choice of the strategy. It is well known that the commitment of the leaders may not be credible when initial strategies can be easily revised over time. However, a commitment represents a credible advantage in markets with a short horizon or when strategies are costly to change. For instance, in some markets a certain production level is associated with preliminary investments in the preparation of projects, machinery, and on the allocation of diﬀerent inputs. It may be costly to change these factors of production afterwards: being a first mover on the output choice in these markets can represent a fundamental strategic advantage. In other markets, prices are sticky in the short run due to small menu costs or to costly acquisition of information, or because a price change can induce adverse reputational eﬀects on the perception of the customers: in these cases, being the first mover in the price choice provides the leader with a credible commitment in the short run. Finally, in sectors where firms compete for the market, a preliminary investment in research and development represents a solid commitment to an innovation strategy. In general, the economic concept of leadership associated with the timing of the decisions can be seen as a simple representation of situations in which preliminary investments, as those studied in the previous chapter, provide a strategic advantage to a firm. The modern game theoretic analysis of competition between market leaders and followers started from the seminal contribution of Dixit (1980),1 who focused, as with most of the subsequent literature, on a duopoly. When a market leader faces a single follower, two basic situations can emerge. If the fixed costs of production for the follower are high, the leader finds it optimal to deter entry, for instance by choosing a high output level that leaves too little demand for the follower, or by choosing a low price against which the follower cannot profitably compete. If the fixed cost of production is low enough, for instance if it is zero, the leader cannot profitably deter entry, and has to compete on the market with the entrant. There are two possible outcomes, and they depend on the form of competition, or more precisely, on the kind 1

See also Spence (1977) and Dixit (1979).

92

3. Stackelberg Competition and Endogenous Entry

of strategic interaction. Under strategic substitutability, that typically holds with competition in quantities, the leader is aggressive: for instance, produces a lot so as to gain market share compared to the rival. Under strategic complementarity, that typically holds with competition in prices, the leader is accommodating: for instance, chooses a high price so as to induce the rival to choose a high price as well. Ultimately, whether strategic complementarity or substitutability holds is an empirical question, but its answer is not obvious, as it is often not obvious what the strategic variables are that are under the control of firms in the real world. For this reason the results of the theory appear too vague to be of practical interest for unambiguous descriptions of the behavior of market leaders and for policy recommendations. The above analysis of the competition between a leader and a follower, as already said, holds when the fixed cost of production for the latter is low, so that entry deterrence is not an option for the leader. However, in this exact situation, net profits for the followers are likely to be high and they could attract other firms in the market. For this reason, an analysis limited to an exogenous number of firms (the leader and a single follower, or two followers, or any other given number of followers) can be quite misleading. In most markets, we can regard the number of competitors as an endogenous variable, which depends on the interaction between the market leader and the other firms, and not as an exogenous variable. In this chapter, we will examine the case in which a leader faces an endogenous number of followers. The results, based on Etro (2002, 2008), are quite simpler: the leader always behaves in an aggressive way, choosing higher production or lower prices than the followers. In particular, if each firm P has a profit function Π(xi , X−i ), where the aggregate statistics X−i = j6=i xj summarize the strategies of the other firms, an interior equilibrium can be characterized quite simply. The choice of each entrant satisfies the normal optimality condition Π1 = 0, while the choice of the leader satisfies Π1 = Π2 . For instance, under competition in quantities and homogenous goods, this implies that the entrants equate marginal cost and marginal revenue, while the leader equates marginal cost and price. Its profits are positive because production is in the region of increasing average costs. We will also verify under which conditions the leader finds it optimal to be so aggressive as to deter entry, and we will see that the conditions for such an outcome are not very demanding: under competition in quantities and homogenous goods the equilibrium implies just one firm, the leader, as long as there are increasing, constant or even slightly decreasing returns to scale.2 The analysis of Stackelberg competition with endogenous entry is somewhat related with three older theoretical frameworks. The first is the initial literature on entry deterrence associated with the so-called Bain-ModiglianiSylos Labini framework. However, even if the initial contributions by Sylos 2

As we have already seen in Chapter 1, with a linear demand p = a − X √ and a constant marginal cost c, the equilibrium implies the limit price p = c + 2 F .

3. Stackelberg Competition and Endogenous Entry

93

Labini (1956), Bain (1956) and Modigliani (1958) took in consideration the eﬀects of entry on the behavior of market leaders, they were not developed in a coherent game theoretic framework and were substantially limited to the case of competition with perfectly substitute goods and constant or decreasing marginal costs (which not by chance, as we will see, are suﬃcient conditions for entry deterrence). The second is the dominant firm theory, which tried to explain the pricing decision of a market leader facing a competitive fringe of firms taking as given the price of the leader.3 Assuming that the supply of this fringe is increasing in the price, the demand of the leader is total market demand net of this supply. The profit maximizing price of the leader is above marginal cost but constrained by the competitive fringe. While such a model is not fully consistent with rational behavior of the parts in a game theoretic perspective, it provides interesting insights on the behavior of market leaders under competitive pressure. The third is the theory of contestable markets by Baumol et al. (1982), which focuses mainly on homogenous goods and shows that, in the absence of sunk costs of entry, the possibility of “hit and run” strategies by potential entrants is compatible only with an equilibrium price equal to the average cost. One of the main implications of this result is that “one firm can be enough” for competition when there are aggressive potential entrants.4 None of these frameworks provides indications on the behavior of market leaders in general contexts, but nevertheless they have been quite helpful in providing insights on the role of competitive pressure in markets with leaders. 3

4

See Carlton and Perloﬀ (2004) and Viscusi et al. (2005, Ch. 6) for an introduction and Kahai et al. (1996) for an empirical application to the case of AT&T. See also the work of Gaskins (1971) on dynamic limit pricing under threat of entry; I am grateful to Avinash Dixit for attracting my attention on this work. Baumol et al. (1982) note that the contestable outcome can be described as the game in which firms first choose prices simultaneously and then choose output (or capacity) if they enter (choosing positive output implies entry decision). They also claim that the theory of perfect contestable market can be viewed as a generalization of the Bertrand game to markets with increasing returns to scale. In the case of a linear demand p = a − X and a constant marginal cost c, the contestable-market equilibrium requires a price of the incumbent equal to the average cost (p = a − x = c + F/x), therefore: p=

1 a+c− 2

(a − c)2 − 4F

which is always lower than the equilibrium price under Stackelberg competition in quantities with endogenous entry. The contestable-market equilibrium can be also interpreted as a Stackelberg equilibrium in prices with endogenous entry and homogenous goods. Of course, our theory applies beyond the case of homogenous goods.

94

3. Stackelberg Competition and Endogenous Entry

In this chapter we will develop a general theory of Stackelberg competition with endogenous entry within the framework developed in the previous chapter, and we will analyze complex situations where there are multiple leaders, where the leadership itself is endogenous, where there are multiple strategies to be chosen, and where there are more general profit functions. Finally we will analyze a few applications concerning collusive cartels and antitrust policy, strategic export promotion and privatizations. The chapter is organized as follows. Section 3.1 studies pure Stackelberg competition where entry is exogenous, while Section 3.2 studies Stackelberg competition with endogenous entry. Section 3.3 applies these models to general forms of competition in quantities and in prices. Section 3.4 extends the model in diﬀerent directions. Section 3.5 derives some implications for collusion between firms. Section 3.6-7 concludes our analysis with a digression on commitments created by government policy as state aids to exporting firms and privatizations. Section 3.8 concludes.

3.1 Stackelberg Equilibrium In this section we will study a general version of a simple and well known game: Stackelberg competition. The number of firms in the market, n, is exogenous, for instance because legal or institutional constraints limit entry, or because a certain technology is available only for a limited number of firms, or is protected by intellectual property rights. What is crucial for the following analysis is that no other firms can enter in the market even if this is profitable. One of the firms, the leader, can choose its own strategy before the other firms. These other firms, defined as followers, choose simultaneously their own strategies taking as given the strategy of the leader. Therefore, this is a Stackelberg game with one leader and n − 1 followers, and we are looking for its subgame perfect equilibrium. Imagine that each firm i has the profit function: πi = Π(xi , β i ) − F

with β i =

n X

h(xj )

(3.1)

j=1,j6=i

where Π is unimodal in the first argument xi , which is the strategy of the same firm, and decreasing in the second argument β i , which summarizes the strategies of the other firms through a positive and increasing function h(·). In Chapter 1 we analyzed a few examples of this environment: models of Stackelberg competition in quantities with linear demand and with homogenous goods or imperfect substitutability between goods, models with U-shaped average cost functions, models of competition in prices with a Logit demand, and simple models of competition for the market. In those examples the leader in the market was exploiting the first mover advantage in diﬀerent

3.1 Stackelberg Equilibrium

95

ways. For instance, in models of competition in quantities and of competition for the market we found out that the leader was aggressive compared to the followers (producing or investing more), while in models of competition in prices the leader was accommodating (choosing higher prices and producing less). Here we generalize those findings in a rule for the behavior of the market leaders. We will focus on the case in which interior equilibria emerge, that is all firms are active in the market and obtain positive profits, and the leader does not find it optimal to deter entry. This case emerges whenever the fixed costs are low enough.5 We can define the equilibrium in the following way: Definition 3.1. A Stackelberg Equilibrium between n firms is such that 1) each follower chooses its strategy x to maximize its profits given the spillovers β from the other firms and the strategy of the leader xL ; 2) the leader chooses its strategy xL to maximize its profits under rational expectations on β L ; 3) β = (n − 2)h(x) + h(xL ) and β L = (n − 1)h(x).

As usual, the equilibrium can be solved by backward induction. Given the strategy of the leader, defined as xL , all the followers choose their own strategies to satisfy the first order conditions: Π1 (xi , β i ) = 0 for any i

(3.2)

In this kind of game, for a given number of firms, a pure-strategy equilibrium exists if the reaction functions are continuous or do not have downward jumps (see Vives, 1999). Unfortunately this may not be the case due to the presence of fixed costs, but weak conditions for existence have been studied for many applications.6 In this general framework we will just assume the existence of a unique symmetric equilibrium where all the followers choose the same strategy x.7 In the symmetric equilibrium we have: Π1 [x, (n − 2)h(x) + h(xL )] = 0

(3.3)

This expression provides the strategy of the follower x as a function of the strategy of the leader and of the number of firms, x = x(xL , n). Totally diﬀerentiating the equilibrium first order condition, it follows that: Π12 (x, β) h0 (xL ) dx = dxL − [Π11 (x, β) + (n − 2)h0 (x)Π12 (x, β)] 5

6

7

The next section will deal with the case in which the fixed costs of production are high enough (or the number of potential entrants is high enough), that only a limited and endogenous number of firms actually enters in the market. For instance, see Amir and Lambson (2000) on Cournot games with perfectly substitute goods and Vives (1999) for a survey. This happens in all of our examples and, in general, under a standard contraction condition, Π11 + (n − 2)h0 (x) |Π12 | < 0. This always holds for n = 2. With more than one follower, weaker conditions for uniqueness are available for particular models.

96

3. Stackelberg Competition and Endogenous Entry

whose denominator is positive under the assumption of stability. Hence, a more aggressive strategy of the leader (an increase in xL ) makes the followers more aggressive under the assumption of SC (Π12 > 0), and less aggressive under SS (Π12 < 0). In the first stage, the leader takes this into account and maximizes: πL = Π L (xL , β L ) − F

(3.4)

where β L = (n − 1)h [x(xL , n)]. Therefore, in the case of an interior solution, we obtain the first order condition: ∂β Π1L (xL , β L ) + Π2L (xL , β L ) L = 0 (3.5) ∂xL and we assume that the second order condition is satisfied. Using our expression for dx/dxL we have: Π1L (xL , β L ) =

(n − 1)h0 (x)h0 (xL )Π12 (x, β) Π2L (xL , β L ) [Π11 (x, β) + (n − 2)h0 (x)Π12 (x, β)]

(3.6)

whose term on the right hand side has the sign of Π12 (x, β). Comparing the equilibrium condition for the followers and that for the leader, it is immediate to derive: Proposition 3.1. A Stackelberg equilibrium with exogenous entry implies that the leader is aggressive compared to the followers under strategic substitutability and accommodating under strategic complementarity. The intuition for this result is straightforward.8 When the leader foresees that a more aggressive strategy will induce the followers to be more aggressive, it is optimal to be accommodating, which happens under SC. When the leader foresees that a more aggressive strategy will induce the followers to be more accommodating, it is then optimal to be aggressive, which happens under SS. From this general principle we can make sense of our results in Chapter 1: in the models of competition in quantities, the leader was aggressive because higher production was pushing toward a lower production for the followers, while in the model of competition in prices, the leader was accommodating because a higher price was pushing toward higher prices for the followers as well, increasing the profits of all firms. As we will see later on in detail, these are the typical outcomes of these two forms of competition, while competition for the market can lead to a diﬀerent behavior of the leader depending on many market features, a point that we will revisit in the next chapter. 8

Contrary to the model of Fudenberg and Tirole (1984), here we do not have a preliminary investment that aﬀects the strategy, but we have a preliminary strategy tout court. In the terminology of the last chapter, it is as if we are L > 0. always in the case where Π13

3.2 Stackelberg Equilibrium with Endogenous Entry

97

3.2 Stackelberg Equilibrium with Endogenous Entry Let us move now to the case in which the number of firms in the market is not an exogenous variable, but it actually depends on the profitable opportunities in the market. As long as there are positive profits to be made in the market, firms enter and compete with the leader and the other firms.9 Therefore, the number of competitors is endogenously determined by the technological conditions, by the nature of the strategic interaction, and by the preliminary strategy of the leader. More precisely, following Etro (2002, 2008), we will look at the subgame perfect equilibrium of the game with the following sequence of moves: 1) in the first stage, a leader, firm L, enters, pays the fixed cost F and chooses its own strategy xL ; 2) in the second stage, after knowing the strategy of the leader, all potential entrants simultaneously decide “in” or “out”: if a firm decides “in”, it pays the fixed cost F ; 3) in the third stage all the followers that have entered choose their own strategy xi (hence, the followers play simultaneously). We can define the new equilibrium in the following way: Definition 3.2. A Stackelberg equilibrium with endogenous entry is such that 1) each follower chooses its strategy x to maximize its profits given the spillovers β from the other firms; 2) the number of firms n is such that all followers make non negative profits and entry of another follower would induce negative profits for all of them; 3) the leader chooses its strategy xL to maximize its profits under rational expectations on x and n; 4) β = (n − 2)h(x) + h(xL ) and β L = (n − 1)h(x). To characterize this equilibrium we look at the last stage again. In this stage, in the case of an interior equilibrium, we still have a standard first order condition for the followers: Π1 [x, (n − 2)h(x) + h(xL )] = 0

(3.7)

Since dΠ/∂dn = Π2 h(x) < 0 under our assumptions, entry reduces gross profits until they reach the fixed costs and further entry is not profitable anymore. Therefore, ignoring the integer constraint on the number of firms, we can impose the endogenous entry condition as a zero profit condition: 9

The exogeneity of the leadership, that is of the identity of the leader and also of the number of leaders, can be a realistic description for markets with an established dominant firm, or where entry at an earlier stage was not possible for technological or legal reasons, for liberalized markets that were once considered natural monopolies or those where intellectual property rights play an important role. Later, we will extend the model to multiple leaders and to endogenous leadership.

98

3. Stackelberg Competition and Endogenous Entry

Π [x, (n − 2)h(x) + h(xL )] = F

(3.8)

Leaving a formal treatment to the Appendix, we will provide here an intuitive and constructive argument to characterize the Stackelberg equilibrium with endogenous entry which will be useful in the applications of the next section. The system (3.7)-(3.8) can be thought of as determining the behavior of the followers in the second and third stages, namely as determining x and n as functions of the leader’s first stage action. But we can also look at these two equations in a diﬀerent way: they can be solved for the two unknowns x and β. The pair (x, β) will only depend on the fixed cost of production and not on the strategy of the leader. Given (x, β), there is a unique locus of (xL , n) pairs that satisfy the equilibrium relation β = (n − 2)h(x) + h(xL ). In other words, the strategy of the followers is independent from the strategy of the leader, while their number must change with the latter. The invariance property (dx/dxL = 0) is quite important since it shows that what matters for the leader is not the reaction of each single follower to its strategy, but the eﬀect on entry. This is exactly the opposite of what happened in the Stackelberg equilibrium. When entry is exogenous the leader takes as given the number of followers and looks at the reaction of their strategies to its own strategy. When entry is endogenous the leader takes as given the strategies of the followers and looks at the reaction of their number to its own strategy. Let us now move to the first stage and study the choice of the leader. As long as entry takes place, the perceived spillovers of the leader can be written as β L = (n − 1)h(x) = (n − 2)h(x) + h(x) + h(xL ) − h(xL ) = = β + h(x) − h(xL )

(3.9)

which depends on xL only through the last term, since we have just seen that the pair (x, β) does not depend on xL . We can use this result to verify when entry of followers takes place or does not. It is immediate that entry does not occur for any strategy of the leader xL above a cut-oﬀ x ¯L such that n = 2 or, substituting in (3.9), such that: β = h(¯ xL )

(3.10)

which clearly implies x ¯L ≥ x. Entry occurs whenever xL < x ¯L . In such a case, the leader chooses the optimal strategy to maximize: πL = Π L [xL , β + h(x) − h(xL )] − F which delivers the first order condition:10 10

Notice that the second order condition is: L L 0 L 0 DL = Π11 − 2Π12 h (xL ) − Π2L h00 (xL ) + Π22 h (xL )2 < 0

that we assume to be satisfied at the interior optimum.

(3.11)

3.2 Stackelberg Equilibrium with Endogenous Entry

Π1L [xL , (n − 1)h(x)] = Π2L [xL , (n − 1)h(x)] h0 (xL )

99

(3.12)

In this case the equilibrium values for xL , x and n are given by the system of three equations (3.7)-(3.8) and (3.12). In general, the profit function perceived by the leader is an inverted U relation in xL for any strategy below the entry deterrence level x ¯L , and it takes positive values just for xL > x. Beyond the cut-oﬀ x ¯L , it is downward sloping (as long as the market is not a natural monopoly). Hence, the strategy x ¯L is optimal only if it provides higher profits than at the local optimal strategy for xL < x ¯L (see the Appendix for the details). If we focus our attention on the qualitative behavior of the firms, we can conclude as follows: Proposition 3.2. A Stackelberg equilibrium with endogenous entry always implies that the leader is aggressive compared to each follower, and each follower either does not enter or chooses the same strategy as in the Marshall equilibrium. The main result is that when entry in a market is endogenous, the leader of this market behaves always in an aggressive way, independently from the kind of strategic interaction that takes place with the followers. In particular, an accommodating behavior, which is typical of models of price competition (where SC holds) when entry is exogenously limited, will never emerge when the decision to enter in the market is endogenously taken by a suﬃciently large number of potential entrants. Of course, this result is reminiscent of what we found in the previous chapter: there leaders were always undertaking preliminary investments that were inducing an aggressive behavior in the market, here they directly undertake aggressive strategies in a preliminary stage. We can conclude that the aggressiveness of leaders facing endogenous entry is a fairly general result. Comparative statics. We could now investigate the way our equilibria are aﬀected when we change some of the parameters, as we did in the previous chapter for the Nash and Marshall equilibria. Unfortunately, the comparative statics with respect to a generic parameter aﬀecting the profit functions are quite complicated for both the Stackelberg equilibrium and the Stackelberg equilibrium with endogenous entry. In the second case, we can make some progress focusing on changes in the fixed cost. It turns out that results are typically the opposite if SS or SC holds. For simplicity, let us assume Π22 ≥ 0, which will hold in most of our examples.11 The main results are summarized in: Proposition 3.3. Consider a Stackelberg equilibrium with endogenous entry where entry occurs. Under SS, a) if Π12 > Π11 /h0 (x), 11

Π22 > 0 holds in the case of quantity competition and perfectly substitute goods as long as demand is convex, in our examples of price competition, and in the patent races of the next chapter.

100

3. Stackelberg Competition and Endogenous Entry

the strategy of each firm is increasing and the number of firms is decreasing in F , b) otherwise, the strategy of entrants (leader) is L L increasing (decreasing) in F . Under SC, c) if Π12 < (=)Π22 Π1L /Π2L , the strategy of entrants and their number are decreasing while the strategy of the leader is increasing in (independent from) F , d) otherwise, the strategy of each firm is decreasing in F . These results are more interesting when we interpret entry as a “general equilibrium” phenomenon determined by the profits available in other sectors. In this case, F can be re-interpreted as the profits available in another sector and a no arbitrage condition between sectors determine the entry decisions. As in the Marshall equilibrium case, a positive shock in another sector (increasing F ) tends to reduce entry and induce more aggressive strategies by the entrants under SS and more accommodating strategies under SC, but the strategies of the leaders may react in the opposite way (or remain unchanged). In the next section we will verify these results in models of quantity and price competition, and briefly in a simple model of competition for the market (generalized in the next chapter).

3.3 Competition in Quantities, in Prices and for the Market In the previous sections we characterized equilibria in markets with pure Stackelberg competition and with Stackelberg competition and endogenous entry in a general way. In Chapter 1 we analyzed a number of simple applications. In this section we will adopt an intermediate level of sophistication. 3.3.1 Competition in Quantities The classic model of leadership due to Stackelberg (1934) is associated with competition in quantities and one firm committing to its own output before the other firms. Let us consider this situation under the following specification of the profit function: πi = xi p (xi , β i ) − c(xi ) − F

(3.13)

where xi is the output of firm i, we allow for imperfect substitutability between goods (the inverse demand is decreasing in both arguments) and we employ a general cost function. Exogenous entry. Let us first focus on the case of exogenous entry. Given the output of the leader xL , the equilibrium output of each follower will satisfy the profit maximizing condition: p (x, β) + xp1 (x, β) = c0 (x)

3.3 Competition in Quantities, in Prices and for the Market

101

where we remember that β = (n − 2)h(x) + h(xL ). The leader is aware that its strategy aﬀects the choice of the followers according to the impact dx/dxL that can be derived from the above condition, and can choose its output taking this into account.12 In Chapter 1 we solved for the Stackelberg equilibrium in the cases of a quadratic cost function with a linear demand and in the case of a linear cost function with a linear demand and imperfect substitutability between goods. Beyond those examples things are already quite complex. To obtain more useful results, let us focus on the standard case of homogenous goods and constant marginal costs. Totally diﬀerentiating the equilibrium condition: p(X) + xp0 (X) = c where X is total output, we obtain: −(1 − E) dx = dxL [n − E(n − 1)] Here E ≡ −xp00 (X)/p0 (X) is the elasticity of the slope of the inverse demand with respect to the production of a follower, which we already encountered in the previous chapter, and which measures the degree of convexity of the demand function. For instance, in the case of a linear demand, like the one we studied in the example of Chapter 1, this elasticity was zero: in that case, an increase in the output of the leader was reducing the output of each follower by 1/n. A negative impact emerges whenever this elasticity is small enough, but for a high enough elasticity, the impact may turn out to be positive. Given the perceived reaction of the followers, the leader chooses its output to maximize profits πL = [p(X) − c] xL − F , which provides the optimality condition: · ¸ dx 0 =c p(X) + xL p (X) 1 + (n − 1) dxL Joining the two equilibrium first order conditions and using the slope of the reaction function, we can easily obtain a new general expression for the equilibrium output of the leader as a function of the equilibrium output of the followers:13 12

13

If fixed costs of production are high enough, the leader can engage in entry deterrence, but now we focus on the case in which entry takes place. We can also solve for the equilibrium price under Stackelberg competition: p(X) =

1 − 1/

L

c [n − E(n − 1)]

where L = −p(X)/p0 (X)xL is the elasticity of demand perceived by the leader. We could also calculate the market share of the leader, which is larger than 50% whenever E < 1/(n − 1), that includes the linear demand case.

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3. Stackelberg Competition and Endogenous Entry

xL = x [n − E(n − 1)]

(3.14)

We can easily verify that in the case of a linear demand (E = 0), the leader produces n times the output of the followers, a result we already encountered in Chapter 1. When the demand is concave the leader produces even more than that, while in case of a convex demand the leader produces less than that. Finally, notice that in the particular case in which E = 1 the first mover advantage disappears and the leader produces exactly the same as each one of the followers. This is not such an extreme result, as we will see in the following example. Consider the case of a hyperbolic demand p = 1/X, which can be derived from the logarithmic utility (2.16). After some tedious calculations, the Stackelberg equilibrium can be solved for the production levels: xL =

2n − 3 4c(n − 1)

x=

2n − 3 4c(n − 1)2

Accordingly, the equilibrium price and the gross profits for the leader and the followers are: p=

2c(n − 1) 2n − 3

ΠL =

1 4(n − 1)

Π=

1 4(n − 1)2

First of all, notice that in the case where there are just two firms, the first mover advantage disappears: the choices of the two firms are strategically neutral in the Cournot duopolistic equilibrium (rather than complements or substitutes), and there is not an alternative commitment that can increase the profits of the leader.14 When the number of firms increases, the output of the leader increases compared to the one of the followers: indeed, we can verify that xL = (n − 1)x, which satisfies our general rule (3.14) for any number of firms. It follows that, with the exception of the duopoly case, we are always in a region where SS holds. Finally, one can also verify that total production is the same as under Cournot competition when there are just two firms, but it is higher whenever the number of firms is larger than two. Endogenous entry. Let us move to the case of endogenous entry in the model of quantity competition with a leadership. Consider again the general profit function (3.13). The equilibrium first order condition for the followers and the endogenous entry condition are: p (x, β) + xp1 (x, β) = c0 (x) xp (x, β) = c(x) + F 14

This is in line with our previous general result, since under this demand function the elasticity of the inverse demand is E = 2x/X, which satisfies our general rule (3.14) for n = 2 only when xL = x.

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103

and they pin down the production of the followers x and their spillovers β independently from the production of the leader. Consequently, the profits of the leader can be rewritten as: πL = xL p (xL , β L ) − c(xL ) − F = xL p [xL , β + h(x) − h(xL )] − c(xL ) − F whose maximization delivers the optimality condition: p(xL , β L ) + xL [p1 (xL , β L ) − p2 (xL , β L )h0 (xL )] = c0 (xL )

(3.15)

This relation provides the equilibrium production of the leader if goods are poor substitutes or the marginal cost is increasing enough, conditions that guarantee the existence of an interior solution. It emerges quite clearly that the leader is going to produce more than any follower. In particular, when goods are homogenous and the inverse demand is simply p(X), the equilibrium condition for the leader boils down to an equation between the price and its marginal cost. In such a case, the equilibrium is fully charcterized by the following conditions: p(X) =

c0 (x) c(x) + F = = c0 (xL ) 1 − 1/ x

(3.16)

where the first equality is a traditional mark up rule for the followers (with elasticity of demand), the second equality is the endogenous entry condition, and the third one defines the pricing rule of the leader. Notice that while the followers produce below the optimal scale (defined by the equality between marginal and average cost), the leader produces above this scale and obtains positive profits thanks to the increasing marginal costs. In Chapter 1 we studied an example of this result in the case of linear demand (p = a − X) and linearly increasing marginal cost (equal to dx), where profits were given by (1.18). The equilibrium output of the leader and the followers were: r r 1+d 2F 2F xL = x= d 2+d 2+d This simple set up with homogenous goods allows us to compare welfare under alternative forms of competition, namely Marshallian competition and Stackelberg competition with endogenous entry. Since we know from Mankiw and Whinston (1986) that the Cournot case is characterized by too many firms producing too little, it is clear that Stackelberg competition does better on both dimensions. Hence, it is welfare improving to assign a leadership position to some firms despite this will give them a dominant position with associated extra-profits. This is a general result since our model implies that total production is always the same under Stackelberg and Cournot competition when there is endogenous entry, but a leader produces more than the

104

3. Stackelberg Competition and Endogenous Entry

followers and consequently there are fewer firms in the Stackelberg case. The associated reduction in wasted fixed costs comes back in the form of profits for the leader. In conclusion, consumer surplus is the same, but welfare is higher under Stackelberg competition with endogenous entry: Proposition 3.4. Under endogenous entry and homogenous goods, as long as there is entry of some followers, Stackelberg competition in quantities is always Pareto superior with respect to Cournot competition. Another simple example of the aggressive behavior of the leader that we analyzed in Chapter 1 emerged in the model with product diﬀerentiation (demand pi = a − (1 − b)xi − bX) and constant marginal cost (c), where profits were given by (1.25), and the equilibrium output of the leader and the followers were: √ 2−b √ xL = F x= F 2(1 − b) Again the leader produces more than the follower and sells at a price above its marginal cost. The consequence is that entry of followers is reduced. Since consumers value product diﬀerentiation in such a model the welfare consequences are more complex. Nevertheless, the reduction in the price of the leader more than compensates the reduction in the number of varieties and consumer surplus is strictly increased by the leadership.15 Therefore, in this case the consumers strictly gain from the aggressive pricing strategy of the leader even if this induces some firms to exit and reduces the number of varieties provided in the market. Let us now move to the kind of equilibrium that can emerge when the interior solution characterized above does not maximize the profits of the leader. When goods are homogenous or highly substitute, or when the marginal cost is decreasing, constant or not too much increasing, the optimality for the leader implies a corner solution with entry deterrence and: 15

Using the quadratic utility function (2.11) and the related demand function, in equilibrium we have:   n 1 U =Y + x2 + b xi xj  2 i=1 i i j6=i

where Y is the exogenous income of the representative agent. One can verify that the gain in consumer surplus from the presence of a leader when entry is endogenous is: ∆U =

b(2 − b)F >0 8(1 − b)

and the gain in welfare is ∆W = ∆U + πL . I am thankful to Nisvan Erkal and Daniel Piccinin for insightful discussions on this point.

3.3 Competition in Quantities, in Prices and for the Market

xp [x, h(¯ xL )] = c(x) + F

⇐⇒

x ¯L = β − x

105

(3.17)

We saw an example of this outcome in Chapter 1 within the basic model with homogeneous goods, linear demand (p = a − X) and constant marginal costs c, where profits were given by (1.2). In that case, the equilibrium output, produced entirely by the leader was: √ x ¯L = a − c − 2 F Moreover, in that case we noticed that welfare was greater under Stackelberg competition with entry deterrence rather than Cournot competition with free entry because total production was reduced but the profits of the leader and the savings in fixed costs were enough to compensate the lower consumer surplus. Another simple case emerges with the hyperbolic demand (p = 1/X) and with constant marginal cost c. Now, the Stackelberg equilibrium with endogenous entry requires entry deterrence with production: ³ √ ´2 1− F x ¯L = c In the case of general demand functions for homogenous goods, we can actually find a simple suﬃcient condition for entry-deterrence which only depends on the shape of the cost function: Proposition 3.5. Under endogenous entry and homogenous goods, whenever marginal costs of production are constant or decreasing, Stackelberg competition in quantities always delivers entrydeterrence with only the leader in the market. This result can contribute to clarify the old debate on limit pricing. Entry deterrence through this forms of limit pricing is the equilibrium strategy for leaders facing endogenous entry for any demand function as long as goods are homogenous (or highly substitutable) and returns to scale are constant or decreasing.16 As both our examples show, the entry deterrence production is decreasing in the fixed cost, since this cost helps the leader to exclude the rivals. When the fixed cost diminishes the equilibrium output of the leader increases, and when it approaches zero, the equilibrium approaches the competitive outcome with a price equal to the marginal cost (indeed both x ¯L = a − c in the case of linear demand and x ¯L = 1/c in the case of hyperbolic demand correspond to a price p = c). Nevertheless, this eﬃcient output level is still entirely produced by one single firm, the leader. 16

This corresponds to the result of the contestable markets theory of Baumol et al. (1982). However, that theory generates a limit price which implies zero profits for the leader. For instance, with the hyperbolic demand the limit pricing would equate inverse demand and average cost (p = 1/x = c + F/x), which implies x = (1 − F )/c > x ¯L .

106

3. Stackelberg Competition and Endogenous Entry

3.3.2 Competition in Prices The role of price leadership is often underestimated for two main reasons. The first is that commitments to prices are hardly credible when it is easy and relatively inexpensive to change prices. While this is true for long term commitments, it is also true that short term commitments can be credible in most markets. The macroeconomic literature on price stickiness has developed a number of arguments on why this may be the case, ranging from small menu costs of price adjustments to costs in the acquisition of information to reoptimize. The second reason for which a price leadership may poorly describe the behavior of market leaders is probably more pervasive and relies on the absence of a first mover advantage in simple models of competition in prices. For instance, in standard duopolies, a price leader obtains lower profits than its follower, and for this reason neither one nor the other firm would like to be a leader: there is actually a second mover advantage. As we will see, this result disappears and the first mover advantage is back when entry in the market is endogenous. In our general class of models with price competition the profit function is given by: πi = (pi − c) D (pi , β i ) − F

(3.18)

where pi is of course the price of firm P i, and the demand function is decreasing in both arguments, with β i = j6=i g(p) for some positive and decreasing function g. Notice that the model is nested in our framework (3.1) after setting xi = 1/pi as the strategic variable (see Section 2.4.2 for a discussion). Exogenous entry. Let us consider first the case of exogenous entry. Stackelberg equilibrium with n firms is characterized by the following equilibrium optimality conditions for the followers and the leader:17 D (p, β) + (p − c)D1 (p, β) = 0 · µ ¶¸ dβ L D (pL , β L ) + (pL − c) D1 (pL , β L ) + D2 (pL , β L ) =0 dpL

(3.19)

where dβ L /dpL < 0 can be derived by the optimality condition of the followers as long as SC holds. While the equilibrium conditions soon become quite complex, the positive last term shows that the leader chooses a price above the one of the followers, inducing a general increase in prices compared to the Nash-Bertrand equilibrium between the same firms. The choice of a high price by the leader is aimed at softening price competition, but it also leads the followers to make more profits by choosing a lower price and stealing market shares from the leader. 17

If fixed costs of production are high enough, the leader can engage in entry deterrence, but here we will focus on the case in which entry is accommodated.

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107

Endogenous entry. Let us now look at the Stackelberg equilibrium with endogenous entry. The optimality condition for the followers and the endogenous entry condition are: D (p, β) + (p − c)D1 (p, β) = 0 (p − c) D (p, β) = F and they pin down the price of the followers p and their spillovers β = (n − 1)g(p), so that the profit of the leader becomes: π L = (pL − c)D [pL , (n − 1)g(p) − g(pL )] − F = = (pL − c)D [pL , β + g(p) − g(pL )] − F Profit maximization delivers the equilibrium condition: D(pL , β L ) + (pL − c) [D1 (pL , β L ) − D2 (pL , β L )g 0 (pL )] = 0

(3.20)

which implies a lower price pL than the price of the followers, since the last term is negative. This is a crucial result by itself since we are quite familiar with associating price competition and accommodating leaders setting higher prices than the followers: this standard outcome collapses under endogenous entry. Moreover, the leader is now obtaining positive profits, while each follower does not gain any profits: the first mover advantage is back. In Chapter 1 we have seen an example based on the Logit demand (2.21), where the equilibrium prices were: pL = c +

1 λ

p=c+

1 F + λ N

Moreover, using the microfoundation pointed out by Anderson et al. (1992) in terms of the quasilinear utility (2.22), one can show that this equilibrium is Pareto eﬃcient compared to the correspondent Marshall equilibrium: the reduction in the price of the leader reduces entry, leaves unchanged consumer surplus and increases firms’ profits, inducing an increase in total welfare. In the case of the isoelastic demand (2.24) derived in the last chapter from the utility function (2.23), we obtain the following prices: pL =

c θ

p=

cY θ [Y − F (1 + α)]

where of course the leader applies a lower mark up than each follower.18 It can be verified that in any version of the Dixit-Stiglitz model where 1/(1 − θ) 18

As we already noticed, we could analyze competition in quantities within the same model - one can obtain the inverse demand from (2.23). Since there is product diﬀerentiation, also that case would entail a higher output for the leader, and consequently a lower price.

108

3. Stackelberg Competition and Endogenous Entry

is the constant elasticity of substitution between goods and c is the marginal cost of production, as long as entry is endogenous, the leader will choose the price pL = c/θ and the followers will choose a higher price. Indeed, free entry pins down the price index that is perceived by the leader, whose optimization problem is of the following kind: −

1

max(pL − c)DL ∝ (pL − c)pL 1−θ which always delivers the price above. As a consequence, the leader produces more than each follower and the number of followers is reduced compared to the Marshall equilibrium. Once again, however, consumer surplus is not changed because the price index is unaﬀected. Since the leader obtains positive profits, overall welfare is increased. We summarize these results as follows: Proposition 3.6. In a model of price competition with Logit demand or Dixit-Stiglitz demand and endogenous entry, a leader sells its variety at a lower price than the entrants, inducing a Pareto improvement in the allocation of resources. In all of these models we can verify the existence of an unambiguous ranking of market structures from a welfare point of view. Indeed, from the best to the worst case for welfare we have: 1) endogenous entry with a leader; 2) endogenous entry without a leader; 3) barriers to entry without a leader; 4) barriers to entry with a leader. If we look at consumer surplus only, case 1) and 2) deliver the same utility for the consumers, but the rest of the ranking is unchanged. This welfare results have important consequences for the evaluation of market leaders and for antitrust policy: we will return on them in Chapter 5. 3.3.3 Competition for the Market In Chapter 1 we studied a simple model of competition for the market where firms were investing to obtain a reward V . Under the specification: πi = xi

n Y

j=1,j6=i

(1 − xj ) V −

x2i 2

(3.21)

with xi investment in R&D for firm i, we found that because of SS, a Stackelberg equilibrium was characterized by a leader investing more than each follower, while a Stackelberg equilibrium with endogenous entry was characterized by only the leader investing: √ 2F x ¯L = 1 − V These results are not general, since more realistic descriptions of the market for innovations can lead to diﬀerent results. Nevertheless, as we will see in the next chapter, which focuses entirely on competition for the market, a leader always invests more than any other firm when entry is endogenous.

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109

3.4 Asymmetries, Multiple Leaders and Multiple Strategies The results of the previous sections can be extended in many directions to be able to describe market structures in a more realistic way. This section will consider a few directions: introducing a technological asymmetry between the leader and the followers, extending the model to multiple leaders, endogenizing the same leadership status, allowing for multiple strategies and considering more general profit functions. Our main focus, at this point, will be on the case where entry is endogenous, which we believe to be more relevant in most markets. 3.4.1 Asymmetries Between Leader and Followers In this section, following Etro (2002), we assume that the leader has the profit function: πL = Π L (xL , β L , K) − F where K is a new parameter specific to the leader (it may well be a vector of parameters). The basic assumptions are Π3L ≡ ∂Π L /∂K > 0 and Π L (x, β, 0) = Π i (x, β). Notice that, while this specification may look like the one analyzed in Chapter 2, here we are talking about an exogenous parameter K, not an endogenous one. We are interested in understanding how exogenous asymmetries aﬀect the behavior of market leaders, and not how market leaders endogenously create asymmetries to aﬀect their behavior (which was the purpose of the analysis of the previous chapter). A first mover advantage is often associated with some asymmetry between the leader and the followers. For instance, in the simple model of competition for the market of Chapter 1 we extended the basic model to consider leaders that were also incumbent monopolists with a flow of current profits aﬀecting their expected profits. In other cases, it is natural to link the first mover advantage with some technological or market advantage, for instance a lower marginal cost c(K) for the leader (with c0 (K) < 0), or other diﬀerences as those suggested in the previous chapter. In general, when entry is endogenous we obtain a strategy of the leader which depends on K, xL = xL (K), and hence the number of entrants, but not their individual strategy, also depends on K. One can show: Proposition 3.7. An asymmetric Stackelberg equilibrium with endogenous entry implies that the leader is aggressive whenever L L Π13 ≥ Π23 (Π1L /Π2L ) or K is small enough. The intuition is the following: an increase in the advantage of the leader (that is in K) induces a higher incentive to aggressiveness if it raises the

110

3. Stackelberg Competition and Endogenous Entry

marginal benefit from it more than the change in its marginal cost. Indeed the suﬃcient condition could be rewritten as ∂(Π1L /Π2L )/∂K ≤ 0, that is the marginal rate of substitution between xL and β L is decreasing in K. If this condition does not hold, it means that x0L (K) < 0, therefore for a great enough K (a strong enough asymmetry) the leader may be accommodating (xL (K) < x). To exemplify how one can apply this result, notice that the leader with a lower marginal cost than its followers will always be aggressive because L (as one can easily verify) under competition in quantities we have Π13 > L L 0 and Π23 = 0, and under competition in prices we have Π13 > 0 and L Π23 < 0. Similarly one can examine other kinds of exogenous asymmetries (as those we examined in the previous chapter on the demand side, in the financial structure, in complementary markets, and so on) and verify how the incentives of the leader to be aggressive are changed. 3.4.2 Multiple Leaders Until now we considered a simple game with just one leader playing in the first stage. Here we will consider the case in which multiple leaders play simultaneously in the first stage. Hence the timing of the game becomes the following: 1) in the first stage, m leaders simultaneously choose their own strategies; 2) in the second stage, potential entrants decide whether to enter or not; 3) in the third stage each one of the n − m followers that entered chooses its own strategy. In the next section we will discuss how to endogenize m. When entry is endogenous we should consider two diﬀerent situations: one in which entry of followers is not deterred in equilibrium and one in which the leaders deter entry. Consider first the case in which the number of leaders m is small enough, or the cost of deterrence is large enough that entry of followers takes place in equilibrium. In such a case, the behavior of the leaders can be characterized in a similar fashion to our basic analysis. Moreover, contrary to what happens when the number of firms n in the market is exogenous (in that case the number of leaders m aﬀects their strategic interaction, their strategies and their profits), with endogenous entry the number of leaders does not aﬀect their strategies, still given by (3.12), and their profits: Proposition 3.8. Under Stackelberg competition with m leaders, as long as there is endogenous entry of some followers, each leader is aggressive compared to each follower and its strategy and profits are independent from m. This confirms the spirit of our results with a single leader. Each one of the leaders now behaves in an aggressive way compared to the followers and also independently from the other leaders. For instance, under competition in quantities and increasing marginal cost, each leader produces the same

3.4 Asymmetries, Multiple Leaders and Multiple Strategies

111

output that equates the marginal cost to the price, and the equilibrium price equates the optimal mark up of the followers to the fixed cost of production. While the profit of each leader is not aﬀected by the number of leaders, the number of entrants is clearly decreased by an increase in the number of leaders. The situation is more complicated if there is entry deterrence in equilibrium. In the case of an exogenous number of firms, entry deterrence is a sort of public good for the leaders, which may introduce free-riding issues in their behavior. Gilbert and Vives (1986) have analyzed this issue in a model with m leaders facing a potential entrant, while Tesoriere (2006) has extended the model in Etro (2002) to analyze the case of m leaders facing endogenous entry. The result can easily be seen through a simple example with two leaders. Let us analyze a model of competition in quantities with a linear inverse demand p = a − X, constant marginal cost c, m = 2 and endogenous entry of followers. ¯= √ Remember that the entry deterring output in this model is x a − c − 2 F . Consider the best response of one leader, say L1 . If the output of the other leader, say L2 , is already above the entry deterrence level, xL2 > x ¯, the best strategy is clearly xL1 = 0. However, whenever the output of the second leader is below the entry deterring level, it is always optimal to produce at least enough to deter the entry of any follower, which implies xL1 ≥ x ¯ − xL2 . Nevertheless, it may be optimal to produce more than this when the standard Cournot best response, namely xL1 = (a − c − xL2 ) /2, generates a higher output than √ the level that is suﬃcient to deter entry, which happens for xL2 > a − c − 4 F . An analogous rule drives the best response for the second leader. In summary, the best response function for a leader Li with i, j = 1, 2 is: ( ) 0 ¯ i if xLj ≥ x h √ xLi (xLj ) = a−c−xLj ¯ if xLj < x max a − c − 2 F − xLj ; 2 that can be rewritten as: √   c − 2 F √  0 xLj ≥ a −  √ xLi (xLj ) = (a − c −√xLj ) /2 if xLj ∈ [a − c − 4 F ; a −√c − 2 F )   a − c − 2 F − xLj xLj < a − c − 4 F

This analysis has generated two best responses that are slightly more complex than what we have seen before. Nevertheless, it is relatively easy to characterize the equilibria where the two best responses are consistent with each other. Under all circumstances there are two equilibria in which just one of the two leaders produces all the entry deterring output and only this:19 19

The profits of the single firm active in the market are positive if F < 4(a−c)2 /25. As it will be clear in what follows, the two polar equilibria with just one leader deterring entry are the only possible equilibria when F ∈ (a − c)2 /9; 4(a − c)2 /25 .

112

3. Stackelberg Competition and Endogenous Entry

√ xLi = a − c − 2 F , xLj = 0 Moreover, there are other possible equilibria with both the leaders active in the market. We need to distinguish two cases depending on the size of the fixed cost. When the fixed cost is high enough, the standard equilibrium of the Cournot duopoly is an equilibrium of Stackelberg competition in quantities with endogenous entry and two leaders, since it implies a high enough output so that further entry is deterred. Since in a symmetric Cournot duopoly each firm (each leader here) produces: xL1 = xL2 =

a−c 3

this equilibrium requires that profits are positive for both firms, or F < (a − c)2 /9, and that total output is enough to deter entry of any follower, 2(a − c)/3 > x ¯ or F > (a − c)2 /36. When the fixed cost is lower than this last cut-oﬀ, however, the two best response functions overlap in an intermediate region where aggregate production is just enough to deter √ entry, and we have a continuum of equilibria with xL1 + xL2 = a − c − 2 F and such that both firms produce enough to obtain positive profits. This requires: h √ √ √ i xL1 = a − c − 2 F − xL2 and xL2 ∈ a − c − 4 F ; 2 F In summary, Stackelberg equilibria in quantities with two leaders and endogenous entry in the case of linear demand and marginal cost are always characterized by entry deterrence with the following possible configurations of production by the leaders:   √ 2   xLi = a − c − 2 F , xLj = 0 for any F h< 4(a−c)   25 i   (a−c)2 (a−c)2 xL1 = (a − c) /3 and xL2 = (a − c) /3 if F ∈ ; 9 h i36     any x = a − c − 2√F − x ∈ a − c − 4√F ; 2√F if F < (a−c)2   Li

Lj

36

Tesoriere (2006) generalizes this example to m leaders, showing that endogenous entry of followers is always deterred,20 and there is always an equilibrium with just one leader producing the entry deterrence output and the remaining leaders producing zero. Furthermore, the symmetric Cournot equilibrium between all the m leaders can be an equilibrium when total Cournot output of the m leaders exceeds the entry deterrent output, and there can be a continuum of equilibria with aggregate production equal to the entry deterrent level when the fixed cost of production is low enough. Hence, underinvestment in entry deterrence cannot occur when entry is endogenous, while overinvestment in entry deterrence can occur (but leaders always obtain strictly positive profits). Once again, this outcome remains in the spirit of our results about the aggressive behavior of market leaders. 20

As we have seen from the case of a single leader, under constant marginal costs, entry deterrence occurs for any demand function.

3.4 Asymmetries, Multiple Leaders and Multiple Strategies

113

3.4.3 Endogenous Leadership After developing a Stackelberg model with multiple leaders and endogenous entry of followers, it is natural to verify what happens when there is endogenous entry of leaders as well. The simplest way to endogenize the number of leaders is by adding an initial stage of the game where firms decide simultaneously whether or not to become a leader.21 Any firm can make an investment, say I, which provides the status of a leader in the market, while any firm that does not invest can only enter in the market as a follower: in other words, commitment to strategies is costly. As Prop. 3.8 suggests, as long as there is entry of followers, it must be that all leaders obtain the same level of positive profits (which is independent from the number of leaders m). Therefore, if the investment needed to become a leader is small enough, there must always be incentives to invest to become leaders when this does not deter entry of followers. Then, consider the largest number of leaders compatible with some entry, say M . Given this number of leaders, another firm may invest in leadership and subsequently engage in Nash competition with only the other leaders (entry of followers is now deterred by construction). If such an entry is profitable, the equilibrium must imply only leaders in the market and an endogenous number m∗ > M derived from a free entry condition with a fixed cost F + I (clearly this happens whenever the cost of leadership is zero or small enough). If this is not the case, the only equilibrium implies m∗ = M firms investing in leadership and a residual competitive fringe of followers: once again, as Prop. 3.8 still implies, all leaders would be aggressive compared to each follower. Another interesting situation emerges when entry is sequential, leading to a hierarchical leadership. While a general treatment of sequential games is complex, Vives (1988) and Anderson and Engers (1994) have fully characterized sequential competition in quantities with linear costs and isoelastic demand, and with an exogenous number of firms.22 Their analysis makes clear that in the case of endogenous entry the only possible equilibrium would imply entry deterrence.23 21 22

23

See Hamilton and Slutsky (1990). See Prescott and Visscher (1977) for an early discussion. Economides (1993) studies free entry in a game with simultaneous entry at the first stage and sequential quantity decisions between the entrants. Tesoriere (2006) studies the following extension of Etro (2002): at a first preplay stage firms simultaneously decide whether or not to enter the market and at which period t ∈ T , then at each stage t = 1, 2, ..., T , each firm that has chosen to enter at stage t decides how much to produce, knowing the production chosen by all the firms that entered in the previous periods, taking as given that of the other firms that enter at the same time t, and anticipating correctly the strategies of the later movers. Focusing on the case of constant marginal costs, he shows that at any Subgame Perfect Nash Equilibrium, endogenous entry occurs

114

3. Stackelberg Competition and Endogenous Entry

3.4.4 Multiple Strategies In this section we will show that a weaker version of the result on aggressive leaders generalizes when firms choose multiple strategic variables. Imagine that each firm chooses a vector of K ≥ 1 strategic variables xi = [xi1 , xi2 , ..., xiK ] ∈
with h : h(xj ). Then, in equilibrium we have a vector x for the followers which is independent from the leader’s strategies, and the following equilibrium conditions for the strategies of the leader: µ ¶ ∂h(x) ∂Π L (x, β L ) ∂Π L (xL , β L ) = ≤ 0 for all k (3.23) ∂xLk ∂xLk ∂β L These conditions do not imply that the leader is more aggressive in all the strategies, but that it must be more aggressive in some strategies. Moreover, they allow us to derive: immediately and simultaneously, and that any of the following configurations is an equilibrium: 1) one of the firms enters in t = 1 and produces the entry deterring output; 2) m firms enter in t = 1 and produce the entry deterring output in aggregate, when the Cournot equilibrium with m firms would imply a lower aggregate output than the entry deterring output; 3) m firms enter in t = 1 and produce as in a Cournot equilibrium with m firms, when this implies an aggregate output which is larger than the entry deterring output. No other configuration is sustainable as equilibrium, but the above characterization of equilibria already exhibits multiplicity. At any of the possible equilibria, however, only market leaders produce: when the leadership is endogenous, sequential production is never observed.

3.4 Asymmetries, Multiple Leaders and Multiple Strategies

115

Proposition 3.9. A Stackelberg equilibrium with endogenous entry and multiple strategic variables always implies that the leader is on average more aggressive than each follower. To see how to use this result we develop two examples. Capital/labour choices. Let us extend the simplest model of competition in quantities with a production function using two inputs, say capital ki and labour li according to a Cobb-Douglas specification xi = kiα liη with 0 < α ≤ 1 − η < 1. Suppose that the rate of return on capital is r and the wage rate is w. Then, the profit function can be written as:   X η η η πi = kiα li · p kiα li , kjα lj  − rki − wli − F j6=i

where the usual inverse demand function p(·) is decreasing in both arguments. We can apply Prop. 3.9 after setting h(ki , li ) = kiα liη . On this basis, we cannot immediately say whether a leader facing endogenous entry will hire more workers than the followers or will employ more capital than them. What we can say is that the leader will produce more (and employ more of one or both inputs). Fortunately, in this case we can also verify that all firms choose the same capital-labor ratio k/l = αw/ηr, therefore we can conclude that the leader must employ more labor and also more capital than each follower. Quality/price choices. Let us extend our basic model of price competition with the choice of a second strategy, the quality of the product. In such a model with vertical diﬀerentiation, each firm can oﬀer a product of quality qi at a price pi , and the marginal cost for this quality level, c(qi ), is increasing and convex in quality. Let us assume that consumers allocate their demand by comparing the quality-price ratios of the diﬀerent products. Then, expected profits are:   µ ¶ X pi pj  πi = D  , g [pi − c(qi )] − F qi qj j6=i

Defining θi = qi /pi as the quality/price ratio for firm i, this model satisfies our conditions with:     · ¸ X X 1 qi     h(θj , qj ) = D , h(θj , qj ) − c(qi ) Π θ i , qi ; θi θi j6=i

j6=i

where h(θi , qi ) = g(1/θi ). We cannot say whether the leader will oﬀer a good with both a lower price and a higher quality, but only that the good of the leader will be better than the goods oﬀered by the followers at least in one of these two dimensions. Nevertheless, we can also infer from Prop. 3.8 that the

116

3. Stackelberg Competition and Endogenous Entry

leader will be more aggressive than the followers on average, which means that h(θL , qL ) > h(θ, q). But this implies g(1/θL ) > g(1/θ) or, using the fact that g is a decreasing function, that θL > θ. We can then conclude that in a Stackelberg equilibrium in price and quality with endogenous entry the leader supplies a good with a better quality-price ratio than each other follower.24 3.4.5 General Profit Functions In this chapter we examined the behavior of firms with a first mover advantage over their competitors in the choice of the market strategy. A general result that emerges in the presence of endogenous entry is that leaders tend to behave in an aggressive way, in particular they choose lower prices and higher output than their followers. While we noticed that the spirit of this result is robust to a number of extensions, at least under some regularity conditions, we are aware that we had to impose a considerable amount of symmetry in the general model adopted in this book to obtain the simple results described until now.25 For instance, our simple results do not apply to models where profits depend on the number of firms in a more complex way26 or when conjectural variations of the firms are not restricted to the Nash case. Nevertheless, as shown in Etro (2008), also in a more general framework there is still a tendency of the market leaders to be aggressive toward a fringe of competitors that endogenously enter in the market. In particular, generalizing our analysis to the case of demand functions exhibiting strong forms of love for variety, we have verified that the tendency toward an aggressive pricing of the leaders facing endogenous entry remains, but the behavior of the followers is now aﬀected. For instance, consider theP classic case of imperfect substitutability with linear demands pi = a − xi + b j6=i xj , that we studied many times in this book and that can be derived from a quadratic utility function as (2.11). Inverting the system, we obtain the direct demands: P b a − pi + 1−b j6=i (pj − pi ) Di = (3.24) 1 + b(n − 1) 24

25

26

Similarly, in a generalized version of the Logit model (1.34) with demand for good n uj , where ui = qi − λpi parameterizes utility i equal to Di = Neui / j=1 e from purchasing good i, a leader facing endogenous entry would choose quality and price so as to provide higher utility to the consumers than the followers. Analogous results emerge if quality does not aﬀect marginal costs but it aﬀects fixed costs. On quality choices in the Logit model see also Anderson et al. (1992, Ch. 7). For a critique to the generality of our characterization of Stackelberg equilibria with endogenous entry, and to the implications that can be drawn from it, see Encaoua (2006). As with the demand function of Shubik (1980), which, however, does not generate love for variety (see Erkal and Piccinin, 2007a).

3.4 Asymmetries, Multiple Leaders and Multiple Strategies

117

It can be verified that the profit function associated with this case is not nested in our general framework. Nevertheless, it is well behaved and it is decreasing in the number of firms for given strategies. Since prices are strategic complements, the Stackelberg equilibrium with an exogenous number of firms is characterized by a higher price for the leader compared to the followers. Contrary to this, the Stackelberg equilibrium with endogenous entry is characterized by a lower price for the leader compared to the followers. Moreover, the price of the leader is below the equilibrium price in the Marshall equilibrium, while the price of the followers is above it and the number of products is reduced.27 In the long run, prices turn into strategic substitutes: the reduction in the price of the leader induces the followers to increase their prices.28 Finally, we hope that these simple models of market leadership could be useful for normative purposes. Understanding the way markets work under diﬀerent entry conditions is important not only to derive policy implications for competition policy, a topic on which we will turn in Section 3.5 and in Chapter 5, but also to understand how government policy should deal with a number of issues concerning foreign markets and domestic ones, a hot topic in the days of intense globalization, on which we will focus in Sections 3.6 and 3.7. 27

Assume zero marginal costs. The optimality condition of the followers and the endogenous entry condition imply the following equilibrium relation between the price of the followers p and the number of firms n: p=

F (1 − b)[1 + b(n − 1)] [1 + b(n − 2)

A reduction in the price of the leader pL reduces entry and, according to this relation, it increases the price of the followers. The profit of the leader is: πL =

28

pL b(n − 1) (p − pL ) − F a − pL + 1 + b(n − 1) 1−b

where both n and p depend on pL . Since ∂πL /∂nbpL =p < 0, it is optimal for the leader to reduce the number of firms compared to the Marshall equilibrium. This implies a lower price of the leader and a higher price of the followers in the Stackelberg equilibrium with endogenous entry compared to the price of the Marshall equilibrium. These result derive from joint work with Nisvan Erkal and Daniel Piccinin. Notice that with a Shubik demand a leader facing endogenous entry would reduce its price and the followers would reduce their prices as well (prices are strategic complements in both the short and long run). As a consequence the number of varieties provided in the market would decrease. Nevertheless, consumer surplus would strictly increase because of the generalized reduction in prices.

118

3. Stackelberg Competition and Endogenous Entry

3.5 Antitrust and Collusion Our analysis of the behavior of a market leader and of multiple market leaders in this and in the previous chapter has been useful to introduce our discussions of antitrust issues concerning abuse of dominance. Nevertheless, the same principles can be exploited to investigate other antitrust issues as well. In this section we will focus on price fixing cartels. One of the main objectives of antitrust policy is the elimination of forms of collusion between firms aimed at increasing prices. As we have seen in Chapter 1, a collusive cartel for the choice of prices or quantities between an exogenous number of firms ends up increasing prices and harming consumers. When a restricted number of firms collude, they can still implement accommodating strategies and increase their equilibrium prices and profits (especially if they act as leaders). The reaction of the other firms to their collusive strategies can be either aggressive under SS or accommodating under SC, but the outcome is qualitatively similar to the previous one: when it takes place, collusion in a market with an exogenous number of firms tends to harm consumers. This book does not have much to add to this important principle. In this section we will examine a diﬀerent, but related, issue: the impact of collusion between a restricted number of firms in a market where entry is endogenous. In such a case, collusion has unusual eﬀects. More formally, let us consider a collusive cartel between m firms, where their strategies xk for k = 1, 2, ..., m, are chosen to maximize the joint profits: πCartel =

m X

k=1

Π(xk , β k ) − mF

(3.25)

while the other firms i = m + 1, ..., n, maximize their simple profits π i = Π(xi , β i ) − F and enter until these net profits are zero. In a hypothetical Nash equilibrium between the cartel and the outsider firms, each member of the cartel would implement an accommodating strategy according to the joint optimality conditions: Π1 (xk , β k ) +

m X

Π2 (xq , β q )h0 (xk ) = 0 for k = 1, 2, ..., m

(3.26)

q=1,q6=k

while the outsiders would stick to the usual optimality conditions Π1 (xi , β i ) = 0. Notice that the accommodating strategies of the members of the cartel would attract entry until the cartel becomes a lossmaker: in Marshall equilibrium, a simple commitment to collusion is not profitable when entry is endogenous (this is another application of our results in Chapter 2, since the collusive commitment makes the members of the cartel more accommodating). However, a commitment to join in a cartel can be profitable when the members of the cartel act as leaders in the competition with the other firms.

3.5 Antitrust and Collusion

119

More formally, consider a game in which the cartel plays first, then the followers enter, and finally the followers play simultaneously. In this case, the optimality condition of the followers and their zero profit condition pin down their strategy x and their spillovers β independently from the strategies of the cartel.29 Therefore, taking P into account that the expected spillover of a member of the cartel is β k = j6=k h(xj ) = β + h(x) − h(xk ), the optimal strategies of the cartel solve the problem: max π Cartel =

x1 ,...,xm

m X

k=1

Π [xk , β + h(x) − h(xk )] − mF

(3.27)

The corresponding optimality conditions are: Π1 (xk , β k ) = Π2 (xk , β k )h0 (xk ) for k = 1, 2, ..., m

(3.28)

But these conditions exactly correspond to the condition defining the equilibrium strategy of a leader (or more leaders) in the Stackelberg equilibrium with endogenous entry, namely (3.12). On this basis, we can apply all the results derived in the rest of this chapter. In the case of competition in quantities, a collusive cartel in a market where entry is endogenous would coordinate an increase in the output of its members so as to increase their market shares and improve the allocation of resources. In the case of competition in prices, the cartel would coordinate a reduction of the prices of its members to increase their market shares, and this would lead to an improvement in the allocation of resources.30 We can summarize our result as follows: Proposition 3.10. In a market with endogenous entry, a collusive cartel is not eﬀective unless it acts as a leader: in such a case, as long as there is endogenous entry of some followers, each member of the cartel is aggressive compared to each follower. Paradoxically, collusion by cartels acting as leaders in markets where entry is endogenous turns out to be profitable, sustainable31 and also procompetitive. This result should not be overemphasized from a policy point of view. It suggests that harmful collusion between a restricted number of firms of a market cannot occur when there is endogenous entry of other firms in the market - as already pointed out within the Chicago view (Bork, 1993, Posner, 2001). However, most of the time, collusive cartels involve all the firms of an oligopolistic market and are harmful to consumers: their avoidance should be the main focus of antitrust authorities. 29

30

31

We focus on the case in which the number of members of the cartel is small and entry takes place in equilibrium. If this is not the case, the cartel deters entry. Under competition for the market an R&D cartel acting as a leader under endogenous entry would enhance investments in R&D for its members. Since the cartel with m members implements the same strategies as in the Stackelberg equilibrium with m leaders and endogenous entry, collusion is always sustainable.

120

3. Stackelberg Competition and Endogenous Entry

3.6 State-Aids and Strategic Export Promotion Globalization leads to the intensification of competition on international markets and requires a deeper understanding of the eﬀects of industrial policy at large in the international environment. In this section we will present a digression on the optimal state aid policy for exporting firms with particular reference to subsidies for exports, a topic on which there are contrasting views at both the policy and theoretical level. In the EU there are strong limitations to state aids distorting competition and aﬀecting trade among member countries. Nevertheless, the EU heavily subsidizes exports of agricultural products and the aircraft industry (Airbus), France has a long tradition in supporting its “national champions” with public funding, Italy in supporting the Made in Italy. The US have implemented strong forms of export subsidization through tax exemptions for a fraction of export profits, foreign tax credits, export credit subsidies and even an exemption from antitrust law for export cartels (the Webb-Pomerene Act exempts export associations from antitrust investigations as long as their actions do not restrain trade in the US and do not restrain the export trade of other domestic competitors). Nevertheless, at least in theory, the WTO forbids direct forms of export subsidization for industrial production. In front of such a complex and contradictory scenario, it is important to understand whether state aids to exporting firms and export subsidies are beneficial (as unilateral policies) and what are their consequences for international markets. Economic theory is largely ambiguous on this point. In the neoclassical trade theory with perfect competition, for instance, export subsidies are not optimal because they deteriorate the terms of trade; more precisely, since export taxes are equivalent to import tariﬀs, their optimal value can be derived as 1/ , where is the elasticity of demand (see Helpman and Krugman, 1989). In case of imperfect competition, export promotion assumes a strategic dimension, so its main aim becomes shifting profits toward the domestic firms. A large body of literature has studied oligopolistic models with a fixed number of firms competing in a third market. In this case, the optimal unilateral policy is an export tax under price competition (or whenever SC holds; see Eaton and Grossman, 1986). Under quantity competition, an export subsidy can be optimal (Spencer and Brander, 1983), but only under restrictive conditions. The ambiguity of these results represents a major problem to derive policy implications.32 When entry in the international market is free, however, the theory of market leaders suggests that only a commitment able to turn the strategy of the domestic firm into a more aggressive one is going to increase its profits. More precisely we can apply Prop. 2.3 and conclude that it is (unilaterally) optimal to implement any form of strategic export promotion that increases 32

See Maggi (1996) for an important contribution which endogenizes the mode of competition in the strategic trade literature.

3.6 State-Aids and Strategic Export Promotion

121

the marginal profitability of the domestic firms: this may include direct or indirect state aids for exporting firms, policies that boost demand or decrease transport costs, export subsidies, R&D subsidies for exporting firms or related strengthening of their IPRs (Etro, 2007,a). Here we will focus our attention on the optimal export subsidies following Etro (2006,f). To fix ideas with an example, imagine Harley & Davidson, Ducati and Honda selling their motorbikes in a third unrelated market, say Australia. Consider the optimal unilateral policy of the US government toward H&D. According to the traditional view, the US government should tax exports of H&D. This would force H&D to increase its prices in Australia, which would lead Honda to increase its prices as well, and would generate higher American net profits from sales of H&D bikes in Australia, together with a tax revenue to be distributed between American citizens. The fallacy of this argument relies on neglecting that other international companies, say Yamaha, Suzuki, Kawasaki, BMW or Aprilia, would be ready to enter in the Australian market for motorbikes whenever prices are high enough to promise positive profits. And when this is the case an export tax can only penalize H&D. When entry in the Australian motorbike market is endogenous, as we actually could expect, the optimal US trade policy is to subsidize Harley’s exports. Always. More formally, adopting the usual notation, it is immediate to verify that a (specific) export subsidy s increases the marginal profitability of the domestic firm, say firm H. For instance, under competition in quantities we have: Π(xH , β H , s) = [p(xH , β H ) + s] xH − c(xH )

(3.29)

and Π13 = 1, while under competition in prices we have: Π(xH , β H , s) = (pH + s − c) D (pH , β H )

with xH = 1/pH

(3.30)

and Π13 = −D1 p2H > 0. Now, the optimal unilateral policy does not maximize the total profits of the domestic firm, but these profits net of the subsidy (notice that prices aﬀect only foreign consumers). Therefore, the optimal policy must simply maximize the strategic impact on the domestic profits: it follows that, as long as entry in the international market is free, an export subsidy is always optimal. We can say something more than this: the optimal policy must implement nothing else than the Stackelberg equilibrium with endogenous entry in which the domestic firm is the leader, exactly the kind of equilibrium we have characterized in this chapter. Why this equilibrium? Simply because it is the best equilibrium that the domestic firm can aim for. It is now relatively simple to derive the subsidies that implement this equilibrium. For instance, with homogenous goods, increasing marginal costs and competition in quantities, the general expression for the optimal specific subsidy is (Etro, 2006,f):33 33

One can verify that the first order condition for the domestic subsidized firm:

122

3. Stackelberg Competition and Endogenous Entry

s∗ =

pH

>0

(3.31)

where pH is the equilibrium price of the domestic firm and = − (pH /xH ) (dxH /dpH ) the corresponding elasticity of demand. It is important to notice that this optimal subsidy rate is exactly the opposite of the optimal export tax rate in the neoclassical theory of trade policy. We can also derive the optimal specific subsidy under price competition. In our framework this is given by (Etro, 2006,f):34 s∗ =

(pH − c)D2 (pH , β H ) g 0 (pH ) >0 [−D1 (pH , β H )]

(3.32)

It is important to notice that the traditional optimal policy in the same model with exogenous entry would have required, according to the result of Eaton and Grossman (1986), a negative subsidy, that is an export tax. At this point, the intuition for the general optimality of export promoting policies should be straightforward. While firms are playing some kind of Nash competition in the foreign market, a government can give a strategic advantage to its domestic firm with an appropriate trade policy. When entry is free, an incentive to be accommodating is always counterproductive, because it just promotes entry by other foreign firms and shifts profits away from the domestic firm. It is instead optimal to provide an incentive to be aggressive, to expand production or (equivalently) reduce the price, since this behavior limits entry increasing the market share of the domestic firm. This is only possible by subsidizing exports.35 Of course, we need to remind the reader that we are here referring to the optimal unilateral policy: as well known, s + p(X) + xH p0 (X) = c0 (xH )

34

satisfies the equilibrium condition (3.16) when the subsidy is the one in the text. As it should be clear after the discussion in this chapter, in the case of constant or decreasing marginal costs, the optimal subsidy must implement an entry deterrence equilibrium. Again, one can verify that the first order condition for the domestic firm: (pH − c + s)D1 (pH , β H ) + D(pH , β H ) = 0

35

corresponds to the pricing rule of a Stackelberg leader facing endogenous entry (3.20) when the subsidy is the one in the text. ˇ c (2006) For related investigations on strategic trade policy see Kováˇc and Zigi´ and Boone et al. (2006). The first work analyzes strategic trade policy in markets where leaders choose the quality of their products before the followers. The second work shows that when domestic firms are leaders in the domestic market and invest in cost reducing innovations, but the protection of intellectual property rights on these innovation is limited abroad, positive tariﬀs can enhance ˇ c, 1998, 2000). The reason is that tariﬀs induce consumer welfare (see also Zigi´ market leaders to be aggressive toward foreign imitators, whose entry is limited.

3.7 Privatizations

123

if all countries were going to implement their optimal unilateral policies, an ineﬃcient equilibrium would emerge. This may explain why international coordination tends to limit export subsidies. If we interpret globalization as the opening up of new markets to international competition we can restate the main result as follows: in a globalized word, there are strong strategic incentives to conquer market shares abroad by promoting exports.

3.7 Privatizations A final application to privatizations deserves some comments. Recent decades have witnessed a huge sequence of privatizations, especially in Western European countries and in former communist countries. In many cases, public enterprises active in traditional markets were the subject of privatizations and an intense debate emerged on the conditions under which private or public property was better (see Boycko et al., 1997). In this section, following an important early contribution by Anderson et al. (1997) we provide an alternative way to approach this debate. Broadly speaking, a public firm is characterized by a diﬀerent objective function, which we can (generously) identify with the welfare function, and by likely ineﬃciencies associated with the lack of an optimal allocation of incentives within public institutions. If this is the case, we can evaluate the behavior of the same firm when public and when privatized. A crucial issue in this case, is whether a process of liberalization, meaning of opening to endogenous entry of other private firms, occurs as well. As a benchmark case, consider the production of a homogenous good. A single public firm would maximize welfare by pricing at the marginal cost. If the same public firm faces a process of liberalization with entry of profit maximizing firms, it is immediate that the Marshall equilibrium will correspond exactly to the one under Stackelberg competition with endogenous entry. In such a case, the public firm would still price at marginal cost,36 and the private firms will apply a markup to cover their fixed costs of production: the profits of the public firm would be positive only if its cost ineﬃciency is limited relative to the private firms. Consider privatization now. If the privatized firm is symmetric with respect to the other firms, it will end up obtaining zero profits as the others. If the privatized firm gains the role of the leader, it can keep pricing at its marginal cost while obtaining positive profits: the privatization does not aﬀect the equilibrium price, but it increases profits for the privatized company. Overall, the privatization enhances welfare when 36

X

The objective function of the public firm corresponds to πP ubl = 0 p(j)dj − i6=P c(xi ) − cP ubl (xP ) − nF where X is total production and the cost function of the public firm cP ubl (·) can be diﬀerent from that of the private firms because of some ineﬃciencies. Maximization of this function leads to p(X) = c0P ubl (xP ).

124

3. Stackelberg Competition and Endogenous Entry

the former public enterprise becomes the leader of a market with endogenous entry. Two remarks are in order. First, if products are diﬀerentiated or firms compete in prices (see Anderson et al., 1997) the gains from privatization may be larger because product variety flourishes. Second, if the privatization is not associated with a process of liberalization, it may lead to ambiguous results: for instance a privatized firm may increase its prices and induce other private firms to do the same. This cannot happen when entry is endogenous: liberalization is crucial to gain from privatizations.

3.8 Conclusions In this chapter we analyzed diﬀerent forms of competition in the market where leaders can exploit a strategic advantage to increase their profits. We noticed that their behavior depends on the entry conditions in a crucial way. The diﬀerence is quite evident under competition in prices. In markets where entry is limited exogenously leaders tend to behave in an accommodating way choosing high prices, which leads the followers to chose high prices as well. All firms obtain large profits but a second mover advantage emerges: the followers obtain larger profits than the leader. When entry is endogenous (and determined by the opportunities to make profits in the market), new firms are attracted into the market from a similar accommodating strategy of both the leader and the followers. Since entry occurs until the net profits of the followers are driven to zero, the accommodating leader ends up with negative profits because of the second mover advantage (its profits must be lower than the profits of the followers, which in turn have been entirely dissipated by free entry). This implies that a leader can only gain from an aggressive pricing strategy: in equilibrium, the price of the leader is lower than the price of the followers and the first mover advantage is restored. With this chapter we have concluded our excursus on the diﬀerent modes of competition in the market (in the choice of output or price variables). All sectors have such a component of competition. Nevertheless, in some sectors such a conponent plays a minor role in the interaction between firms and in the entry process: these are sectors in which competition is mainly for the market and entry of new products or new firms derives from successful innovations. These sectors are the subject of the next chapter.

3.9 Appendix

125

3.9 Appendix Proof of Prop 3.2: The system (3.7)-(3.8) defines the impact on x and n to changes in xL . Totally diﬀerentiating the system we have:      dx −Π12 h(x) Π12 h0 (xL )dxL Π2 h(x) 1  =−    ∆ 0 0 0 dn −(n − 2)Π2 h (x) Π11 + (n − 2)Π12 h (x) Π2 h (xL )dxL where ∆ = Π11 Π2 h(x) and Π11 + (n − 2)Π12 h0 (x) + Π2 h(x) < 0 (under the contraction condition in case of SC), which implies stability. It follows that: dx =0 dxL

dn −h0 (s) = <0 dxL h(x)

dβ =0 dxL

dβ L = −h0 (xL ) < 0 dxL

which shows that the strategy of the followers is independent from the one of the leader. Since this holds also for xL = x, which replicates the Marshall equilibrium, in a Stackelberg equilbrium with endogenous entry any active follower adopts the same strategy as in the Marshall equilibrium. At the entry stage, entry of at least one follower takes place for any xL < x ¯L , where x ¯L is such that: Π [x(h(¯ xL )), h(¯ xL )] = F and the profit of the leader is: πL =

Π L [xL , (n − 1)h(x)] − F if xL < x ¯L Π L (xL , 0) − F if xL > x ¯L

hence, the optimal strategy is x∗L that satisfies the first order condition: Π1L [x∗L , (n − 1)h(x)] = Π2L [x∗L , (n − 1)h(x)] h0 (x∗L ) if it is smaller than x ¯L and such that: Π L {x∗L , (n − 1) h(x)} > Π L (¯ xL , 0) Otherwise the global optimum is the corner solution x ¯L . We will show that in equilibrium xL > x always. In case of corner solution, this is trivial. Consider the case of an interior solution x∗L as defined above. Assume that x∗L ≤ x; then it must be that β = (n − 2)h(x) + h(x∗L ) ≤ (n − 1)h(x) = β L , which implies Π(x∗L , β L ) ≤ Π(x∗L , β) from the assumption Π2 < 0. But the optimality of x and the free entry condition imply Π(x∗L , β) < Π(x, β) = F . From these inequalities it follows that Π(x∗L , β L ) < F , which implies negative profits for the leader, contradicting the optimality of the interior solution. This implies that the profit function of the leader must have a global optimum larger than x. Q.E.D.

126

3. Stackelberg Competition and Endogenous Entry

Proof of Proposition 3.3. The eﬀect of a change in the fixed cost on the strategy and the number of firms are: dx [−Π12 ] = dF [Π11 Π2 ]

· ¸ dn Π11 + (n − 2)Π12 h0 (x) ∂n ∂xL = + dF Π11 Π2 h(x) ∂xL ∂F

The first derivative has the opposite sign of Π12 . The second has a first negative term (under the contraction condition when Π12 > 0) and a second ambiguous term. It follows that d[β + h(x)]/dF = [Π11 − h0 (x)Π12 ]/Π11 Π2 h(x). Totally diﬀerentiating (3.12) we have: ¤ £ L L [Π11 − Π12 h0 (x)] Π12 − h0 (xL )Π22 ∂xL =− ∂F DL Π11 Π2 h(x) where DL < 0 from the assumption that the second order condition is satisfied. It follows that: ¸ · £ L ¤ dn h0 (xL ) 0 0 L [Π − Π h (x)] Π − h (x )Π ∝ Π11 + (n − 2)Π12 h0 (x) + 11 12 L 12 22 dF h(x)DL The Proposition follows immediately after noticing from (3.12) that h0 (xL ) = Π1L /Π2L . Q.E.D.

Proof of Prop 3.4: In a Marshall equilibrium, the number of firms is nm and each one produces xm , with welfare: Wm =

m m nZ x

p(j)dj − nm [c(xm ) + F ] =

0

m m nZ x

p(j)dj − p(nm xm )nm xm

0

where we used the zero profit condition p(nm xm )xm = c(xm ) + F . Under Stackelberg competition when there is endogenous entry by some followers, the strategy of each follower remains xm by Prop. 3.2, while the number of firms ns satisfies the zero profit condition: p [xL + (ns − 1)xm ] xm = c(xm ) + F which implies the same total production in the two cases xL + (ns − 1)xm = nm xm . Hence the welfare will be: s m xL +(n Z −1)x Ws = p(j)dj − (nm − 1)c(xm ) − c(xL ) − ns F = 0

=

m m nZ x

p(j)dj − p(nm xm )nm xm + [xL + (ns − 1)xm ] p(nm xm )

0

−(ns − 1)c(xm ) − c(xL ) − ns F = W m + xL p [xL + (ns − 1)xm ] − c(xL ) − F = W m + πL > W m

3.9 Appendix

127

which proves the claim. Q.E.D. Proof of Prop 3.5: Adopt a generic cost function c(x) with c00 (x) ≤ 0. Imagine an equilibrium without entry deterrence. The zero profit condition, stated in the proof of Prop. 3.4, sets total production and hence the inverse demand at the level: p[xm (ns − 1) + xL ] =

F + c(xm ) xm

where xm is always the equilibrium production of the followers, which corresponds to the equilibrium production in the Marshall equilibrium. Then, the profit function of the leader becomes: · ¸ F + c(xm ) L m s Π (xL ) = xL p[x (n − 1) + xL ] − c(xL ) = xL − c(xL ) xm with: Π L0 (xL ) =

F + c(xm ) − c0 (xL ) > 0 xm

Π L00 (xL ) = −c00 (xL ) ≥ 0

since p(·) > c0 (xm ) > c0 (xL ) for any xL > xm . Hence, the leader always gains from increasing its production all the way to the level at which entry is deterred. This level satisfies the zero profit condition for ns = 2, that is p (xm + x ¯L ) = [F + c(xm )] /xm . Since the right hand side is also equal to m m p(n x ) by the zero profit condition in the Marshall equilibrium (see the proof of Prop. 3.4), it follows that the entry deterrence strategy is exactly x ¯L = (nm − 1)xm . Q.E.D. Proof of Prop 3.6: Total expenditure Y¯ for the representative agent is Pn given by an exogenous part Y and the net profits of the firms i=1 π i , which is zero in the Marshall equilibria, but equal to the positive profits of the leader πL in the Stackelberg equilibrium with endogenous entry. The welfare comparison derives from the calculation of indirect utilities (2.22) for the Logit model and (2.23) for the Dixit-Stiglitz model in both cases. Labeling with W (Y¯ ) the indirect utility in function of total expenditure Y¯ , in the Logit case we have for both equilibria: µ ¶ N N W (Y¯ ) = Y¯ + ln 1 + − N (1 + λc) − λF λ λF and in the Dixit-Stiglitz case we also have for both equilibria: ¡ ¢α £ ¤ ¸ 1−θ θ ¯ ¯ − F (1 + α) · (1 − θ)Y¯ θ α Y Y W (Y¯ ) = +θ 1+α (1 + α)F c (1 + α)

128

3. Stackelberg Competition and Endogenous Entry

Since they are both increasing in total expenditure, the utility of the representative agent must be higher under Stackelberg competition with endogenous entry. Q.E.D. Proof of Prop 3.7: The analysis of the last stage is the same as before, and in particular dx/dxL = 0. Now, the leader’s first order condition becomes: Π1L [xL , β + h(x) − h(xL ), k] = Π2L [xL , β + h(x) − h(xL ), k] h0 (xL ) which defines a continuous function xL = xL (k). It follows that: L L [xL , β + h(x) − h(xL ), k]−Π23 [xL , β + h(x) − h(xL ), k] h0 (xL ) x0L (k) ∝ Π13

Clearly, when the condition in the proposition holds x0L (k) ≥ 0 and xL (k) ≥ xL (0) > x by Prop. 3.2. Otherwise, since xL (0) > x , continuity implies that there is a neighborhood of xL (0) for k small enough where xL (0) > xL (k) > x. Q.E.D. Proof of Prop 3.8: The analysis is similar to the basic one, but now we have: 



  Π12 h0 (xL )dxL + [h(xL ) − h(x)]Π12 dm 1  = − Ω  ∆ 0 dn Π2 h (xL )dxL + [h(xL ) − h(x)]Π2 dm dx

with:



Ω≡

Π2 h(x)

−Π12 h(x) 0

0

−(n − m − 1)Π2 h (x) Π11 + (n − m − 1)Π12 h (x)

 

which again implies dx/dxL = 0 and dn/dxL = −h0 (xL )/h0 (x). Moreover we have: dx dm

= 0,

dn dm

=1−

h(xL ) h(x)

<0

The first order conditions for each one of the leaders become: Π1L (xL , β L ) = Π2L (xL , β L ) h0 (xL ) where β L = (n−m)h(x)+(m−1)h(xL ). Totally diﬀerentiating this condition and using dn/dm it follows that dxL /dm = 0. The profit of each leader is not aﬀected by the number of leaders since: · ¸ dπ L dn L = Π2 h(xL ) − h(x) + h(x) =0 dm dm

3.9 Appendix

129

which concludes the proof. Q.E.D. Proof of Prop 3.9: Denote with xi = [xi1 , xi2 , ..., xiK ] the strategies of a firm i. Assume again that a symmetric equilibrium in the strategies of the followers exist. The system of K + 1 equilibrium conditions for the second stage: ∂Π [x, (n − 2)h(x) + h(xL )] = 0 for k = 1, 2, .., K ∂xk Π [x, (n − 2)h(x) + h(xL )] = F pins down the vector x and β = (n − 2)h(x) + h(xL ). Consequently the profit of the leader is: πL = Π L [xL , (n − 1)h(x)] − F = Π L [xL , β + h(x) − h(xL )] − F which is maximized by the vector xL which satisfies the system of K first order conditions: ∂Π L (xL , β L ) ∂h(xL ) ∂Π L (xL , β L ) = ∂xLk ∂xLk ∂β L where clearly β L = (n − 1)h(x). Imagine that there is such an interior equilibrium with h(xL ) ≤ h(x). Then it must be that β ≤ β L , which implies Π(xL , β L ) ≤ Π(xL , β) from the assumption ∂Π/∂β < 0. But the optimality of x and the free entry condition imply Π(xL , β) < Π(x, β) = F , hence Π(xL , β L ) < F , which contradicts the optimality of the interior solution. This implies that h(xL ) > h(x). Q.E.D.

4. Dynamic Competition and Endogenous Entry

Static analysis of market structures as those studied in the previous two chapters are not particularly relevant for fast-moving markets of high-tech and New Economy industries (computer hardware and software, online businesses, mobile telephony and biotechnology). These industries are often characterized by massive R&D investments, strong reliance on IPRs and other intangible assets, network eﬀects, high fixed sunk costs and low marginal costs. Competition in these markets is often dynamic in the sense that it takes place for the market in a winner-takes-all race. Leading firms in these markets might enjoy high market shares yet be subject to massive competitive pressure to constantly create better products at lower prices due to threats from innovative competitors and potential entrants. Companies that hold a significant share of the market at any given point of time may see this share decrease rapidly and significantly following the development and supply of a new and more attractive product by an actual or potential competitor (the launches of the iPod and the iPhone by Apple and their impact on the distribution of MP3 players and smart phones are good examples of such rapid and drastic market developments), or they may persist in their leading position thanks to heavy investments in R&D (think of Intel whose large and increasing investments induced sequential innovations in the development of chips).1 This chapter analyzes competition for the market through models where firms invest to obtain innovations and conquer a market. Since innovations often lead to patents or other forms of intellectual property rights that guarantee exploitation for a certain period, we often refer to this kind of competition as to a patent race. In Chapter 1 we analyzed a simple form of competition for the market, but here we augment it with a number of realistic additions: we introduce a time dimension, so that firms discount profits from future innovations, we allow for explicit forms of dynamic investment, we consider sequential innovations and endogenize expected profits in partial equilibrium, and finally we evaluate the impact of alternative forms of product market competition on the incentives to invest in R&D. 1

The innovation process of Intel has been so systematic that the rule of thumb for which the number of transistors on an Intel chip doubles every two years has been labeled Moore’s Law from the intuition of Intel co-founder Gordon Moore.

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4. Dynamic Competition and Endogenous Entry

A central focus of this chapter will be on the role of incumbents in innovative sectors, and we will show under what conditions these firms invest in R&D and when their technological leadership persists. The first economist to forcefully emphasize the fundamental role of established large firms in driving technological progress has probably been Schumpeter: “As soon as we go into details and inquire into the individual items in which progress was most conspicuous, the trail leads not to the doors of those firms that work under conditions of comparatively free competition but precisely to the doors of the large concerns which, as in the case of agricultural machinery, also account for much of the progress in the competitive sector - and a shocking suspicion dawns upon us that big business may have had more to do with creating that standard of life than with keeping it down” (Schumpeter, 1943). Related analysis of modern capitalism as driven by the innovative and persistent leadership of large firms is also in the classic works of Galbraith (1952) and Chandler (1990). Recent evidence confirms that incumbents do a lot of research and their leadership persists through a number of innovations. One of the industry leaders investing more in innovation is Microsoft, the leading firm in operating systems: in 2000, its expenditure in R&D was $ 3.7 billion, corresponding to 16.4% of its total sales. High investments can also be found in many other major firms of high tech sectors. In the same year, the R&D/Sales ratio was 15% for Pfizer and 5.8% for Merck, two leaders in the pharmaceutical sector, 11.5% for Intel, leader in the chips market and 5.8% for IBM, and 5.4% for Hewlett-Packard, two leaders in computer technologies and services, 11.8% for Motorola and 8.5% for Nokia, leaders in wireless, broadband and automotive communications technologies, 10% for Johnson & Johnson, the world’s most comprehensive manufacturer of health care products and services, 6.6% for 3M and 6.3% for Du Pont, which are active in many fields with a leading role, 5.6% for Xerox and for Kodak, leaders in the markets for printers and photographs. Things did not change much since then. Today American corporations spend around $ 200 billion on R&D every year, much of it on computing and communications: in 2006 Microsoft spent around $ 6.6 billion, IBM and Intel about $6 billion each, Cisco Systems and Hewlett-Packard around $4 billion each (The Economist, 2007, “Out of the dusty labs”, March 1). More systematic evidence on the R&D activity by market leaders comes from patented innovations and expenditure on licenses. The comprehensive study by Malerba and Orsenigo (1999) on EU patents provides clear evidence on this point.2 For instance, they show that the percentage of patents granted to firms that had already innovated within their sectors is 70 % in Germany, 2

See also Malerba et al. (1997).

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133

68 % in US, 62 % in Japan, 60 % in France, 57 % in UK and 39 % in Italy; moreover, they conclude that: “a large fraction of new innovators is composed by occasional innovators that exit soon from the innovative scene [...] Only a fraction of entrants survives and grows larger (in terms of patents) as times goes by: they become persistent innovators. Older firms who survive and continue to patent are few in number but represent an important contribution to total patenting activities in any period. Here, cumulativeness of knowledge and competencies play a major role in aﬀecting the continuity of innovative activity of these firms.” Czarnitzki and Kraft (2007a) is the first study looking at who purchases licenses on patents: on the basis of German data they show that incumbents invest more in licensing expenditures than eﬀective and potential entrants, and that the investment of these incumbents is higher when the entry threats are stronger.3 The literature on patent races has studied equilibrium outcomes in the market for innovations starting with Loury (1979) and Dasgupta and Stiglitz (1980).4 The standard hypotheses of this literature are decreasing returns to scale, fixed costs of innovations and Nash competition between firms. The participants of the patent race are the current monopolists of the market, who have a patent on the leading-edge product, and a number of entrant firms trying to replace the patentholder. A main result is that the patentholder does less research than any other entrant and zero research under free entry because its incentives to invest in R&D are lower due to the Arrow (1962) eﬀect: the expected gain of the patentholder is just the diﬀerence between expected profits obtained with the next technology and the current one, while the expected gain for each outsider is given by all the expected profits obtained with the next technology. In the presence of sequential innovations, the fact that patentholders do not invest in R&D implies a continuous leapfrogging and no persistence of monopolistic positions between one innovation and another, which is a quite counterintuitive picture of what is going on in the real world: that’s why the result is sometimes called the Arrow’s paradox. A number of solutions to the Arrow paradox have been proposed, most of which are based on some technological advantage of the patentholder, often derived from a gradual accumulation of knowledge.5 Despite the fact that 3

4

5

The empirical research on the reaction of the investment of incumbents to entry is limited. Scherer and Keun (1992) look at the increase in high-tech imports in US and find that incumbents in sectors without barriers to entry react more aggressively to endogenous entry, increasing R&D/sales more than other firms. See also Lee and Wilde (1980), Reinganum (1982, 1983, 1985a,b), Harris and Vickers (1985) and Beath et al. (1989). For a survey, see Tirole (1988, Ch.10). See also Reinganum (1982), Fudenberg et al. (1983), Harris and Vickers (1985) and Vickers (1986) for detailed analysis.

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4. Dynamic Competition and Endogenous Entry

these are reasonable explanations for the puzzle, they do not seem to tell the whole story, as we see monopolists investing in R&D even if they do not have consistent technological advantage to the outsiders. Here we will study patent races where the patentholder has the opportunity to make a strategic precommitment to a flow of investment in R&D. This may happen through a specific investment in laboratories and related equipment for R&D, by hiring researchers or in a number of other ways. In the case of “contractual costs” of R&D, that is, when a fixed initial investment determines the arrival rate of the innovation, the interpretation of a strategic precommitment for the incumbent monopolist is very standard. The leader can choose to invest before the other firms, and since the leader is by definition the firm that has discovered the latest technology, it is reasonable to assume that such a discovery is associated with a first mover advantage in the following patent race. When the number of entrants is exogenous, the behavior of the incumbent is hard to predict: on one side the Arrow eﬀect pushes toward a low investment, on the other side the strategic eﬀect is ambiguous. Under reasonable conditions, however, a first mover advantage does not give strong incentives to invest for an incumbent monopolist, and the traditional view that monopolists stifle innovation is preserved: without competitive pressure, monopolists are not very innovative indeed.6 Under endogenous entry, the outcome is completely changed and generates a crucial result: the incumbent leader always invests in R&D and more so than any other firm, thus the Stackelberg assumption with endogenous entry delivers a new rationale for the persistence of a monopoly (Etro, 2004). The rationale for endogenous innovation by leaders is similar to the general rationale for aggressive strategies by leaders facing endogenous entry: competitive pressure determines the aggregate rate of innovation and the investment of the leader cannot aﬀect this or the expected length of the current rent. Since the expected profits from the current technology are not aﬀected by the leader’s strategy, the Arrow eﬀect disappears and, as we also know from our general analysis in Chapter 3, the optimal behavior for a Stackelberg leader facing endogenous entry is always aggressive. The empirical results of Blundell et al. (1999) “are in line with models where high market share firms 6

In the pre-industrial world, barriers to entry in the innovative sectors, monopolized for centuries by guilds, have represented a substantial limit to innovation. Dutch guilds opposed progress in shipbuilding, Swiss printers obtained laws to avoid improvements in printing press and French paper producers sabotaged machines that could speed up pulp production. Interesting historical evidence is described by Ogilvie (2004a,b) in a study on merchant guilds between the XVI and the XVIII century. These kinds of guilds, spread for centuries around Europe, were strongly restricting entry in many sectors and were detrimental to innovation activity. Finally, the English Luddites, organized in trade unions, had a similar role at the beginning of the Industrial Revolution.

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135

have greater incentives to preemptively innovate”. Their conclusion is rather explicit: “It is often asserted that the superior performance of large firms in innovating is because they have higher cash flows from which to finance investment in R&D. Our findings suggest that this is not the whole story - dominant firms innovate because they have a relatively greater incentive to do so. Firm with high market shares who innovate get a higher valuation on the stock market than those who do not.” However, notice that, contrary to purely-preemptive models of innovation, in our environment incumbents do not necessarily deter entry, but they typically invest more than other firms, so that their leadership is only partially persistent. When innovations are sequential, not only incumbent monopolists keep investing under the pressure of endogenous entry, but the same value of their leadership is enhanced, which in turn increases the aggregate incentives to invest in R&D. Contrary to a common belief for which monopolies would stifle innovation, the persistence of monopoly can be caused by innovative pressure and can enhance technological progress. This result appears in line with the original ideas of Schumpeter (1943) on the role of large established firms in fostering innovation, and we will use it to sketch a model of technological progress driven by market leaders. The chapter is organized as follows. Section 4.1 presents a simple model of patent races, Section 4.2 extends it in more realistic ways and Sections 4.3 considers sequential innovations. Finally, Section 4.4. discusses the relation between competition in the market and competition for the market and Section 4.5 concludes.

4.1 A Simple Patent Race with Contractual Costs of R&D In this chapter we will develop models of competition for the market. We already developed an example in Chapter 1, but in that case we assumed a very simple technology of investment in innovations. Investment could be just successful or not (and by investing enough a firm could even innovate with certainty), while in the real world it takes time and risk to innovate, and future gains are properly discounted taking into account alternative investment opportunities. In this section we will introduce a time dimension developing a simple patent race in which investment can only increase the chances of innovating early on. Of course this is crucial in a competition where the first to innovate wins a patent and the associated profits, while all the others get nothing. Nevertheless, we still assume that an initial investment determines the future chances to innovate, therefore we are still dealing with a form of

136

4. Dynamic Competition and Endogenous Entry

competition which is partially static (in the next section we will augment the model with a genuinely dynamic investment). Following the pathbreaking contribution of Loury (1979) and Dasgupta and Stiglitz (1980) we will adopt a particular R&D technology, assuming that, given the investment choices of the firms, innovations arrive according to a stochastic Poisson process in the continuum. According to this process, the probability that a single firm i will obtain the innovation before a certain amount of time t ∈ [0, ∞) is independent across firms, memoryless and given by: G(t, i) = 1 − e−hi t where hi is a firm specific parameter. Notice that this probability does not depend on the corresponding probability of other firms and does not depend on the probability of innovation of the same firm i before time t. The density function is g(t, i) = hi e−hi t . Another property of a Poisson process is that the so-called hazard rate, the instantaneous probability of innovation in t conditioned to previous failure, corresponds to the firm specific parameter hi > 0. Indeed, we have: Pr(i innovates in t) =

g(t, i) = hi 1 − G(t, i)

The simplest kind of investment we can consider is a fixed investments, usually called a contractual cost of innovation. In this case, at the beginning of the race, each firm i invests a fixed amount F to participate to the contest, and decides a variable amount, xi , so that the arrival rate of an innovation is: ˆ hi = h(xi ) with h(0) = 0, h0 (x) > 0 and h00 (x) R 0 for x S x If we look at h(x) as to a stochastic production function of innovation, loosely speaking we are allowing for increasing returns to scale for low investment, but we assume decreasing returns for investment greater than a cut oﬀ x ˆ ≥ 0. Using basic properties of probability theory, we can calculate the probability that firm i wins the race at time t as:7 Sn Y Pr(i wins in t) = g(t, i) [1 − G(t, j)] = hi e− j=1 hj j6=i

The exogenous value of the innovation is V . In most of our discussion, for simplicity, we will refer to this as to the value of a patent. More generally, we may think of this as the expected value of the profits obtained by the innovation. For instance, the innovation could be kept secret and exploited 7

Since we work in the continuum, the probability that two firms innovate at the same time is zero: there will always be a unique winner in these contests.

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137

until other innovations will replace it, or it could be disclosed with the innovator enjoying a first mover advantage in the marketing of the invention (even when facing free entry of imitators, as we have seen in the models of the previous chapters). Nevertheless, it should be clear that a strengthening of the protection of IPRs will increase the value of the innovation V . Since we have introduced a time dimension, we need to take in consideration the present discounted value of the expected profits. Given the exogenous interest rate r, expected profits from the patent race are: Z ∞ πi = e−rt V Pr(i wins in t)dt − xi − F = t=0

h(xi )V − xi − F = r+p

Pn where we defined with p = j=1 h(xj ) the aggregate instantaneous probability of innovation. Also this profit function is nested in the general version P (2.1) employed in the previous chapters. Rearranging and defining β i = nk=1,k6=i h(xk ), we have: Π (xi , β i ) =

h(xi )V − xi r + h(xi ) + β i

Here it can be verified that expected profits for firm i are an inverted U function of the investment of the same firm xi and are decreasing in the investment of each other firm, since the relative probability of winning the race is what matters. However, in this case the cross derivative (Π12 ) has an ambiguous sign. When another competitor invests more, the relative probability of winning is reduced, which makes a marginal investment less profitable, but at the same time the aggregate probability of innovation in the market is increased and this creates an eﬀect in the opposite direction. If the first eﬀect prevails R&D investments are strategic substitutes, as in our simple example of Chapter 1. In such a case, we would expect that a firm with a first mover advantage over a rival would invest more because of what we called the Stackelberg eﬀect: a higher investment reduces the incentives of the competitor to invest and increases the relative probability of winning the contest. We can also easily incorporate an asymmetric position for the incumbent monopolist. Assume that this monopolist has a flow of profits K from its own leading edge technology. Assume also that the innovation is drastic, so the incumbent obtains nothing in case of innovation by another firm: this characterizes a situation where the “winner takes all”. The expected profits of the monopolist are now: Π (xM , β M , K) =

h(xM )V + K − xM r + h(xM ) + β M

What in Chapter 1 we called the Arrow’s eﬀect is again at work: this eﬀect tells us that current profits reduce the marginal profitability of R&D

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4. Dynamic Competition and Endogenous Entry

investment (Π13 < 0), and consequently they reduce the incentives of the incumbent monopolist to invest in innovation. Therefore, in any Nash equilibrium with an exogenous number of firms, the incumbent monopolist will invest less than any other firm.8 The behavior of the incumbent monopolist acting as a leader in this model is complex because the Arrow eﬀect and the Stackelberg eﬀect may work in opposite directions. If the fixed costs of entry are high enough, an entry deterring strategy can be optimal, but when this is not the case, the optimal strategy for the incumbent monopolist will be biased toward a lower investment if the Arrow eﬀect prevails. 4.1.1 Endogenous Entry As shown in Etro (2004, 2008), any ambiguity of the results disappears in equilibria with endogenous entry. Consider first a Marshall equilibrium, where all firms compete in Nash strategies and entry takes place as long as there are profitable opportunities. In this environment, as we noticed, the incumbent monopolist is always investing less than the rivals because of the Arrow eﬀect. When entry has dissipated all profitable opportunities for the other firms, the optimality condition for the outsiders and the free entry condition are: h0 (x)V h0 (x)h(x)V + 1, = 2 r+p (r + p)

h(x)V =x+F r+p

(4.1)

These conditions determine the equilibrium investment of each outsider and the aggregate probability of innovation independently from the equilibrium strategy of the monopolist. In particular, the investment of each outsider can be implicitly expressed as: µ ¶ x+F h(x) 0 = (4.2) h (x) 1 − V x+F and it can be verified to increase in the value of innovation.9 Let us now look at the equilibrium behavior of the incumbent monopolist, and in particular at its incentives to invest in this competition. First of all, notice that the aggregate probability of innovation is going to be independent from the investment of the incumbent monopolist. Therefore, the expected profits from the leading edge technology will be the same whether the monopolist invests or not to innovate. Consider now its expected profits from the 8

9

This can be easily seen comparing the respective first order conditions in a Nash equilibrium where the fixed costs are assumed low enough that all firms invest: the marginal cost of investment is higher for the monopolist because an increase in the aggregate probability of innovation reduces the expected lenght of exploitation of the current technology. A simple example with linear technology, h(x) = √ x, can be solved analytically. In this case the Marshall equilibrium implies x = V F − F .

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139

actual patent race. Because of the Arrow eﬀect, the monopolist is going to invest less than the outsiders. On the other side, the outsiders are investing to maximize the expected profits from the actual patent race. Nevertheless, endogenous entry reduces to zero these expected profits. Consequently, it must be that the alternative strategy of the monopolist can only reach negative expected profits in the actual patent race. In conclusion, it is better for the monopolist to withdraw from the competition and retain the current flow of profits until some other firms will innovate. Finally, we will study the case in which the incumbent monopolist is the leader of the patent race. In a Stackelberg equilibrium with endogenous entry, as long as entry takes place, the first order condition and the free entry condition at the second stage are the same as before, and they generate the same investment for the outsiders (4.2), and the same aggregate probability of innovation implicit in the free entry condition in (4.1). As a consequence of the usual neutrality result emerging under endogenous entry, the strategy of the leader is not going to aﬀect the strategy of the active followers, but just their number. Using (4.1), we can now re-express the expected profits of the incumbent monopolist as: h(xM )V + K − xM − F = r+p h(xM )(x + F ) K(x + F ) = + − xM − F h(x) h(x)V

πM =

where the investment of the outsiders x is now taken as given according to the equilibrium condition (4.2). The incumbent monopolist can now exploit its first mover advantage choosing its investment according to the optimality condition: h0 (xM ) =

h(x) x+F

(4.3)

which defines a local maximum when h00 (xM ) < 0, as we will assume, and it is associated with a higher investment than the one of the outsiders defined in (4.2). Since the monopolist could still invest as much as the outsiders and obtain zero expected profits from the actual patent race, the optimality condition above, which diﬀers from that of the outsiders, implies that the monopolist can do even better and obtain positive profits from the patent race. This also implies that the strategy defined by (4.3) is always preferred to the corner strategy of not participating to the race. However, it may not be preferred to the corner strategy that deters entry. Such an entry deterring strategy would require an investment high enough to deter entry, that is h(xM ) = (V − F − x)h(x)/(x + F ) − r.10 The possibility of entry deterrence 10

For instance, this is what happens in the case of a linear technology, h(x) = x. Given the expected behavior of the outsiders, the expected profits of the

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4. Dynamic Competition and Endogenous Entry

by the monopolist was pointed out by Gilbert and Newbery (1982) in a diﬀerent duopolistic framework.11 . Notice that the level of current profits does not aﬀect the equilibrium outcome,12 which confirms two results. First, the Arrow’s paradox disappears: the monopolist that is leader in a patent race with free entry takes as given the expected value of the current monopoly and simply exploits its strategic advantage to increase the relative probability of success in the patent race. Second, the escape competition eﬀect associated with Aghion and Griﬃth (2005) disappears: an increase in the intensity of product market competition associated with a decrease in the profits before a drastic innovation does not aﬀect the aggregate level of innovation. In this model, eﬀective competition for the market leads the incentives to innovate, and competition in the market cannot enhance further these incentives. In conclusion, our extension of the simple model of competition for the market analyzed in Chapter 1 allows to generalize the result obtained in that simpler environment: incumbent monopolists facing a competitive pressure in the competition for future markets behave in an aggressive way and invest more than each other rival, but they do not necessarily deter entry. We can summarize our findings as follows: Proposition 4.1. In a competition for the market with contractual costs of R&D, the incumbent monopolist invests more than any other firm and independently from its current profits when has a leadership and entry is endogenous. As intuitive, entry deterrence can be optimal when investment is not too costly or its marginal productivity is constant (or not too much decreasing). However, when the marginal productivity of investment diminishes strongly with the same investment, entry deterrence requires a very large and costly

11

12

monopolist turn out to be linearly increasing in its investment. The monopolist √ is better oﬀ deterring entry with the limit investment x ¯M = V + F − 2 V F − r. Gilbert and Newbery (1982) obtained entry deterrence by the monopolist in a deterministic contest, where investment reduces the waiting time for innovation in a deterministic way. They also suggested that a similar result could occur in stochastic patent races, providing an early insight for our result (see also Gilbert and Newbery, 1984). However, they did not move one step further and show that even when entry deterrence is not optimal, the monopolist with a first mover advantage invests more than any outsider as long as entry is free. For this reason, their result was forced to suggest a rationale for “sleeping patents” without innovative purposes and used by monopolists to preempt entry. Our point here is the exact opposite: under competitive pressure incumbent monopolists are led to invest a lot in R&D to conquer useful patents and generally without exclusionary purposes. L This is a consequence of Prop. 3.7 since in equilibrium we have Π13 = −(r + −2 L 0 p) = Π23 h (xM ).

4.1 A Simple Patent Race with Contractual Costs of R&D

141

investment and becomes suboptimal. As noticed by Kortum (1993), Griliches (1994), Cohen and Klepper (1996) and other empirical works, investments in R&D are characterized by decreasing marginal productivity at the firm level. Cohen and Klepper (1996) show that “the assumption of diminishing returns to R&D is well grounded empirically” for a broad sample of industries.13 Even Aghion and Howitt (1998, Ch.12) accept this as a stylized fact. Therefore, it is reasonable to focus on this case where the marginal productivity of investment is decreasing and, accordingly, both the monopolist and some outsiders invest in R&D. 4.1.2 Welfare Analysis Before, moving on in our discussion, we want to analyze our equilibria from a welfare point of view. Assuming that V ∗ is the social value of innovations, potentially higher than its private value, a social planner would maximize a welfare function based on the discounted expected social value of the innovation net of the total investment costs: Pn n X h(x )V ∗ i=1 Pn i W = (xi + F ) − r + i=1 h(xi ) i=1 The social planner problem amounts to choosing n∗ firms and an investment x∗ for each firm to solve: max W = x,n

nh(x)V ∗ − n(x + F ) r + nh(x)

Combining the optimality conditions, one obtains the optimal investment as satisfying: h(x∗ ) = h0 (x∗ ) x∗ + F which implies that the investment of each firm is too low in Marshall equilibrium. Moreover, the number of firms is too high when the social value of the innovation is small, for instance when it coincides with its private value (Wn < 0 at the number of firms which makes net profits equal to zero), and it is too low when the social value of the innovation is large enough. In Stackelberg equilibrium with endogenous entry the incumbent monopolist invests more than the outsiders, reducing the number of firms but not the aggregate 13

From a theoretical point of view, notice that, while in most of the productive sectors there are good reasons to believe that doubling the amount of input total production will double (constant returns to scale hold), there are no reasons to believe that doubling the amount of inputs in the R&D activity will double the expected amount of innovations.

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4. Dynamic Competition and Endogenous Entry

probability of innovation, which remains the same. This leads to a simple welfare comparison (Etro, 2008): Proposition 4.2. In the competition for the market with contractual costs of R&D and endogenous entry, the allocation of resources in the Stackelberg equilibrium with endogenous entry is Pareto superior compared to the Marshall equilibrium.

4.2 Dynamic Competition for the Market Competition for the market is an intrinsically dynamic phenomenon and not a static one, as we often remarked. Nevertheless, until now we considered simple forms of this competition where an initial investment by each firm was exhausting the research activity. In reality, firms invest over time and keep investing until one of them innovates: just at that point the race is over and all firms stop spending for that innovation. In the rest of this chapter we will study patent races where firms continuously invest a flow of resources in R&D and their probability of innovation depends on this flow. Following Lee and Wilde (1980), if xi is now the flow of investment of firm i determining an instantaneous probability of innovation h(xi ) assumed positive, increasing and strictly concave, the expected profits of a generic outsider are given by: Z ∞ πi = e−rt [V Pr(i wins in t)dt − xi Pr(no one wins in t)] − F = t=0

h(xi )V − xi −F = r+p

which again can be rewritten as a particular case of our general formulation (2.1) employed in the previous chapters, with:

Π(xi , β i ) =

h(xi )V − xi [r + h(xi ) + β i ]

(4.4)

An interesting feature of this model is that now we can determine unambiguously the sign of the cross derivative. In particular, when firm i maximizes its expected profits, the impact of a change in the strategy of the other firms on its marginal profit is: Π12 ≡

[h0 (xi )V − 1]

[r + h(xi ) + β i ]

2

>0

Contrary to the simple example of Chapter 1, where investments of the firms were strategic substitutes, and to the ambiguous case of the previous section, we now realize that under more realistic conditions, investment strategies

4.2 Dynamic Competition for the Market

143

are strategic complements. When a firm invests more in R&D, the aggregate probability of innovation in the sector increases and this reduces expected profits of the other firms, but it also increases their expected marginal profits, and therefore their incentives to invest. Finally, we can derive the objective function of the incumbent monopolist with a flow of current profits K as follows: Π (xM , β M , K) =

h(xM )V + K − xM r + h(xM ) + β M

(4.5)

which is again characterized by Π13 < 0: an increase in current profits reduces the marginal profitability of investment. In what follows, we will describe in detail the equilibrium of the competition for the market under alternative forms of strategic interaction. 4.2.1 Nash Equilibrium Under Nash competition the equilibrium symmetric optimality condition for the investment of each entrant is: [h0 (x)V − 1] (r + p) = h0 (x) [h(x)V − x]

(4.6)

where p = h(xM ) + (n − 1)h(x) is the aggregate probability of innovation. Straightforward diﬀerentiation shows that the investment of each entrant is increasing in the expected value of innovation, in the interest rate and in the number of firms (since SC holds). If the incumbent invests, its choice xM satisfies the first order condition: [h0 (xM )V − 1] (r + p) = h0 (xM ) [h(xM )V + K − xM ]

(4.7)

which diﬀers from the previous one just because the flow of current profits increases the marginal cost of investment: this is a consequence of the Arrow eﬀect and it implies that, ceteris paribus, the incumbent invests less than each entrant and has lower expected profits from participating to the patent race (Reinganum, 1983). Because of SC, a change in K aﬀects all firms in the same way: for instance if we interpret an increase in the intensity of product market competition as a reduction in current profits K, all firms invest more in R&D according to the escape competition eﬀect. Summarizing we have: Proposition 4.3. A Nash equilibrium in the competition for the market implies a lower investment by the incumbent monopolist than any other firm and an investment for each firm which is decreasing in the current profits.

144

4. Dynamic Competition and Endogenous Entry

4.2.2 Marshall Equilibrium Let us assume free entry now. Since the expected profit functions of all firms derived in the Nash equilibrium are decreasing in the number of firms, and the incumbent expects lower profits from the R&D investment than the others, we can conclude that the incumbent will stop researching if the number of firms is great enough: the Arrow eﬀect induces the incumbent to withdraw from the competition for the market. Moreover, the entrants will break even if the number of firms achieves a still higher bound. This bound is defined by the free entry condition: r+p=

h(x)V − x F

(4.8)

Rearranging the equilibrium first order condition for the outsiders and this free entry condition, we can re-express the equilibrium flow of investment in the following implicit way: h0 (x) =

1 V −F

(4.9)

which is increasing in the diﬀerence between the expected value of the innovation and the fixed cost, but independent from the interest rate. Moreover, the equilibrium number of firms is increasing in the value of innovation and decreasing in the fixed cost of entry and in the interest rate, while it is independent from the current profits of the incumbent monopolist. Summing up, we have: Proposition 4.4. A Marshall equilibrium in the competition for the market implies that the incumbent monopolist does not invest and the investment of the outsiders and the aggregate probability of innovation do not depend on the current profits. In general, if the social value of innovation is higher enough than its private value, equilibrium investment is too low and there are too few firms. Nevertheless, if the social value of innovation is close enough to its private value, the equilibrium number of firms can be excessive. 4.2.3 Stackelberg Equilibrium We will now assume that the patentholder has the opportunity to make a strategic precommitment to a level of investment in R&D. This may happen through a specific investment in R&D laboratories, by hiring researchers or in a number of other ways. Our strategic assumption seems a natural one since the patentholder can be easily seen in a diﬀerent perspective from all the other entrants in the patent race. Assume that the fixed costs are low enough that the entry deterrence strategy is not optimal. Then, the incumbent leader will commit to a low

4.2 Dynamic Competition for the Market

145

level of investment because such a strategy will induce a reduction in the investment of the other firms and a longer expected lifespan of the current patent (Reinganum, 1985,b). The reason of this unambiguous result is that now the Stackelberg eﬀect and the Arrow eﬀect work in the same direction. The first pushes toward a low investment by the monopolist because it reduces the incentives of the followers to invest as well. The second pushes in the same direction because a lower investment by the monopolist reduces the aggregate probability of innovation so as to increase the length of time in which the monopolist enjoys the profit flow from the current patent. More formally, each entrant chooses its own investment according to the optimality condition (4.6). In the initial stage, the choice of the leader xM satisfies the optimality condition: · ¸ ∂h(x) [h0 (xM )V − 1] (r + p) = h0 (xM ) + (n − 1) [h(xM )V + K − xM ] ∂xM (4.10) unless current profits are so high that the incumbent leader prefers to withdraw from the race. The system (4.6)-(4.10) defines the interior equilibrium. The eﬀect of SC is now strengthened by the Arrow eﬀect and leads to a low investment of the incumbent monopolist compared to the entrants. In the Appendix we show that the investment by each firm is increasing in the interest rate r and decreasing in the flow of current profits, but ambiguously dependent on the value of the innovation V and the number of firms n. Summarizing: Proposition 4.5. A Stackelberg equilibrium in the competition for the market implies a lower investment for the incumbent monopolist than for the other firms as long as entry is accommodated; investment by each firm is decreasing in the current profits. An immediate corollary of this result is that a Stackelberg equilibrium implies an aggregate investment in R&D which is increasing in the interest rate and decreasing in the current profits of the incumbent, and an expected lifespan of the current patent which is aﬀected in the opposite way. Compared to the Nash equilibrium, both the incumbent and each entrant invest less, and, since the number of firms is exogenous, the aggregate investment must be lower. In conclusion, a Stackelberg leadership with a fixed number of firms does not give a rationale for incumbents’ investment in R&D. Finally, notice that the escape competition eﬀect is now working: if we imagine that an increase in product market competition decreases current profits K but not the value of the innovation (because this is a drastic innovation), then a more intense competition increases individual and aggregate investment in R&D.

146

4. Dynamic Competition and Endogenous Entry

4.2.4 Stackelberg Equilibrium with Endogenous Entry Let us now consider the endogenous entry case, in which the leader has to foresee the eﬀects of its investment choice on the equilibrium number of entrants. In this case, as shown by Etro (2004), the results of the previous three market structures are radically modified: the incumbent monopolist has incentives to invest more than any other firm, the Arrow’s paradox disappears and the escape competition eﬀect disappears as well. Once again, we focus on the realistic case in which entry of followers occurs in equilibrium. In the last stage all the entrants choose the same flow of investment x determined by the symmetric optimality condition: [h0 (x)V − 1] [r + (n − 1)h(x) + h(xM )] = h0 (x) [h(x)V − x]

(4.11)

Using symmetry, the zero profit condition becomes: h(x)V − x =F r + (n − 1)h(x) + h(xM )

(4.12)

Substituting this in (4.11) we obtain the same implicit expression for the entrant’s investment as under Marshall competition (4.9): h0 (x) =

1 V −F

which does not depend on the leader’s decision. However, the equilibrium number of firms does depend on the leader’s choice as predicted by the free entry condition. Totally diﬀerentiating the latter, using the fact that x does not depend on xM , delivers the expected change of investment in R&D of each entrant for a change in the leader’s investment: ∂ [(n − 1)h(x)] = −h0 (xM ) ∂xM which shows that a higher investment of the incumbent reduces the aggregate investment of the other firms through a reduction in the number of entrants. In the initial stage, the incumbent monopolist maximizes profits according to the optimality condition: · ¸ ∂ [(n − 1)h(x)] 0 0 [h(xM )V + K − xM ] [h (xM )V − 1] (r + p) = h (xM ) + ∂xM and, substituting our expression for the indirect impact ∂ [(n − 1)h(x)] /∂xM we obtain a simple equilibrium expression: h0 (xM ) =

1 V

(4.13)

4.2 Dynamic Competition for the Market

147

which shows a larger investment than the one of the entrants. This also implies that the equilibrium number of firms is lower than in the Marshall equilibrium.14 Summarizing, we have: Proposition 4.6. A Stackelberg equilibrium with endogenous entry in the competition for the market implies a) the same investment as in Marshall equilibrium for the entrants with a lower number of entrants, b) a higher investment for the incumbent monopolist than for each of the other firms, and c) a higher total investment than in Marshall equilibrium. Once again, Stackelberg competition with endogenous entry induces the aggressive behavior of the incumbent. The intuition is related to the perception the leader has of the entry process. It is understood that any profitable opportunity for doing R&D left open by the leader will be seized by new entrants until their expected profits are zero. The aggregate probability of innovation is determined by the free entry constraint independently from the investment of the leader and is thus taken as given by the latter. So, the monopolist looses the strategic incentive to keep its investment low: the latter is not going to aﬀect the expected lifespan of the current patent. The Arrow eﬀect disappears. Therefore, the only purpose of investing in R&D for the leader is to actually win the patent race, and the incentives to do it are now higher than those of any other entrant. An intuitive way to see this asymmetry relies on the fact that the leader maximizes its profits taking as given the aggregate probability of innovation, which is equivalent to maximize h(xM )V − xM , without taking into account the impact on the aggregate arrival rate of innovation. This impact, instead, is taken into account by each entrant and reduces the marginal profits of each entrant, explaining why the entrants invest less than the leader.15 We finally derive some comparative statics in the following proposition: Proposition 4.7. A Stackelberg equilibrium with endogenous entry in the competition for the market implies an investment for each entrant firm which is increasing in the value of the innovation and decreasing in the fixed cost, and an investment for the incumbent monopolist which is increasing in the value of innovation while none of them is aﬀected by changes in the current profits. An immediate corollary of this result is that a Stackelberg equilibrium with endogenous entry implies an aggregate investment in R&D which is decreasing in the interest rate and independent from current profits. We confirm 14

15

Also in this model we have entry deterrence when the marginal productivity of investment is not too decreasing. In this case, the equilibrium investment of the monopolist satisfies h(¯ xM ) = (V −F )h(x)/F −x/F −r. In the rest of the chapter we will focus on the case in which there is entry of outsiders in equilibrium. The result holds even when the leader has a lower gain from innovation than the outsiders as long this gain is higher than V − F (Lee and Sung, 2004).

148

4. Dynamic Competition and Endogenous Entry

that the escape competition eﬀect emphasized by Aghion and Griﬃth (2005) disappears when there is endogenous innovation by leaders: here competition for the market eliminates the impact of product market competition on the incentives to innovate. We will discuss later on the implications of this result. Finally, from a welfare point of view, a leadership reduces the number of firms and hence the expenditure in fixed costs, but it increases the total flow of investment, maintaining the aggregate probability of innovation at the same level. This makes ambiguous a welfare comparison between the Marshall outcome and the Stackelberg outcome with endogenous entry. 4.2.5 Non-drastic Innovations Until now we confined our analysis to drastic innovations. Often times, once an outsider has introduced an innovation, the previous leader is not completely replaced, and both firms can still obtain positive profits; in these cases we have non-drastic innovations. Imagine that if the incumbent loses the patent race a duopoly between the winner and the incumbent sets in. Let us denote the value of winning the patent race for the incumbent with V W . When an outsider wins, the previous incumbent obtains V L and the entrant obtains V ≤ V W . The standard assumption is that, even if the innovation is drastic and the duopoly is characterized by perfect collusion, the sum of the discounted profits obtained by the two duopolists cannot be greater than the discounted profits obtained by the incumbent who wins the patent race V W ≥ V + V L . Notice that the case of drastic innovations is a particular case for V W = V and V L = 0. Using the properties of Poisson processes in a standard fashion, the objective function of each outsider is the same as before, (4.4), with a value of innovation V , while the gross expected profits of the incumbent monopolist are now: Π (xM , β M , K) =

h(xM )V W + K + β M V L − xM r + h(xM ) + β M

(4.14)

In Nash and Stackelberg equilibria the comparison between the incentives of the incumbent monopolist and the outsiders to invest are ambiguous because, beyond the usual Arrow and Stackelberg eﬀects, we now have two new eﬀects. On one side the gain from innovating for the incumbent is larger than for an outsider (V W > V ), which increases the relative marginal benefit of innovating for the incumbent. On the other side the gain from the duopolistic profits of the incumbent in the case in which another firm innovates (V L > 0) increases the marginal cost of innovating for the incumbent. Of course, if the first eﬀect is strong enough, the incumbent may be the only firm to invest.16 16

Gilbert and Newbery (1982) studied an auction for a non drastic innovation between an incumbent and an entrant and noticed that the incumbent is willing to pay more for the innovation than an outsider. In theory, their deterministic

4.2 Dynamic Competition for the Market

149

However, in what follows we will not deal with entry deterring strategies, but we will focus on the more realistic case where both the leader and the followers invest in R&D. Consider equilibria with endogenous entry. In a Marshall equilibrium, as long as entry of outsiders drives expected profits to zero, we can obtain the same equilibrium condition for the investment of each outsider (4.9) as obtained earlier, h0 (x) = 1/ (V − F ). In a Stackelberg equilibrium with endogenous entry, when the incumbent monopolist is the leader, the equilibrium is characterized by this same investment for the outsiders and by an aggregate probability of innovation p = h(xM ) + β M which is again independent from the strategy of the incumbent. Accordingly, the incumbent monopolist maximizes: πM =

h(xM )V W + K + [p − h(xM )] V L − xM −F r+p

which is equivalent to maximize h(xM )V W − h(xM )V L − xM , and implies the optimal investment: h0 (xM ) =

1 VW −VL

(4.15)

Clearly, condition V W ≥ V + V L always implies that that the monopolist invests more than each outsider. The investment of the leader is directly related to the net perspective value of innovating V W − V L , which is strictly higher than the one of the entrant V E . Assuming for simplicity that a symmetric duopoly takes place in case of innovation by an outsider, V = V L ∈ (F, V W /2), we can conclude with: Proposition 4.8. With non-drastic innovations, a Stackelberg equilibrium with endogenous entry in the competition for the market implies that the incumbent monopolist invests more than any other firm, all investments are not aﬀected by changes in current profits, and the investment of the monopolist (outsiders) is decreasing (increasing) in the value of the duopolistic competition. Also in this case, the basic escape competition eﬀect disappears: an increase in product market competition leading to lower current profits for the incumbent does not aﬀect the investment in R&D of any firm, including the same incumbent. However, in this case, we can extend our analysis to another interesting experiment. When tougher product market competition reduces the duopolistic profits expected by an innovative outsider and model would apply to cases in which firms can license existing innovations, however Salant (1984) has shown that the result collapses if any firm can license the patented innovation, and Czarnitzki and Kraft (2007b) have extended the model to entry of challengers (endogenizing the number of licenses) obtaining ambiguous results.

150

4. Dynamic Competition and Endogenous Entry

the incumbent (V ), the investment of the former is always reduced and the one of the latter is always increased: a standard Schumpeterian eﬀect impacts on the outsider, and an escape competition eﬀect à la Aghion et al. (2005) impacts on the incumbent monopolist. As we have seen, this happens also when entry in the competition for the market is endogenous. However, the aggregate impact of a higher intensity of product market competition is unambiguously in favor of the Schumpeterian eﬀect. Formally, remembering that p = h(xM ) + (n − 1)h(x), we have: h(x) ∂p = − h00 (x) (V − F )2 > 0 ∂V F Once again, we realize that when competition for the market is free, product market competition cannot increase the aggregate incentives to innovate through the escape competition eﬀect. In a sense, when leaders are endogenously innovating to escape from the innovative pressure of the outsiders, they cannot escape also from product market competition. 4.2.6 Strategic Commitments The model can also be extended to the case in which the size of innovations is actually endogenous. A widespread view claims that the innovations of the outsiders are more radical since patentholders may have a technological advantage in obtaining small improvements on their technologies, so as to induce entrants to try replacing the patentholder with radical innovations. Etro (2004) questions such a view showing that in this model the incumbent monopolist invests also in more radical innovations than the other firms as long as it is the leader in the competition for the market. Before moving on, we should notice that in this chapter we focus on a purely strategic advantage for the incumbent monopolist. As we know from Chapter 2, however, similar results would emerge if we allowed the incumbent to engage in preliminary investments that could induce an aggressive behavior. For instance, the incumbent could commit to invest in R&D more than its rivals through a strategic investment that reduces the variable costs of R&D (Section 2.6), or one that increases the value of innovation (Section 2.7): examples include research eﬀorts aimed at obtaining more radical innovations, entry in related sectors where the same innovation could be fruitfully exploited in the future, or expansion of the market for the future innovation. According to our general analysis of debt financing in Section 2.8, competition for the market is the typical case in which a bias toward debt financing in the financial structure (for instance through venture capital financing) would lead to aggressive investment in a risky activity as R&D: this would endogenously reduce the cost of innovation, since in case of failure, debtholders would bear those costs. Finally, a recent interesting work by Erkal and Piccinin (2007,b) has studied R&D cartels, which are aimed at coordinating R&D investments, and

4.3 Sequential Innovations

151

research joint ventures (RJV) cartels which are aimed at sharing the results of cooperative R&D investment, in the presence of endogenous entry.17 As we have seen in the more general case of Section 2.13, R&D cartels are ineﬀective as any other form of horizontal collusion, because they induce less investment for the members of the cartel than for the outsiders, which leads to lower profits under endogenous entry. On the contrary, RJV cartels between a small number of members can manage to increase their profits by coordinating on a larger investment level than the other firms. This happens because RJV cartels increase the expected value of innovation: as long as one of the members wins the race, the right of exploiting the innovation is awarded to all of them. Under endogenous entry, these cartels do not aﬀect the aggregate arrival rate of innovations: therefore, when RJV cartels take place, they can increase welfare if an increase of the number of firms with the new technology is expected to create gains for the consumers. In other words, antitrust authorities evaluating RJV cartels should focus their attention on the foreseen impact on the product market.

4.3 Sequential Innovations Many innovative markets are characterized by a continuous development through sequential innovations. It has been sometimes argued that, in the presence of sequential technological advances, patents may stifle innovation because they may refrain outsiders from improving the existing technologies leaving the burden of innovation to slacker monopolists.18 On the contrary, we will show that in an environment where innovations are sequential, patents and intellectual property rights play a crucial role in fostering innovation because they can start a virtuous circle of incentives to innovate, and this happens exactly when incumbent monopolists are the leaders in the patent races. The idea, fully developed in Etro (2001, 2007,a), is quite simple. In a one shot patent race the value of the expected monopolistic profits provides the incentives to invest in R&D, and, when entry is endogenous, the aggregate incentives are unchanged when the outsiders or the incumbent monopolist invest. However, in a sequential patent race, the value of becoming a monopolist patentholder is what provides the incentives to invest, and that value is crucially aﬀected by the role of the incumbent monopolist. If 17

18

In a related work, De Bondt and Vandekerckhove (2007) have extended the model of Etro (2004) to the case where the players may commit to share their rewards. The larger investment by the leaders is confirmed when sharing may occur among all entrants, but not necessarily when the leader shares with all the entrants (“winner does not take all”). For instance, see Bessen and Maskin (2002). On this issue, see also Erkal (2005), Etro (2005d), Denicolò (2007), and Scotchmer (2004, Ch. 5) for a survey.

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4. Dynamic Competition and Endogenous Entry

the latter does not invest, the market is characterized by systematic replacement of the monopolist with a new one and the value of being a patentholder coincides with the expected profit flow of a single patent. If the incumbent monopolist is the leader in the patent race and hence, as we know by now, invests in R&D more than any other firm, there is a chance that its monopolistic position will be preserved at the time of the new innovation, and then at the time of the following one, and so on. This possibility of a persistent innovation dramatically increases the value of being a patentholder, which in turn enhances the incentives to invest by all firms, the incumbent and the outsiders. In this case, we will have to associate a (partial) persistence of monopolies with stronger incentives to invest in R&D and therefore with a faster technological progress. This process is at the source of technologically driven growth in the global economy. In this section we will examine this mechanism, dividing it in two separate steps: the first is to endogenize the value of a patent as function of the related innovation and all the subsequent innovations, and the second is to endogenize the value of technological progress in a partial equilibrium production economy. One could also take a third step and endogenize the interest rate in a general equilibrium framework, but this is beyond the scope of this book, whose analysis is limited to a partial equilibrium context. 4.3.1 Endogenous Value of Innovations Consider a sequence of drastic innovations τ = 1, 2, ...T − 1, T , each one associated with the exogenous profit flow Kτ . Every innovation can be obtained after winning a patent race as the one we studied in the previous section. Participation to the patent race for the innovation τ requires a fixed cost Fτ and an investment xτ , which induces an instantaneous probability of innovation hτ (xτ ) with the same properties as before, but potentially changing for diﬀerent innovations. The interest rate is always exogenous and constant at the level r. The value of conquering the patent on innovation τ is defined Vτ and for now will be taken as given. This is natural since it does not depend on investment choices during the regime of innovation τ − 1, and all firms will consider it as exogenous while choosing their investments to conquer it. Accordingly, the expected profit of an outsider firm i participating to the patent race for the innovation τ is: hτ (xiτ )Vτ − xiτ − Fτ (4.16) r + pτ P where pτ = hτ (xjτ ) is the aggregate probability of innovation in this patent race. Of course, while this patent race takes place, the current monopolist has a patent on the previous innovation τ − 1, which is associated with a flow of profits Kτ −1 . The expected profit of this incumbent monopolist can be expressed analogously, taking into account the flow of profits from the current patent: πiτ =

4.3 Sequential Innovations

πM τ −1 =

hτ (xMτ )Vτ + Kτ −1 − xMτ − Fτ · I[xMτ > 0] r + pτ

153

(4.17)

where I[xMτ > 0] is an indicator function with value 1 if xMτ > 0 and 0 otherwise. While the value of the innovation, the current flow of profits and the fixed cost of production may change over time, each patent race can be characterized exactly as in our previous analysis. In equilibrium, the investment of each firm and, in case of endogenous entry, the number of firms investing in R&D will depend (positively) on the value of the innovation in ways that we have examined earlier and that change with the kind of competition. In particular, the incumbent monopolist will not invest in a Marshall equilibrium, but will invest more than any other outsider when is leader in the patent race, as we have seen for the Stackelberg equilibrium with endogenous entry. However, following Reinganum (1985a) and Etro (2004), we can now endogenize the value of these innovations, because the value of holding patent τ must correspond to the equilibrium expected profit of the incumbent monopolist with the patent on the innovation τ , and the value of patent τ − 1 must correspond to the equilibrium expected profit of the incumbent monopolist with the patent on innovation τ − 1, and so on. Accordingly, Vs = πMs for any s = τ − 1, τ , ... For instance, if Marshall competition takes place in every patent race, we know that the incumbent monopolist will not participate, each outsider will invest in the patent race for innovation τ an amount xτ (Vτ ) satisfying the condition h0τ (xτ ) (Vτ − Fτ ) = 1, and the aggregate probability of innovation will be determined by the zero profit condition for the outsiders. Using these equilibrium conditions, the dynamic relation that links the value of subsequent innovations becomes simply: Vτ −1 =

Kτ −1 Fτ hτ [xτ (Vτ )]Vτ − xτ (Vτ )

(4.18)

whose right hand side is decreasing in Vτ . Given the value of the last innovation (say VT = KT /r at time T ), one can recursively obtain the value of all the previous innovations.19 Something analogous emerges with Stackelberg competition and endogenous entry. In this case the incumbent monopolist participates always to the patent race and, assuming that entry deterrence is not optimal (which 19

Notice that this implies a negative relation between the value of subsequent innovations. The intuition is straightforward: if the value of innovation τ is expected to be large, there will be more investment in the patent race to obtain this innovation, which reduces the expected length of the monopoly associated with the previous patent τ − 1, whose value will be smaller as a consequence. This may lead to innovation cycles (see Etro, 2004).

154

4. Dynamic Competition and Endogenous Entry

requires the hτ function to be concave enough),20 its investment xMτ (Vτ ) satisfies h0τ (xMτ ) Vτ = 1, while the equilibrium investment of the outsiders and the aggregate probability of innovation are given by the same conditions as before. The relation between subsequent values of innovations becomes: ½ ¾ hτ [xMτ (Vτ )]Vτ + Kτ −1 − xMτ (Vτ ) Vτ −1 = (4.19) − 1 Fτ hτ [xτ (Vτ )]Vτ − xτ (Vτ ) which implies an important consequence. Since the first mover advantage represents a strategic advantage for the incumbent monopolist and increases its expected profits compared to the outcome without such an advantage, the value of being the incumbent monopolist is endogenously increased.21 But, since the value of being the current monopolist is what provides the incentives to invest in R&D, also the total investment and the aggregate probability of innovation must endogenously increase. More precisely, for every innovation except the last one, the value of becoming the incumbent monopolist is higher under Stackelberg competition with endogenous entry rather than under Marshallian competition. This induces a larger investment by each firm and a larger aggregate investment when the incumbent monopolist has a first mover advantage. Summarizing, we have: Proposition 4.9. With sequential innovations, competition for the market with endogenous entry implies that the aggregate probability of innovation is higher when the incumbent monopolist has a leadership in the patent races. The bottom line is that, far from stifling innovation, incumbent monopolists facing endogenous entry of competitors enhance aggregate investment in R&D. Of course, the first mover advantage of these monopolists is a precondition for both a larger investment in R&D and a more likely persistence of technological leadership. Therefore, we obtain the paradoxical result for which endogenous entry in the competition for the market is associated with persistent monopolies. Notice that our theory suggests a way to discriminate between diﬀerent degrees of persistence of leadership in innovative sectors. As we have seen, when entry of firms in the competition for the market is endogenous we should expect that technological leaders invest a lot and their persistence is more likely. Of course, when there is no competition for the market we would also expect that the leadership is persistent. However, when the degree of competition for the market is intermediate, we expect that the incumbent does not 20

21

The analysis of sequential patent races in case of entry deterrence can be found in Denicolò (2001) in a related framework with linear technology, and an additional externality from aggregate investment, and in Etro (2001) within our framework. See also Cozzi (2007) for further discussion. The right hand side of (4.19) is always larger than the right hand side of (4.18).

4.3 Sequential Innovations

155

invest much in R&D and its leadership is more likely to be replaced. This suggests an inverted U curve between the degree of persistence of technological leadership and the degree of competition for the market. This may explain why it is so diﬃcult to find empirical support for the dynamic view of competition which suggests that a leadership position should rapidly vanish.22 In the last part of the chapter, we will discuss the relation between competition in the market and for the market, and draw some policy implications. 4.3.2 Endogenous Technological Progress In all our static and dynamic description of patent races we have kept exogenous the flow of profits obtained by the incumbent monopolists. It is now time to endogenize it and, for this purpose, we need to describe explicitly the market through which firms exploit their innovations, employ their patents and derive their profits. We will do it in a framework where innovations improve the productivity of intermediate goods that are used in the production of final goods. This implies that the incentives to invest to improve the quality of these intermediate goods derive from the profits obtained from sales to the market for final goods. Following the pathbreaking analysis of Romer (1990), Segerstrom et al. (1990) and Aghion and Howitt (1992, 1998), consider a competitive market for final goods with a production function as:23 Z Y = (q τ j Xj )α dj (4.20) j∈J

where output Y is produced employing intermediate goods of diﬀerent kinds (from a set J). Each one of these intermediate goods is produced by a monopolist with a patent on its leading technology at a constant and unitary marginal cost. An infinite sequence of product innovations characterizes these intermediate goods: an innovation τ j for the intermediate good j implies that Xj units of this input are equivalent to qXj units produced with the preexisting technology τ j − 1, with q > 1/α, which guarantees that the innovation is drastic. Demand for an input sold at a price 1 + µj , that is with a mark up £ ¤1/(1−α) µj > 0, can be derived as Dτ j = αq ατ j /(1 + µj ) . This implies that the profit maximizing price of a monopolist producing this input would be 1 + µj = 1/α, however, we will maintain a general expression for the equilibrium price to encompass alternative assumptions.24 Since each sector works 22 23

24

See Cable and Mueller (2006). Other inputs are held constant and normalized to unity for simplicity. As long as their markets are perfectly competitive the analysis is not aﬀected by them. See Barro and Sala i Martin (1995) for a discussion. Our result generalizes to non-drastic innovations if Bertrand competition with free entry takes place. In such a case, the equilibrium implies limit pricing by

156

4. Dynamic Competition and Endogenous Entry

in the same way, in what follows we will disregard the sector index j. Hence, each patent τ for any intermediate good gives the right to a flow of profits: Kτ = µDτ = µ

µ

αq ατ 1+µ

1 ¶ 1−α

(4.21)

Suppose that the probability of innovation is given by: hτ (xτ ) = (φτ xτ )

(4.22)

where ∈ (0, 1). To have an idea of the realistic shape of this function, notice that the first estimate of the elasticity of the number of innovations with respect to investment in R&D by Pakes an Griliches (1980) was 0.6, while the time series study of Hausman et al. (1984) estimated an elasticity of 0.87 using the Poisson distribution, decreased to 0.5 with the larger sample used by Hall et al. (1986). More recently, Kortum (1993) suggests a range between 0.1 and 0.6 and Blundell et al. (2002) find a long-run elasticity close to 0.5. Most of these estimates are based on the relation between investment and the number of patented innovations, which is not necessarily a good measure of innovation (since only a small percentage of patents are really valuable).25 Acemoglu and Linn (2004) have focused on the new drugs obtained in the pharmaceutical industry (rather than the new patents) obtaining an implicit estimate of the elasticity of the innovations with respect to R&D investment around 0.8. Finally, assume that new ideas are more diﬃcult to obtain when there is an increase in the scale of the sector, as represented by expected production with the new technology. Furthermore, assume that the fixed cost is a constant fraction of the expected cost of production with the new technology. Summarizing, assume φτ = 1/ζDτ and Fτ = ηDτ /(r + pτ +1 ), where ζ > 0 and η ∈ (0, µ) parametrize how costly are innovations. With these last assumptions we want to capture the idea that the larger is the scale of expected production of a firm, the larger are the costs necessary to discover and

25

the last innovator (1 + µj = q for any j) and no other firms active in the market. Cournot competition with free entry would imply that more than one firm would produce intermediate goods, but Stackelberg competition in quantities with free entry would result again in having only the last innovator producing for the market and obtaining positive profits (something quite similar to the idea of the first mover avantage of the innovators in a world without patents advanced by Boldrin and Levine, 2005). Moreover, as Scotchmer (2004) notices, “these estimates should be interpreted with caution, due to the noisiness of the data. It is not clear that the estimated coeﬃcients address the experiment of increasing the R&D spending in firms, since other circumstances of the invention environment change.” See also the discussion in Denicolò (2007). Notice that Segerstrom (2007) assumes = 0.3 in his model.

4.3 Sequential Innovations

157

develop the associated technology (construction of prototypes and samples, new assembly lines and training of workers).26 These ingredients allow us to fully characterize the equilibria of the sequential patent races in function of the interest rate r.27 Under Marshall competition in the patent races the incumbent monopolist never invests in R&D and is systematically replaced by a new firm when the subsequent innovation is obtained: this process of continuous “leapfrogging” between firms implies that monopolies are not persistent and technological progress is driven by outsider firms. This is the standard result in the literature on Schumpeterian growth (Barro and Sala-i-Martin, 1995; Aghion and Howitt, 1998), even if it has little to do with the original ideas of the late Schumpeter (1943), for which large established firms are the main drivers of innovation and technological progress. The original Schumpeterian characterization of the innovation process emerges when Stackelberg competition with endogenous entry takes place in the competition for the market: when the incumbent monopolist has a first mover advantage in the patent races and invests in R&D more than any other firm, its leadership is partially persistent and technological progress is driven by both the outsiders and the incumbent monopolists.28 Moreover, as we have seen in the previous section, the partial persistence of monopoly associated with this leadership must increase the incentives to invest for all firms. As long as entry in the competition for the market is free, under both forms of competition, the aggregate probability of innovation is positively correlated to the mark up and negatively correlated to the interest rate. In particular, as shown in the Appendix, in steady state the probability of innovation for each patent race is: p=

·

(µ∗ − η) ζ

¸ ·

¸1− (1 − ) (µ∗ − η) −r +1 η

(4.23)

where µ∗ can be interpreted as the eﬀective gross return on a patent. Under Marshall competition this is simply equal to the mark up µ, since this is the only gain expected by a patentholder. Under Stackelberg competition, µ∗ is 26

27

28

See Peretto and Connolly (2005) on the role of these kinds of fixed costs in endogenous growth models, and Peretto (2007) for further applications. Full fledged patent races with decreasing marginal productivity have been introduced in the Schumpeterian growth model in Etro (2004). The previous literature, starting with the pathbreaking contribution of Aghion and Howitt (1992) assumed linear technology of innovation so that a no-arbitrage condition was able to pin down the aggregate investment in R&D without any insights on the industrial organization of the patent races. For a related treatment of patent races in growth models see Zeira (2004). Here we focus on the case where is realistically low. When is high enough, the incumbent monopolist deters entry.

158

4. Dynamic Competition and Endogenous Entry

higher and includes the value of a partially persistent leadership, which is also increasing in the size of innovations. Summarizing, we have: Proposition 4.10. With sequential innovations, competition for the market with endogenous entry implies a steady state aggregate probability of innovation that is increasing in the mark up on patented products and that is higher when the incumbent monopolist has a leadership in the patent races. The relation (4.23) provides an implicit equilibrium relation between the interest rate and the investment in innovation, which is expressed in terms of the aggregate probability of innovation that the firms can support. Of course, a higher interest rate reduces the incentives to invest in R&D since it increases the return on alternative investments. To evaluate the consequences for growth, one could endogenize savings of the consumers as a (decreasing) function of the interest rate, and determine the equilibrium interest rate that clears the credit market (equating investments and savings) and consequently the growth rate of the economy.29 This framework can be used for a number of macroeconomic experiments, that are however beyond the scope of this book.30 Here, we will summarize a few results that are relevant for our purposes. First, one can show that the decentralized equilibrium is always characterized by dynamic ineﬃciency because of a bias in the R&D sector toward firms investing too little - essentially because, for a given total investment in R&D, too many firms do research, since they do not consider the negative externality induced by their entry on the expected profits of the other firms. The presence of incumbent monopolists doing a lot of research limits this ineﬃciency, but does not eliminate it. Dynamic ineﬃciency means that a reallocation of resources in the innovation sector (inducing larger research units) could increase both current and future consumption, and a consequence of this is that the optimal innovation policy 29

If the final good is consumed by a representative agent with logarithmic utility, the Euler condition for utility maximization implies the growth rate of consumption gC = r − ρ, where ρ is the time preference rate. Since the equilibrium α 1−α

30

κj α

α q 1−α dj, its production of the final good must amount to Y = 1+µ j∈J growth rate can be approximated as gY = (pα ln q) /(1 − α). Equating these two expressions for the unique steady state growth rate, one obtains an implicit expression for the savings that the agent is willing to provide at a given interest rate, expressed in terms of the aggregate probability of innovation that these savings can support p = (1 − α) (r − ρ) /α ln q. Equating this with (4.23) one obtains the equilibrium interest rate, and consequently the general equilibrium growth rate of the economy. On macroeconomic policy and the eﬀect of aggregate demand shocks in this framework see Etro (2001).

4.4 Competition in the Market and Competition for the Market

159

requires always R&D subsidies.31 Nevertheless, the equilibrium growth rate may well be below its socially optimal level (essentially because the private value of innovations can be lower than their social value), therefore the optimal innovation policy may require also subsidies to entry in the competition for the market. Segerstrom (2007) has introduced the possibility of imitation by the followers (which drives industry profits to zero), showing that an increase in the probability of imitation can increase the incentives to invest of the leader whose innovation has been copied (through a sort of escape competition effect), but it reduces the value of the endogenous leadership and hence the aggregate incentives to invest (that are always determined by the free entry condition for the outsiders in the competition for the market). One can also explore in more details the markets for inputs, which we assumed to be perfectly competitive in our discussion, 32 and introduce other forms of productivity growth to study their impact on the innovation activity in general equilibrium.33 Finally, one could also extend the analysis to a multicountry framework to study global growth and the diﬀerence between strategic (unilateral) innovation policy and optimal international coordination of the same policy (in terms of R&D subsidies and protection of IPRs as well).34

4.4 Competition in the Market and Competition for the Market The basic theories of innovation, as those described until now, suggest that competition in the patent races increases investment in R&D, but also the 31

32 33

34

See Etro (2007a). The interesting work of Minniti (2006) has introduced the first complete analysis of multiproduct firms in the Schumpeterian framework, showing that the equilibrium is characterized by too many firms (too much interfirm diversity) and too few products per firm (too little intra-firm diversity). On the eﬀectiveness of R&D subsidies in promoting investment in innovation see the empirical work of Aerts and Schmidt (2007). See Koulovatianos (2005) and Grieben (2005). In general, an increase in an exogenous growth rate of total factor productivity has a positive direct eﬀect (since directly enhances the value of innovations) and a negative general equilibrium eﬀect due to the increase in the interest rate (needed to increase savings to sustain a higher growth). This implies that an increase in total factor productivity growth increases the growth rate of the economy, but has an ambiguous impact on the percentage of income spent in R&D activity. This may explain the lack of a clear correlation between R&D per capita and growth over time and across countries (see Scotchmer, 2004, Ch. 9). For related investigations see Kornprobsty (2006). See Etro (2007a), and Impullitti (2006 a,b, 2007).

160

4. Dynamic Competition and Endogenous Entry

market power of the innovators in the product market is positively related with investment in R&D. While the first result is consistent with the evidence, the second one is, to some extent, at odd with empirical evidence. This shows a positive relation between competition and technological progress (Blundell et al., 1999), or at most a non monotone relation, positive for low levels of competition and negative for high levels (Aghion et al., 2005). Aghion and Griﬃth (2005) have provided a possible explanation for this relation in a model of Schumpeterian growth with exogenous innovation by leaders. They consider step by step innovations, that is they assume that frontier technologies can be used by their developers while other firms have to develop them before trying to expand the frontier. In this set up, tougher competition may increase the incentives of the leaders to innovate with the aim of escaping competition. The intuition of this “escape competition eﬀect” is simple because, as usual, the incentives to invest for the leaders depend on the diﬀerence between the profits with innovation and those without innovation: competition reduces both, but tends to reduce more the profits of a leader that does not innovate, since a leader that obtains a drastic innovation is less constrained by competition.35 While this theory is fascinating, it is not entirely convincing. In particular, Aghion and Griﬃth (2005) do not derive innovation by leaders endogenously, but assume that the technological leaders invest in innovation and there is not entry of outsiders in the competition for the market.36 Since we have seen that innovation by incumbent monopolists emerges endogenously exactly when there is free entry in the competition for the market and the incumbents are leaders in this competition, leaving entry aside does not appear neutral: the escape competition eﬀect heavily depends on the hypothesis that the leaders undertake the research activity, since standard incentives would drive the investment of the outsiders (namely less investment when competition is tougher). As we have noticed in a number of models, the escape competition eﬀect works when competition for the market is exogenously limited, but when competition for the market is free we noticed that the behavior of outsiders determines the rate of innovation (constraining in a way or another the strategy of the leaders), and the escape competition eﬀect vanishes. Finally, Aghion and Griﬃth (2005) do not associate the intensity of competition with more competitive structures in the product market, but with a lower price of the competitive fringe of firms, with a higher probability of entry (see also Aghion et al., 2006) or with other exogenous elements. The crucial interaction between competition in the market and for the market 35

36

This does not happen always but just when firms are neck-and-neck, that is when the technology of the leader is similar to that of the other firms and the leader has strong incentives to escape competition. The result is strengthened when competition increases the fraction of neck-and-neck sectors. Aghion et al. (2005) augment the model with a single follower, but still without free entry in the competition for the market.

4.4 Competition in the Market and Competition for the Market

161

remains to be studied for the escape competition eﬀect to be convincing from a theoretical point of view. Denicolò and Zanchettin (2006) adopt an alternative approach and compare alternative forms of competition in the market for intermediate goods when innovations are non drastic. They describe a sort of “Darwinian selection eﬀect” induced by competition. When this is weak many ineﬃcient firms can be active in the product market, while tough competition is consistent with just few eﬃcient firms. In other words, when the intensity of competition increases, ineﬃcient firms have to exit the market leaving the most eﬃcient ones in it. Moreover, this process gradually shifts profits from less eﬃcient to more eﬃcient firms (“front-loading eﬀect”), that are the most recent innovators. As a result of these eﬀects, industry profits for the eﬃcient firms may increase in such a way that also the incentives to invest in R&D are strengthened. More formally, let us extend our model of section 4.3.2 with diﬀerent forms of competition in the market for intermediate products. In case of innovations of limited size (q < 1/α), the producer of the latest vintage of an intermediate good (with a patent on it) will face competition from the previous innovators, who still have patents on slightly inferior technologies. In case of Bertrand competition with free entry the outcome is simple: only the latest innovator is on the market, pricing its intermediate goods at the limit price 1 + µ = q, and the previous analysis goes through. In case of Cournot competition, which can be regarded as a less competitive form of competition, the equilibrium implies a higher price but the latest innovator is not anymore alone in the market: previous innovators with their inferior technologies produce part of the intermediate goods.37 This implies ineﬃcient production, since the previous innovators are less productive, and this may even lead to a decrease in the total profit of the sector compared to the outcome under Bertrand competition. √ For instance, imagine that q ∈ (1/ α, 1/α), which implies that at most two firms (the last two innovators) can profitably produce any intermediate good. The latest innovator and the previous one compete in quantities as if the marginal cost of the former was unitary and that of the latter was q > 1, and it is easy to verify that with our demand function this leads to the equilibrium price 1 + µ = (1 + q)/(1 + α). This price is always higher than the limit price under Bertrand competition 1 + µ = q, but may generate lower industry profits and lower profits for the technological leader, because part of the production of the latest innovator is replaced by the production of a less eﬃcient firm. This always happens when q is close to the monopolistic price 1/α, since industry profits under Bertrand competition remain close to their monopolistic level, while industry profits (and the profits of the latest 37

As we know by now, a leadership for the latest innovator also in the product market competition would lead to limit pricing as well, leaving our analysis unchanged again.

162

4. Dynamic Competition and Endogenous Entry

innovator) under Cournot competition have a first order reduction due to the entry of a less eﬃcient firm.38 More in general, whenever industry profits are lower with Cournot competition than with Bertrand competition, and they are shifted toward the less eﬃcient firms, the incentives to innovate are lower as well - even if Cournot competition generates higher prices than Bertrand competition. In particular, in our duopolistic example, the value of becoming the last innovator is a weighted discounted average of the profits expected as a producer with the leading technology and with the second best technology (once a better one is invented), and under Marshall competition in the patent races, this value is what drives the investment of the outsiders (current producers do not invest because of the Arrow eﬀect once again). Denicolò and Zanchettin (2006) show that the same positive relation between the intensity of competition and growth can emerge when there is endogenous persistence of technological leadership due to Stackelberg competition with endogenous entry in the patent races. As we have seen before, non drastic innovations that give raise to duopolies between the last two innovators do not aﬀect the general principle for which the leader invests more than any other firm. Denicolò and Zanchettin focus on the extreme case where only the last innovator invests ( = 1) and the persistence of technological leadership is complete. Notice that the incentives to invest of the outsiders determine the entry deterrence investment of the technological leader and those incentives depend again on a weighted discounted average of the expected profits in the potential duopoly. This implies that, under the same circumstances as before, Cournot competition in the product market leads to lower industry profits and lower investments in R&D than Bertrand competition. Nevertheless, in this case duopolistic competition in the market for intermediate goods does not take place in equilibrium since all innovations are due to a single leading firm with eternal leadership. Similar results are likely to emerge in the more realistic case where investment by outsiders takes place and the persistence of technological leadership is only partial.

4.5 Conclusions In their Epilogue, Aghion and Griﬃth (2005) address some policy issues and emphasize two contrasting views: “some commentators have argued there is a specificity of innovative markets with respect to competition. They see the role of antitrust action in innovative sectors as one of counteracting incumbent firms that try to prevent innovation by new entrants by issuing 38

Denicolò and Zanchettin (2006) prove that this outcome emerges under more general conditions.

4.5 Conclusions

163

and accumulating (unjustified) patents. In other words, antitrust action should focus on fostering competition for the market, but not so much on increasing competition in the market, since this would reduce innovation incentives by reducing rents. In innovative markets where incumbents innovate, antitrust action should be restrained so as not to stamp out monopoly power in such markets. Instead, our analysis suggests that stimulating competition in the market, especially in sectors that are close to the corresponding world frontier and/or where incumbent innovators are neck-and-neck, can also foster competition for the market through the escape competition eﬀect. Incumbent firms innovate precisely as a response to increased product market competition or to increased entry threat, at least up to some level.”39 We are not sure that this distinction is properly motivated. First, we do believe that there is a specificity of innovative markets with respect to competition, because firms in high-tech markets compete mainly with investments to create better products rather than with standard price strategies, and this should be taken into account. Second, we do not see any contradiction between the claim of the theory of market leaders and endogenous entry for which strong competition for the market enhances technological progress and the fact that competition in the market may enhance it as well under certain conditions: when this is the case, antitrust policy should be aimed at promoting both forms of competition in innovative markets. Nevertheless, we have shown that when competition for the market is characterized by endogenous entry (and by a leadership position), the incentives to invest in R&D are maximized and there is a limited space for competition in the market to enhance investment: to a large extent, competition for the market is a good substitute for competition in the market in dynamic sectors. An interesting exception to this principle derives from the Darwinian selection eﬀect, which implies that tougher product market competition can endogenously exclude ineﬃcient firms from production and constrain the price of the eﬃcient ones, while still promoting innovation (of the most eﬃcient firms) through the gains in production eﬃciency.40 Finally, it is clear, and in no way contradicted by the results of Aghion and Griﬃth (2005), that the ultimate engine of market-driven innovations is associated with the possibility of exploiting the fruits of uncertain investments through intellectual property rights. Therefore, we believe that a main policy implication of this research is that antitrust policy should promote competi39

40

Aghion and Griﬃth (2005, p. 91) associate the two positions respectively with Etro (2004) and Vickers (2001). This is another case in which competition leads to exit of the competitors of the leader, but it enhances consumer welfare as well.

164

4. Dynamic Competition and Endogenous Entry

tion both for and in the market,41 but should never interfere with the legal protection of patents and trade secrets, which drive the private incentives to invest in R&D. With this chapter we have concluded the theoretical part of the book. In the following chapters we will move on to the policy implications of the theories we have examined.

41

For a policy analysis on the benefits of product market reform taking in considerations the eﬀects on innovation see Faini et al. (2006), Parascandolo and Sgarra (2006), Barone and Cingano (2007) and Leiner-Killinger et al. (2007).

4.6 Appendix

165

4.6 Appendix Proof of Prop. 4.2. Imagine that the social value of the innovation is V ∗ . Under Marshall competition with n firms investing x each, welfare is: WN =

nh(x)V ∗ − nx − nF r + nh(x)

Under Stackelberg competition with a leader investing xM and ns −1 followers investing x, using the fact that nh(x) = h(xM ) + (ns − 1)h(x), we have an increase in welfare: [h(xM ) + (ns − 1)h(x)] V ∗ WS = − xM + (ns − 1)x − ns F r + h(xM ) + (ns − 1)h(x) · ¸ (x + F ) (xM + F ) h(xM ) h(x) N − > WN =W + h(x) xM + F x+F since the second term is positive because xM > x. Notice that this second term corresponds to the expected profit of the leader from the patent race. Q.E.D. Proof of Prop 4.5. Symmetry between the entrants in the second stage implies the equilibrium system: f (·) ≡ [h0 (x)V − 1] [r + (n − 1)h(x) + h(xM )] − h0 (x) [h(x)V − x] = 0 g(·) ≡ [h0 (xM )V − 1] [r + (n − 1)h(x) + h(xM )]+ ¸ · ∂nh(x) [h(xM )V + K − xM ] = 0 − h0 (xM ) + ∂xM

with ∂nh(x)/∂xM = nh0 (x)φ0 (xM ) where x = φ(xM ) is the common reaction function for x as a function of xM and increasing in it: φ0 (xM ) =

− [h0 (xM )V − 1] h0 (xM ) h” (x) {V [r + (n − 1)h(x) + h(xM )] + x}

Since ∂φ0 (xM )/∂r < 0, ∂φ0 (xM )/∂K = 0 and ∂φ0 (xM )/∂n > 0 , while the sign of ∂φ0 (xM )/∂V is ambiguous, by totally diﬀerentiating the system above we obtain the comparative statics for y = r, n, K, V : # " ¸· ¸ · dx 1 gxM −fxM fy dy =− dxM −g f gy ∆ x x dy where ∆ ≡ fx gxM − fxM gx > 0 by assumption of stability, and assuming fx < 0 and noting that fxM > 0, fr > 0, fK = 0, fn > 0, fV > 0, gx > 0, gxM < 0, gr > 0, gK < 0 while gn and gV have the only ambiguous signs. It follows that comparative statics for n and V is ambiguous, but dxM /dr > 0, dx/dr > 0, dxM /dK < 0, and dx/dK < 0. Q.E.D.

166

4. Dynamic Competition and Endogenous Entry

Proof of Prop. 4.6: To complete the proof we need to rigorously show that the choice of the leader is indeed a global maximum, or, in other words, that the option of zero investment is dominated by that choice. If we use the equilibrium free entry condition of the second stage to rewrite the objective function of the leader as: ΠL =

h(xM )V + K − xM h(xM )V + K − xM −F = F −F [r + (n − 1) h(x) + h(xM )] h(x)V − x

we notice that the local maximum satisfying the first order equilibrium condition h0 (xM ) V = 1 is a global maximum if: h(xM )V +K−xM h(x)V −x

F −F >

K h(x)V −x F

⇔

h(xM )V −xM h(x)V −x

>1

but this is always true since we know that h(xM )V − xM > h(x)V − x. The last part follows noticing that nh(x) = h(xM ) + (ns − 1)h(x) implies: · ¸ h(xM )x xM x h(xM ) h(x) s nx − [xM + (n − 1)x] = − − xM = <0 h(x) h(x) xM x since h00 (x) < 0. Q.E.D. Proof of Prop. 4.9. Consider first the case of Marshall competition in each patent race, so that incumbent monopolists do not invest and are replaced at each innovation. Under our functional form assumptions every patent race will be characterized by an investment for each outsider: xτ =

1 1−

1

φτ1− (Vτ − Fτ ) 1−

and by a zero profit condition: (φτ xτ ) Vτ − xτ = Fτ r + pτ The value of innovation is simply: Vτ =

µDτ r + pτ +1

where Dτ is the demand of the corresponding intermediate good sold to the final good sector as in (4.21). Solving the endogenous entry condition we have: (φ xτ ) Vτ − xτ r + pτ = τ = Fτ 1 1−

[(φτ ) (Vτ − Fτ )] 1− Vτ − Fτ

=

( /ζ) 1− (µ − η) 1− [µ − (µ − η)] η (r + pτ +1 ) 1−

1

φτ1− (Vτ − Fτ ) 1−

=

=

4.6 Appendix

167

which shows a negative relation between probabilities of innovation of subsequent patent races, exactly as in the model of sequential patent races with an exogenous flow of profits for each innovation. Focusing on the steady state with a constant probability of innovation p, we can solve the above relation for the eﬀective discount factor in steady state, r + p, that satisfies: (r + p) =

( /ζ) 1− (µ − η) 1− [µ − (µ − η)] η (r + p) 1−

from which we obtain: · ¸ · ¸1− (µ − η) µ(1 − ) + η r+p= ζ η This is increasing in the mark up, and it allows to derive explicitly the investment for each firm: µ ¶ 1− · ¸ 1−1 1 1 (µ − η) D τ xτ = 1− = ζDτ r + pτ +1 η (µ − η) Dτ = µ − (µ − η) that is increasing in the mark up and also in the size of demand for the corresponding product. The explicit equilibrium expression for the value of innovations is: Vτ =

µ (ζ/ ) η1− Dτ 1−

(µ − η) [µ(1 − ) + η]

Consider now the case of Stackelberg competition with endogenous entry. In each patent race we still have the same general rules for the investment of the outsiders in function of the value of innovation, and the same free entry condition as before. However, also the incumbent monopolist participates to the patent race, investing according to the following rule: xMτ =

1 1−

1

φτ1− Vτ 1−

and the value of being a monopolist with the patent τ − 1 is now given by the following recursive relation: Vτ −1 =

(φτ xMτ ) Vτ + Kτ −1 − xMτ − Fτ r + pτ

While this is general a complex relation, our modeling assumptions on technological progress allow us to derive a complete solution. First of all, notice that free entry by the outsiders determines the aggregate probability of innovation in each patent race independently from the behavior of the incumbent, while the value of innovation depends on the behavior of the leader as well.

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4. Dynamic Competition and Endogenous Entry

The profit function of the producers of intermediate goods implies that demand increases in a deterministic way through subsequent innovations: Dτ = q α/(1−α) Dτ −1 . Because of this, it turns out that also the value of innovation increases at the same rate between subsequent innovations. We can solve for this using the method of undetermined coeﬃcients. Guessing a functional form Vτ = ψDτ /(r + pτ +1 ) we have also: α

Vτ −1

ψq − 1−α Dτ = r + pτ

Substituting the equilibrium investment of the incumbent monopolist in the recursive relation above, we obtain: i h 1 1 1 1 (φτ ) 1− Vτ 1− Vτ + Kτ −1 − 1− φτ1− Vτ 1− ηDτ − Vτ −1 = r + pτ r + pτ +1 Equating the two expressions for Vτ −1 and solving in steady state we have: #1− µ ¶ " α (1 − ) q 1−α ψ−r p= α ζ ψ − µ + ηq 1−α which provides a negative relation between the aggregate probability of innovation p and the rate of return from the leadership ψ (for ψ small enough): the higher is the probability of innovation, the shorter is the lifetime of an innovation, and, consequently, the lower is the value of being a leader. Moreover, using again our guess, we can solve for the free entry condition for the outsiders as before: · ¸ · ¸1− (ψ − η) ψ(1 − ) + η p= −r ζ η This is a positive relation between the aggregate probability of innovation p and the rate of return from leadership ψ: the higher is the value of being a leader, the larger will be the investment in R&D and hence the probability of innovation. Finally, putting together these last two relations we can derive an implicit expression for the equilibrium value of ψ: α

ψ(µ) = µ +

1

(1 − ) ηq 1−α ψ 1−

(ψ − η)

1−

[ψ(1 − ) + η]

α

− ηq 1−α

which must be larger than µ for our guess to be consistent (otherwise the incumbent monopolist would not find it convenient to invest), which can be verified to be the case for a wide set of parameter values. To close our equilibrium description, the investments of the incumbent monopolists and of each outsider for any patent race are:

4.6 Appendix

xMτ =

ηψDτ ψ − (ψ − η)

xτ =

169

η (ψ − η) Dτ ψ − (ψ − η)

where the first is 1/(1 − η/ψ) times the second. The expression for the aggregate probability of innovation can be obtained with µ∗ = µ in case of Marshall equilibrium and µ∗ = ψ in case of Stackelberg equilibrium with endogenous entry. Q.E.D.

5. Antitrust and Abuse of Dominance

The scope of antitrust policy is to avoid distortions of competition that may negatively aﬀect consumers, like collusive arrangements aimed at fixing prices above their competitive level, mergers aimed at creating a dominant position, and abuse of dominance by market leaders against the interests of consumers. Given the particular focus on market leaders in this book, our attention in this chapter will be mainly on the last aspect of antitrust policy: abuse of dominance with anticompetitive purposes.1 In the United States the main federal antitrust statute is the Sherman Act of 1890, which was developed in reaction to the widespread growth of large scale business cartels and trusts. Section 1 of the Sherman Act prohibits restraints of trade in general, while Section 2 deals with monopolization stating that: “Every person who shall monopolize, or attempt to monopolize, or combine or conspire with any other person or persons, to monopolize any part of trade or commerce among the several States, or with foreign nations, shall be deemed guilty of a felony”. Enforcement at the federal level is shared by the Antitrust Division of the Department of Justice and by the Federal Trade Commission. The current interpretation of US antitrust law associates abusive conduct with predatory or anticompetitive actions having the specific intent to acquire, preserve or enhance monopoly power distinguished from acquisition through a superior product, business acumen or historical accident (hence monopoly per se is not illegal). It is generally accepted that an action is anticompetitive when it harms consumers. In Europe, competition policy has a more recent history which is mostly associated with the creation of the European Union and its coordination of policies for the promotion of free competition in the internal market. The main provisions of European Competition Law concerning abuse of domi1

On the first two aspects of antitrust, see Motta (2004, Ch. 4-5) for a wide survey of the economic literature, and Sections 2.13 and 3.5 for some implications of the endogenous entry approach. Recently, Rhee (2006) has applied aspects of the theory of market leaders to merger policy for the New Economy.

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5. Antitrust and Abuse of Dominance

nance are contained in the Article 82 of the Treaty of the European Communities which states that: “Any abuse by one or more undertakings of a dominant position within the common market or in a substantial part of it shall be prohibited as incompatible with the common market in so far as it may aﬀect trade between Member States. Such abuse may, in particular, consist in: (a) directly or indirectly imposing unfair purchase or selling prices or other unfair trading conditions; (b) limiting production, markets or technical development to the prejudice of consumers; (c) applying dissimilar conditions to equivalent transactions with other trading parties, thereby placing them at competitive disadvantage; (d) making the conclusion of contracts subject to acceptance by other parties of supplementary obligations which, by their nature or according to commercial usage, have no connection with the subject of such contracts.” This article on abuse of dominance is part of the law of each member state and is enforced by the European Commission and by all the National Competition Authorities (as Article 81 on horizontal and vertical agreements and the Merger Regulation).2 The application of EU competition law on abuse of dominance involves the finding of a dominant position and of an abusive behavior of the dominant firm, usually associated with exploitative practices such as excessive pricing,3 and with exclusionary practices such as predatory pricing, rebates, tying or bundling, exclusive dealing or refusal to supply. However, the analysis of both dominance and abusive behaviors entails complex economic considerations and its reform in the EU is the subject of an ongoing debate. Many economists have pointed out the necessity of a closer focus on consumer welfare in the implementation of competition policy with specific reference to abuses of dominance. While antitrust legislation was written with this objective in mind, its concrete application has sometimes been biased against market leaders and in defense of their competitors rather than toward the defense of competition and of the interests of consumers. The two objectives do not necessarily overlap. The development of the New Economy, characterized by very dynamic and innovative markets, has increased the pressure for a new approach, already somewhat developed in the United States, and in progress in Europe. An important EU Report by Rey et al. (2005), has 2

3

The Commission acts both as a prosecutor and judge at a first level. The Court of First Instance has jurisdiction in all actions brought against the decisions of the Commission, while the European Court of Justice decides on appeal actions brought against the judgments of the Court of First Instance. Motta (2004) provides a careful treatment of competition policy in the EU. For a non-technical treatment see Riela (2005). On this point see Katsoulacos (2006).

5. Antitrust and Abuse of Dominance

173

recently argued in favor of an eﬀects-based approach to competition policy, which associates abuses of dominant positions with anti-competitive strategies that harm consumers. In line with this proposal, we believe that a new approach to competition policy should be based on rigorous economic analysis, from both a theoretical and an empirical point of view. Rey et al. (2005) emphasize this element in the antitrust procedure: “a natural process would consist of asking the competition authority to first identify a consistent story of competitive harm, identifying the economic theory or theories on which the story is based, as well as the facts which support the theory as opposed to competing theories. Next, the firm should have the opportunity to present its defence, presumably to provide a counter-story indicating that the practice in question is not anticompetitive, but is in fact a legitimate, perhaps even pro-competitive business practice.” Moreover, any theory of the market structure able to provide guidance in detecting abuses of dominant positions should take into account the role and the strategies of market leaders, describe the equilibrium outcomes as a function of the entry conditions and of the demand and supply conditions, and provide welfare comparisons under alternative set-ups. In this chapter we will try to argue that, while the Chicago school and the post-Chicago approach had problems in providing a unified framework which matches these requirements, the theory of market leaders formalized in the previous chapters has provided alternative insights that may be useful for this purpose. The general principle derived until now is that market leaders may behave in an anti-competitive way, accommodating or predatory, in markets where the number of firms is exogenous (meaning that outsiders cannot overcome barriers to entry even when there are profitable opportunities), while they always behave in an aggressive way when entry into the market is endogenous (meaning that it depends on the profit opportunities). In the first situation a large market share of the leader can be the fruit of anti-competitive strategies, but in the second situation a large market share of the leader is a consequence of its aggressive strategies and of the entry conditions, and not of market power. Therefore, there should be no presumption of a positive association between market shares and market power unless the lack of free entry conditions has been established. This has a main implication: while the old approach to abuses of dominant positions needs to verify dominance through structural indicators and the existence of a certain abusive behavior, a new economic approach would simply need to verify the existence of harm to consumers. As Rey et al. (2005) correctly point out, “the case law tradition of having separate assessments of dominance and of abusiveness of behavior simplifies procedures, but this simplification involves a loss of precision in the implementation of the legal

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5. Antitrust and Abuse of Dominance

norm. The structural indicators which traditionally serve as proxies for ‘dominance’ provide an appropriate measure of power in some markets, but not in others”, in particular not in markets where entry is an important factor (a concentration index is uniquely concerned with actual competition and ignores potential competition) and when innovation is important (a concentration index can deal with competition in the market, not for the market). In this chapter we review the traditional approaches to antitrust analysis in Section 5.1 and the market leaders approach in Section 5.2, while Section 5.3 contains a digression on the protection of IPRs. We apply our results to a profound policy oriented discussion in Section 5.4 and conclude in Section 5.5.

5.1 The Traditional Approaches to Abuse of Dominance In this section, we review some aspects of the traditional approaches to antitrust policy on abuse of dominance and start comparing them with the insights of the recent theoretical attempts to build a comprehensive theory of market leadership and competition policy. 5.1.1 The Chicago School The so-called pre-Chicago approach was mostly based on the simplistic insights of the early studies on imperfect competition, which associated monopolistic behavior and abusive conduct with firms having large market shares. Such a naïve view has been challenged since the 50s- 60s by what we now call the “Chicago school”, led by Aaron Director and other exponents of the Law School of the University of Chicago, whose main merit has been to introduce a systematic economic approach to antitrust - as opposed to what Posner (2001) calls the “populist” approach and Bork (1993) associates with a “farrago of amorphous and leftist political and sociological propositions”.4 While the Chicago school was seriously attacking collusive agreements as conducive to large welfare losses, it was less critical of mergers and exclusionary practices. Many scholars were (and still are) convinced that, when there are potential entrants in a given sector, mergers are mostly aimed at creating beneficial 4

Bork (1993) cites the following two primary characteristics of the early Chicago school. “The first is the insistence that the exclusive goal of antitrust adjudication, the sole consideration the judge must bear in mind, is the maximization of consumer welfare. The judge must not weigh against consumer welfare any other goal, such as the supposed social benefits of preserving small businesses against superior eﬃciency. Second, the Chicagoans applied economic analysis more rigorously than was common at the time to test the propositions of the law and to understand the impact of business behavior on consumer welfare” (p. xi).

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175

cost eﬃciencies, while aggressive strategies such as bundling, price discrimination and exclusive dealing, are not necessarily anti-competitive but may instead have a strong eﬃciency rationale behind them. For instance, bundling is typically used for price discrimination purposes and not for exclusionary purposes. Moreover, according to a widespread view in the Chicago school, there is no such a thing as predatory pricing, which is a reduction of the price below cost to induce exit by the competitors in order to compensate for the initial losses with future monopolistic profits. The main reason is that, if the predator can sustain such initial losses, any other prey can also sustain the induced losses (which are smaller since its output is lower) as long as credit markets are properly working, therefore predatory pricing would not be eﬀective to start with.5 More recently, Posner (2001) has taken a less extreme position, claiming that: “there is an economic basis for concern with at least some exclusionary practices, in at least some circumstances; and a few practices that are not exclusionary (though so classified in the law), like persistent price discrimination, may still be undesirable on strictly economic grounds” (Posner, 2001, p. 4) Accordingly, Posner proposes a moderate standard for judging practices claimed to be exclusionary: “in every case in which such a practice is alleged, the plaintiﬀ must prove first that the defendant has monopoly power and second that the challenged practice is likely in the circumstances to exclude from the defendant’s market an equally or more eﬃcient competitor. The defendant can rebut by proving that although it is a monopolist and the challenged practice exclusionary, the practice is, on balance, eﬃcient” (ibidem, pp. 194-5). This eﬃciency defense is at the basis of the rule of reason approach, for which a business practice is not per se illegal, but can be justified if it does not harm consumers or creates eﬃciencies. In the modern economic debate, the Chicago school has been criticized for failing to provide results that were robust enough to withstand full-fledged game theoretic analysis of dynamic competition between incumbents and 5

See McGee (1958) on the Standard Oil Trust (1911), a famous US case of predatory pricing which led to the break up of the Rockefeller’s oil refining company into thirty four small companies. Beyond what pointed out in the text, another reason why firms should not engage in predatory pricing is that a merger would be a better solution. Of course this alternative is not viable if the merger is prohibited by the same antitrust law (but in the US, mergers capable of reducing competition became the subject of antitrust investigations only after the Clayton Act of 1914).

176

5. Antitrust and Abuse of Dominance

entrants. The so-called “post-Chicago” approach has shown that in the presence of strategic asymmetries between incumbents and entrants and pervasive market imperfections, strategies such as price-cuts, bundling or vertical restraints can be anti-competitive because they can successfully deter entry in the short run and protect monopolistic rents in the long run. Broadly speaking, US antitrust authorities have been highly influenced by all of these approaches over time, while it is hard to claim that the same is true of the EU antitrust authorities. It has recently been pointed out by Ahlborn et al. (2004) that “in Europe it has taken longer for new developments in economic theory to aﬀect competition policy. While U.S. antitrust has been influenced by Chicago school and post-Chicago school theories, pre-Chicago school considerations still play a role in Europe, albeit at times dressed up in post-Chicago clothing”.6 We believe that the Chicago school provided fundamental insights into many antitrust issues, but it failed to provide a complete understanding of the behavior of market leaders. In particular, it limited most of its analysis to the understanding of how monopolistic and perfectly competitive markets work, and in a few cases it focused on markets characterized by a monopolist facing a competitive fringe of potential entrants.7 Dismissing the useful progress in the applications of game theory, the Chicago school ignored the important role of the strategic interactions between incumbents and entrants. Consequently, its approach to exclusionary practices has often been biased toward a competitive role of the incumbents without an updated theoretical support. 5.1.2 The Post-Chicago Approach In the 80s, while the Chicago school was succeeding in reducing the enforcement attitudes of US antitrust law, especially under the Reagan Administration, a new school of thought started to expand its influence between economists and, in the following decade, also between antitrust scholars. The socalled post-Chicago approach introduced new game theoretic tools to study complex market structures and derive sound normative implications, which 6

7

A symptom of the pervasive European approach, which is more against market leaders than in favor of free entry, emerges in basic business and industrial regulation. For instance, in many European countries the development of large chains of supermarkets is condemned as an unfair threat to small retail businesses. Similarly, it is hard to liberalize entry in the markets for taxicabs even if the eﬃciency gains for the consumers would be quite clear. Somewhat related to this literature is the theory of contestable markets by Baumol et al. (1982), which, however, was mostly limited to simple forms of price competition with homogenous goods. The theory of Stackelberg competition with endogenous entry generalizes that theory to product diﬀerentiation and other forms of competition.

5.1 The Traditional Approaches to Abuse of Dominance

177

represents one of the main contributions of this line of research. With reference to exclusionary practices, the post-Chicago approach has shown that in the presence of strategic commitments to undertake preliminary investments, of asymmetric information between firms, of credit market imperfections or in the presence of limited forms of irrationality, predatory pricing can be an equilibrium strategy for the incumbent, can deter entry and it can harm consumers. Similarly, it has shown that bundling can be used to strengthen price competition and exclude a rival from a secondary market. Analogously, many other strategies can have an exclusionary purpose. One should keep in mind that many of the results of the post-Chicago approach (summarized in the early but still unsurpassed work of Tirole, 1988) are quite weak, and they largely depend on a number of restrictive assumptions. For example, predatory pricing has been shown to be exclusionary under extreme circumstances, including forms of irrational behavior (in reputation models) or pervasive market imperfections, and, even when exclusion emerges under more plausible conditions, it is not necessarily associated with a pricing below cost or even with reductions in consumer welfare (in signalling models), which is what should matter in drawing antitrust implications. Nevertheless, the intellectual achievements of the post-Chicago approach, especially the introduction of game theory as the ultimate tool of industrial organization and the proof of the possibility of profitable exclusionary strategies, are remarkable. Our critique of the post-Chicago approach is not focused on its game theoretic foundation or on its specific results, but on the general applicability of these results for policy purposes. In most cases, the modern game theoretic literature in industrial organization has studied the behavior of incumbent monopolists facing a single potential entrant. To cite the most known theoretical works with strong relevance for antitrust issues, this was the case of the Dixit (1980) model of entry deterrence, of the models by Kreps and Wilson (1982) and Milgrom and Roberts (1982) of predatory pricing, by Fudenberg and Tirole (1984) and by Bulow et al. (1985) on strategic investment, by Brander and Lewis (1986) on strategic debt financing, by Rey and Stiglitz (1988) and Bonanno and Vickers (1988) on vertical restraints, by Whinston (1990) on bundling for entry deterrence purposes, and many other subsequent works based on the analysis of duopolies with an incumbent and an entrant.8 Most of the standard results on the behavior of incumbents in terms of pricing, R&D investments, mergers, quality choices and vertical and horizontal diﬀerentiation are derived in duopolistic models, where the incumbent chooses its own strategies in competition with a single entrant. While this analysis simplifies the interaction between incumbents and competitors, it can be highly misleading, since it assumes away the possibility of endogenous entry, and hence limits its relevance to situations where the incumbent already has an exogenous amount of market power. 8

See Motta (2004) and Whinston (2006) on the post-Chicago approach.

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5. Antitrust and Abuse of Dominance

It is not surprising that the results of the post-Chicago approach are often biased toward an anti-competitive role of the incumbents: these incumbents engage in predatory pricing, threaten or undertake overinvestments in complementary markets and patent new technologies only to preempt entry, impose exclusive dealing contracts, or bundle their goods with the sole purpose of deterring the entry of the competitor. Otherwise they are accommodating, engaging in excessive pricing or in anticompetitive mergers aimed at increasing prices, or stifling innovation to preserve their power. In such a simple scenario, what antitrust authorities should do is unambiguously fight against incumbents: punish their aggressive pricing strategies as predatory, and their accommodating pricing strategies as exploitative, punish investments in complementary markets as attempts to monopolize them, weaken their intellectual property rights, forbid bundling strategies, prohibit mergers and so on. The bottom line is that, according to this view, antitrust authorities should sanction virtually any behavior of the incumbents which does not conform to that of their competitors. The fallacy of this line of thought, in our view, derives from a simple fact: it is based on a partial theory of oligopoly limited to the analysis of duopolies with an incumbent and an entrant which does not take into account that, at least in most cases, entry by competitors is not an exogenous fact, but an endogenous choice. Whether entry is more or less costly, it is typically the fruit of an endogenous decision by the potential competitors. Of course, entry can be regarded as an exogenous phenomenon in the case of a natural monopoly or when there are legal barriers to entry, but these cases should not be a subject of antitrust analysis, but of regulatory analysis. When entry can be regarded as an endogenous element which depends on the technological conditions that constrain the profitability of the firms, we need a complete understanding of the behavior of leaders facing endogenous entry.

5.2 The Theory of Market Leaders and Endogenous Entry The theory of market leaders studied in the previous chapters clarifies the role of market leaders and of the entry conditions in a game theoretic framework that is more general than most analysis within the post-Chicago approach. In this section we will review its results and compare its implications for antitrust with those of the traditional approaches, but before doing that, we need to clarify a few concepts concerning the determinants of entry in a market.9 The industrial organization literature has emphasized diﬀerent kinds of constraints on entry. The definition of barriers to entry has been quite debated in the literature. Bain (1956) associated them with the situation in 9

This section is partly derived from Etro (2006b).

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179

which established firms can elevate their selling prices above minimal average costs of production without inducing entry in the long run. Broadly speaking, such a situation corresponds to what we define as competition between an exogenous number of firms: even if profits can be obtained in the market, entry is not possible. Stigler (1968) has proposed a diﬀerent definition of barriers to entry, associating them with costs of production which must be borne by firms seeking to enter an industry but not borne by the incumbents; a similar approach has prevailed more recently (Baumol et al., 1982), so that we can talk of barriers to entry as sunk costs of entry for the competitors which are above the corresponding costs of the incumbent (or have been already paid by the incumbent). According to this definition, sunk costs can be binding on the entry decision of the followers, therefore, they can be a crucial determinant of the endogeneity of entry in a market.10 A final category is that of the fixed costs of entry: these are equally faced by the incumbent and the followers to produce in the market, but they can also represent a binding constraint on entry. While there is a fundamental difference in the concepts of sunk costs and fixed costs of entry, their role in endogenizing entry is virtually the same, and we will not stress the diﬀerence in what follows.11 5.2.1 Competition in the Market and Policy Implications The main point emerging from our analysis of the behavior of market leaders facing or not facing endogenous entry is that standard measures of the concentration of a market have no relation to the market power of the leaders of a market, and may lead to misleading welfare comparisons. 10

11

There is a relation between the theory of market leaders and the “bounds approach” by Sutton (1998, 2005). His approach is largely based on the concept of endogenous sunk costs as strategic investments - see Etro (2006,b) and Chapter 1 for an attempt to endogenize sunk costs in the theory of market leaders. However, his focus is more on explaining market concentration rather than the strategies of market leaders. The two approaches could be seen as complementary. Another important aspect is about the source of these barriers and costs. As we noticed before, they can constitute a source of antitrust examination if they have been artificially created or enlarged by the incumbent; they cannot if their source is purely technological. Nevertheless, it is hard to imagine how artificial barriers could be erected under normal circumstances. The Chicago school is quite clear on this point, as we can conclude from the following position of Bork (1993): “If everything that makes entry more diﬃcult is viewed as a barrier, and if barriers are bad, then eﬃciency is evil. That conclusion is inconsistent with consumer-oriented policy. What must be proved to exist, therefore, is a class of barriers that do not reflect superior eﬃciency and can be erected by firms to inhibit rivals. I think it clear that no such class of artificial barriers exists.”

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5. Antitrust and Abuse of Dominance

Competition in Quantities. The irrelevance of market shares for the evaluation of the market power of leaders emerges quite clearly in the simplest environment we studied, that of competition in quantities with homogenous goods, constant marginal costs and a fixed cost of production. Such a simple structure approximates the situation of many sectors where product diﬀerentiation is not very important but there are high costs to starting production (as in many high-tech sectors). In such markets the characterization of the equilibrium structure is drastically diﬀerent when entry conditions change. First of all, as long as the number of firms is exogenously given and the fixed costs of production are not too high, the leader is aggressive but leaves space for the followers to be active in the market. As external observers, we would look at this as a market characterized by an incumbent with a market share typically larger than its rivals, but with a certain number of competitors whose supply of goods reduces the equilibrium market price. The higher the number of these competitors, the lower the price will be: in such a case, lower concentration would be correctly associated with higher welfare. Radical changes occur when entry in the market is endogenous, and is determined by the existence of profitable opportunities in the same market. In such a case (as we have seen in Section 1.1) the leader would expand production until no one of the potential entrants has incentives to supply its goods in the market. The intuition for this extremely aggressive behavior of the market leader is simple. When entry is endogenous, the leader understands that a low production creates a large space for entry in the market while a high production reduces entry opportunities. More precisely, knowing how technological constraints govern the incentives to enter in the industry, the leader is aware that its output exactly crowds out the output of the competitors leaving unchanged the aggregate supply and hence the equilibrium price. However, taking this equilibrium price for the market as given, the leader can increase its profits by increasing its output and reducing the average costs of production. Here the fixed costs of production (associated with constant marginal costs) are crucial: on one side they constrain the profitability of entry, while on the other side they create scale economies in the production process that can be exploited by the leader through an expansion of its output. Actually, it is always optimal for the leader to produce enough to crowd out all output by the competitors: exploiting the economies of scale over the entire market allows the leader to enjoy positive profits even if no entrant could obtain positive profits in this market. As external observers, in this case, we would simply see a single firm obtaining positive profits in a market where no one else enters, and, following traditional paradigms, we would associate this situation with a monopolistic environment, or at least with a dominant position derived by some barriers to entry. But this association is not correct, since entry is indeed free in this market: it is the competitive pressure of the potential entrants that induces the leader to produce so much to drive down the equilibrium price until no other firm can enter. We are

5.2 The Theory of Market Leaders and Endogenous Entry

181

referring to firms that are as eﬃcient as the leader (assuming identical cost technologies). Finally, in Chapter 1, we even noticed that this equilibrium with only the leader in the market is associated with a higher welfare than the free entry equilibrium without a leadership - the Marshall equilibrium, which involves many firms active in the market and earning zero profits. Let us now consider a related situation with a diﬀerent cost pattern for the firms (see Section 1.2.1). When marginal costs are substantially increasing in the production level or, more generally, when the average costs have a Ushape, a market leader facing endogenous entry of competitors may not have incentives to deter entry, but would still behave in an aggressive way. In such a case, given the strategy of the leader, all the entrants maximize their own profits and therefore they price above the marginal cost. However, endogenous entry reduces the equilibrium price to a level that is just high enough to cover the fixed costs of production. Notice that this equilibrium generates a production below the eﬃcient scale (which should equate marginal and average costs). Also in this case, the leader takes into account these elements and, in particular, takes as given the equilibrium price emerging from the endogenous entry of the competitors. Accordingly, the leader finds it optimal to produce as much to equate its marginal cost to the price, which requires a production above the eﬃcient scale. Since marginal costs are increasing for such a high production level, the leader is pricing above its average cost, and hence obtains positive profits. In this case the strategy of the leader does not even aﬀect the market price, which is fully determined by endogenous entry of firms. Nevertheless, the leader obtains a larger market share than its rivals and positive profits. Moreover, we have shown that the aggressive behavior of the leader, that adopts a price equal to the marginal cost, improves the allocation of resources compared to the same market with free entry and no leadership.12 A similar situation emerges when goods are not homogeneous but diﬀer in quality (see Section 1.2.2). This happens when consumer needs or tastes are quite diﬀerentiated, as is the case in many sectors where the design and the inner quality of products play an important role. Under these circumstances, firms often compete in prices by choosing diﬀerent mark-ups for diﬀerent products. When quality diﬀers, it is important to have a number of firms producing diﬀerent varieties of goods. A competitive market typically satisfies 12

As we saw in the general model of Chapter 3, under Stackelberg competition with endogenous entry, the followers equate the price to their average total cost following the standard mark-up rule, and the leader equates the price to its own marginal cost: p=

c(q) + F c0 (q) = = c0 (qL ) 1 − 1/ q

where is the elasticity of demand. It follows that the equilibrium output of the leader, qL , is always higher than the one of the followers, q.

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this requirement, but it tends to induce excessive proliferation of products. The presence of market leaders is again beneficial: they will not conquer the entire market, but they will expand production and consequently reduce their prices below the prices of their competitors, some of which will be driven out of the market. Consumers will then face a lower variety of alternative products, but pay less for some of them.13 The crucial lesson from this analysis is that we should be careful in drawing any conclusion from indexes of concentration or from the market shares. We have seen examples in which the equilibrium outcome of a market with free entry was characterized by a single active firm enjoying positive profits, and other examples where the outcome was less drastic, but not too diﬀerent. Notice that in all these cases, the market leader was adopting aggressive strategies which were reducing entry but increasing welfare nevertheless. It is important to emphasize that strategies that are aimed at reducing entry are not necessarily negative for consumers, especially when entry is not fully deterred, but simply limited due to a low level of the prices, so that some competitors are still active in the market and able to exert a competitive pressure on the leader. As a matter of fact, this is a good example of how real competition works. Of course, a predatory behavior can still be associated with aggressive strategies aimed at foreclosure and with negative consequences on consumers. This can be the case under two circumstances: 1) when these strategies are implemented by leaders with genuine market power which is not constrained by eﬀective entry, and 2) when the same leader has built barriers to artificially constrain entry without eﬃciency reasons (see the Appendix in Chapter 1).14 Finally, notice that a complete analysis of the consequences of entry deterrence would require a dynamic model taking into account the behavior of the 13

Consider a generalization of the examples of Chapter 1 with both product differentiation and U-shaped costs. Under the profit function: πi = qi (a − qi − b

j6=i

qj ) − cqi − dqi2 /2 − F

a Stackelberg equilibrium with endogenous entry is characterized by followers producing: q=

2F 2+d

and a leader producing: qL = 14

2−b+d 2 − 2b + d

2F 2+d

Artifical barriers associated with bureaucracy and lobbying activity on government processes are emphasized by the Chicago school as well (see Bork, 1993, Ch. 18).

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leader before and after deterrence, which is beyond the scope of this book. However, simple models can reveal a lot. Our point here is simply to warn against the risk of directly associating aggressive price strategies that reduce entry with strategies that harm consumers. Competition in Prices. Another important implication of the theory of market leaders emerges quite clearly under competition in prices. In this typical situation, the traditional analysis of Stackelberg oligopolies shows that dominant firms are either accommodating (setting high prices) or trying to exclude rivals by setting low enough prices: the first case happens when the fixed costs of entry are small (and predation would be too costly), the second when they are high enough.15 Such an outcome implies the risk of erroneously associating an aggressive price strategy with an entry deterring strategy in a systematic fashion. As we have seen (in Section 1.3), when we endogenize entry in the market, leaders never adopt accommodating pricing strategies while they are always aggressive. Again, in equilibrium with endogenous entry, leaders increase their market shares and obtain positive profits. Of course an aggressive pricing strategy will still reduce entry, even if it will not exclude all rivals. Nevertheless, we must be more careful in associating aggressive pricing with predatory purposes. The reason why predatory strategies are anti-competitive is that they exclude competition in the future allowing the dominant firm to behave in a monopolistic fashion once competitors are out of the market. Clearly, if an aggressive pricing strategy is aimed at excluding some but not all competitors, this anti-competitive element is more limited. Notice that competition in prices is quite typical of markets where product diﬀerentiation is relevant and firms have more autonomy in choosing their prices directly. The results are also relevant in oligopolistic markets in which prices determine the volume of business, as in the banking sector, where the interest rates on loans determine how much firms borrow from a bank, and the interest rates on deposits determine how much households lend to a bank.16 15

16

Accommodating high prices are chosen by the leader when fixed costs of entry are small. The problem is that this is exactly when there are incentives for other firms to enter, hence the duopolistic equilibrium is quite weak, and the study of endogenous entry becomes crucial. Price competition is typical of the banking sector, where banks choose both the interest rates on loans, ι, and on deposits, r (see Freixas and Rochet, 1997). When entry in the sector is exogenous we would expect leaders to oﬀer worse terms to their customers, when it is endogenous we would expect the opposite. For instance, imagine that banks compete only on the deposit side, and the supply of deposit for firm i is S(ri , j6=i h(rj )) with S1 > 0 and S2 < 0. Adopting the usual notation, profits for bank i are: πi = (ι − ri − c)S (ri , β i ) − F where c is the marginal cost of intermediation. A Stackelberg equilibrium with endogenous entry is characterized by the optimality and free entry conditions for

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Strategic Commitments. In general, as we have seen in Chapter 2, the spirit of our result on the aggressive behavior of leaders goes through when leaders cannot commit to output or price strategies, but can undertake preliminary investments that change their incentives in the market. For instance, a market leader facing an exogenous number of competitors may want to underinvest or overinvest strategically in cost reducing R&D according to the kind of competition (in prices or in quantities), because it may want to commit through these investments to adopt an accommodating or an aggressive strategy in the market: in particular, underinvesting is optimal before price competition, while overinvesting is optimal before quantity competition. However, this ambiguity collapses if the leader is facing endogenous entry of competitors. In such a case, it is always optimal to adopt the strategy that allows one to be aggressive in the market: strategic overinvestment in cost reducing R&D is optimal independently from the form of competition, because it allows one to be aggressive against competitors (see Section 2.6).17 A similar role is attached to investment in production capacity, to debt as a financing tool issued to commit management to produce higher output, and to many other strategic investments. An interesting situation for antitrust purposes emerges when demand is characterized by network eﬀects. In such a case, market leaders tend to underprice their products initially to attract customers in the future. As known, these strategies may induce pricing below marginal cost without entry deterrence purposes. Moreover, in Section 2.9 we have seen that leaders facing endogenous entry may have further strategic incentives to reduce initial prices (or expand initial production): by doing so, they enhance network externalities and are able to reduce their prices also in the future. Therefore, antitrust authorities should be careful in evaluating aggressive pricing in the presence the followers: ι−r−c=

F S(r, β) = S1 (r, β) S(r, β)

and by the optimality condition for the leader: ι − rL − c =

17

S(rL , β L ) S1 (rL , β L ) − S2 (rL , β L )h0 (rL )

which implies rL > r. Only under the pressure of free entry, the leader aﬀords to compensate deposits with a high rate than its followers. Both eﬀective and potential competition are crucial here. On this point, we are close to early informal insights of the Chicago school. For instance, Posner (2001, p. 145) notices that “notions of potential competition cannot and should not be banished entirely from antitrust law... a monopolist who creates excess capacity in order to reduce his marginal cost, so that entrants (who have to be able to cover their average total cost if they are to make a go of entry) are deterred, is reacting to potential competition.”

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of network eﬀects. Finally, this point applies in particular to multi-sided markets, where network eﬀects take place between diﬀerent kinds of customers, and firms can charge their diﬀerent customers diﬀerently. In such an environment market leaders tend to price quite aggressively one of the sides, but again without exclusionary purposes. We will return to this point with more details in the next chapter. The same care in judging aggressive strategies is needed in cases of complementary strategies that virtually induce aggressive behaviors. One of these is bundling. In an influential paper, Whinston (1990) has studied bundling in a market with two goods. The primary good is monopolized by one firm, which competes with a single rival in the market for the secondary good. Under price competition in the secondary market, the monopolist becomes more aggressive in its price choice in the case of bundling of its two goods. Since a more aggressive strategy leads to lower prices for both firms as long as both are producing, the only reason why the monopolist may want to bundle its two goods is to deter entry of the rival in the secondary market. This conclusion can be highly misleading because it neglects the possibility of further entry in the market. As we have seen in Section 2.10, if the secondary market is characterized by endogenous entry, the monopolist would always like to be aggressive in this market and bundling may be the right way to commit to an aggressive strategy. Bundling would not necessarily deter entry in this case, especially if there is a high degree of product diﬀerentiation in the secondary market, but may increase competition in this market and reduce prices with positive eﬀects on the consumers.18 Another application of the theory of market leaders concerns vertical restraints aﬀecting inter-brand competition (Bonanno and Vickers, 1988; Rey and Stiglitz, 1988). Also in this case, the behavior of the market leader can be anticompetitive depending on the entry conditions. In particular, under price competition, a contract delegating distribution to a downstream firm tends to soften price competition when entry in the market is exogenous (because the upstream firm imposes high prices through direct or indirect contractual restraints), but it strengthens price competition when entry is endogenous (in which case the upstream firm can only gain by inducing an aggressive behavior of the downstream firm): the consequences on consumers tend to be negative in the former case and positive in the latter case (Section 2.11). We encounter a more complex situation when we consider price discrimination versus uniform pricing, since they can both soften or strengthen price competition in diﬀerent markets. However, we have shown an example where, when price discrimination emerges between two groups of customers, it is also likely to soften price competition compared to uniform pricing (Section 2.12). If this is the case, price discrimination is adopted by a firm competing with 18

Notice that the same limit of the analysis of Whinston, namely the exogenous assumption that there are just two firms and further endogenous entry is not taken into account, applies to many other duopolistic models of bundling.

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an exogenous number of competitors, but not when entry is endogenous. Accordingly, when it takes place price discrimination is likely to harm at least some consumers. Conclusion. Our final remark is about the presence of high and sustained profits (sometimes called supernormal profits) of the market leaders. These high profits are frequently, but sometimes erroneously, associated by the traditional approaches with a situation of market dominance and barriers to entry that prevents competition from driving down the rate of return to its competitive level. As we have seen repeatedly, even in the presence of free entry market leaders with a first mover advantage or with a more reasonable chance to undertake preliminary investments are able to obtain positive profits, or, in other words, they are able to preserve a rate of return above the opportunity cost of capital. Evidently, these sustained profits in a market where entry is free are not a symptom of dominance per se. Notice that there are other important reasons why sustained profits may persist in innovative markets, but we will look at them in the next section on the competition for the market and its implications. The bottom line of this discussion on competition in the market is that in evaluating market structures and the behavior of market leaders we should give special attention to the entry conditions. Standard results on aggressive price and non-price strategies with exclusionary purposes emerging for markets with an incumbent and an entrant can change in radical ways when we take in consideration the possibility of endogenous entry by other firms. After all, antitrust policy in an uncertain world should derive from a comparison of the expected losses from incorrectly challenging a practice that benefits consumers (a Type I error ) versus the expected losses from incorrectly failing to challenge a practice that harms consumers (a Type II error). We believe that while the Chicago School has been extremely biased to reduce the first kind of losses (exactly because it largely ignored strategic interactions), the postChicago approach has been excessively biased in the opposite sense (exactly because it often neglected endogenous entry).19 5.2.2 Competition for the Market and Policy Implications Competition in high-tech markets is dynamic in the Schumpeterian sense that it takes place as competition for the market in a so-called winner-takes-allrace, and such an element requires a deeper evaluation of competition policy than that suggested in the analysis of the previous section, which was mostly focused on a static concept of competition in the market.20 19

20

On the design of optimal procedures for competition policy see Katsoulacos and Ulph (2007). In the terminology of the famous growth-share matrix popularized by the Boston Consulting Group, new products in the growing high-tech markets are Stars (for

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Economic research has emphasized the positive relationship linking patents to investments in innovation and these investments to technological progress and growth. In high-tech sectors (hardware, software, pharmaceuticals, biotechnology) firms compete mainly by innovating. This is possible as long as there are well defined intellectual property rights (IPRs), and especially patents, protecting their innovations and investments, which is ultimately what leads to technological progress in our economies. In Section 1.4 we have even suggested that this form of dynamic competition can be a valid substitute for the competition in the market: when entry in the competition for the market is free, an increase in the degree of competition in the market cannot provide further incentives to invest in innovation (because any escape competition eﬀect disappears). Moreover, even if most economists are used to thinking about market leaders as firms with weaker incentives to invest in R&D, recent theoretical and empirical research has also found support for an old idea associated with the institutional work of Schumpeter (1943), Galbraith (1952) and Chandler (1990), according to which market leaders play a crucial role in the innovative activity. The theory of market leaders has clarified the mechanics of these results. IPRs drive competition through innovation in these markets and induce technological progress led by incumbent monopolists under two conditions: their leadership in the contest to innovate and free entry of outsiders in this same contest. In particular, in Chapter 4 we contrasted two scenarios. According to traditional theories, in the absence of strategic advantages, a technological leader that is also an incumbent monopolist in its market, would have less incentives to invest in R&D compared to other firms, since its relative gain from improving its own technology is smaller than the gain of the outsiders from replacing the incumbent monopolist. This result, sometimes called the Arrow’s paradox, has often been used to suggest that incumbent patent-holders invest less than other firms and stifle innovation. However, we have also seen that when an incumbent monopolist is the leader in the contest for innovating, the pressure of a competitive fringe of potential innovators leads this monopolist to invest more than any other firm. The competitive environment spurs investment by leaders and consequently induces a chance that their leadership persists. Finally, we have also suggested that when the leadership persists because of the endogenous investment in R&D by the leaders, the same value of becoming a leader is increased, which strengthens even further the incentives for any other firm to invest, and so on. Paradoxically, the persistence of a leadership in high-tech sectors can be a sign of eﬀective dynamic competition for the market, which leads to a faster rate of technological progress in the interest of consumers. market leaders) or Question Marks (for the followers), as opposed to the mature markets typical of the traditional sectors that can be characterized by products with high market shares (Cash Cows) or low market shares (Dogs).

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Notice that our results on the relation between entry in the competition for the market and investment by the incumbent monopolists can be seen as strengthening our initial claim that standard indices of market concentration or market shares should not be related to the degree of competition in a market. In high-tech markets where competition is mostly for the market, it is natural that better products conquer large shares and, exactly when entry is free, incumbent patent-holders have more incentives to invest and their leadership is more likely to persist. There is no basis to relate in a significant way market shares and market power in dynamic sectors. This mechanism is even more radical in markets with network eﬀects, where the natural outcome is a sequence of dominant paradigms associated with market leaders whose behavior is still constrained by innovative competitive pressure. Scotchmer (2004, p. 296), in her discussion of network eﬀects, emphasizes this point neatly: “All this calls into question whether an incumbent’s share of a network market is a good test of market power for antitrust purposes. With tippy markets, any snapshot of the market will find some firm with a dominant market share. But sequential monopoly is only a problem for competition policy if the price charged by each sequential monopolist is high [...] the price is constrained at first by the proprietor’s need to attract users of the previous product, and later by a fear of scaring users into embracing a successor. The same fears will cause the incumbent to keep innovating.” Of course, we do not want to give the message that persistent monopolies are necessarily the fruit of eﬀective competition for the market, but rather that they can be the fruit of eﬀective competition. What we would like to emphasize is the importance of entry conditions in the market for innovations. This is in line with an old Chicago-style position associated with Demsetz (1973), who pointed out that:21 “Under the pressure of competitive rivalry, and in the apparent absence of eﬀective barriers to entry, it would seem that the concentration of an industry’s output in a few firms could only derive from their superiority in producing and marketing products ... an industry will become more concentrated under competitive conditions only if a diﬀerential advantage in expanding output develops in some firms ... The cost advantage that gives rise to increased concentration may be reflected in scale economies or in downward shifts in positively sloped marginal cost curves, or it may be reflected in better products which satisfy demand at a lower cost” (Demsetz, 1973). Consequently, industrial policy, including antitrust policy, should primarily promote, and possibly subsidize, investment in R&D, and it should be less 21

See Hughes (2007) for a recent and successful test of the Demsetz hypothesis.

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relevant whether the incumbent monopolist or new comers invest in R&D and innovate once entry is free. On the other side, the protection of IPRs should be established at a legislative level (possibly even coordinated at an international level) because its stability is essential to foster investments, while the discretionary activity of antitrust authorities should not aﬀect the basic principles of IPRs protection. The credibility of innovation policy is crucial to give incentives to firms to innovate, because investment in R&D depends mainly on the expectations on the protection of IPRs. This point is quite similar to standard results in monetary and fiscal policy. A commitment to low inflation is essential because price setting decisions are based on the expectations of inflation: surprise inflation may push the economy in the short run, but will just increase inflation in the long run. A commitment to a capital income tax is essential because savings decisions are based on the expectations of capital income taxes: unexpected higher capital taxation can raise more tax revenue in the short run, but it will mainly reduce savings and tax revenue in the long run. Analogously, a commitment to a level of protection of IPRs is essential because investment decisions are based on the expectation of this protection: forcing disclosure of IPRs can have some positive eﬀects for outsider firms in the short run, but will have devastating eﬀects on innovation and growth in the long run. This leads us to another important aspect of industrial policy, the protection of IPRs, which has an old and well recognized tradition in developed market economies.22

5.3 A Digression on IPRs Protection To understand the crucial role of IPRs and patents in promoting technological progress and growth we rely on an old important theory developed by Nordhaus (1969). In general, patents assign a temporary monopolistic power for the innovators which creates price distortions and hence carries a social cost, but also constitutes an incentive for many firms to invest and try to gain market leadership through innovations. This eﬀect leads to social benefits because innovations have a social value that can be higher than the 22

Patent protection was recognized in Renaissance Italy. In 1474 the Republic of Venice issued a decree by which new and inventive devices, once they had been put into practice, had to be communicated to the Republic in order to obtain legal protection against potential infringers. Galileo applied for a patent on an hydraulic system in 1593 noticing that “it does not suit me that the invention, which is my property and was created by me with great eﬀort and cost, should become the common property of just anyone.” The Venetian Senate assigned him a patent valid for twenty years. For more on the history of innovations and IPRs see Scotchmer (2004).

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private value (and that cannot be fully appropriated by the innovators)23 and because they drive technological progress and growth. Clearly social benefits and costs can be diﬀerent for diﬀerent inventions and generally for diﬀerent fields of technology, so, in theory, the optimal length and breadth of patents should depend on the field it applies to. For simplicity, and to avoid discriminations between fields of technology, patents typically have a uniform length and common principles on infringement regulation. Nevertheless, from a strictly economic point of view, one may question this uniformity and consider the advantages of providing diﬀerent terms of protection in diﬀerent sectors (at least this could avoid the ineﬃcient choice of radically excluding certain innovations from patentability rather than allowing a more limited protection). More importantly, an evaluation of the social benefits and costs of patents for diﬀerent fields is essential in judging the net benefit of a patent system.24 5.3.1 Patents in Dynamic Sectors and Innovations Consider the pharmaceutical sector, where the role of patents on new drugs is, to say the least, at the basis of competition in the market and of scientific progress in the world. These kinds of patents have been often criticized for jeopardizing health defense around the world and especially in developing countries, where western drugs are very important but very expensive. Nevertheless, one should not forget that those same patents induced many firms to invest and some of them to invent new drugs which are now available, something which would have hardly happened or would have happened later without patent protection: in other words the social benefit of patents on drugs is very high. Fortunately, there are ways to reduce the problems related with the pricing of drugs and their adoption depends mostly on the public sector. For instance, governments could buy drugs and distribute them at lower prices through the medical system, or just pay part of the prices. They may even directly buy the same patents from the innovators and produce the drugs (or outsource their production) and sell them at lower prices. Finally, western governments could redirect their international aid toward similar initiatives in favor of developing countries. These solutions, widely discussed between economists, may preserve the proper incentives to invest and discover new drugs while spreading their eﬀects globally. Ultimately, this suggests that patents in the pharmaceutical sectors are a crucial determinant of innovation and progress and should be protected while finding alternative solutions to guarantee health defense for poor classes and poor countries. 23

24

For a “public choice” perspective on this and the relation with the theory of market leaders see Reksulak et al. (2006). When the social value of patents is very high, public sponsorship of R&D activities and public-private partnership can be useful (on the latter experience see the empirical works by Baarsma et al., 2004, and Ambrosanio et al., 2004).

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Another field in which patents are particularly valuable and induce high investments in R&D is the New Economy. In the last few years the European Union tried (without success) to complete a process of harmonization of the patent system for computer-implemented inventions (CIIs).25 We believe that the rationale for these patents is strong: while their main social gain is to promote innovation in the most dynamic sectors, the social cost is smaller than for other patents since in these sectors competition mainly works through frequent price-reducing and quality-improving innovations, therefore price distortions are less relevant and do not last long anyway. Neglecting these traditional economic insights, opponents of the patent system have often claimed that patents stifle innovation. There is not, however, consistent theory or empirical evidence behind these claims. In US, the extension of patent protection to CIIs started in 1980 (the first patent of this kind was granted by the US Patent and Trademark Oﬃce in 1981), and it was associated with a clear increase in R&D investment during the eighties. The R&D/sales ratio for US firms innovating on computer, telecommunications and electronic components (the relevant field here) increased from 5.5% to above 8% in 1989 (see Etro, 2007c). In a careful empirical study Mann (2005) has shown that patents bestow significant benefits, especially for start up companies, in terms of traditional appropriability, information signalling and cross-licensing revenue, while Merges (2006), looking at patent data in the US software market, finds out that “new firms entry remains robust, despite the presence of patents (and, in some cases, perhaps because of them). Successful incumbent firms have adjusted to the advent of patents by learning to put a reasonable amount of eﬀort into the acquisition of patents and the building of patent portfolios. Patent data on incumbent firms shows that several well-accepted measures of ‘patent eﬀort’ correlate closely with indicators of market success such as revenue and employee growth.”26 5.3.2 Open-Source Innovations While IPRs are fundamental drivers of innovation in all sectors, software development has recently been characterized by a large amount of innovation 25

26

After a long procedure, the Common Position adopted by the European Council in March 2005 proposed the patentability of CIIs when they provide a technical contribution to a field of technology. While this positive proposal simply reaffirmed the requirements already adopted in Europe for the previous two decades and it excluded from patentability any pure software, business methods and consulting practices (which are patentable in US), the European Parliament ended up rejecting the Directive in July 2005. See Etro (2005a,b). See Bessen and Maskin (2002) for a theoretical and empirical position against software patents, and Etro (2007c) for a critical view of their theoretical and empirical results.

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obtained in a decentralized, voluntary and uncompensated way by programmers within the so-called open source movement.27 While many private corporations support it because they supply products that are complementary to open source software (IBM first of all, but also Hewlett-Packard, Intel, Sun, Oracle,...), it remains surprising that such a large innovative process can take place, at least in part, through directly unrewarded eﬀorts.28 Lerner and Tirole (2002, 2006) have provided a few explanations for the incentives of these individual programmers: career concern, ego gratification and signalling activity are quite powerful and eﬀective in this field. Unfortunately, the same nature of these incentives shows the possible limitations of the innovative activity in the open source community: it is limited by the usual free riding problems emerging in the private provision of public goods, it requires a complementary activity in the for-profit sector (to motivate the career concern and the signalling activity), it may be biased by research efforts that are diﬀerent from general consumer needs and by adverse selection of the contributors, and it may be eﬀective to solve a number of small and short term problems, but less eﬀective to solve multi-sided challenges and approach long term projects.29 While the development of this new form of user-driven innovation is a symptom of high competitive pressure in the sec27

28

29

Open source software is made available for direct use and modification (through direct access to the source code) under limited protection. For instance, the GPL (General Public License, first used in 1981 by Richard Stallman, the leader of the Free Software Movement) grants unlimited right to use, modify and distribute software as long as its redistribution makes available the modified source code and does not impose further restrictions on the rights granted by the GPL. These enforcement mechanisms make cooperative innovation quite eﬀective and immune from free riding, but can create problems when an innovation includes both open source software and licensed proprietary software. Major results of the open source movement are Linux, an operating system based on Unix (an old OS first created at Bell Labs) and developed in 1991 by Linus Torvalds, Apache, a world wide web (HTTP) server, and Mozilla Firefox, a web browser. Besides software that is freely distributed, there is an increasing number of companies, like Red Hat and Novell, that profit from collateral services supplied jointly with free software. In theory, any rival could resell Red Hat software at a lower price because it is under GPL (and some firms actually do it), but Red Hat managed to sidestep this problem protecting its products with trademark law. In this sense, the diﬀerence between proprietary software and open source software appears much less relevant: the former earns from licenses to end-users, the latter mainly licenses software free of charge and earns from selling support description needed by end-users to install and run the software. For empirical evidence on the open source development see Koski (2007). It is often claimed that open source software is more eﬀective than proprietary software in debugging activity (since many programmers find and solve many defects within a software and make the solutions freely available), but may have

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tor, it does not provide any evidence against the fundamental role of IPRs in driving core innovations.30 Actually, we believe that the current coexistence of open source software and proprietary software exerts a positive impact on innovation on both sides.31 In a fascinating work, Boldrin and Levine (2005) adopted open source software as a main example of innovation created without commercialization of IPRs, and collected some anecdotal evidence suggesting that innovations can perfectly take place in the absence of what they call “intellectual monopoly”. Their idea is that the first mover advantage of the innovator in the competition in the market preserves a certain amount of profits even when entry of imitators is free, and this Stackelberg advantage can be suﬃcient to pro-

30

31

big problems confronting issues as synchronization of upgrades and eﬃcient levels of backward compatibility. In a debate on the Financial Times, the author of this book expressed a related point: “It is true that the competitive pressure from open source software has led technological leaders to continue investing in research and development, but major advances such as the iPhone or Microsoft Surface keep arriving from the commercial software world. Moreover, restrictive open source software creates a fundamental asymmetry. On one side, open source software companies (allied with big business, such as IBM) can use proprietary software within their products and freely distribute them while covering licence expenditures through customer support services. On the other side, commercial companies cannot pursue their business model when including open source within their software, because they would infringe the "copyleft" if they apply a price to the licence. This asymmetry can create substantial problems for the conventional business model, and may inhibit or bias consumer-driven innovation. Finally, the notion that European competitiveness vis a vis China will be enhanced by the promotion of the open source software model is preposterous. The general public licence is built on the proposition that anything you do and distribute can be freely appropriated by anyone within or outside Europe, in fact handing over the result of your investment to China on a silver platter. Rather than democratising innovation, we should protect it.” (Etro, 2007,e). To see why, think of a diﬀerent sort of open source activity: Wikipedia is a famous and successful online encyclopedia where anybody can post a new voice or edit an old one (www.wikipedia.org). While it contains a lot of useful and constantly updated information (especially in certain fields, like those related to the online community), it often includes unmotivated and misleading references or mistakes that are the normal consequences of overlapping additions by heterogeneous contributors whose preparation is not properly controlled and whose eﬀort is not rewarded. Traditional encyclopedias based on rewarded contributions by selected experts are not constantly updated like Wikipedia, but they provide a standard of quality and a balanced unifying structure that Wikipedia lacks. The tradeoﬀ for the end users is clear, and coexistence appears natural. See Aghion and Modica (2006).

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mote innovation. Since a main leitmotif of our book has been showing that market leaders with a first mover advantage can obtain positive profits even in markets where entry is free by adopting aggressive strategies (Chapters 2-3), and since our formalization of competition for the market was perfectly compatible with incentives deriving from the profits of a market leader facing free entry, rather than deriving from a monopolistic position (Chapter 4), we certainly do not dislike the idea of Boldrin and Levine. But the point is: how much innovation can be promoted by the simple first mover advantage? Without an analysis of the industrial organization of the competition for the market it is quite hard to answer this question, and the general equilibrium analysis of Boldrin and Levine (1998) concluding that perfectly competitive innovations can achieve the first best amount of innovation neglects, to a large extent, the industrial organization of the market for innovations. Unfortunately, whether the incentives to invest are eﬃcient or not is more an empirical question than a theoretical one, and we still do not see a consistent piece of evidence showing that current patent systems provide excessive incentives in a systematic way, or that we should totally eliminate IPRs legalizing “intellectual expropriation”- as Boldrin and Levine (2005) actually suggest. As a matter of fact, the opposite may be true. Recently, Denicolò (2007) analyzed a general model of the organization of innovations and obtained a simple rule for the optimal level of patent protection: his empirical estimates suggest that current patent systems do not over-compensate innovators, while they may actually induce too limited incentives to invest in R&D.32 5.3.3 Conclusions on IPRs Protection Before returning to the core discussion on antitrust issues, we list a number of implications of the economic debate on IPR protection that in our opinion are quite relevant: 1) the optimal patent system should trade-oﬀ the social benefits of the incentives to innovate and the social costs due to temporary price distortions, and the protection of IPRs is crucial in those fields, such as in the New Economy, where the net benefits of patents are higher or in those fields, like the pharmaceutical sector, where social benefits are higher and there are proper policies which can reduce the social costs; 2) restrictions to the patentability of innovations in high-tech sectors for one country or a group of countries could severely jeopardize investment in innovation and technological progress in the leading high-tech sectors with negative consequences on growth and competition in the global economy and would shift investments toward other countries where IPRs are better protected without regard for comparative advantage; 32

On the same point see Erkal (2005) and Cozzi and Galli (2007).

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3) improvements of the eﬀectiveness of the current patent systems should rather promote access to patents, especially for small and medium size enterprises which are traditionally less able to exploit this opportunity, and enhance the spillovers created by the patent system on the diﬀusion of knowledge through further requirements on a disclosure of the patented inventions which should be suﬃciently clear and complete to be carried out by a person skilled in the art; 4) a proper industrial policy promoting competition for the market should adequately protect and subsidize R&D investments, and at the same time guarantee open access to the markets for innovations.

5.4 Reforming Antitrust In the last few years there has been a lot of academic and political debate on how to reform the EU approach to antitrust, and in particular on issues concerning abuse of dominance, moving toward an economic based approach more similar to the US approach. European Commission (2005) proposed a new approach to exclusionary abuses under Article 82 which is the subject of an open debate and gives an important indication as to how the Commission may approach antitrust cases of abuse of dominance in the future. We will comment on this debate focusing on the general principles of EU antitrust policy, but our discussion tries to provide principles for antitrust policy that could be applied to any national antitrust authority. The EU approach appears to move toward a purpose of competition policy associated with the protection of competition in the market as a means of enhancing consumer welfare and of ensuring an eﬃcient allocation of resources. This implies that antitrust should protect competition and not competitors, and be based on an economic analysis aimed at the maximization of consumer welfare and allocative eﬃciency rather than based on a legalistic analysis, a new direction which appears much more in line with the consolidated US approach. While the aim is to enhance consumer welfare and to protect competition and not competitors, we have some concern that these principles are not fully carried through into certain aspects of the current EU competition policy and of the proposal of European Commission (2005).33 As a matter of fact, until now the approach of the European Commission has often been in line with outdated views, for instance when stressing an excessive reliance on market 33

This section is partly derived by Etro (2006c). See International Chamber of Commerce (2006,2007) for a more extensive and related treatment. Here we will focus on issues related to our previous theoretical analysis, namely market dominance, predatory pricing, bundling and protection of IPRs. I am grateful to Martti Virtanen of the Finnish Competition authority for precious comments on this section.

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shares in determining dominance. The analysis of whether an undertaking has engaged in abusive conduct under Article 82 should ultimately turn on the conduct’s actual eﬀects on eﬃciency and consumer welfare. Thus, we believe that, if the pro-consumer benefits of a dominant undertaking’s conduct are significant, it should be immune from liability even if it disadvantages certain competitors. Inventing better products or more eﬃcient methods of distribution, reducing prices or oﬀering better terms of trade, and more quickly adapting to changes in the market can disadvantage rivals and maybe even cause them to exit the market. Yet, these forms of conduct often also enhance eﬃciency and consumer welfare. The focus on the eﬀects for consumers is particularly important with respect to fast-moving markets such as those commonly found in high-tech and New Economy industries which are often characterized by massive R&D investments, strong reliance on IPRs and other intangible assets, network effects, high sunk costs and low marginal costs. As we already noticed, under competition for the market, leading firms might enjoy high market shares yet be subject to massive competitive pressure to constantly create better products at lower prices due to threats from innovative competitors and potential entrants. Undertakings that hold a significant share of the market at any given point in time may see this share decrease rapidly and significantly following the development and supply of a new and more attractive product by an actual or potential competitor. Nevertheless, the current EU approach is still characterized by a close association between market shares and market dominance without any reference to the kind of market that is under consideration. 5.4.1 Eﬃciency Defense Since the main purpose of antitrust policy should be the protection of consumers and of the eﬃcient allocation of resources within sectors, it is important that strategies that create eﬃciency gains remain outside the realm of abusive strategies. The proposal on the eﬃciency defenses for dominant firms contained in European Commission (2005) appears to be going in the right direction since it allows otherwise abusive strategies if they create a net eﬃciency gain (which benefits consumers).34 In our view, conduct that generates eﬃciencies should not be deemed abusive unless it is demonstrated that the impact of this conduct on competition will result in consumer harm outweighing these eﬃcien34

This can happen in two ways: through an objective necessity defense “where the dominant company is able to show that the otherwise abusive conduct is actually necessary conduct on the basis of objective factors external to the parties involved and in particular external to the dominant company”, or a meeting competition defense “where the dominant company is able to show that the otherwise abusive conduct is actually a loss-minimising reaction to competition from others”.

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cies. Nevertheless, the proposal of the European Commission (2005) provides relatively limited scope for taking eﬃciencies into account. First, according to the proposed approach, it will fall on dominant undertakings to prove the extent to which their conduct was justified on grounds of eﬃciency. However, such a system would send the wrong signal to the business community: investigations would often move quite far along before eﬃciency considerations fully come into play. Placing the burden of proof on competition authorities, by contrast, would make more sense as they are likely to be in a better position to obtain relevant evidence from the dominant undertaking as well as other market participants (such as consumer organizations) on whether challenged conduct promotes eﬃciency. Second, to assert a successful eﬃciency defense under the proposed framework, dominant undertakings will be required to show that there are no other economically practicable and less anticompetitive alternatives to achieve the claimed eﬃciencies. This condition means that liability could be imposed even on conduct whose eﬃciency and consumer benefits far outweigh its adverse eﬀect on competitors simply because there exists an alternative that would have disadvantaged rivals less. We doubt that such a rule would have any economic justification and any basis in commercial reality. Finally, the eﬀectiveness of these rules in safeguarding consumer welfare would be weakened under the proposal of European Commission (2005) for which some firms are virtually excluded from the possibility of an eﬃciency defense: according to this proposal, the protection of competitors would be given priority over eﬃciency when the dominant undertaking holds a market share above seventy-five per cent. In our view, eﬃciencies should be assessed in the same manner in all cases, regardless of the defendant’s market share: undertakings that generate pro-competitive eﬃciencies that benefit consumers should not be penalized regardless of the level of market share or potential impact on less eﬃcient competitors. 5.4.2 Predatory Pricing Predatory pricing is defined by European Commission (2005) as “the practice where a dominant company lowers its prices and thereby deliberately incurs losses or foregoes profits in the short run so as to eliminate or discipline one or more rivals or to prevent entry by one or more potential rivals thereby hindering the maintenance or the degree of competition still existing in the market or the growth of that competition”. The standard antitrust approach uses a number of cost benchmarks in order to assess whether “predatory pricing” by a dominant undertaking has actually taken place, and in particular it sets a cut-oﬀ such that pricing below this cut-oﬀ gives rise to a rebuttable presumption that the pricing is predatory. This strategy is supported by the traditional idea that pricing below marginal cost should have an exclusionary purpose in standard markets, while pricing above marginal cost should not.

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The theory of market leaders emphasizes some limits of this way of thinking: pricing at or below marginal cost by the market leader does not need to exclude (equally eﬃcient) competitors and it does not even need to induce short run losses for the same leader. To see why, let us remember that, as we noticed in Chapter 3 and in Section 5.2.1, a leader in a standard market with quantity competition and endogenous entry can generally choose between two alternative strategies. The first one is to price below the rivals and allow their entry with a price equal to their average cost but above the marginal cost. The second strategy is to choose a limit price such that entry is not profitable for any firm. The former strategy is optimal when marginal costs are increasing enough in the production level and/or products are differentiated, while the latter strategy is optimal in the case of decreasing or constant marginal costs and/or homogenous goods. Let us focus on the first situation. When goods are homogenous, the equilibrium strategy of the leader is simply to price at marginal cost, and its profits are positive because production is in the region where average total costs are increasing. When goods are diﬀerentiated, the equilibrium price of the leader is above its marginal cost, and profits are again positive. As we have seen, in this equilibrium entry occurs, and is not deterred. Moreover, if the leader can obtain positive profits in equilibrium by pricing at marginal cost, positive profits could be preserved even by pricing slightly below marginal cost as long as the scale of production is large enough. Let us focus on the second situation now. The leader can deter entry when marginal costs are constant or decreasing and/or goods are homogenous, and this happens with a price of the leader above the marginal cost. Nevertheless, when entry is endogenous this is a normal competitive strategy of a firm able to exploit scale economies and reduce average costs of production (and, as we have seen in Section 1.1, this strategy does not even reduce welfare). Finally, in Section 2.9 we saw that in dynamic (and multi-sided) markets where demand is characterized by network externalities or supply is characterized by learning by doing, leaders may want to price below the marginal cost without entry deterrence purposes. The purpose of pricing below marginal cost would be to develop network eﬀects or decrease costs for the future and to be more aggressive in the future competition. In conclusion, it is highly questionable that the marginal cost should be the right theoretical cut-oﬀ below which predation can be presumed, and we do believe that a rule of reason should be applied also in this case, because diﬀerent sectors and diﬀerent cost and demand structures require diﬀerent approaches to the definition of predatory pricing. For the sake of argument, suppose we could agree that marginal cost pricing represents a crucial cut-oﬀ under some circumstances. The problem is that it is quite diﬃcult to measure such a figure. Therefore, many antitrust scholars, notably Areeda and Turner (1974), have proposed to substitute it with the average variable cost:

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“the incremental cost of making and selling the last unit cannot readily be inferred from conventional business accounts, which typically go no further than showing observed average variable cost. Consequently it may well be necessary to use the latter as an indicator of marginal cost” This rule has influenced antitrust policy worldwide, but one should always keep in mind that there are (demand and technological) conditions under which its premise, the marginal cost as a cut-oﬀ below which pricing is predatory, is not valid. On the basis of our theoretical discussion, we can now try to draw our conclusions on the proper approach to predatory pricing. As we have noticed repeatedly in this book, one can not judge the pricing behavior of a market leader in a correct way without taking the entry conditions into account. When entry is endogenous, in the practical sense that entry is driven by profitable opportunities and it is rapid, no firm can manipulate the market at its will. As McGee (1958) noticed in his pioneering work on predatory pricing, a necessary condition for the success, and therefore the viability, of a predatory strategy is that entry must be exogenously blocked: “Obstacles to entry are necessary conditions for success. Entry is the nemesis of monopoly. It is foolish to monopolize an area or market into which entry is quick and easy. Moreover, monopolization that produces a firm of greater than optimum size is in for trouble if entry can occur even over a longer period. In general, monopolization will not pay if there is no special qualification for entry, or no relatively long gestation period for the facilities that must be committed for successful entry.” Only when entry is not feasible (even when it could be profitable), a leader can hope to exclude the current rivals and monopolize the market. On the basis of these considerations, we propose the following rule based on two steps: 1) the Antitrust Authority should evaluate whether the undertaking is eﬀectively constrained by endogenous entry of competitors in his strategic choices: if entry is endogenous dismiss the case, otherwise proceed. 2) the Antitrust Authority should evaluate the relation between price, average total cost (ATC) and average variable cost (AVC): a) a price above ATC should be lawful without exceptions; b) a price below ATC but above AVC should be presumed lawful with the burden of proving the contrary on the Antitrust Authority, and on the basis of the consequences on consumers and allocative eﬃciency; c) a price below AVC should be presumed unlawful with the burden of proving the contrary on the undertaking, through an eﬃciency defense or proving that demand or technological conditions reduce the relevant cut-oﬀ below the AVC.

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Notice that the first step we propose is diﬀerent from the traditional one, which simply evaluates whether there is a dominant position in the relevant market.35 The traditional step is based on the idea that after excluding the rivals, a dominant firm can monopolize the market and recoup its initial losses with higher prices. But, this is impossible when entry in the competition in the market is endogenous (there is no way to recoup losses by increasing future prices if a price increase attracts entry), and it is extremely unlikely when entry in the competition for the market is endogenous (there is a low probability to recoup losses by increasing future prices of goods that may be soon replaced by innovations of other firms). The traditional definition of dominance (associated with the market share and the related indexes of concentration) should not be the relevant element to establish the likelihood of recoupment, particularly in high-tech markets. We believe that the focus should not be on the market leader in the first step of an antitrust investigation for abuse of dominance, but on the followers and on the chances that these followers have to exploit profitable opportunities in the market. Concerning the second step in the evaluation of predatory strategies, EU antitrust has also adopted a similar approach (but an eﬃciency defense still needs to be formally introduced). However, the recent proposal by European Commission (2005) has suggested to substitute the AVC with an average avoidable cost (AAC), the average of the costs that could have been avoided if the undertaking had not produced a discrete amount of extra output (this extra output is usually the amount allegedly subject to abusive conduct), a sort of average marginal (or incremental) cost of the extra output to serve the predatory sales. Unfortunately, the AAC can be quite higher than the right theoretical concept whenever it accounts for fixed costs. Moreover, the AAC can be much more diﬃcult to measure than the AVC, since it is almost always impossible to precisely define which costs are sustained for a given output and isolate the extra output (supposedly the predatory output) from the total one. Finally, there are well known conditions, as in the presence of network externalities and multi-sided markets, under which extremely ag35

The definition of the relevant market generally depends on an empirical analysis of the way demand of substitute products changes with changes in the price of the hypothetical dominant firm. Such an analysis can be problematic because the market price could be above its competitive level. For instance, a widely used method is the SSNIP-test, which defines the relevant market as the smallest market where a Small but Significant Non-transitory Increase in Prices (say of 5-10%) increases the profits of a hypothetical monopolist. This test is ideal when prices are close to the competitive level, but otherwise it is biased and leads to a too-wide market definition (which in turn may lead to a finding of no dominance in a wide market). This problem is known as the ‘cellophane fallacy’, from the subject of the du Pont case (1956). It should be noticed that such bias should not emerge (and the SSNIP-test at the prevailing prices should be valid) when the market leader is constrained by endogenous entry (see Etro, 2007,b).

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gressive pricing is a normal competitive strategy for a market leader. For instance, it is a standard practice for multi-sided markets to charge less one side of the market (as readers for a newspaper or end-users for video game consoles) and more the other side (advertisers and game developers in these examples),36 without an exclusionary purpose but only to create network effects and increase the value of the interactions between the two sides. Often, the price on one side is not only below cost, but even below zero (the sale is subsidized with free add ons), and nevertheless even such a strategy is not necessarily predatory. For these reasons, we believe that the traditional AVC remains a better reference than the AAC.37 5.4.3 Bundling Looking at the approach of the European Commission (2005) on bundling, again it appears that its positive principles are not fully carried through. Indeed, economists today generally acknowledge that tying can produce positive eﬃciencies and consumer benefits, and that a rule of reason should be adopted in evaluating its anti-competitive eﬀects. The pro-competitive eﬀects are particularly pronounced in the case of technical tying (when companies innovate by linking formerly separate technologies or products, eﬃciencies often emerge through improved performance and quality). Moreover, they can also emerge because tying strengthens price competition, and so it can be used as an aggressive strategy by leaders facing endogenous entry in the secondary market: as we have seen in Section 2.10, under product diﬀerentiation in this market, such an aggressive strategy by the leader would induce low prices without eliminating product diversification in the secondary market. The current EU approach, however, perpetuates a biased position against bundling per se. 36

37

According to the Rochet-Tirole (2003) rule, the higher price should be for the market side with higher elasticity of demand and vice versa. But this goes right against the fundamental principle of monopoly pricing for which a higher price should be for the market side with lower elasticity of demand and vice versa. In certain sectors, the same proposal uses a long-run average incremental cost benchmark (LAIC), instead of AAC. This is usually the case in industries where fixed costs are high and variable costs very low. In these cases, the LAIC benchmark is used as the benchmark below which predation is presumed. The same considerations as before hold also here: there are not economic justifications for a change of standard from AVC to LAIC. Moreover, we believe that the LAIC standard is inconsistent with business reality because it requires companies to price to cover their own average sunk fixed costs that are unrecoverable: this approach ignores the economic reality that, when market leaders decide how to price a product, they do not consider their own costs that are sunk or unrecoverable, even if not a single product is sold.

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We have many doubts on the same definition of tying adopted in the EU approach, which places too much emphasis on consumer demand for the tied product in the context of its “distinct products test” as a proxy for determining whether the tying arrangement produces eﬃciencies. To exemplify our doubts, notice that, while there is clearly consumer demand for shoelaces, this should not mean that shoes and shoelaces are distinct products for the purposes of tying analysis. This issue can only be addressed by asking whether there is consumer demand for shoes without shoelaces. In sum, whether or not consumer demand exists for the tied product is the wrong question; the correct question is whether there is any significant consumer demand for the tying product without the tied product. Unless the analysis focuses on this question, there is a danger that the mere existence of consumer demand for the tied product may prevent the emergence of eﬃcient tying arrangements and end up protecting suppliers of tied products at the expense of consumers and innovation. Moreover, in the case of technical integration of two products that were previously distinct, the distinct products test itself may not be helpful for understanding market dynamics because, by definition, this test is backwardlooking. A better approach in these cases would be simply to ask whether the company integrating the previously distinct products can make a plausible showing of eﬃciency gains: since technical tying is normally eﬃcient, market leaders would be able to continue producing innovative products benefiting consumers without running afoul of the prohibitions on tying. Finally, since tying usually enhances price competition, it should never be abusive when it is standard commercial practice (which is also indirect evidence that such tying generates eﬃciencies, or that there is no demand for the unbundled product). We are also concerned that the current approach fails to acknowledge that bundling can be used to create value for consumers in markets that experience network eﬀects and in multi-sided markets (further analyzed in the next chapter). For instance, bundling is a valuable strategy to gain broader distribution of the products or services that are subject to network eﬀects. And the broader the distribution, the greater the value produced for all consumers. This is particularly true when the product or service in question has low (or zero) marginal costs, because the supplier can include the product or service in bundles with other products at no cost. In a multi-sided market multiple types of customers gain from reciprocal interaction, as in the case of advertisers and readers for a journal: complex business models resulting from multi-sided markets often require bundling practices because the consumption on one side of the market is being “sold” on the other side of the market, and piece-meal consumption on one side of the market would break down the interdependent ecosystem.38 38

On the antitrust implications of multi-sided markets see Evans (2003b).

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Finally, in the EU approach the standard of proof the antitrust authority is required to meet to establish harmful foreclosure eﬀects is too low, particularly in light of the fact that the analysis of foreclosure eﬀects can be speculative in nature. According to the current EU approach to bundling, actual market foreclosure eﬀects are not required: it is enough that such effects are “likely” to occur. In other words, the mere risk of foreclosure can result in a finding against a dominant company. A standard of proof that requires convincing evidence would rather help ensure that companies will not be deterred from bringing new products to market as a result of concerns about remote and potential foreclosure eﬀects. 5.4.4 Intellectual Property Rights Finally, we want to look at the relationship between antitrust and the protection of IPRs. While we noticed that the latter should be the focus of legislation and not of the discretionary behavior of antitrust authorities, the current EU approach deals with IPRs in the discipline on refusals to supply, that is, situations where a dominant company denies a buyer access to an input in order to exclude that buyer from participating in an economic activity. In general, four conditions have to be fulfilled in order to find a refusal to supply be abusive: i) the behavior must be properly characterized as a termination of a previous supply arrangement; ii) the refusing undertaking must be dominant; iii) the refusal must be likely to have a negative eﬀect on competition; and iv) the refusal must not be justified objectively or by eﬃciencies. Only when the dominant supplier has not previously supplied the input to a potential buyer, as for IPRs, an additional criterion is added: v) the input must be “indispensable” to carry on normal economic activity in the downstream market (a so-called “essential facility”). Nevertheless, the European Commission (2005) correctly points out that “to maintain incentives to invest and innovate, the dominant firm must not be unduly restricted in the exploitation of valuable results of the investment. For these reasons the dominant firm should normally be free to seek compensation for successful projects that is suﬃcient to maintain investment incentives, taking the risk of failed projects into account. To achieve such compensation, it may be necessary for the dominant firm to exclude others from access to the input for a certain period of time.” The proposal clearly states the priority of IPR protection, saying that “imposing on the holder of the rights the obligation to grant to third parties a licence for the supply of products incorporating the IPR, even in return for a reasonable royalty, would lead to the holder being deprived of the substance of the exclusive right”. Therefore, another more restrictive criterion is added in the case of a refusal to license IPRs: the undertaking which requests the licence should intend to produce new goods or services not oﬀered by the owner of the IPRs and for which there is a potential consumer demand. This additional criterion is in line with established case law, but an exception to this criterion is

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introduced by the European Commission (2005). This states that a refusal to license IPR-protected technology which is indispensable for follow-on innovation may be abusive even if the license is not sought to directly incorporate the technology in clearly identifiable new goods and services, since the refusal to license an IPR-protected technology “should not impair consumers’ ability to benefit from innovation brought about by the dominant undertaking’s competitors”. This exception is inconsistent with economic analysis. As we have seen in Chapter 4, there are no clear economic arguments supporting the view that weakening IPRs could ever strengthen innovation in the long run, even when innovation is sequential. As a matter of fact, the opposite is true: the protection of IPRs for sequential innovations is more important to promote innovation and growth because it creates a multiplicative eﬀect on the incentives to innovate and it fosters technological progress and growth. Finally, concerning the refusal to supply information needed for interoperability, the proposal in European Commission (2005) states that leveraging market power from one market to another may be an abuse of a dominant position and it may not be appropriate to apply the same high standards for intervention even if such information may be considered a trade secret. The framework for assessing how such leveraging may occur or when trade secrets do not deserve the same high standards for protection has not been developed yet. Again, such a broad policy intervention could have chilling eﬀects on the incentives to invest and innovate and could ultimately end up protecting ineﬃcient competitors that may free ride on the risks and investments of the dominant undertaking, therefore in contradiction with the objective of protecting competition on the merits.

5.5 Conclusions In this book we have proposed an alternative approach to antitrust policy. Taking into account the endogeneity of entry, we have seen that standard results of the post-Chicago literature can be radically modified. The main implications, analyzed in this chapter, concern the behavior of market leaders and, consequently, the antitrust approach to abuse of dominance. In other parts of this book, we have also derived implications for the antitrust approach to mergers, collusion and state aids. The overall flavor of our approach to antitrust is reminiscent of the Chicago school. Nevertheless, our analysis is based on solid game theoretic foundations that the original Chicago view did not have. The theory of market leaders has shown that whether entry in a market is exogenous or endogenous makes a lot of diﬀerence for the way leaders behave. In markets where entry is independent from the profitability conditions, market leaders can adopt accommodating strategies to increase prices or aggressive ones to exclude rivals, and their strategies can harm consumers.

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When entry is endogenously dependent on the profitability conditions in the market, the leaders always adopt aggressive strategies which typically do not harm consumers. For instance, a firm competing with a single rival could engage in accommodating pricing to increase mark ups, or could engage in predatory pricing to induce the exit of the rival, but a firm facing endogenous entry of competitors will ordinarily engage in aggressive pricing strategies without exclusionary purposes. A monopolist in a primary market competing with a single rival on a secondary market may bundle its goods to monopolize the secondary market as well, but when the secondary market is characterized by endogenous entry the only purpose of bundling can be the strengthening of price competition. A firm facing a single rival could adopt vertical restraints on its retailers or price discrimination strategies to soften price competition, but when the same firm faces endogenous entry of rivals these anti-competitive practices will not be in its interest. Of course, notice that eﬃciency reasons can still motivate the adoption of bundling, vertical restraints, price discrimination or other strategies. The theory of endogenous entry delivers a related and strong result on horizontal mergers (see Section 2.13). As well known, even in the absence of cost eﬃciencies, these mergers are often profitable when entry is exogenous because they allow the merged entity to increase prices or restrict production so as to enhance profitability. These eﬀects are counterproductive when entry is endogenous because any accommodating strategy attracts entry. Therefore, the only rationale for mergers in markets with endogenous entry must be a cost eﬃciency large enough to (more than) compensate the strategic disadvantages associated with the merger. In these cases, mergers are welfare improving. The theory of endogenous entry also has some implications for the case in which collusive cartels are organized between a restricted number of firms (see Section 3.5). These cartels, as with any price fixing agreements, always lead to higher prices and lower welfare when the number of firms in the market is exogenous. However, when entry in the market is endogenous collusive cartels are ineﬀective, unless they act as leaders. In this last case, the cartels coordinate aggressive strategies aimed at increasing the market shares of their members through low prices, and their implementation is always sustainable and does not harm consumers. The theory of market leaders and endogenous entry can be applied to standard problems of strategic policy to evaluate the role of state aids aimed at promoting exports. These are always optimal when the domestic firms export in markets where entry is endogenous, and they do not harm domestic or foreign consumers. Therefore limitations to state aids and export subsidies should be exempted when they concern firms competing in international markets where entry is free. Finally, the theory of market leaders and endogenous entry has implications also in the case of competition for the market. Market leaders invest

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more in R&D when threatened by a competitive pressure, while they tend to stifle innovation in the absence of such a pressure: hence, persistence of a leadership in high-tech sectors can be consistent with eﬀective dynamic competition for the market, which leads to a faster rate of technological progress in the interest of consumers. It is clear that the relevance of our results depends on the relevance of the hypothesis that entry is endogenous. As we repeatedly pointed out, it does not matter what constrains entry, but simply that some fixed costs of production or some opportunity costs of participating to the competition endogenously limit entry of firms in the market. One may argue that entry can be regarded as endogenous in the medium and long run, but not in the short run. If this is the case, and if antitrust policy is aimed at correcting distortions in the medium and long run (as opposed to short run distortions), then our results are potentially relevant. In the next chapter we move on to examine in more detail the markets of the New Economy. A recent important article by Segerstrom (2007) on technological progress in the New Economy has a simple and suggestive title, “Intel Economics”. This title emphasizes the importance of market leaders of the high-tech sectors in driving innovation and global growth. In the next chapter, we will borrow the style of that title to refer to what is probably the major market leader of the New Economy and the subject of some of the most representative antitrust cases in recent history.

6. Microsoft Economics

After examining theoretical and institutional aspects of the behavior of market leaders and of the role of antitrust policy, this chapter approaches an important example of market leadership and technological leadership which is also associated with well known antitrust issues. The choice of Microsoft as a symbol of market leadership is somewhat natural: Microsoft is one of the most visible and relevant companies in the New Economy, one of the most innovative firms in one of the most dynamic industries. The antitrust cases in which this company has been involved in both the US and the EU attracted primary attention of media, policymakers and observers. Many important economists were involved in these antitrust cases in both the US and the EU, and many others were inspired by them while developing theoretical and empirical analysis on the structure of the software market, on the role of Microsoft in this market and on the role of antitrust policy for the New Economy. In a recent important book, Evans et al. (2006) have emphasized the crucial role that software platforms are playing in shaping our economies, in enhancing the development of many traditional sectors, and ultimately in aﬀecting our way of living. These “invisible engines”, as they call the software platforms, power not only the PC industry but also other industries like those associated with mobile phones and other handheld devices, video games, digital music, and (with strong externalities for the rest of the economy) on-line auctions, online searches and web-based advertising. Their claim is that software platforms and microprocessors are at the basis of a new industrial revolution, exactly as the steam engine had been at the basis of the first industrial revolution (1760-1830) and electric power at the basis of the second industrial revolution (1850-1930). The third industrial revolution began with the introduction of commercial PCs in the early 80s and had a second phase starting in the mid 90s with the diﬀusion of the Internet.1 Ob1

The Internet is a global network of interconnected computer networks (linked by copper wires, fiber-optic cables and wireless connections) that transmit data by packet switching using the standard Internet Protocol (IP) and the Transfer Control Protocol (TCP). The World Wide Web (WWW) is a collection of interconnected documents and other resources (linked by hyperlinks and Uniform Resource Locators, or URLs) that is accessible via the Internet, as are many

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servers have talked about “Intel economics”, “Microsoft economics” or the “Internet economics” to refer to this period of innovations in general purpose technologies, and to describe the ultimate engine of growth in the New Economy.2 What follows in this chapter surveys the wide academic debate on these issues. Our aim is not to provide a comprehensive analysis of the software market or of the role of Microsoft, but to point out relations between our theoretical results on the behavior of market leaders and the structure of this market, and use this theoretical background to evaluate antitrust issues involving Microsoft. The chapter is organized as follows. Section 6.1 describes the development of the software market within the New Economy, and the role of Microsoft in this environment. Section 6.2 describes the genesis of the antitrust cases which involved Microsoft and the remaining sections adopt our theoretical instruments in evaluating the basic issues emerging in these cases: whether Microsoft is a monopoly in Section 6.3, whether its bundling strategies are predatory in Section 6.4, and whether its innovations should be disclosed to promote interoperability in Section 6.5. We conclude in Section 6.6.

6.1 The Software Market The software market was developed in the last few decades.3 In the 1960s, the computer industry was dominated by IBM, which manufactured mainframe computers used by large enterprise customers. These computers were expensive to purchase and expensive to maintain. As a result, very few consumers had access to computers. Apart from IBM, mainframes were oﬀered by firms such as Sperry, Control Data, Philco, Burroughs, General Electric, NCR, ect.

2

3

other services like the emails. Other protocols or applications run on top of this structure. In 1958 United States created the Advanced Research Projects Agency, which supported first the research of the MIT Lincoln Laboratory in networking country-wide radar systems, and then the development of ARPANET, the main predecessor of the Internet, activated in 1969 at UCLA. The first TCP/IP wide area network was operational by 1983, when the American National Science Foundation constructed a university network backbone that would later become the NSFNet. In 1991 the European CERN launched the new WWW project after having created the Hypertext markup language (html), the predominant language for the creation of web pages, the Hypertext transfer protocol (http), the application that links and provides access to the files, documents and other resources of the WWW, and the first web pages. Popular web browsers emerged soon after that. On the role of the Information and Communication Technology in the recent growth experience see Dosi et al. (2007) Part of this section is based on Etro (2007d).

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In the mid 70s the US market was still dominated by IBM followed by Honeywell, Burroughs, Sperry, Control Data, NCR, Digital, G.E. and HewlettPackard (see Sutton, 1998, Ch. 15). There was little or no interoperability among mainframes from diﬀerent vendors. For the most part, an enterprise customer was required to choose an all IBM solution or an all Sperry solution. In the 1970s, Digital Equipment achieved considerable success with a line of less expensive minicomputers that were well-suited to engineering and scientific tasks. Again, however, there was little or no interoperability between these minicomputers and mainframes oﬀered by IBM and others. The structure of the industry at that time was still largely vertical. By 1980, a number of companies had started oﬀering less expensive microcomputers which, again, were not interoperable with one another. Early PCs by Altair, Tandy, Apple, Texas Instruments, Commodore and Atari ran their own operating systems, meaning that applications written for one brand of PC would not run on any other brand: the industry was fragmented. Apple, founded by Steve Jobs and Steve Wozniak in 1976, developed a very successful software platform, especially because of VisiCalc, an electronic spreadsheet which was introduced in 1979 and soon became a killer application for Apple II. In the early 80s, IBM announced plans to introduce an IBM personal computer. The first one was oﬀered with operating systems (OSs) produced by others: CP/M-86 from Digital Research (a rewrite of the leading OS at the time), UCSD-p System by Softech Microsystems, and PC-DOS developed by Microsoft, a company founded by Bill Gates, a young software architect who dropped out of Harvard University to create what was going to become a symbol of market leadership in the New Economy. Microsoft’s OS won the race mainly because it was cheaper than CP/M-86 ($ 40 against $ 240) and faster than p-System. Moreover, Microsoft managed to keep the right to license its OS to other PC makers, under the name MS-DOS: this drove its success in the software market. As Evans et al. (2006) noticed, “having multiple operating systems run on a hardware platform is a poor strategy. The idea, of course, was to ensure that the hardware, not the operating system, became the standard that defined the platform and determined its evolution. Indeed, IBM followed an important economic principle for traditional industries: all firms would like everyone else in the supply chain to be competitive. IBM didn’t seem to recognize that this was far from a traditional industry... Applications are generally written for software platforms, not the underlying hardware. The more fragmented the installed base of operating systems, the less attractive it is to write an application for any one of them.” Not surprisingly, IBM’s multiple-OS strategy did not work, the hardware sector became always more fragmented, with many PC manufacturers producing clones of the IBM PC and most of them running MS-DOS, the exact replica of the operating system running on IBM PCs. In the second half of

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the 80s IBM reacted by developing a new operating system, OS/2, while Microsoft independently developed Windows, whose lead at that point became unreachable. According to some observers, IBM based its strategy on its brand name and its research capacity, while Microsoft invested more in supporting the developers of software applications and in what is often called “evangelization”: convincing software producers to develop applications for Windows. This was the winning strategy: the share of IBM in the market for the so-called IBM-compatible PCs decreased over time (in 2004 IBM arrived to the point of selling its PC division to Lenovo), while the market share of Microsoft in the software market increased. Over time, the computer industry had moved from the old vertical structure toward a horizontal structure. This was characterized by a market for chips (Intel as a leader, Motorola, ARM, TI, AMD,..), one for hardware and peripheral equipment (IBM, Dell, Hewlett-Packard, Packard Bell, Compaq, Gateway, Acer, Fujitsu,...), one for operating systems (Windows as a leader, OS/2, Unix, Linux, Solaris,..), one for application software (Oﬃce, Scientific Workplace, Adobe Acrobat, Macromedia Dreamweaver,..) and one for sales and distribution, with competition within horizontal levels and higher interoperability across levels. A similar horizontal structure has emerged in the industries for mobile phones and personal organizers. This is not by chance: such decentralized structures can work well when technical interactions between complementary products are stable and well defined, while vertical structures would become too rigid to control them. Apple, the only large player remaining a fully integrated structure producing both hardware and software for its PCs and for other devices, had to become quite active in attracting applications from other software developers, in order to build network externalities.4 6.1.1 Network Eﬀects A software platform is a software program that makes services available to other software programs through external “hooks” called Application Programming Interfaces (APIs). Examples are the operating systems running on PCs as Windows, Mac OS or Linux, those employed by videogame consoles as the Sony one for PlayStation or Windows 2000 for the Xbox, the Symbian 4

Famous is the 1985 letter by Bill Gates to Apple, which advised its future main competitor to license the Mac OS to PC manufacturers to create network eﬀects and establish a standard (at the time Microsoft was still earning its revenues mainly from software applications, most of which, like Word and Excel, were important applications for the Macintosh). As well known, Apple chose the harder way, but it is still a strong and extremely innovative company in the PC industry today.

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operating system for cellular phones,5 Palm OS for personal digital assistants (PDAs), RIM for the BlackBerry, Mac OS for the Apple iPod and iPhone, and so forth. To understand the peculiarities of the software market in general it is convenient to focus briefly on the main functions of PC operating systems. The main one is to serve as a platform on which applications can be created by software developers. OSs supply diﬀerent types of functionality, referred to as system services, that software developers can call upon in creating their applications. These system services are made available through APIs. When an application calls a particular API, the operating system supplies the system service associated with that API by causing the microprocessor to execute a specified set of instructions. Software developers need well-defined platforms that remain stable over time. They need to know whether the system services on which their applications rely will be present on any given PC. Otherwise they would have to write the software code to provide equivalent functionality in their own applications, generating redundancy, ineﬃciency and a lack of interoperability. Moreover, modern OSs provide a user interface, the means by which users interact with their computers. User interfaces for computers have evolved dramatically over the last decades, from punch card readers, to teletype terminals, to character-based user interfaces, to graphical user interfaces, first introduced (at a low price) by Apple with Macintosh in 1984. Finally, OSs enable users to find and use information contained in various storage devices: local ones, such as a floppy diskette, a CD-ROM drive, a jump drive or the hard drive built into a PC, or remote ones, such as local area networks that connect computers in a particular oﬃce, wide area networks that connect computers in geographically separated oﬃces, and the Internet. Over time, the OS of Microsoft became the most popular because Microsoft continually added new functionality and licensed it to a wide range of computer manufacturers with extremely aggressive price strategies. Microsoft recognized early on that an OS that served as a common platform for developing applications and could run on a wide range of PCs would provide substantial benefits to consumers. Among other advantages, development costs would fall and a broader array of products would become available because products could be developed for the common platform rather than for a large number of diﬀerent platforms. By providing a single OS that ran on multiple brands of PCs, Microsoft enabled software developers to create applications, confident that users could run those applications on PCs from many diﬀerent computer manufacturers. In addition, applications developed for a single platform are more easily interoperable because they rely on the same functionality supplied by the underlying OS. 5

Symbian is a joint venture founded by Nokia, Ericsson and Motorola (which left it in 2003). It is currently owned (in order of shares of stocks) by Nokia, Ericsson, Sony Ericsson, Panasonic, Siemens AG and Samsung.

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The original winning strategy of Microsoft was the creation of these network eﬀects between hardware producers, software developers and consumers: computer manufacturers benefit because their PCs can run the many applications written for Windows and because users are familiar with the Windows user interface; software developers benefit because their applications can rely on system services exposed by Windows via published APIs and because they can write applications with assurance that they will run on a broad range of PCs; consumers benefit because they can choose from among thousands of PC models and applications that will all work well with one another and because such broad compatibility fosters intense competition among computer manufacturers and software developers to deliver improved products at attractive prices. But this argument should not be overemphasized: for many years, PC-DOS and OS/2 had as many applications as Windows, but IBM’s decline did not stop. There is indeed another and more traditional element that is fundamental also in the software market: the other crucial aspect of the strategy of Microsoft was its aggressive pricing strategy. This was strengthened through the development of the same network eﬀects: conquering market shares, Microsoft could spread its huge fixed costs of production over a larger market and reduce the price, which in turn could enhance the network eﬀects. 6.1.2 Multi-sided Platforms Software platforms, as we have seen, deal with multiple sides. Microsoft deals with at least three: consumers, software developers and PC manufacturers. Apple produces hardware internally, hence it deals with the remaining two sides: consumers and software developers. Sometimes relationships are even more complex, as in the platform for smart mobile phones where, beyond OSs, software developers and handset makers, there are network operators (as Vodafone, NTT, T-Mobile, Orange, China Mobile, Telecom Italia Mobile,..) playing a coordinating role.6 In the presence of multiple sides with network eﬀects between them, the choice of which ones should be charged more to use the platform is not simple. Rochet and Tirole (2003), Caillaud and Jullien (2003) and Evans (2003a) have noticed that software platforms, as other similar multi-sided platforms, give rise to market structures that are quite diﬀerent from the traditional ones. For simplicity, here we will refer to two-sided platforms, which connect two sides in such a way that for each side the valuation of the interactions with the other side depends on the number of agents on the others side. These network externalities, and in particular the non neutral impact of the pricing structure on both sides (and therefore on these externalities) distinguishes a two-sided 6

Moreover in this ecosystem not only competition within layers is strong, but also competition between layers is relevant.

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market from a traditional one-sided market with diﬀerent consumers (and possibly price-discrimination between them).7 An analogous situation to software platforms emerges in many completely diﬀerent contexts. A classic example, useful to understand the implications of any kind of platforms, is given by newspapers. They are sold to readers, but they also sell advertising space to advertisers: the reader is not only a “customer” of the newspaper, the reader is also a supplier of “eyeballs” that the newspaper sells to advertisers. In this case network eﬀects emerge because advertisers value their advertising more in a newspaper when the number of its readers is higher (the eﬀect in the other direction may exist but is typically less important). This has crucial consequences on the pricing structure since a low price for the readers increases the number of sold copies and in turn enhances the value of advertising. Such a phenomenon is stronger when a newspaper is competing with other newspapers, and a low price reduces the readers of competing newspapers and the value of advertising on these competing newspapers. Other two-sided platforms include other media networks as television channels, real estate agencies, traditional auction houses, shopping malls, night clubs, payment card systems, telephone networks and many industries of the New Economy as those related with video game consoles, smart phones, digital music, PDAs, i-Mode, search engines (Google), on line communication (Yahoo! and Skype), on line social networks (MySpace, asmallworld, or Second Life), on line academic articles (JSTORE or SSRN) and on line shopping (Amazon and eBay). In many of these markets, multi-homing on at least one of the two sides is common: people often buy more than one journal or watch more TV channels (as companies advertise on multiple medias), hold multiple credit cards (as merchants accept multiple cards) and software developers prepare applications for multiple OSs (while individuals typically use only one). In each one of these examples, network externalities are crucial to the success of a software platform, and the pricing structure toward buyers and sellers is crucial to the creation of these network eﬀects. In particular, a platform typically ends up charging one of the two sides less than the other, taking into account demand elasticities and which side values the other side more: the aim is to get on board as many agents as possible from one side, so as to increase the value of the platform for the other side and earn more revenue from it. For instance, when the price is the strategic variable, it is optimal to charge the side whose demand is more elastic, because this allows one to maximize the total volume of interactions.8 Prices will be constrained downward 7

8

See Section 2.9 for a theoretical analysis of this aspect. An early contribution on two-sided markets is due to Baxter (1983). Consider the simplest case of a monopolistic platform charging a group, say the buyers, a price pB per interaction with the other group, say the sellers, and charging the sellers a price pS per interaction with the buyers. If total demand

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when there are competing platforms (especially in the case of multi-homing), and further bias may emerge for strategic reasons,9 but the general principles on the balanced price structure between the two sides remain unchanged. In extreme cases, one side may even receive its goods or its services for free or even be subsidized so as to maximize earnings from the other side. The above theoretical results are fully confirmed by what happens in the above mentioned two-sided markets, whose companies typically settle on pricing structures that are heavily skewed toward one side of the market or, in other words, adopt what is sometimes called a “divide and conquer” strategy. Newspapers, television networks and even websites typically earn more from advertisers than from consumers, real estate agencies earn more from sellers (or from landlords) than from buyers (or renters), auction houses from sellers rather than from the buyers, shopping malls from stores rather than from the shoppers, night clubs from men rather than from women and payment card companies from merchants rather than from cardholders. Similarly, phone operators earn more from originating calls rather than from receiving ones, video game platforms from royalties on game developers rather than from of interactions is D(pB ) for the buyers and D(pS ) for the sellers, the number of interactions is D(pB )D(pS ). Given a marginal cost per interaction c the profits of the platform are: π = (pB + pS − c)D(pB )D(pS )

9

whose maximization provides the following Rochet-Tirole (2003) rule pB + pS − c = pB / B = pS / S , where i is the elasticity of demand for i = B, S. Similar outcomes emerge in case demand on each side depends on demand on the other side, with more complex pricing structures and with competition between platforms (see Armstrong, 2006, Rochet and Tirole, 2006, and Goldfain and Kováˇc, 2007). Strategic reasons may bias the pricing structure of platform leaders. In the example of the previous footnote, suppose product diﬀerentiation on one side occurs and, with the usual notation, profits of a representative firm are: π = (pB + pS − c)D(pB )D(pS , β S ) Suppose that the leader can commit to a price for the buyers, while, for simplicity, the others are given. Firms compete on the prices for the sellers. To verify the incentives of the leader, notice that, with the usual notation of Chapter 2 (with k = 1/pB as preliminary commitment), we have: L (1/pS , β S , 1/pB ) = (pS pB )2 D(pB )D1 (pS , β S ) < 0 Π13

Assuming that SC holds, this implies that when entry is not free the leader will tend to underprice buyers to be accomodating in the competition for the sellers. However, when entry in the platform competition is endogenous, the leader will tend to overprice buyers to be aggressive in the competition for the sellers.

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buyers of consoles (that are often sold below cost), while most of the other software platforms, including PC OSs, earn more from end users rather than from software developers.10 Notice that, in spite of the network eﬀects, most of these two-sided markets are also characterized by a certain degree of fragmentation between platform providers, often associated with a certain degree of diﬀerentiation. Only when technological innovation is particularly important and fixed costs of investment in R&D are high, while marginal costs of production are particularly low, the number of competing platforms is endogenously reduced, as in the above mentioned markets of the New Economy. Nevertheless, tipping on a single leader rarely happens, especially when product diﬀerentiation and multi-homing have a role, as for video games. And even in these cases competition for the market can be quite eﬀective and induce periods of persistent leadership with occasional replacement of the leader: pathbreaking innovations (or “killer applications”) are what competitive firms really look for. For instance, in the console video game industry, sequential innovations brought to leadership a number of companies as Atari (that reached 80% share of the market in 1980), Nintendo (90% of the market in 1987), Sega (leader in the early 90s), Nintendo again (in the mid 90s) and Sony with the PlayStation in diﬀerent improved versions (during the last decade): recently Microsoft Xbox started gaining market shares, and Nintendo is still active, but the leadership of Sony (65% market share in 2004) does not appear under threat yet, especially after the recent successful launch of PlayStation 3. Similarly, after a number of unsuccessful attempts by many companies, Palm’s PDA gained success and leadership in the market for OSs for organizers thanks to a simple handwriting recognition system (65% market share in 2000) until Microsoft competing platform and other handheld devices, including Blackberry and (in perspective) Apple’s iPhone, started gaining success. Having described the role of network eﬀects and multi-sided relations, it is now time to return to the software market, where these elements play a crucial role. 6.1.3 Microsoft Microsoft was founded in 1975 by Bill Gates and Paul Allen to develop BASIC interpreters for the first PC, Altair 8800, and then other programming languages. Only later, did it start producing major software programs. In 1981, Microsoft released its first operating system, MS-DOS, which had a 10

This happens in diﬀerent ways however: Microsoft licenses Windows, Palm and Symbian license their OSs to manufacturers of PCs, PDAs and cellular phones, while RealNetworks licenses access to digital content and Apple sells PCs and iPods, but none of these companies charges content owners (Apple and RealNetworks actually pay them) or software developers (which are typically subsidized).

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character-based user interface that required users to type specific instructions to perform tasks. In 1985, Microsoft introduced a new product called Windows that included a graphical user interface, enabling users to perform tasks by clicking on icons on the screen using a pointing device called a mouse (basically the only piece of hardware produced by Microsoft for PCs). Windows 3.0, shipped in 1990, was the first commercially successful version of Windows. In 1995, Microsoft released Windows 95, which integrated the functionality of Windows 3.1 and MS-DOS in a single operating system. In 2000, Microsoft shipped Windows 2000 Professional, a new generation of PC operating system built on a more stable and reliable software code base than earlier versions of Windows. Windows XP represented a further evolution with a range of added functionality for both business and home users. In 2007 Windows Vista has been released worldwide: it was the fruit of five years of work by eight thousand designers, programmers and testers and of an estimated investment of $ 10 billion to rewrite from scratch a new code. This impressive eﬀort was probably related to the competitive pressure coming from the open source community, which is strongly supported by many large corporations willing to strengthen valid alternatives to Windows. Even if complete and homogenous data are unavailable, consistent evidence suggests that the market share of Windows on sales of OSs for PCs rapidly increased towards 80% in the first half of the 90s to gradually arrive at 92% in 1996, 94% in 1997, 95% in 1999, 96% 2001, and remained above 90% since then (while the average consumer price of Windows, calculated as average revenue per licence to PC manufacturers based on Microsoft sales, remained around $ 44-45). Nevertheless, one should keep in mind that Linux, after having made inroads into corporations’ server computers, is now expanding into a much broader market, that of employees’ PCs, that a minor group of PC users (but strongly increasing in number, especially between expert users) downloads open source OSs from the Internet,11 and that on the 11

Estimates for the percentage of server computers running Linux worldwide are in the range of 20-25%, while desktop computers running Linux are around 3%. According to the Wall Street Journal (March13, 2007, Linux Starts to Find Home on Desktops), “market researcher IDC said licenses of both free and purchased versions of Linux software going into PCs world-wide rose 20.8% in 2006 over the previous year and forecast that licenses will increase 30% this year over last. That compares with 10.5% growth in 2004, according to IDC. Whether Linux gains a stronger footing in PCs depends partly on whether PC makers start supporting it more strongly. To date, neither Dell Inc. nor Hewlett-Packard Co. have oﬀered PCs preloaded with Linux. But Dell has been soliciting input from its customers to help guide its plans for Linux — which some industry observers say could lead the company to start making Linux PCs [...] H-P says it has recently signed deals — on an ad hoc, custom basis — to provide Linux PCs to large customers.”

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top of this market there are Apple computers running Mac OS.12 It is clear that Microsoft has reached a robust leadership in the PC operating systems market for Intel-compatible computers. In line with our previous discussion, Evans et al. (2006) state four key strategies that have driven Microsoft to become the leader of the PC industry: “(1) oﬀering lower prices to users than its competitors; (2) intensely promoting API-based software services to developers; (3) promoting the development the development of peripherals, sometimes through direct subsidies, in order to increase the value of the Windows platform to developers and users; and (4) continually developing software services that provide value to developers directly and to end users indirectly.” Beyond OSs, Microsoft is the leader in other markets for software applications. Some essential applications have been freely bundled with the operating system: for instance a basic word processing software (WordPad), a browser to access Internet (Internet Explorer) and media player functionality (Windows Media Player) have been gradually added for free to subsequent versions of Windows when they became standard components of a modern OS. Other more sophisticated applications are supplied separately. Most notably this is the case of the Oﬃce Suite consisting of the word processor Word (first edition released in 1983), the spreadsheet Excel (1985), the presentation software PowerPoint (1987) and more. The main two applications, Word and Excel, have been successfully competing against alternative products like WordPerfect, WordStar, AmiPro and others on one side and Lotus 1-2-3, Quattro and others on the other side. Liebowitz and Margolis (1999) have shown convincing evidence for which a better quality-price ratio together with network eﬀects were at the basis of this evolution (it is important to note that Microsoft achieved leadership in the Macintosh market, hence without exploiting the presence of its own OS, considerably earlier than in the PC market). In the market for word processing applications, Microsoft’s market share was hardly above 10% at the end of the 80s, but gradually increased to 28% in 1990, 40% in 1991, 45% in 1992, 50% in 1993, 65% in 1994, 79% in 1995, 90% in 1996, 94% in 1997 and arrived to 95% in 1998, remaining around this level afterward. Meanwhile the average consumer price of Word (calculated as average revenue per license) decreased from $ 235 in 1988 to $ 39 in 2001. In the market for spreadsheet applications, Microsoft followed a similar progress, with a market share of 18% in 1990, 34% in 1991, 43% in 1992, 46% in 1993, 68% in 1994, 77% in 1995, 84% in 1996, 92% in 1997 and 94% in 1998, with 12

As pointed out by Foncel and Ivaldi (2005), there is a certain variability between countries. The DOS/Windows platform is on 88 % of PC sales in Japan and 98% in Germany. Data for the second half of the 90s are from International Data Corporation.

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minor progress in the following years, while the average consumer price of Excel was decreasing from $ 249 in 1988 to $ 42 in 2001. Finally, Microsoft is also active in other strategic markets as a follower, in particular with the personal finance software Money (the leader being Intuit Quicken), the operating systems for smart phones Windows Mobile (the leader being Symbian, with a 60% market share in 2004), the video game console Xbox (the leader being Sony PlayStation, with a 65% market share in 2004), the search engine based portal Windows Live (the leader being Google, with more than 80% of searches on the Internet) and more. In 2006, Microsoft, led by the CEO Steve Ballmer, had revenues of $ 44.2 billion, 60% of which derives from Windows and Oﬃce, and net income of $ 12.4 billion, 80-90% of which derives from Windows and Oﬃce.

6.2 The Antitrust Cases Microsoft’s leading position induced large opposition in the industry and the emergence of multiple antitrust cases with importance at the global level.13 Microsoft has been under investigations in the US by the Federal Trade Commission and the Department of Justice since 1990, primarily for its contracts with computer manufacturers and for bundling secondary products with its OSs.14 However, the most important US case began only in the late ’90s under the Democratic Clinton Administration, followed after a few years by the EU case. 6.2.1 The US Case In the main Microsoft vs. US case, started in 1998, the software company was accused of protecting its monopoly in the OS market from the joint threat of the Internet browser Netscape Navigator and the Java programming language,15 which could have developed a potential substitute for OSs allowing 13 14

15

This section is partly derived from Etro (2006d). Already in the mid 90s we could see important economists in action in these early cases. In 1995 the Nobel prize Kenneth Arrow intervened saying that “Microsoft appears to have achieved its dominant position in its market as a consequence of good fortune and possibly superior products and business acumen” and that Microsoft’s licensing practices toward original equipment manufacturers “made only a minor contribution to the growth of Microsoft’s installed base. Even this minor contribution overstates the impact of Microsoft’s licensing practices on its installed base barrier to the entry and growth of competing operating systems” (Declaration of Kenneth Arrow, U.S.. v. Microsoft Corp., Civil Action No. 941564 (SS), January 17, p. 11-12). The dramatic expansion of the World Wide Web started in 1993 after the development, by a team from the University of Illinois, of the first graphical web

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software applications to run on hardware independently from the desktop OS. Basically, the hypothetical threat for Microsoft was the development of an alternative to the software platform based on the OS, a sort of middleware platform or a web-based platform leading to the “commoditization” of the OS (as ten years before the software platform led to the commoditization of hardware), and hence to the loss of leadership of Microsoft. Microsoft reacted by improving its Internet Explorer (IE) browser, engaging in contractual agreements with computer manufacturers and Internet service providers to promote preferential treatment for IE (notably AOL, whose “You’ve got mail” sound track was attracting more than 20 millions Americans at the time), and finally tying Windows with IE. For perspectives by economists who were active in the case see Fisher and Rubinfeld (2001) and Bresnahan (2001) on the side of US Government, and the essays in Evans (2002), especially Elzinga et al. (2002), on the opposite side.16 As Klein (2001) pointed out in an academic survey on the Journal of Economic Perspectives (Symposium on the Microsoft case), “Microsoft spent hundreds of millions of dollars developing an improved version of its browser software and then marketed it aggressively, most importantly by integrating it into Windows, pricing it at zero and paying online service providers and personal computer manufacturers for distribution. All of this was aimed at increasing use of Microsoft’s Internet Explorer browser technology, both by end users and software developers, to blunt Netscape’s threat to the dominance by Windows of the market for personal computer operating systems.” Microsoft’s investments in browser technology, which largely improved IE until it became a superior product compared to Netscape Navigator (see the empirical analysis in Liebowitz and Margolis, 1999), and Microsoft’s pricing of IE at zero (as always since then) appear to us as examples of aggressive strategic investment and aggressive pricing by a market leader facing competition, and not as anti-competitive strategies.17 According to Klein (2001),

16

17

browser, Mosaic. Netscape, founded in 1994, hired most of its developers to create Navigator. Java was developed at the same time by Sun as a middleware product to allow programmers to write applications that would run on line on any computer regardless of the underlying OS. For economic surveys on the case see Gilbert and Katz (2001), Klein (2001) and Economides (2001). For retrospective views see Motta (2004, Ch. 7) and Evans et al. (2005). In our view, the US case was characterized by a too limited focus on rigorous economic arguments in support of the diﬀerent thesis. It is ironic that Microsoft’s internal documents and emails including aggressive expressions toward competitors were used to support the idea that Microsoft undertook its browser development for entry deterrence purposes. It is hard to see how the aggressive language of business people can prove more than competitive intent (on the use of internal documents to prove antitrust violations, see Manne and Williamson, 2005).

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“a crucial condition for anticompetitive behavior in such cases is that the competitive process is not open. In particular, we should be concerned only if a dominant firm abuses its market power in a way that places rivals at a significant competitive disadvantage without any reasonable business justification. Only under these circumstances can more eﬃcient rivals be driven out of the market and consumers not receive the full benefits of competition for dominance. The only Microsoft conduct ... that may fit this criteria for anticompetitive behavior are the actions Microsoft took in obtaining browser distribution through personal computer manufacturers” This is correct: a number of contractual restraints imposed by Microsoft on its distributors were potentially harmful and have been correctly forbidden. After a failed attempt by Judge Richad Posner to mediate in settlement negotiations, Judge Thomas Penfield Jackson decided to impose heavy behavioral and structural remedies on Microsoft, including the break up in an operating system and an application company (the so-called “Baby Bills”, as Baby Bells were the companies derived from the 1984 break up of AT&T). At the time, this draconian remedy was criticized by many economists with diﬀerent perspectives on the case, for excessively penalizing the company without a clear relation between the punishment and the alleged crime, and for inducing perverse consequences for consumers. For instance, on the pages of The New York Times, Paul Krugman pointed out the risk of creating two monopolists engaging in double marginalization: “The now ‘naked’ operating-system company would abandon its traditional pricing restraints and use its still formidable monopoly power to charge much more. And at the same time applications software that now comes free would also start to carry heftly price tags” (Krugman, 2000a).18 18

Judge Jackson was later disqualified for violating a number of ethical precepts and being manifestly biased against Microsoft. The government proposal of splitting Microsoft into two companies, which was adopted by the Judge without substantive changes, had been supported by declarations of important economists, including Paul Romer and Carl Shapiro. For instance, Shapiro declared that, while “network monopolies can be very strong, they are most vulnerable to attack by firms with a strong position in the provision of a widely-used complementary product ”, hence “the proposed reorganization of Microsoft into separate applications and operating systems businesses will lower entry barriers, encourage competition and promote innovation” (Declaration of Carl Shapiro, U.S. v. Microsoft Corp., Civil Action N0. 98-1232 (TPJ), p. 7 and p 29). Nevertheless, other economists were critical of the consequences of the break up on innovation. Krugman (2000b) again criticized a systematic reference to the promotion of innovation as a vague justification for the remedy: “we don’t know very much

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After the appeal phase and the return of the Republican Administration with George W. Bush, the DOJ changed attitude looking for a settlement. The November 2002 ruling of the District of Court decided on behavioral remedies aimed at preventing Microsoft from adopting exclusionary strategies against firms challenging its market power in the market for OSs. Moreover, the Court adopted forward looking remedies that required limited disclosure of APIs, communication protocols, and related technical information in order to facilitate interoperability, and created a system of monitoring of Microsoft’s compliance which has been working quite well in the last years. Since other derivative private actions have also been dismissed or settled, it seems that this long-standing conflict has arrived to its end in the US. 6.2.2 The EU Case The Microsoft vs. EU case was subsequently developed on somewhat similar issues. In particular, Microsoft has been accused of abuse of dominance in the market for OSs through technological leveraging and in particular in two ways: first, by bundling Windows with Media Player, a software for downloading audio/video content, and, second, by refusing to supply competitors with the interface information needed to achieve interoperability between work group server OSs19 and Windows. Contrary to the US case, the bundling part of the EU case is a traditional case of bundling, since the competitors in the secondary market, notably RealNetworks, do not represent a threat for Windows, the primary product of Microsoft. In the famous antitrust decision of March 24, 2004, Competition Commissioner Mario Monti imposed on Microsoft the largest fine in the history of antitrust (€ 497 million), required Microsoft to issue a version of its Windows operating system without Media Player, and mandated the licensing of intellectual property to enable interoperability between Windows PCs and

19

about what promotes innovation, and even some of what we think we know may not be true. For example, advocates of the breakup of Microsoft like to point to the breakup of AT&T, which everyone thinks was purely positive in its effects on innovation. It’s a bad parallel in many ways, but still it is interesting to notice that next-generation telecommunications is not yet a hot issue in the United States, because thanks to the fragmentation of our cellular system we are lagging well behind Europe and Japan in mobile phone technology. And that fragmentation is in part a legacy of the AT&T breakup. My point is not that it is wrong to consider the impact of policy on innovation; it is that because the determinants of innovation are not well understood, clever advocates can invoke technological progress as an all-purpose justification for whatever policy they favor”. A work group server OS is a software providing services to share files and printers and other administration services to a group of users connected in a network, typically in oﬃce environments.

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work group servers on one side, and competitor products on the other side. After this decision, Microsoft paid the fine, developed and released a version of Windows without Media Player, and entered into extensive discussions with the Commission about the implementation of the remedies concerning interoperability. In the original decision this required to prepare a complete and accurate interface documentation describing portions of Microsoft server operating system software and to license innovations created by Microsoft under “reasonable and non discriminatory” (so-called RAND) terms to competitors. These imply that the royalties should be set at levels that enable use by other developers in a commercially practicable way with reference to standard valuation techniques, to an assessment of whether the protocols are innovative, and with reference to market rates for comparable technologies. Over time, the new Competition Commissioner Neelie Kroes has continued to extend the scope of the information required, from information that would enable interoperability with Windows PCs and servers for the purpose of creating new products for which there is unmet consumer demand, to information that would allow a competitor to produce clones or “drop-in replacements” of the Windows server OS. Even more controversially, the Commission’s Competition Directorate-General has sought to loosen the terms under which Microsoft would be able to licence its information, so as to allow products implementing its technical specifications to be released under so-called Open Source licences (DG Competition was prepared to make an exception for technologies that involved an inventive step and were considered novel by comparison with the prior art, thus meeting the criteria for patentability). Such release, by revealing to the world Microsoft’s own implementations of its technical specifications, would irreparably undermine the trade secret protection to which these technologies, some of which are not patented, are subject. In a further shift, the Commission made clear in Spring of 2007 that it expected Microsoft to forego royalty payments on any technologies that were not covered by patents. With the compliance process made more diﬃcult on both sides by the technical complexity of the material and key policy diﬀerences (e.g. over the intellectual property issues), DG Competition challenged Microsoft to comply with the interoperability remedy by 15 December 2005, on pain of massive penalty payments for noncompliance. In early 2006, Microsoft provided further information needed for interoperability purposes, and even made available to its competitors selective access to the source code of Windows. Nevertheless, in July 2006 the Commission levied fines of € 1.5 million a day from the December hearing onwards (for a total of other € 280.5 million), and threatened to double the fine if the company did not comply. At the time of writing, the case is still unresolved: Microsoft’s Appeal of the Commission’s 2004 landmark decision

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was heard by the European Court of First Instance in April 2006,20 and a decision is expected by September 2007, after this book will be completed. In either case, both Microsoft and the Commission may also appeal to the European Court of Justice, which is the EU’s highest court.21 A common element in both the US and EU cases has been the substantial involvement of competitors of Microsoft on the side of the antitrust authorities. In a neat article about the US vs. Microsoft case on Business Week, Robert Barro noticed that: “a sad sidelight in the Microsoft case is the cooperation of its competitors, Netscape, Sun and Oracle Corp., with the government. One might have expected these robust innovators to rise above the category of whiner corporations [...] The real problem is that whining can sometimes be profitable, because the political process makes it so. The remedy requires a shift in public policies to provide less reward for whining. The bottom line is that the best policy for the government in the computer industry is to stay out of it” (Barro, 1998) Nevertheless, IBM, Sun, Oracle, Novell and the wide open source movement have also been active against Microsoft in the EU case.

6.3 Is Microsoft a Monopolist? While a comprehensive analysis on the PC operating system market and of the role of Microsoft is beyond our scope, we can try to provide a basic interpretation of a few features of this market through the simple ideas developed in the theoretical part of this book. The technological conditions in the software market are relatively simple. Production of an operating system, as any other software, takes a very high up-front investment and a roughly constant and low (close to zero) marginal cost.22 Demand conditions are 20

21

22

Also in this case important economists played a crucial role: for instance with Joseph Stiglitz on the European Commission side and David Evans on the Microsoft side. Another antitrust case focused on bundling issues has taken place in South Korea: in 2005 Microsoft had to pay a fine of $ 32 million and produce more than one version of Windows for the country (one with Windows Media Player and Windows Messenger and one without them). However, notice that the initial fixed costs of production are not independent from the future scale of production: higher production requires a better product, which requires higher R&D investments. Moreover, diminishing returns to scale are typical in the production of new software, which may explain why the price of software has not been declining as much as the price of hardware in the last decades.

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more complex. What drives demand is not the traditional concept of product diﬀerentiation, which is of course present, but the development of network externalities: network eﬀects are crucial in the development of a market for an OS and the pricing structure is fundamental to get on board both end users and application developers. Beyond this, a firm producing OSs faces competitors: the entry conditions in the market for OSs are quite debated, but there are good reasons to believe that even though entry into the software market may entail large costs, it is substantially endogenous. First of all, there are already many companies distributing OSs (for instance Solaris by Sun Microsystems, many versions of Unix and Linux, those by Red Hat and Novell), there are many firms producing OSs for related industries (smart phones, PDAs and videogames) which could be scaled-up to run on desktop computers (especially on low cost PCs), and there are even more potential entrants (think of the giants in adjacent sectors of the New Economy, hardware and telecommunications in particular). Second, it is hard to think of a market which is more “global” than the software market: demand comes from all over the world, transport costs are virtually zero, and the knowledge required to build software is accessible worldwide. Nevertheless, it has been claimed that in the market for OSs, the high number of applications developed by many diﬀerent firms for Windows represents a substantial barrier to entry. It is probably true that high quality products make life harder to the competing products, but this should not lead to the conclusion that quality is a barrier to entry, especially in sectors where innovation should drive competition. Moreover, it is true that competitors need to oﬀer a number of standard and technologically mature applications upon entry to match the high quality of the Windows package and create network eﬀects (and some do oﬀer many already), but the cost of oﬀering these applications is unlikely to be prohibitive compared to the global size of this market.23 There are at least two reasons for this. First, notice that the alleged “applications barrier to entry” is often erroneously associated with thousands of applications written for Windows, while it is actually limited to a handful of applications such as word processing, spreadsheet, graphics, internet access and media player software, which really satisfy the needs of most active computer users (McKenzie, 2001). Second, the competitors of Microsoft should not (and the existing ones do not) even finance the development of all the needed applications: they should just fund and encourage 23

There are many examples of markets with network eﬀects where subsequent entrants managed to create network eﬀects and challenge incumbents. Within traditional sectors, examples abound in the fashion industry and many industries where creating new successful brands requires building network eﬀects. In the New Economy a clear example emerges in the case of payment cards (where network eﬀects are crucial, to say the least), which absorbed sequential entry by Diners Club (1950), American Express (1958), Visa (1966), MasterCard (1966) and Discover (1985), to name the most famous actors of this market.

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other firms to write applications for their OSs, or have old applications originally written for other OSs “ported to” theirs, which is what already happens since multi-homing is common practice on the side of software developers.24 In essence, the software market is characterized by network eﬀects, high fixed costs of R&D, constant marginal costs of production close to zero and substantially open access by competitors able to create new software. According to the theory of market leaders, these are the ideal conditions under which we should expect a leader to produce for the whole market with very aggressive (low) prices. Hence, it should not be surprising that, at least in the market for operating systems, a single firm, Microsoft, has such a large market share. We can see the same fact from a diﬀerent perspective: since entry into the software market is endogenous, the leader has to keep prices low enough to expand its market share to almost the whole market. 6.3.1 Why Is the Price of Windows so Low? Many economists agree on the fact that Microsoft sells Windows at an extremely low price. For instance, Fudenberg and Tirole (2000) notice that both sides in the US Microsoft case admit that “Microsoft’s pricing of Windows does not correspond to short run profit maximization by a monopolist. Schmalensee’s direct testimony argues that Microsoft’s low prices are due at least in part to its concern that higher prices would encourage other firms to develop competing operating systems” even if, they add, “neither side has proposed a formal model where such ‘limit pricing’ would make sense.” To verify in the simplest way that the price of Windows does not correspond to the monopolistic price for the OS market, assume for simplicity that the marginal cost of producing Windows is zero, and that the price of hardware is constant and independent from the price of Windows. Demand for Windows is clearly a derived demand, in the sense that it depends on the demand for PCs and on the total price of PCs in particular. Standard economic theory implies that the monopolistic price for an operating system should be the price of the hardware divided by − 1, where is the elasticity of demand for PCs (including both hardware and software): it means that a 1% increase in the price of PCs reduces demand by %.25 Now, this rela24

25

In 2000, it has been estimated that 68 % of software companies developed applications for Windows, 19 % for Apple (which requires adapting to both unique software and hardware), 48 % for various versions of Unix and Linux and 36 % for other proprietary OSs (see Lerner, 2001). Notice that the respective percentages in 1992 were 71%, 12%, 33%and 31%, therefore competing OSs experienced an increase in software developers compared to Microsoft during the 90s. Formally, let us assume that the price of the hardware is fixed and independent from that of the software. Given a demand D(h + w) decreasing in the price of the hardware h plus the price of Windows w, the gross profit of a monopolist in the OS market would be wD(h + w) and would be maximized by a price of

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tionship tells us that, if the basic price of the hardware is € 1000, which is about the current average price for a PC, the monopolistic price for Windows would be other € 1000 if = 2, it would be € 500 if = 3, it would be € 333 if = 4 and so on. Foncel and Ivaldi (2005) estimate this elasticity on the basis of a panel data of all PC brands sold in the G7 countries over the period 1995-1999 and derive a value between = 1.5 and = 3 with a best guess slightly above two. The moral is that it would take really unreasonable values of demand elasticity to even get close to the real price of Windows, which is around € 50.26 Moreover, the above estimate of the monopolistic price is very conservative. In the real world, we can imagine that the price of hardware is not completely independent from the price of Windows: if the latter would double tomorrow, hardware producers would be forced to somewhat reduce their prices (eventually switching to lower cost techniques and/or lower quality products).27 Even if this eﬀect may be limited by the high level of competition in the hardware sector, it works in the direction of further increasing the hypothetical monopolistic price, that is, even beyond the actual price of Windows. Finally, let us remember what we pointed out in our previous discussion on the software platforms: a two-sided platform like Windows earns its revenue entirely from end-users, and not from software developers, which are typically subsidized by Microsoft to develop new and better applications to strengthen network externalities. Hence, the low Windows w∗ such that D(h + w∗ ) + w∗ D0 (h + w∗ ) = 0 or: w∗ =

26

27

h −1

with elasticity of demand. This point was first made by Richard Schmalensee, a testimony in the Microsoft vs. US case on behalf of the Microsoft Corporation (see Schmalensee, 2000). It was criticized by the US Government’s economic witnesses at the trial (see Fisher and Rubinfeld, 2001), who argued that Microsoft did not maximize short run profits, but did actually maximize long run profits taking into account the positive impact of a lower price on network eﬀects. This last point may have been correct for the initial pricing strategies of Microsoft, but it does not explain why the price of Windows has remained so low after two decades. Formally, think that the price of hardware h(w) is decreasing in that of Windows (we could endogenize the actual eﬀect but this is beyond the scope of this discussion). Then, we can rework the monopolistic price of Windows as: w∗ =

h(w∗ ) [1 + h0 (w∗ )] − 1

which is higher that in absence of this translation eﬀect (remember that h0 (w∗ ) < 0): a monopolist would price Windows even more because part of the potential reduction in demand due to a higher price would be avoided thanks to an induced reduction in the price of the hardware.

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price of Windows appears further away from what should be the hypothetical monopolistic price. Hall and Hall (2000) developed similar calculations to the one above assuming Nash competition in quantities in the hardware market and suggested that Microsoft has to adopt a low price for Windows as a rational strategy in front of endogenous entry in the PC market. Their conclusion is consistent with the results of the theory of market leaders and endogenous entry: “not only is the price of Windows brought down to a small fraction of its monopoly price, but the social waste of duplicative investment in operating systems is avoided as well.” It has been claimed that low Windows pricing may be explained with higher pricing of the complementary applications, as the Microsoft Oﬃce suite. However, the combined price of Windows and the average application package sold with it is still below the monopolistic price. Moreover, these applications are not sold at lower prices for other OSs. As Nicholas Economides pointed out: “Windows has the ability to collect surplus from the whole assortment of applications that run on top of it. Keeping Windows’ price artificially low would subsidize not only MS-Oﬃce, but also the whole array of tens of thousands of Windows applications that are not produced by Microsoft. Therefore, even if Microsoft had a monopoly power in the Oﬃce market, keeping the price of Windows low is definitely not the optimal way to collect surplus” (Economides, 2001). What does all this tell us? Simply that Microsoft is not an unconstrained price-setter, while its prices are limited well below the monopolistic price to compete aggressively with the other firms active in the operating system market and with the potential entrants in it. Economides (2001) concludes in a similar fashion: “Microsoft priced low because of the threat of competition. This means that Microsoft believed that it could not price higher if it were to maintain its market position.” The empirical work of Foncel and Ivaldi (2005) supports the same conjecture: “Microsoft seems to behave as if it fears that charging monopoly prices today would cause it to lose substantial profits to competitors in the future.” Indeed, we can say more than just that Microsoft is not a monopoly. What the post-Chicago approach suggested about leaders in markets with price competition was that they should be accommodating and exploit their market power, setting higher prices than competitors, or otherwise engage in predatory pricing and, after having conquered the whole market, increase prices. But in the last 10-15 years of global leadership, Microsoft has done neither of these things. Microsoft has been constantly aggressive, which, according to the theory of market leaders developed in this book, is exactly what a leader under the threat of competitive pressure would do.

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The theory of market leaders has shown that a market leader in these conditions would price above marginal cost in such a way to compensate for the fixed costs of investment and obtain a profit margin (over the average costs of production) thanks to the economies of scale derived from the large (worldwide in the case of Microsoft) scale of production. Its (quality adjusted) price should be below that of its immediate competitors, or just low enough to avoid that they can exploit profitable opportunities in the market.28 The low price of Windows induced by competitive pressure and network eﬀects explains its large market share. As Posner (2001, p. 278) has pointed out acutely, in such a market “a firm may have a monopoly market share only because it is not charging a monopoly price.” The significant preference that customers attribute to Windows even in the presence of good alternative products, some of which are supplied at no charge (!), suggests that Microsoft is still providing the package with the best quality-price ratio in the software market, at least if we believe in the rationality of consumers.29 6.3.2 Does Microsoft Stifle Innovation? It is also important to look at competition in the software market in a dynamic sense, that is competition for the market, as opposed to the competition in the market examined until now. As we have emphasized many times, high-tech sectors can be seen as races to develop new products before others and conquer large market shares with the new products. On the basis of the so-called Arrow eﬀect, we know that incumbent monopolists that do not face endogenous pressure in the competition for the market have small incentives to invest in R&D because, by innovating, they only obtain the diﬀerence between the value of the next technology and that of their current technology, 28

29

IBM initially priced its OS/2 at $ 325 against $ 149 for Windows 3.0. It would be more interesting to compare the price of Windows and Mac OS, but the latter is integrated in Apple computers. However, as Evans et al. (2006) notice, “there is a clue: the 1990 upgrade to Windows 3.0 was $ 50, about half the price ($ 99) of a 1991 upgrade to Apple’s System 7.0. Another useful clue comes from a comparison between computers with similar hardware: in this same period the average price of an Apple PC was over $ 200 more than the average price of a similarly equipped and powerful Compaq PC sold with Microsoft operating systems.” Nevertheless, it is sometimes claimed, also between economists, that there are better OSs that provide better services, and that a lack of information and myopic behavior induce collective hysteresis in the choice of Windows. It is hard to imagine how irrational choices could last so long, and it is even more surprising that economists, always ready to assume rational behavior under the most extreme circumstances, can believe that consumers suddenly become irrational or myopic when choosing software.

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while outsiders obtain the full value of replacing the incumbents. However, the theory of market leaders developed in Chapter 4 has shown that, when leaders face competitive pressure, they are induced to invest more in R&D than any other competitor, with the incentive of defending their leadership from a rapid replacement. Let us look at the incentives to invest in the software market. Of course, the overall expected value of Windows Vista for Microsoft can be quite high, but the net value of replacing Windows XP with Vista has been only a small percentage of that value, especially if we take into account that the real price is not likely to increase and that the introduction of Vista is only gradual (and associated to the change of hardware for most customers). At the same time, the value of developing a successful OS for a competitor of Microsoft is incomparably higher. The Arrow eﬀect would suggest that Microsoft has lower incentives to invest in R&D than the other active firms if further entry in the competition for the OS market is not possible. However, the theory of market leaders replies that this is not the case when entry is endogenous. Accordingly, this supports the idea that only strong pressure in the competition for the market could have led Microsoft to undertake an unprecedented investment to rewrite from scratch, develop and release a brand new OS as Windows Vista. This pressure, we conjecture, comes mainly from the new actors in the software market, the open source community and the commercial companies that are active around this community. At the same time, it is reasonable to conjecture that the wide and fast growing open source community and the commercial companies behind it are investing so much in R&D exactly because they envision the possibility of replacing the leadership of Microsoft. In light of this, the software market appears as a dynamic sector characterized by strong competition for the market and by a leader that is both a source and a cause of innovation, quite the opposite of how it is sometimes depicted. Similar ideas appear behind the words of the leading scholar of the Chicago school on the software industry: “We have seen all manner of firms rise and fall in this industry– falling sometimes from what had seemed a secure monopoly position. The gale of creative destruction that Schumpeter described, in which a sequence of temporary monopolies operates to maximize innovation that confers social benefits far in excess of the social costs of the short-lived monopoly prices that the process also gives rise to, may be the reality of the new economy. This is especially likely because quality competition tends to dominate price competition in the software market industry. The quality-adjusted price of software has fallen steadily simply because quality improvements have vastly outrun price increases” (Posner, 2001, pp 249-50). In spring 2007 Microsoft unveiled a revolutionary new product called Microsoft Surface, a combination of ground breaking software and hardware

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technology that will change the way we interact with digital content.30 Sooner or later the technological leadership of Microsoft in the software market will end, but other companies will have to be more innovative to replace its products.

6.4 Bundling Virtually any product is a bundle, since it combines multiple basic products which could be or are sold separately: drugs bundle diﬀerent molecules, shoes bundle shoes without laces and shoelaces, a car bundles many separate components, a computer bundles hardware, an operating system and basic software applications of general interest. In some cases, bundling is just a contractual restriction used to force customers to purchase an ancillary product in an aftermarket for goods or services, while in other cases bundling improves a finished product by integrating new components or features into it: of course, only the first situation should be subject to antitrust investigation. In all of its main antitrust cases, Microsoft has been accused of abusive leveraging through bundling strategies, first between Windows and the browser Internet Explorer, and then between Windows and the Windows Media Player software. As we noticed in the previous chapter, there are contrasting views on bundling. The Chicago school has advanced eﬃciency rationales in its favor with positive, or at worst ambiguous, consequences on welfare, including production or distribution cost savings, reduction in transaction costs for customers, protection of intellectual property, product improvements, quality assurance and legitimate price responses. In the case of bundling of software applications in an OS, in particular, there are eﬃciencies in internal software design due to componentization and code sharing (which facilitate product development, design and testing), there are network externalities made available encouraging and facilitating the development of applications that rely on a bundled functionality and there are reductions in customer support costs which ultimately lead to cost savings for final end-users, whose experience is also largely simplified by bundling.31 Moreover, according to the Chicago view only eﬃciency purposes can motivate bundling because a firm cannot monopolize another market by bundling two products: according to the so-called “single monopoly profit 30

31

Microsoft Surface is a display in a table-like form that is easy for individuals or small groups to interact with in a way that feels familiar. It can recognize dozens of movements such as multiple touches, gestures and actual unique objects that have identification tags similar to bar codes, it eliminates the need for a mouse and a keyboard and allows multiple users to directly interact through the screen. See Davis et al. (2002).

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231

theorem”, as long as the secondary market is competitive, not even a monopolist in a separate market can increase its profits in the former by tying the two products. Actually, in the presence of complementarities, it can only gain from having competition and high sales in the secondary market to enhance demand in its monopolistic market. A similar idea has been advanced at a theoretical level by Davis and Murphy (2000) to explain the tying strategies of Microsoft: they also emphasize a well known basic principle, for which a monopolist will choose lower prices for two complement goods than the prices chosen by two separate monopolists, which suggests that the bundling strategies of Microsoft reduce permanently the prices of both Windows and the bundled products. Motta (2004) adds that a positive impact on prices emerges also for independent products when there are network eﬀects, because in the secondary market “it might be very diﬃcult to leapfrog the current leader, and a firm that can rely on important R&D, marketing and financial assets might manage to achieve what a small firm might not have.” With particular reference to the US case, Economides (2001) notes that Microsoft could not have been interested in the browser market when this was perfectly competitive, but only when this market became dominated by Netscape for two main reasons. “First, Netscape had a dominant position in the browser market, thereby taking away from Microsoft’s operating system profits to the extent that Windows was used together with the Navigator. Second, as the markets for Internet applications and electronic commerce exploded, the potential loss to Microsoft from not having a top browser increased significantly... Clearly, Microsoft had a pro-competitive incentive to freely distribute IE since that would stimulate demand for the Windows platform.” The very same point could be made for the more recent bundling of Media Player with Windows oﬀers a very low price.32 Actually, this motivation for bundling Windows and Media Player (aimed at increasing the attractiveness of the former and promoting applications for the latter) appears the main direct driver in the European case. Today there are no serious threats on Windows that could come from an alternative media player software (while browsers could represent a potential threat for Windows in the mid 90s). However, there is a diﬀerent class of motivations for bundling that we need to examine: these are the indirect or strategic motivations. 32

Notice that, since at the time of launch we were in front of cases of pure (and not mixed) bundling, we do not know the implicit prices of IE and MediaPlayer in the bundled versions of Windows. However, they must have been quite low or close to zero because there were not apparent increases in the price of the new versions of Windows. Moreover, the recent unbundled version (without Media Player) is sold at the same price as the bundled version.

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6.4.1 Strategic Bundling The post-Chicago approach has shown that, when the bundling firm has some market power in the primary market, commitment to bundling can only be used for exclusionary purposes since it enhances competition in the secondary market and increases the profits of the leader only if it excludes rivals from this secondary market (Whinston, 1990). Nevertheless, even the same proponent of this theory has expressed doubts on its applicability to the case of Microsoft: evaluating the tying of Windows and IE, Whinston (2001) notes that “Microsoft seems to have introduced relatively little incompatibility with other browsers. Since marginal cost is essentially zero, bundling could exclude Netscape only if consumers, or computer manufacturers for them, faced other constraints on adding Navigator to their system”, which did not appear to be the case. The same holds in the case of Windows Media Player. It is true that Microsoft bundling in both markets reduced the average prices of browsers33 and media players, but this did not lead to the deterrence of entry (new successful browsers such as Firefox have appeared). As we have formally shown (in Section 2.10), the theory of market leaders emphasizes that when entry in the secondary market is endogenous, an incumbent can gain from bundling exactly because this creates a sort of commitment to apply a low price to the bundle as a whole, which may end up increasing the overall profits for the leader (compared to those obtained only in the primary market without bundling). Nevertheless, the price of the two goods together would be reduced and entry of alternative secondary products would be still viable. This kind of rationale for bundling is more likely to emerge when there are some complementarities between the products, or there are unexploited network eﬀects (which can be enhanced through bundling); ultimately, even sales and profits in the primary market may increase. What matters for our purposes is that bundling is not an extreme strategy adopted by an incumbent firm to deter entry, but a standard aggressive strategy that, by reducing the final prices, may indeed reduce entry of followers, without excluding entry overall. As a matter of fact, under some level of product diﬀerentiation, the impact on the competitors is quite limited and only marginal firms of the secondary market would be driven out of it. Hence, in a world of price competition, it appears hard to conclude that bundling could be used as a predatory strategy when it does not even lead to the exit of all the competitors, but just to a permanent reduction of the price level. 33

Netscape charged many private and corporate users for its browser until started facing substantial competition. Prices ranged between $ 39 in 1995 to $ 79 in 1996 for a premium version. This was quite a high price if we think that the average price of the entire OS Windows was in this same range during those years.

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233

To sum up our general point, when approaching a bundling case we suggest verifying the entry conditions of the secondary market. If there is a dominant firm in this market as well, the main problem is not the bundling strategy, but the lack of competition in the secondary market, and it should be addressed within that same market: punishing the bundling strategy would just guarantee the monopolistic (or duopolistic) rents of the dominant firm in the secondary market. However, things are diﬀerent when the secondary market is not monopolized but open to endogenous entry (even if it is not perfectly competitive, in the sense that firms do not price at marginal cost). In such a case, and especially in the presence of product diﬀerentiation, bundling is a pro-competitive strategy and punishing it would hurt consumers. In the case of Microsoft, in both bundling situations, that of Windows with Internet Explorer and that of Windows with Media Player, the tied market was characterized by endogenous entry. Paradoxically, this became even more evident since Microsoft entered in these markets: just think of new successful browsers as Mozilla Firefox, Netscape, Safari, Opera, Konqueror and media player software as RealPlayer, Apple’s QuickTime, Adobe’s Flash, MusicMatch and many others.34 Consequently the bundling strategy of Microsoft could be simply seen as an aggressive and competitive strategy of a market leader active in a secondary market where entry is indeed endogenous. Moreover, in these markets the standard strategy is to provide free software to enhance network eﬀects and earn from externalities associated with the use of the software (a typical strategy in multisided markets, as we have seen). For instance, in the case of digital media platforms, Microsoft looks for network eﬀects on licenses of its OS, Real earns from content subscriptions, Apple from sales of digital audio and video devices (the iPod and, in perspective, the iPhone)35 and Adobe from Flash server sales. Even if these companies adopt very diﬀerent business models, competition is quite intense especially because multi-homing is common practice: end users typically use multiple media players (that are characterized by a certain degree of hori34

35

Entry in the market for software applications is definitely easier today, since most software is installed through on line downloading in a few seconds. Since most PCs are endowed with a browser (which, ironically, is largely due to Microsoft bundling IE with Windows), the market for software applications has become one of the most transparent and competitive. This implies diﬀerent levels of platform integration and interoperability with diﬀerent platforms. As Evans et al. (2006) noticed: “At one extreme is Apple. Its iPod/iTunes platform is integrated into the hardware and content-provider sides of the media platform, and its doesn’t interoperate with any other platform. At the other extreme is Microsoft, whose media platform is integrated into neither hardware nor content and which interoperates with all other media platforms that allow it to do so. In the middle are vendors like RealNetworks, which limit interoperability - but not completely - and integrate - but only partially - into the content provider side.”

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zontal diﬀerentiation), and also PC manufacturers typically install multiple competing mediaplayers at their will (while this is not the case for digital music devices and mobile phones). Finally, multi-homing is a clear symptom that media players are horizontally diﬀerentiated (some are better for music content, others for videos, others for storing files, and so on): from our previous discussion on bundling for secondary markets with endogenous entry and product diﬀerentiation, it follows that these are precisely the conditions under which bundling assumes a competitive nature rather than a predatory one. 6.4.2 Technological Bundling Beyond the debate on the nature of the strategic reasons for which firms may engage in bundling strategies, there are technological reasons why bundling may emerge. These have typically been at the base of Microsoft defense in its antitrust cases. In dynamic markets like the software market, the same concept of a good is changing over time, since both demand and supply change. If demand by PC users for media player functionality was limited just a few years ago, now it appears that these functionalities are an essential component of an OS. Because of this, an increasing number of software applications and on line services are associated with media player functionalities, so that demand is strengthened by network eﬀects. If supply of media player functionalities was ineﬃcient through bundling a few years ago, and it was mostly left to specific add ons, improvements in hardware processing power, in the cost of hard disk storage and random access memory, and in the streaming technology made it simple and eﬃcient to bundle media player functionality within current OSs. As a consequence of this, bundling has a natural technological rationale and should emerge endogenously when the size of demand is large enough and the cost of supply is low enough. In other words, while a few years ago an OS and a media player could be regarded as separate goods whose union could be associated with a bundling strategy, nowadays an OS must incorporate media player functionalities (as it must incorporate a browser) so that we cannot even talk of a traditional form of bundling.36 36

This is common for software. For instance, word processors and spell checkers were in separate markets many years ago, not today. Voice recognition is separate today, but we can expect that it will be integrated in word processors at some point. Navigators for cars are still optional tools in the automobile industry, but are likely to become essential components in the near future and bundle new applications and new content. At the same time, videogame consoles and PCs are likely to enter in the television ecosystem and bundle new features and capabilities in the attempt to gain the socalled “control of the living room”. In a sense, bundling creates new industries and is a source of competition for the market in itself.

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In this perspective, attempts of antitrust authorities to stop or delay the evolution of OS through additional features, as browsers and media players, appear quite dangerous: while it is diﬃcult to verify in which moment it would be optimal to bundle secondary products in an evolving primary product, it is not clear why antitrust authorities should have a better guess than market driven firms. Notice that since the 2004 Commission’s decision, Microsoft had to prepare and commercialize a version of Windows without Media Player in Europe.37 Demand for the version of Windows without Media Player has been virtually zero in Europe, a likely sign that Microsoft bundling strategy was at least not hurting consumers.

6.5 Intellectual Property Rights In the previous chapters we discussed the role of market leaders in innovative markets and the importance of the protection of IPRs in stimulating investment in R&D and technological progress. Both aspects are quite relevant in the understanding of the dynamics of the software market and the Microsoft case. The software market is a major example of an industry where competition is mainly for the market, and in such a case, as we have seen, large market shares by single firms are a typical outcome. The counterpart of this, of course, is that these industries can exhibit catastrophic entry where innovators can replace current leaders quite quickly. As we noticed in Chapter 4, in such an environment, it is exactly when competition is open that leaders have incentives to invest deeply to retain their leadership. On the contrary, when competition for the market is limited, technological leaders are able to have a quiet life, invest less in R&D and accept the risk that someone will come up with a better product. When competition for the market is open, this same risk is too high and incumbents prefer to accept the challenge and try to innovate first: this leads to a more persistent leadership. When entry is endogenous, innovation by leaders creates a virtuous circle that also has important implications for the way we can evaluate such a market (see Section 4.3). The endogenous persistence of the technological leadership has a value that creates incentives for all firms to invest even more, which in turn strengthens the same incentives of the leader to invest and retain its leadership, and so on. In other words, persistence of leadership is a source of strong competition for the market (through investments in R&D to replace the current leader), and, given that leaders have higher incentives to invest as long as the race to innovate is open, we can also conclude that 37

The version of Windows XP without Media Player was called Windows XP N, a choice of the European Commission between nine potential names submitted by Microsoft.

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strong competition for the market is a source of persistence of leadership. This circular argument may appear paradoxical, but is the fruit of a radical distinction between static and dynamic competition: once again, there is no consistent correlation between market shares and market power in dynamic markets. The endogenous multiplicative eﬀect of the value of leadership that we have just summarized implies that in dynamic markets the rents of a leader may be spectacularly larger than those of its competitors, and the market value of a leadership may be extremely large even if the market is perfectly competitive in a dynamic sense (see Segerstrom, 2007, for a related point). In our view, this is something not too far from what we can see in the software market and in the leadership of Microsoft, but also in many other high-tech sectors. 6.5.1 Patents, Trade Secrets and Interoperability The source of the value of innovation, the starting point of the chain of value that we just described, must be a fundamental rent associated with innovations and protected through IPRs. Hence, all forms of IPRs are the ultimate source of leadership, innovation and technological progress. As we already noticed, the role of patent legislation is exactly to trade oﬀ the benefits of patents in terms of incentives to innovate with the costs related to temporary monopolistic pricing. In our opinion, there is no reason why antitrust authorities should interfere with this legislation when patent protection appears inconsistent with other goals. And even if these goals are legitimate and relevant, introducing a discretionary evaluation of IPRs would create uncertainty and jeopardize the investment, which, after all, goes against the ultimate objective of the same antitrust authorities. Nevertheless, in the Microsoft case the EU Commission has taken this dangerous direction, asking Microsoft to disclose a wide amount of technologies.38 More recently (Statement of Objections of March 1, 2007), the Commission has asked to make them available royalty free unless they have 38

At the beginning of the Appeal on the Microsoft case on April 24, 2006, the author of this book expressed a similar concern in an interview for La Libre Belgique: “Microsoft a été forcé de révéler certaines informations pour assurer l’interopérabilité entre Windows et d’autres systèmes d’exploitation. Mais les demandes de la Commission Européenne ne sont toujours pas claires; elle ne cesse de réclamer plus de la part de la firme américaine. Microsoft a révélé récemment le code source de son système Windows: c’est la documentation ultime du software. Que peut-on encore demander de plus? L’impact de cette décision serat-il négatif ? Le débat économique futur va porter sur les gains qui résultent du fait que l’on a forcé une entreprise à révéler des secrets technologiques protégés par copyright... Mais y a-t-il des gains? Devait-on le faire? Sur le long terme, c’est contre-productif. Qui va investir dans l’innovation et dans la recherche si

6.5 Intellectual Property Rights

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an innovative nature (meaning that they involve an inventive and novel step compared to the prior art).39 Finally, it has started questioning the same innovative nature (and with it the license pricing) of most technologies that Microsoft was forced to disclose, technologies which are also covered by many patents approved by US and EU patent oﬃces. This creates an even stronger contradiction between patent law and antitrust policy in the EU, and also a substantial divergence between the US approach to IPRs and the EU approach, with the former much more careful in protecting IPRs and promoting R&D. It is important to add that new ideas, including those underlying Microsoft software, are not protected only with patents. Not all inventive and innovative activities fall under the scope of patentability and it is not always in the interest of a firm to patent every single innovation. In most high-tech sectors, firms adopt a combination of patents and trade secrets to protect products that are the result of multiple innovations. Defending (intellectual or material) property rights is one of the fundamental conditions for proper functioning of the market economy: defending trade secrets should not play a minor role in this context. Some of the most famous trade secrets are the formulas of Coca-Cola, Chanel No. 5 and Campari. Consider the first example and imagine that Coca-Cola was required to disclose its secret formula: anyone could reproduce the very same drink, “clone” it under a diﬀerent name if you like, but it is hard to believe that this would create large gains for consumers. Close substitutes to Coke already exist and there are small margins to substantially reduce prices. However, the incentives for any other firm in the same industry to invest and create new products could be drastically reduced if trade secrets were not protected.40 High-tech sectors are more complicated. In these sectors, patents and trade secrets often cover fundamental inventions and protecting those inventions amounts to promoting innovations that today are the main engine of growth. In some fields, however, there maybe, at least apparently, a trade-oﬀ between trade secret protection and “interoperability” between products -

39

40

les droits de propriété intellectuelle sont bafoués? On crée un dangereux précédent d’autant que l’industrie de haute technologie est souvent caractérisée par des investissements massifs en recherche et développement” (Contre-productif, dangereux pour l’innovation et la recherche, by Martin Buxant). Notice that these are features needed for patentability, but not for trade secrets, which may just protect technologies that are not novel or innovative, but nevertheless developed with eﬀort and costs. Therefore, the most recent approach of the Commission forces disclosure of similar technologies, and excludes at the same time that they could be licensed for a positive royalty: this is a way of denying de facto the right of protection of trade secrets. See Kanevid (2007) for a related analysis of compulsory licensing. On the story of Coke’s trade secret and its implications see Etro (2005,c).

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broadly speaking, this is the ability of heterogeneous information technology systems, components and services to exchange and use information and data, especially in networks. Interoperability is important in the PC industry and, as we have seen in Section 6.1, the level of interoperability has strongly increased in the last decades. Problems arise, however, when interoperability is confused with “interchangeability” or with a right to clone the innovations of the competitors. For instance, take in consideration the leading on line search engine in the world, Google. We may look at Google’s patented innovations, starting with the 2001 patent on the invention of the PageRank by Larry Page (founder of Google with Sergey Brin),41 but we would need to know its trade secrets to fully discover the mechanism of its precious algorithms. Forcing disclosure of such trade secrets would help many software companies and websites to interoperate with Google even better than they already do, as it would allow other search engines to improve their performances compared to that of the leading search engine. But after that, surely, few companies would invest huge resources and take substantial risks to create a better search engine or other brilliant ideas like Google when they can just free ride on others’ ideas and/or they can’t be sure of their return. The same argument would apply for the trade secrets of Microsoft or Apple on the source codes of their OSs and to many other trade secrets of innovative leading companies. Any forced disclosure of similar trade secrets represents an expropriation of legitimate investments and establishes inappropriate legal standards with perverse eﬀects on the incentives to innovate. 6.5.2 Licenses and Standards Fortunately, giving up the precious role of IPRs in promoting innovations is not the only way to solve interoperability challenges. The market can do it much better: valuable ideas can be selectively commercialized on a voluntary basis through licenses, for instance under RAND (reasonable and non discriminatory) terms, a type of licensing typically used during standardization processes to promote the rapid adoption of standards and new technologies 41

The abstract of US patent 6285999 (filed in 1998) for a method for node ranking in a linked database, reads as follows: “A method assigns importance ranks to nodes in a linked database, such as any database of documents containing citations, the world wide web or any other hypermedia database. The rank assigned to a document is calculated from the ranks of documents citing it. In addition, the rank of a document is calculated from a constant representing the probability that a browser through the database will randomly jump to the document. The method is particularly useful in enhancing the performance of search engine results for hypermedia databases, such as the world wide web, whose documents have a large variation in quality.” Of course, by now, this is just the beginning of Google’s ranking mechanism.

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and to encourage entry. The RAND terms include a definition of reasonable royalties, and can include further restrictions as field-of-use clauses (that allow licensees to utilize a patented technology in a use that is directly related to the implementation of the standard), reciprocity clauses, or limits to sublicensing.42 Coase (1960) has clarified that whenever there is social value to generate, the market will properly allocate all the property rights. This is also true for the intellectual property rights: market mechanism can allocate them efficiently, insure the accessibility of the information that fuels interoperability and acknowledge legitimate ownership rights of the innovators, so as to enhance R&D investments.43 Suppose firm A invests, innovates and obtains a patent, and firm B has a new idea to improve firm A’s innovation, but this idea cannot be used without infringing the patent. Of course, forced interoperability would lead firm B to implement its idea. However, in such a case firm A will not invest to start with, and no idea will be actually implemented. Consider now private agreements between the two firms. First, firm A could license its patent to firm B for a price between the expected profits that A and B can respectively obtain from marketing alone their respective ideas. The price depends on the respective bargaining power, the best idea is implemented, and firm A has all the interest to invest ex ante. Second, firm B could sell its idea to firm A at a price at most equal to the diﬀerence in expected profits that firm A can obtain respectively with firm B’s idea and without it, with the price again depending on the bargaining power. Also in this case the incentives for firm A to invest ex ante would be preserved. This suggests that it may often be a unique firm to buy others’ innovations (especially if this firm has developed a comparative advantage in marketing products), and it may often happen that only outsiders take the initiative to invest in new fields with the aim of reselling their innovations.44 This is indeed the way technological progress evolves in many industries under protection of IPRs. Finally, in the presence of network eﬀects, dynamic market forces can do even more: as long as IPRs are well protected and firms can invest with the safe confidence that successful innovations will be rewarded, market forces can select the best standard when multiple standards are available and interoperability is only partial. Liebowitz and Margolis (1999) have shown that 42

43

44

Notice that extreme open source licenses can create frictions with RAND terms associated with other licenses, so as to jeopardize useful innovative activity this is the case of the GNU General Public License, which is incompatible with technologies licensed with any positive royalty, field-of-use limitations or other standard restrictions. See Scotchmer (2004, Ch. 6) on an interesting discussion on licensing, R&D joint ventures and antitrust policy. This also suggests that in the presence of sequential innovations, primary innovations deserve stronger patent protection than later ones, since their social value is higher.

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this is the case in many episodes. For instance, in the adoption of the common QWERTY keyboard for PCs (so-called from the first five letters on the top left): for years it has been claimed that the allocation of letters of this keyboard was an ineﬃcient standard, while these researchers found that evidence suggests that the Qwerty keyboard, somehow selected by the market, is not worse than any other alternative.45 In conclusion, also in this field, markets can properly balance the short run and long run interests of consumers better than policymakers: promote innovation, enable an eﬃcient degree of interoperability and select the best standards. It would be better to leave the ruling of intellectual property protection and of its limits to the legislative level rather than creating an important precedent for which antitrust authorities could force firms to reveal their IPRs. Much of the residual contrast between Microsoft and the European Commission depends on the approach to interoperability and on its ambiguity. The Commission’s 2004 antitrust decision mandated the licensing of intellectual property to enable full interoperability between Windows PCs and work group servers and competitor products. This mandate has turned out to be the most problematic in the case. The picture that is emerging is of a Commission that has continued to extend the scope of the information required, and more recently has also tried to control Microsoft pricing (a tool of regulatory authorities, not of antitrust ones), while not spelling out exactly what would constitute compliance with the remedy. Microsoft has been forced to licence more than a hundred technologies, and it has even made available to its competitors selective access to the source code of Windows. Nevertheless in Europe (diﬀerently from the US), not one of its competitors has taken out a license, a likely sign that the existing level of interoperability is not as low as it was depicted.46

6.6 Conclusions In this chapter we have focused our attention on the New Economy, which was developed in the last decades around the PC industry and the Internet. The New Economy has spread rapidly all over the world thanks to what 45 46

Another example is VHS winning out over Betamax for home video recording. One could read the facts in a more negative way. The long eﬀort of the EU Commission to force Microsoft to reveal its technologies at better terms may prevent European firms from licensing any technology at the current terms until the case will be solved. We believe that an antitrust authority that decides the name of the products of a private company (as for Windows XP N), forces public disclosure of its IPRs, and tries to decide its prices as well, is well beyond the limits between antitrust policy and regulatory policy. See Mastrantonio (2005) for an interesting analysis from the law & economics point of view.

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we are used to call globalization. Markets in the New Economy work in a radically diﬀerent way from markets in the Old Economy. First of all, while traditional sectors are often characterized by competition in the market with substantial product diﬀerentiation and U-shaped cost functions, many markets of the New Economy are often driven by competition for the market taking place through high fixed costs of investment in R&D, and production is typically characterized by small and constant marginal costs. Beyond this, many markets of the New Economy exhibit network eﬀects and are often multi-sided, in the sense that firms act as platforms for diﬀerent types of customers with complex network eﬀects between them. These strong diﬀerences require a new approach to the analysis of markets and of the behavior of their leaders. In the absence of such a new approach, it is not surprising that in the last years the attention of antitrust authorities around the world has been often biased against market leaders in the sectors of the New Economy. These dynamic sectors are certainly not less competitive than others, but are often characterized by large market shares for their leaders and aggressive strategies which are the symptom of heavy competition. Leaders might enjoy high market shares yet be subject to massive competitive pressure to constantly create better products at lower prices due to threats from innovative competitors and potential entrants. Following our theoretical analysis, in this chapter we tried to argue that the behavior of leaders as Microsoft and other firms of the New Economy can be better interpreted through the concept of Stackelberg competition with endogenous entry.

7. Epilogue

The objective of this book is to develop a theory of market leadership and endogenous entry. In the previous chapters we analyzed the choice of strategic investments before competition takes place and analyzed first mover advantages under competition in the market where quantities or prices are the strategic variables, and under competition for the market where investments in innovations are the strategic variables. We compared the results in the presence of exogenous and endogenous entry, and we used this theoretical framework to derive normative implications for antitrust policy. In this final chapter we will mainly focus our attention on the descriptive implications of the theory of market leadership and endogenous entry. In Section 7.1 we point out the main empirical predictions of our theory that need future empirical investigations, in Section 7.2 we emphasize a few principles of business administration emerging from our analysis, and in Section 7.3 we suggest directions for future theoretical research. In Section 7.4 we conclude.

7.1 Empirical Predictions of the Theory of Market Leaders The primary empirical implications of the theory of market leaders concern the discrimination between alternative strategies adopted by market leaders facing an exogenous or an endogenous number of competitors.1 Therefore any empirical investigation of our results should be based on a non-trivial analysis of the entry conditions.2 Some markets are clearly characterized by 1

2

A good introduction to empirical studies of industrial organization can be found in Martin (2002). Most of the empirical work on the reaction of incumbents to entry takes entry as given. The problem of endogeneity of entry is briefly discussed in Thomas (1999), who examines the reactions of incumbents in the US ready-to-eat cereal industry. He finds that incumbents are accommodating between themselves, but they adopt aggressive pricing to face new entrants. This result may be due to the typical behavior of market leaders facing endogenous entry: while price competition would lead leaders to be accommodating when facing an exogenous number of firms, an aggressive pricing strategy is forced by endogenous entry.

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exogenous constraints on the number of firms: for instance, when there are legal barriers to entry, when only a restricted number of firms have licenses, patents or other essential inputs needed to produce a certain good or service, or when a certain activity is confined to a predetermined number of subjects with special permission, we are in front of a market where the number of competitors is exogenous. Some other markets are clearly characterized by entry open to domestic and international firms that changes over time, reacts rapidly to variations in demand and supply conditions, and reduces to zero the supra-normal profits of the marginal entrants: when this is the case, we are in front of a market where the number of competitors can be regarded as endogenous. In other markets the situation is not so clear, therefore we need to add a few remarks to clarify how one could approach the concept of entry in an empirical investigation aimed at testing the theory of market leaders. First, there are markets in which processes of liberalization or deregulation have radically changed the entry conditions, from a situation with a fixed number of competitors to one with endogenous entry: these shocks may represent interesting natural experiments for a test of our theory.3 Other exogenous shocks leading to entry of new firms may create interesting natural experiments.4 A related situation emerges in markets with IPRs: when a 3

4

Spiller and Favaro (1984) have studied the behavior of market leaders in the process of deregulation of the commercial banking sector (with data on the Uruguay experience in the late 70s). The “results are consistent with a von Stackelberg type of industry where the degree of oligopolistic interaction among the leading firms is reduced as a consequence of the relaxation of the legal entry barriers.” In recent times, it would be interesting to verify the impact of online banking, which has dramatically increased entry (also of international banks) and competition in the banking sector of many countries: in such a case, the theory of market leaders would imply the emergence of leaders oﬀering better conditions on savings accounts (think of the Orange Savings Account by ING Direct). Goolsbee and Syverson (2006) have examined how incumbents respond to the threat of entry of competitors. They use a case study from the American passenger airline industry, namely the evolution of Southwest Airlines’ route network between 1993 and 2004, to identify routes where the probability of future entry rises suddenly for major US carriers as American, Continental, Delta, Northwest, TWA, United and US Airways. Notice that this is a market characterized by a limited degree of product diﬀerentiation (mostly driven by frequent flyer miles programs), by U-shaped cost functions, and by competition in prices between airlines active on each route. When Southwest begins operating in airports on both sides of a route but not the route itself, the probability that it will start flying that route in the near future increases. Examining the pricing of the incumbents on threatened routes in the period surrounding these events, and controlling for a number of airport-specific operating costs, it emerges that incumbents cut fares significantly when they have faced an exogenous number of competitors in the

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patent or a copyright expire, endogenous entry suddenly takes place, and the eﬀect on the behavior of the incumbents could be used to test our results.5 Another interesting situation that could be used for empirical purposes emerges in markets that, after a period of protection from international competition, are opened to entry of foreign firms: this represents another experiment in

5

past, but expect endogenous entry in the future. More exactly, 3 to 4 quarters before Southwest starts its operations on a new route, the fares of the market leader on that route have fallen about 7 %, and by 1 to 2 quarters prior, they have fallen 10 %, while when Southwest actually starts operating, prices are almost 12 % lower, and after entry the total drop in fares is about 26%. However, price cuts (in the run up to Southwest starting operations) are absent in lowconcentration routes, that is in the routes where, most likely, entry was already free. Furthermore, the empirical analysis of Goolsbee and Syverson (2006) reveals a switch toward the aggressive behavior of market leaders facing endogenous entry and without exclusionary purposes. They test whether there are diﬀerences between the reactions of incumbents when pre-emptive deterrence is possible (Southwest’s entry is likely after starting operations on both sides of a route, but could be avoided through price cuts) and when it is not (Southwest’s entry in the route is announced simultaneously with its start of operations in the airport). The pricing strategies of the incumbent are quite similar in the two samples, and the conclusion is that “even on routes where deterrence is impossible, the incumbents engage in the same pre-emptive price cutting behavior. Thus the behavior cannot be motivated as seeking to deter entry.” Following the traditional theory of price leadership which generates an accommodating behavior of the leaders, Goolsbee and Syverson (2006) are forced to conclude that “the firms are instead accommodating entry”, which can be quite misleading since these leaders are radically reducing their prices rather than increasing them. The paradox disappears once we realize that we are in front of price leaders facing endogenous entry, and that our theory tells us that these leaders should be aggressive and also reduce their prices when they are not trying to deter entry. A similar experiment, which could be re-interpreted in the terms of our theory, is in Ellison and Ellison (2007). They examine the behavior of market leaders in the pharmaceutical industry in the periods around the expiration of patent protection for their patented drugs. Advertising by incumbents declines before entry occurs. Drug prices always decline when entry occurs, and also before the expiration of the patent, but only if the probability of entry is high. Again, these preliminary results are consistent with an aggressive strategy by the leaders, which is induced by endogenous entry. Bergman and Rudholm (2003) examine the Swedish pharmaceutical market where the commitment to a low price is enforced by a particular regulation (for which, if a price is reduced, it is impossible to increase it again). They show that the prices of the incumbent leaders fall at the time of the patent expiration (even before actual entry occurs) by 5-8% for products with small sales volumes.

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which endogenous entry suddenly takes place.6 In all of these examples, one can compare the behavior of market leaders relative to the behavior of the followers before and after endogenous entry takes place. Ideally, any empirical methodology should control for the diﬀerences between the leader and all of the other firms (our basic testable predictions refer to the behavior of leaders facing competition from equally eﬃcient firms).7 Second, there are intermediate situations in which entry can be regarded as exogenous in the short run, but endogenous only in the medium-long run simply because entry takes time. This time can be diﬀerent in diﬀerent sectors: rather than being a limit to the testability of the theory of market leaders, this variability in the degree of reactivity of entry to profit opportunities could be exploited as a useful control variable, especially if one has good instruments available to identify the entry conditions.8 Third, one has to take into consideration entry in the competition in the market but also entry in the competition for the market: the former is visible and active in the same market, while the latter is often not visible because firms may be eﬀectively competing for a market and investing in R&D, but they will not enter in the market until they actually develop a successful product. Fourth, one has to distinguish between eﬀective entry and potential entry: while the former is visible and the latter is not, the existence of potential entry is the essential element of a market in which entry is endogenous compared to a market in which the number of competitors is exogenous. Another important preliminary issue concerns the form of competition in the market. It is well known that the diﬀerence between competition in prices and in quantities is more a theoretical abstraction than a clear-cut element of diﬀerentiation between sectors. However, there are some markets in which price choices are an essential component of competition, and others where production decisions determine, to a large extent, the equilibrium 6

7

8

In a similar vein, Scherer and Keun (1992) looked at the increase in high-tech imports in US and found that incumbents in sectors without barriers to entry react more aggressively to endogenous entry, increasing R&D/sales more than other firms. Thomas (1999) has studied the behavior of incumbents in the ready-to-eat cereal industry, which is characterized by competition in prices, product diﬀerentiation and large advertising. The main result is that “incumbent firms accommodate one another on price but respond aggressively using advertising. Entrants on the other hand are more likely to be met with an aggressive price response.” The diﬀerence in the behavior of market leaders may indicate a switch in strategy from a situation with an exogenous number of competitors (the incumbents) and a situation where entry (of new firms) is endogenous. In this perspective, a good empirical strategy to measure the entry conditions, would involve measuring the likelihood of entry in a market and estimating its determinants.

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price: markets for highly diﬀerentiated goods typically belong to the first group, while markets for homogenous goods belong more often to the second group. These broad diﬀerences should be kept in mind when comparing results from diﬀerent markets. This is particularly important because, as we have seen repeatedly, entry conditions can fundamentally change the behavior of market leaders under competition in prices. Furthermore, when firms compete in multiple strategies, it is important to understand which preliminary investments or commitments can substantially aﬀect competition: the diﬀerent behavior of market leaders in undertaking strategic investments compared to other firms is a crucial element of the theory of market leaders.9 Finally, our predictions refer to the behavior of market leaders versus the behavior of their followers, and the definition of leaders and followers requires some additional specifications. In this case, market shares can be useful because it is normal to associate first mover advantages to the leading firm in terms of market share. One may consider more than one firm as a leader according to the sector under consideration: our analysis has shown that multiple leaders would tend to replicate the behavior of a single leader. Of course, there can be diﬀerences between firms that are beyond the strategic advantages: for instance costs diﬀerences, diﬀerences in product quality or locational diﬀerences. Since our results refer to symmetric firms from a technological point of view, these exogenous diﬀerences should be used as control variables in the analysis. Given these short but important methodological premises, in what follows we will list some of the empirical predictions of the theory of market leaders that distinguish between markets with an exogenous number of firms and markets with endogenous entry. In Chapters 1 and 3 we have seen that, with competition in the market, endogenous entry turns market leaders into more aggressive players compared to a situation in which all firms (leaders and followers) do not face entry threats. In particular, our analysis allows one to discriminate a radical change of strategy under competition in prices: when the number of firms is exogenous, market leaders should choose higher prices than the followers, 9

Röller and Sickles (2000) have performed the first empirical study of a twostage competition with preliminary investment in cost reducing capacity. They considered the European airline industry in the period 1976-1990, before the recent liberalization eﬀorts. On the basis of a panel of the largest carriers (Air France, Alitalia, British Airways, Iberia, KLM, Lufthansa, SABENA and SAS) and a large dataset on cost, network and demand data, they have shown that airline companies behaved as puppy dogs: underinvesting in capacity to keep high prices. It would be interesting to compare that situation with the current situation in which EU liberalization is promoting the entry and competition: according to our the theory of market leaders, we would expect leading carriers to turn into top dogs and overinvest in capacity to reduce their relative marginal costs.

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when entry is endogenous they should choose lower prices. This strong implication does not necessarily hold when firms compete in quantities, but in all cases we would expect that the price of the leaders decreases compared to the price of the followers when endogenous entry occurs. Therefore, our first testable implication is a weak one and can be expressed as follows: P.1a : The gap between the price of the leaders and the average price of the followers decreases with entry. When this prediction is satisfied in the data, one can look at the stronger result, which is supposed to hold for markets with competition in prices, and test the following implication: P.1b: Market leaders facing exogenous entry choose higher prices than the followers; market leaders facing endogenous entry choose lower prices than the followers. Of course, the stronger hypothesis P.1b implies the weaker hypothesis P.1a, while the opposite is not true. Eventually, one could test further predictions of the basic model of Stackelberg competition with endogenous entry. For instance, in the presence of homogenous goods, increasing marginal costs, and competition in quantities we would expect that the equilibrium price corresponds to the marginal cost of the leader but it is higher than its average cost, while the same price is above the marginal cost of the marginal entrant but just enough to match its average cost. This is consistent with positive profits for the leader and endogenous entry. When one introduces product diﬀerentiation, also the equilibrium price for the leader is above its marginal cost according to a mark up which increases in the degree of product diﬀerentiation, but the equilibrium price of the followers is still equal to their average cost. These predictions could be tested against other hypotheses using the tools of the new empirical industrial organization,10 and are summarized as follows: P.2: In a sector with homogenous goods and increasing marginal costs, the equilibrium price of a market leader facing endogenous entry is equal to its marginal cost and above its average cost, and the equilibrium price for the marginal entrant is above its marginal cost and equal to its average cost; an increase in product diﬀerentiation increases the equilibrium price above the marginal cost of the leader. Let us move to the case of strategic investments by market leaders. In Chapter 2 we have seen that, with competition in the market, entry conditions aﬀect the way leaders undertake preliminary investments. In particular, using the classic taxonomy of business strategies, we have seen that leaders facing endogenous entry always act as top dogs or with a lean and hungry look, 10

See Bresnahan (1987) and Berry et al. (2004) on the US automobile market, and Kadiyali (1996) with particular reference to entry deterrence and accommodation in the US consumer market for photographic film in the period 1970-1990, when Kodak was the leader and Fuji the follower.

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and never as puppy dogs or fat cats: ultimately, they are always aggressive compared to the entrants in the competition in the market, which is in line with the previous results. Between the many commitments we analyzed, some can be particularly interesting for empirical investigations. For instance, we analyzed cost reducing and demand enhancing investments. From the first category we obtained neat predictions (leaders invest more in cost reducing activities when facing endogenous entry), and later we will revisit them again when dealing with more general forms of investments in R&D. From the second category we obtained results that depend crucially on the kind of demand enhancing investments under consideration. Consider product quality. Here, our focus will be on the implications of the theory of market leaders in the presence of a double choice on both the quality and the price of the products. Summarizing the strategies with the quality-price ratio, a strong prediction deriving from our characterization (based on Prop. 3.9) would be the following: P.3: Market leaders facing an exogenous number of firms choose a lower quality-price ratio than the followers; market leaders facing endogenous entry choose a higher quality-price ratio than the followers. Given the complex strategic interactions emerging in a situation where firms choose multiple variables, it could be reasonable to limit the analysis to a weaker implication like the following: the quality-price ratio of the leaders increases with entry compared to the quality-price ratio of the followers. Another form of demand enhancing investment is the expenditure on nonprice advertising aimed at increasing demand. If we focus on markets with product diﬀerentiation and competition in prices, our theory (Prop. 2.5) implied the following strong testable prediction: P.4: Market leaders spend more than the followers in nonprice advertising (as a percentage of turnover) when the number of firms is exogenous, and less when entry is endogenous. Finally, after pointing out empirical implications for the policies concerning price, product and promotion, we emphasize an implication for the last strategic investment that characterizes the marketing mix of a firm (the fourth P), place which stands for distribution. From our analysis on the choice of wholesale prices to retailers in the presence of downstream distribution channels (Prop. 2.9), we have the following prediction: P.5: Market leaders set higher wholesale prices for their retailers than their competitors when the number of firms is exogenous, while they set lower prices when entry is endogenous. Concerning financial issues, we need to take care of a more subtle diﬀerentiation on the source of uncertainty in the market, which can be used as an

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additional control variable.11 Then, on the basis of our analysis (Prop. 2.6), we have the following prediction based on the hypothesis of competition in prices: P.6: The financial structure of market leaders is biased toward debt financing compared to the financial structure of the followers when the number of firms is exogenous, while it is biased toward equity financing when entry is endogenous, as long as uncertainty is mainly on the demand side (while uncertainty on costs pushes the predictions in the opposite direction). Notice that under competition in quantities our model always implies a bias toward debt financing for the leader, therefore, once again, we can distinguish a weaker hypothesis from the strong one stated above: the debtequity ratio of the market leaders should increase with entry. As we noticed earlier, investments in cost reductions aimed at reducing the price of a good give rise to neat predictions under competition in prices: in particular, market leaders should spend less than the other firms in R&D investments in cost reductions when the number of firms is exogenous, and they should spend more when entry is endogenous. One should always keep in mind that this hypothesis holds under competition in prices, while under competition in quantities the leader would generally spend more than the followers in cost reductions under both entry conditions. However, we can generalize our result under general forms of competition for the market. In Chapter 4 we have seen that the theory of market leaders provides radical predictions concerning the incentives to invest in R&D by the firms already present in a market with the leading products. We can express the main implications in diﬀerent ways. We start from the weakest possible prediction, which is already in contrast with the traditional result of the theory of innovation:12 P.7: Incumbent market leaders facing endogenous entry in the competition for the market invest in R&D. 11

12

An interesting related analysis on the eﬀect of debt on prices is in Chevalier (1995), but that treatment does not take into account the source of uncertainty and the endogeneity of entry. See Malerba and Orsenigo (1999), Blundell et al. (1999), Czarnitzki and Kraft (2007a) and Hughes (2007) on evidence on the high investment in R&D by market leaders. The empirical study by Blundell et al. (1999) witnesses a positive relationship between market power and innovation activity, which is consistent with strategic investment in R&D by the leaders. This result holds in a panel data with many sectors, but especially in the pharmaceutical sector, which is a sector with a high R&D-sales ratio, strong patent protection and where firms typically recognize that they are in races to develop innovations (in this sector a few drug companies on their own undertake truly innovative research, and a number of mergers in the mid-90s were even motivated to enhance leadership in the patent races).

7.1 Empirical Predictions of the Theory of Market Leaders

251

Of course the theory of market leaders suggests more than this. First of all, we saw that leaders invest more than the followers when entry is endogenous. This was true in all of our models of competition for the market, independently from the kind of strategic interaction between firms (remember that investments could be strategic substitutes or complements in alternative models). Therefore, we state this as an intermediate hypothesis: P.8: The investment rate in R&D of market leaders is higher than the average investment rate in R&D of the followers when entry in the competition for the market is endogenous. We also have a radically strong hypothesis that derives from our favorite model in which the investments of the firms are strategic complements:13 P.9: Market leaders invest less in R&D (as a percentage of turnover) than the followers when the competition for the market is between an exogenous number of firms, they invest more when entry is endogenous. Finally, our theory of sequential innovation by leaders suggests a way to discriminate between diﬀerent degrees of persistence of leadership in innovative sectors. When entry of firms in the competition for the market is endogenous we should expect that technological leaders invest a lot and their persistence is more likely. Of course, when there is no competition for the market we should expect that the monopolistic leadership is also persistent. However, when the degree of competition for the market is intermediate (entry is not free but more than one firm invests), we should expect that the incumbent does not invest much in R&D and that its leadership is more likely to be replaced. This suggests our last prediction: P. 10: The degree of persistence of leadership should follow and inverted U relation with the degree of entry in the competition for the market. These testable implications could be brought to the data in future research. Of course, the analysis of this book was limited to the issues that we considered interesting to understand the behavior of market leaders and to derive implications for antitrust policy. Many other issues could be studied through the market leaders approach and, accordingly, other empirical implications could be derived and eventually tested. 13

Tournaments for team sports are an ideal context to test the theory of innovation by leaders since entry is definitely endogenous in these contests. Casual evidence from Formula 1 racing, the America’s Cup, or the European soccer Champions League suggests that leading teams do invest more than the followers and their leadership is partially persistent. Sport economics may investigate further the issue.

252

7. Epilogue

7.2 Implications for Business Administration In this book we looked at the behavior of market leaders from a descriptive point of view. The attempt was to understand how leaders behave in diﬀerent competitive scenarios. There is another way to read the results of this book. This is the point of view of business administration: our results may suggest a rule of behavior for the management of the leading firms. A vast literature on marketing (see Kotler, 1999) and business strategy (see Porter, 1985) exists which questions what should be the optimal marketing mix and the optimal strategic investments. Here we have emphasized that the right answer may depend on the entry conditions in a crucial way. Consider a generic market where products are highly diﬀerentiated and firms compete in prices. When entry in the market is limited to a predetermined number of firms and there are profitable opportunities for all of these firms, the management should always follow an accommodating philosophy. This requires high prices, high investments in advertising, delegation of the distribution to downstream sellers with high wholesale prices, limited investments in R&D and expansion through horizontal mergers. In such a situation, an aggressive management is counterproductive because it induces retaliation by the rivals and reduces profits in the long run. The optimal management rule changes radically when the market is characterized by high reactivity of entry to the profitable conditions. In such a case, entry is pervasive and can reduce profits at low levels, but a firm can acquire a leadership and preserve high profits by adopting a correct marketing philosophy. This must be an aggressive philosophy, which requires the exact opposite of what we have seen before: low prices, low investments in advertising, delegation of the distribution with wholesale prices below cost and high fees, high investments in R&D and expansion through internal growth. The general principle is that the management should follow an aggressive or an accommodating philosophy according to the entry conditions, be able to monitor these conditions and adopt the right marketing mix and strategies accordingly.

7.3 Implications for Economic Theory In this section we would like to emphasize a few areas where further theoretical research on the theory of market leaders could be fruitful. The model of Stackelberg competition with endogenous entry can be generalized in many other dimensions and applied to other specific forms of market structures. The same holds for the model of strategic investment with endogenous entry. Our discussions of the investments in cost reducing activities, in persuasive advertising and our analysis of the optimal financial structure related to the competition in the market were purely introductory and need further investigations. The literature on multi-sided markets is just taking oﬀ, therefore we

7.3 Implications for Economic Theory

253

look forward to further applications. Concerning bundling, vertical restraints for interbrand competition, price discrimination and horizontal mergers we limited our results to basic attempts to approach these issues within a new perspective: further studies should generalize the outcomes and, most of all, verify their applicability for antitrust purposes. Growing literature on innovation by leaders already exists, but further theoretical work is needed in this field as well, especially for the understanding of the relationship between competition for the market and in the market. Finally, we have seen that the theory of endogenous entry has some general consequences for the approach to antitrust policy, and may limit the validity of some of the implications of the post-Chicago approach. Hopefully, our results will be useful in improving our understanding of the behavior of market leaders under diﬀerent entry conditions, and in deriving a unified economic approach to antitrust issues. Interesting results could be developed in the field of government policy aimed at helping domestic firms in international markets: we briefly analyzed the choice of the optimal state aids and subsidies for exporting firms and some issues concerning privatizations, but many other issues could be investigated. One could extend the analysis to more general forms of export promoting policies, as general forms of strategic trade policy, competitive devaluations in partial equilibrium and R&D subsidies in an international competition for the market.14 The role of non-profit firms could be investigated in an analogous way to our analysis of public firms. Furthermore, it would be interesting to analyze further the Schumpeterian model sketched in our analysis on sequential innovations with leaders driving technological progress and growth. The analysis of full-fledged models of competition for the market with endogenous entry, and eventually with asymmetries between leaders and followers, leads naturally to other applications in macroeconomics. Recent newkeynesian research has been limited to the analysis of competition in prices between an exogenous number of firms (or in situations where the number of firms was indeterminate or irrelevant), and has introduced sticky prices in this environment. We hope that this book contributes to suggest the relevance of endogenous entry under both competition in prices and in quantities, and the relevance of asymmetries between leaders and followers which can have important consequences over the business cycles. Moreover, we believe that the study of sticky entry in these markets can have interesting consequences for the same understanding of the business cycle (maybe more than the usual study of sticky prices). For instance, we have seen that entry heavily aﬀects prices and mark ups in markets with relevant fixed costs of production, and endogenous entry aﬀects the pricing behavior of the existing 14

While we neglected general equilibrium considerations, a deeper analysis of endogenous entry with market leaders in a 2 × 2 × 2 model could be fruitful.

254

7. Epilogue

firms (which can be seen as leaders in such a case). These factors could be fruitfully introduced in the general equilibrium macroeconomic analysis.15 Potentially, one could also apply the principles of the behavior of market leaders in other contexts of economic theory. The simple contest where a leader and its followers exert eﬀort to obtain a compensation can be introduced in a principal-agent framework. A principal could choose the compensation for the agent that achieves the desired result, and could also choose the appropriate hierarchical structure between agents. Assigning a leadership to one of the agents may reduce total eﬀort and the probability of achieving the desired result, but it may also avoid the waste in fixed costs of participation associated with multiple agents. The model of competition for a prize can also be re-interpreted in terms of a rent-seeking contest, and it foresees that incumbent lobbyists should invest more than entrants when there are no barriers to rent seeking. Political leadership can be analyzed in a related way as a function of the entry conditions in the electoral competition. One could think of incumbent politicians running for new elections in a parallel way to our incumbent monopolists that are leaders in the competition for the market. The strategies of competing politicians would aﬀect the incentives of the political leaders to engage in the electoral campaign, spend resources and eﬀort in fund raising, promote the endorsement of opinion makers, and finally (if possible) commit to challenging policies and promises that benefit the citizens. In the case of an electoral competition between two predetermined parties or coalitions where there is no space for the entry of other parties we could expect a systematic leapfrogging of the political opposition on the incumbent party. In the presence of electoral systems allowing for endogenous entry of candidates (when there are chances to replace the political contestants) we could expect the incumbent politicians to engage in more aggressive political campaigns to preserve political power.16 Finally, we cannot exclude that the role of entry conditions in inducing aggressive or accommodating behavior extends to more general interactions between persons, like those emerging in small communities, clubs, or circle of friends where leaders and followers interact to achieve personal satisfaction. The wide development of behavioral and psychological economics in the last years, may find related results in the study of social interactions. These could be the subject of further empirical investigations in experimental economics. 15

16

See Bilbiie et al. (2007) for an important macroeconomic analysis of endogenous entry in the competition in the market, and Etro (2007,a) on endogenous entry also in the competition for the market. Of course, this parallel is limited by the ideological component which is present in political competitions, and it is confined to democratic political systems.

7.4 Conclusions

255

7.4 Conclusions Entry manages to discipline competition more than any government policy. In particular, endogenous entry forces market leaders to act in an aggressive or pro-competitive way that creates benefits for the consumers, avoids welfare reducing mergers and can even reduce the eﬀectiveness of collusive cartels. These results are quite close to those of the Chicago school, but have found a game theoretic formalization in this book and in the emerging literature on endogenous entry. On this basis we believe that industrial policy should be aimed at preserving free entry conditions and promoting competition in and for all the markets. More specifically, antitrust policy should intervene only in markets where entry is exogenously blocked or in which a firm attempts to build artificial barriers to entry. Other than that, we believe that the invisible hand of endogenous entry drives markets better than any other exogenous intervention. With these considerations we have arrived to the end of our book on market leaders and endogenous entry. As Jerry Seinfeld once said, “the big advantage of a book is it’s very easy to rewind: close it and you’re right back at the beginning.”

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1. Competition, Leadership and Entry

Most of the traditional industrial organization literature has studied the way market structure aﬀects the behavior of firms. This book is also about how the behavior of firms aﬀects the market structure. Therefore we will focus on market structures where both the strategies of the firms and their entry choices are endogenous. We will study the strategies and the entry decisions within a general framework and apply the results to diﬀerent environments, characterized by competition in the market and competition for the market. The diﬀerence between these two forms of competition is simple. When firms compete in the market, they choose the price of their products or the production level, or even other auxiliary strategies, but the products of all the firms are exogenously given. When firms compete for the market, they invest in R&D to innovate and create new products or better versions of the existing products. Our ultimate objective will be to employ our theoretical results to derive some insights on policy issues, and in particular on antitrust issues. For this purpose, we will pay a close attention to the behavior of market leaders and to the interaction between these firms and the other firms, the followers. In this chapter we will study the simplest models of competition one can think of. Our purpose is to introduce the reader to the basic tools of the theory of oligopoly. Nevertheless, we will also present new insights on the behavior of leaders in markets where entry is endogenous. In the rest of the book we will generalize these results in many directions, but the spirit of our analysis can be grasped from the examples developed in this chapter. We will focus on four general typologies of competition and their related equilibria. The first typology goes back to the early analysis of Cournot (1838) who was the real pioneer of the modern economic analysis and the first one to study market structures for homogeneous goods where firms choose their output and where the equilibrium between demand by consumers and supply by all firms determines the price. While the analysis of Cournot goes back to the first half of the XIX century, his equilibrium concept corresponds to the one that today we associate with Nash (1950):1 each firm independently chooses its strategy to maximize profits taking as given the strategy of each 1

Nash (1950) introduced mixed strategy equilibria and provided a general proof of the existence of these equilibria.

2

1. Competition, Leadership and Entry

other firm. This idea can be applied to more general market structures and also when firms choose strategies diﬀerent from their output, for instance when they choose their prices, or their investments in R&D. Therefore, we will generally refer to a Nash equilibrium when an exogenous number of firms compete choosing their strategies simultaneously. This equilibrium concept is at the basis of any analysis of strategic interactions between independent agents, and in particular at the basis of the theory of industrial organization. The second typology of competition extends these models of imperfect competition to endogenous entry of firms. A market is in equilibrium only when there are not further incentives for other firms to enter into it and conquer positive extra-profits. This idea is often associated with the studies on competitive markets in partial equilibrium of the second half of the XIX century, in particular with Marshall (1890). Therefore, we will refer to this equilibrium as the Marshall equilibrium. In modern terms, the concept of Nash equilibrium with free entry characterizes this situation. Formal treatments have been provided by von Weizsäcker (1980) and Novshek (1980) for competition in quantities and (neglecting the strategic interactions) by Dixit and Stiglitz (1977) for competition in prices. In general, equilibria with endogenous entry are the natural way to think of medium and long run equilibria both in partial and general equilibrium. Nevertheless, they have been rarely used in industrial organization, where the number of competitors is often assumed exogenous to focus on the strategic interactions between predetermined competitors, and also in general equilibrium macroeconomic analysis with imperfect competition (which often abstracts from entry processes to focus on price rigidities). The third typology of competition was introduced by Stackelberg (1934) who studied markets where a firm has a leadership over the others. While in every day talks a market leadership refers to a vague concept of competitive advantage, in economic jargon a leadership is associated with a first mover advantage, that is the ability to choose strategies and commit to them before the other firms. Under Stackelberg competition, the leader can exploit its first mover advantage taking into account the reactions of the followers.2 Notice that the behavior of a leader in a Stackelberg equilibrium requires a commitment power whose credibility is crucial but sometimes not realistic (see Schelling, 1960). However, Dixit (1980) and Fudenberg and Tirole (1984) have shown that proper preliminary investments can be a valid substitute for this commitment: a firm can invest in cost reductions, in advertising, in R&D or in other strategic investments to obtain a competitive advantage over the other firms. We will return to this possibility in the next chapter, while in this one we will analyze the simpler case in which a leader has indeed the ability 2

Only later on, Selten (1965) introduced the concept of subgame perfect equilibrium for dynamic games (and the Stackelberg equilibrium belongs to this class), while Harsanyi (1967-68) introduced Bayesian equilibria with uncertainty. For an introduction to game theory see Fudenberg and Tirole (1991) or Myerson (1991).

1. Competition, Leadership and Entry

3

to commit to strategies before the other firms. For example, the leader can choose how much to produce before them. Since the equilibrium price depends on the production of all the firms, the followers must take in consideration the production of the leader when they decide their own production: for instance, they may want to produce less if the leader has decided to produce more. But the leader is aware of these reactions, and decides its own production level taking into account the expected behavior of the followers: for example, the leader may want to produce a lot to induce the followers to reduce their production. Similarly, a price leader chooses its own price taking into account the impact of this choice on the prices adopted by the followers. Imagine that the followers are going to increase their prices when they face a price increase by the leader: then, the leader may want to choose a high price to start with, so that all firms will end up with high prices. The last typology of competition completes our taxonomy of the basic forms of market interaction combining the analysis of leadership and entry. In the second half the XX century there have been some attempts to model both these elements. One is the literature on entry deterrence associated with Bain (1956), Sylos Labini (1956) and Modigliani (1958), who took into consideration the eﬀects of entry on the predatory behavior of market leaders mainly in the case of perfectly substitute goods and constant or decreasing marginal costs. Another important attempt is associated with the theory of contestable markets by Baumol et al. (1982), which shows that, in the absence of sunk costs of entry, the possibility of “hit and run” strategies by potential entrants is compatible only with an equilibrium price equal to the average cost. One of the main implications of this result is that “one firm can be enough” for competition when there is at least one aggressive potential entrant. This theory and its implications do not apply when goods are imperfect substitute or firm compete in quantities rather than in prices, which represents a crucial theoretical gap. These and other attempts were not developed in a coherent and general game theoretic framework. The development of such a framework is the focus of this book, whose theoretical contribution is the characterization of the Stackelberg equilibrium with endogenous entry and of its applications. This equilibrium is characterized by rational strategies adopted in diﬀerent stages. In a first stage, the leader chooses its strategy under rational expectations on the strategies that will be adopted by the followers and on the entry decisions of these followers. In a second stage the followers decide whether to enter in the market or not according to their expectations on profitability. In the last stage, the followers simultaneously choose their strategies to maximize profits, knowing the strategy of the leader and taking as given the strategies of the other followers. This introductory chapter presents, in the simplest possible way, some examples of these four diﬀerent forms of competition and equilibria. Our initial focus is on models of competition in quantities. After presenting the

4

1. Competition, Leadership and Entry

basic linear model which assumes constant marginal costs and homogenous goods in Section 1.1, we extend it to U-shaped cost functions and to product diﬀerentiation in Section 1.2. In Section 1.3, we present a simple model of competition in prices with a Logit demand function. Finally, in Section 1.4, we discuss a simple model of competition for the market (a contest where firms compete investing with the purpose of conquering a new market), and we analyze the role of incumbent monopolists (with or without a leadership in the competition for the market). Section 1.5 concludes.

1.1 A Simple Model of Competition in Quantities Our initial example will be about the simplest situation one can think of: a market for a single homogenous good whose supply requires a positive fixed cost of production and a constant additional cost for each unit produced, which means that the marginal cost of production is constant. To be more formal, imagine a good whose demand is linearly decreasing in the price, say D(p) = a−p where a > 0 is a parameter representing the size of the market. If Pn total production by all the firms is Q = i=1 qi , where qi is the production of each firm i = 1, 2, ..., n, in equilibrium between supply and demand we must have Q = D(p) = a − p, which provides the so called inverse demand function in equilibrium:

p=a−Q=a−

n X

qi

(1.1)

i=1

Basically, the larger production is, the smaller the equilibrium price must be. Imagine now that each firm can produce the good with the same standard technology. Producing q units requires a fixed cost of production F ≥ 0 and a variable cost cq where c ∈ [0, a) is a constant marginal cost of production. Notice that, while the average variable cost is constant (equal to c), the average total cost (equal to c+F/q) is decreasing in the output. In conclusion, the profit function of a firm i is the diﬀerence between revenues and costs: πi = pqi − cqi − F = Ã ! n X = a− qi qi − cqi − F

(1.2)

i=1

Before analyzing diﬀerent forms of competition between many firms in this set up, we will investigate a few simple and extreme situations where one or two firms only are active in this market and derive some preliminary implications for antitrust analysis.

1.1 A Simple Model of Competition in Quantities

5

1.1.1 Monopoly and Antitrust Issues Our first investigation of the market described above focuses on a monopoly. Consider a single firm producing q. Its profit must be given by π = (a − q)q − cq − F . Its maximization requires an output satisfying the optimality condition ∂π/∂q = a − 2q − c = 0,3 which can be solved for the monopolistic output: qM =

a−c 2

The monopolistic price can be derived from the inverse demand function as pM = a − qM = (a + c)/2, and the associated profits are:4 πM =

(a − c)2 −F 4

Imagine now that another firm enters in the market. When the two firms compete at the same level, it is natural to imagine that their strategic choices are taken simultaneously. In the equilibrium of this duopoly, both firms must choose their output levels independently, and these output levels must be consistent with each other. The result is a Cournot equilibrium. Consider firms i and j. If they compete choosing independently their outputs, firm i has the following profit function π i = (a − qi − qj )qi − cqi − F , and total production is now Q = qi + qj ; of course the profit of firm j is the same after changing all indexes. Profit maximization by firm i requires ∂π i /∂qi = 0 or a − 2qi − qj = c, from which we obtain the so called reaction function: qi (qj ) =

a − c − qj 2

This is a rule of behavior for firm i which can be interpreted in terms of expectations: the larger is the expected production of firm j, the smaller should be the optimal production of firm i. Firm j will follow a similar rule: qj (qi ) =

a − c − qi 2

The geniality of Cournot’s idea is that in equilibrium the two rules must be consistent with each other. In terms of expectations, the equilibrium production of each firm must be the optimal one given the expectation that the other firm adopts its equilibrium production. Mathematically, we can solve the system of the two reaction functions to find out the production of each firm in 3

4

The second order condition ∂ 2 π/∂q∂q = −2 < 0 guarantees that the profit function is concave, so that the solution corresponds to a maximum. We will assume that F is small enough to allow profitable entry by one firm in the market.

6

1. Competition, Leadership and Entry

equilibrium. It is easy to verify that there is only one consistent equilibrium, and it implies that each firm produces the same amount: q=

a−c 3

Accordingly, the equilibrium price is p = (a + 2c) /3, and the profit of each firm is: πC =

(a − c)2 −F 9

Competition increases total production and reduces the price and the profits compared to the monopolistic case. For this reason, the firms may engage in alternative agreements or strategies that can increase the price and their profits. Any practice that leads to higher prices ends up hurting consumers.5 The scope of antitrust policy is precisely to avoid this kind of anti-competitive behavior. Here, we will sketch the main anti-competitive practices that can emerge in such a simple context. Mergers. As we noticed, the Cournot duopoly generates lower profits for each firm compared to a monopoly. Moreover, also the sum of the profits of both firms is lower than the profits of the monopolist. This implies that there is an incentive for one firm to merge with the other one, monopolize the market and increase total profits. Since this induces a higher final price, antitrust authorities should prevent a similar horizontal merger as an attempt to monopolize the market.6 Abuse of Dominance. There is another possibility for one of the two firms to increase its profits. This possibility emerges when this firm can act as a leader and choose its output before the second firm. In this case, the leader i could chose a output level q¯ which is high enough to convince the second firm j to avoid entry. This entry deterring output level can be calculated as follows. Consider the reaction function of firm j derived above: this tells us that when firm i produces q, firm j finds it optimal to produce qj (q) = (a − c − q)/2 so as to obtain profits πj (q)√= (a − c − q)2 /4 − F . Now, the leader i is aware that producing q¯ = a − c − 2 F will reduce the profits of the other firm j to zero (π j (¯ q ) = 0). This is the entry deterring strategy, and it allows the leader to remain alone in the market. If this firm has the market power to choose its 5

6

In this model with linear demand, consumer surplus is simply the area below the demand curve and above the market price, which corresponds to Q2 /2. Welfare is traditionally defined as the sum of consumer surplus and firms’ profits, W = Q2 /2 + n i=1 π i . Notice, however, that in case the merger between the two firms allows to save one of the two fixed costs, the gain in eﬃciency may overcompensate the loss in consumer surplus after the merger (see Williamson, 1968, and Farrell and Shapiro, 1990, on a more general analysis of eﬃciencies in horizontal mergers).

1.1 A Simple Model of Competition in Quantities

7

strategy before the rival, it can use this power to increase profits excluding entry.7 Moreover, if this firm remains alone in the market, it could be able to restore the monopolistic price in the future. When this is the case, the exclusionary strategy ends up increasing the final price, therefore antitrust authorities should punish it as a predatory strategy. Collusion. A third way to increase profits requires collusion. To see how it works in our simple setup, let us go back to the symmetric duopoly. The reduction in total profits associated with Cournot competition (compared to the monopolistic outcome) was due to the fact that each firm did not take into consideration the impact of its own production on the profits of the other firm, and hence tended to produce too much from the point of view of joint profit maximization. This externality leads to a price reduction and to a decline in total profits. For this reason the two firms may try to collude and agree on limiting their production at a lower level, possibly at the monopolistic level. Under perfect collusion, each one of the two firms produces half of the monopolistic output, q˜ = (a − c)/4, and obtains profits π ˜ = (a − c)2 /8 − F . However, only a strong and reciprocal commitment could guarantee that such a collusive behavior is sustainable, because in the absence of a commitment each firm would have incentives to deviate and produce more than that. For instance, if a firm is sure that the other one produces at the collusive level, this firm can deviate from the collusive strategy and choose an output qD that maximizes π = (a − qD − q˜)qD − cqD − F . The optimal deviation is exactly qD = 3(a − c)/8. After deviating from the collusive strategy, this firm increases its profits to π D = 9(a − c)2 /64 − F , which is above the collusive profits, while the profits of the other firm are reduced below them. This profitable deviation should not surprise, because there must be always a profitable deviation for each firm when we are not in the Cournot equilibrium. Not by chance, we can also provide an alternative definition of the Cournot equilibrium as one in which there are not profitable deviations for any firm. It is important to notice that collusive outcomes can be reached more easily when interactions are repeated over time, because deviations can be punished in the future, and the threat of punishments can reduce the incentives to deviate. The theory of collusion has studied the conditions under which monopolistic profits can be sustained in dynamic games. For instance, if the same competition is repeated infinite times, each firm discounts the future, and each deviation is punished with reversion to the Cournot equilibrium forever, collusion is sustainable if and only if firms are patient enough. 7

Notice, however, that the exclusionary strategy does not necessarily increase the price and, even if it increases the price, it does not necessarily reduce welfare (measured as consumer surplus plus profits). If the fixed cost of production is high enough, entry deterrence may require a higher price but it may be more eﬃcient from a welfare point of view.

8

1. Competition, Leadership and Entry

Of course, collusion could be sustained more easily if harder punishments were available (for instance with a reversion to zero profits forever).8 Since collusive cartels allow firms to set higher equilibrium prices, antitrust authorities should prevent similar agreements. As we have seen, simple games can be useful to understand basic strategic interactions and to approach some of the fundamental antitrust issues. However, a more complete analysis needs to take into account the presence of more than just one or two firms, and possibly also to endogenize entry in the market. To these tasks we now turn. 1.1.2 Nash Equilibrium We now move to the study of a generalized Nash competition between many firms. In particular, imagine that there are n firms in the same market described above. Each firm i will have profits:   n X πi = a − qi − qj  qi − cqi − F (1.3) j=1,j6=i

and Pn will choose its production qi to satisfy the first order condition a − 2qi − j=1,j6=i qj = c, which generates the reaction function: qi =

a−

Pn

j=1,j6=i qj

2

−c

Notice that this is decreasing in the output of each other firm, ∂qi /∂qj < 0. Therefore, when a firm is expected to increase its own production, any other firm has an incentive to choose a lower production level. This is a typical property of models where firms compete in quantities. The system of n conditions provides equilibrium outputs as in the duopoly case. However, its solution is immediate if we notice that all firms will produce 8

Assume that the punishment is reversion to the Cournot equilibrium and that the discount factor is δ ∈ (0, 1). Collusion is sustainable if the discounted payoﬀ ˜ + ... = π ˜ /(1 − δ), is higher than the deviation from collusion forever, π ˜ + δ˜ π + δ2 π payoﬀ in one period plus the Cournot payoﬀ forever after that, π D +δπC /(1−δ). This requires δ > (π D − π ˜ ) / (πD − πC ). Substituting for the payoﬀs, one can find that collusion is sustainable when δ > 9/17. The first generalizations of this result, known as Folk Theorem, are in Friedman (1971) and Aumann and Shapley (1976). Of course, collusion could be sustained more easily if punishment was harder. Considering the maximum punishment which delivers zero expected payoﬀ for the deviator, Abreu (1986) has verified under which conditions such a punishment is itself sustainable, relaxing the condition above (see also Fudenberg and Maskin, 1986). For a wide treatment on supergames and dynamic games see Mailath and Samuelson (2006).

1.1 A Simple Model of Competition in Quantities

9

the same output satisfying a − 2q − (n − 1)q = c. This implies the following output per firm as a function of n:9 q(n) =

a−c n+1

(1.4)

with total production Q(n) = n(a − c)/(n + 1), which is increasing in the number of firms. The equilibrium price can be derived as: p(n) =

a + nc n+1

(1.5)

which is decreasing in the number of firms and approaching the marginal cost of production when the number of firms increases. Nevertheless, the profits of each firm are constrained by the fixed costs of production: µ ¶2 a−c −F π(n) = n+1 The profits of each single firm are clearly decreasing when the number of competitors is increasing. This suggests that in the medium and long run, new firms will enter in the market as long as there are positive profits to be made, and they will stop entering when the number of firms achieves an upper bound. This leads us to the next equilibrium concept. 1.1.3 Marshall Equilibrium It is now extremely simple to extend the model to endogenize entry. Formally, consider the following sequence of moves: 1) in the first stage all potential entrants simultaneously decide “in” or “out”; 2) in the second stage all the firms that have entered choose their own strategy qi . In what follows we will mainly refer to F as to a technological cost of production, but one could think of it as including other concrete fixed costs of entry or opportunity costs of participation to the market, as the profits that an entrepreneur can obtain in another sector. Beyond the particular interpretation, the role in constraining entry is the same. As we have seen, in the case of a Nash equilibrium the entry of a new firm enhances competition leading to a reduction in the profit of each single firm in the market. If we assume that entry takes place as long as positive profits can be obtained, a Marshall equilibrium should be characterized by a number of firms n satisfying a no entry condition π(n + 1) < 0 and a no exit condition π(n) ≥ 0. When the fixed cost of production is small enough, this 9

One can verify that both the cases of a monopoly and of the Cournot duopoly are particular cases for n = 1 and n = 2.

10

1. Competition, Leadership and Entry

equilibrium number is quite large. In these cases it is natural to take a short cut and approximate the endogenous number of firms with the real number satisfying the zero profit condition π(n) = 0, that is: a−c n= √ −1 F This allows one to derive the equilibrium output per firm under Marshall competition: √ q= F (1.6) √ the total production Q = a − c − F , and the equilibrium price: √ p=c+ F (1.7) which implies a mark up on the marginal cost to cover the fixed costs of production. When the fixed costs are zero, the outcome corresponds to the classic equilibrium with perfect competition in which the price is equal to the marginal cost and the number of firms is indeterminate. In the more realistic case in which start up costs for each firm are positive, the equilibrium is ineﬃcient and there are too many firms pricing above their marginal cost.10 1.1.4 Stackelberg Equilibrium Let us now consider the case in which one of the firms has a first mover advantage and can choose its output in a first stage before the followers, while these choose their own output in a second stage and independently from each other. Let us define the production of the leader as qL . In the second stage each follower decides Phow much to produce according to the first order condition a − qL − qi − nj=1,j6=L qj = c, where n is the number of firms (including the leader). Assuming that all the followers find it convenient to be active, in a symmetric equilibrium each follower produces: q(qL , n) = 10

a − qL − c n

Adopting the standard definition of welfare (which here corresponds to the consumer surplus because all firms earn no profits under free entry), we have: √ (a − c − F )2 Q2 = WFE = 2 2 Notice that in this case the first best would require one single firm producing Q = a − c with welfare: WFB =

(a − c)2 −F 2

1.1 A Simple Model of Competition in Quantities

11

As we noticed before, ∂q(qL , n)/∂qL < 0: the production of the leader partially crowds out the production of the other firms. Accordingly, in the first stage the leader perceives its profits as: πL = [a − qL − (n − 1)q(qL , n)] qL − cqL − F We can already see what will be the impact of the behavior of the followers on the leader: since a higher production of the leader reduces the production of the followers, the leader has an indirect (or strategic) incentive to increase its production. Such an aggressive strategy reduces the production of the followers and shifts profits toward the same leader. Formally, we can rewrite the profits of the leader as: · ¸ (n − 1) (a − qL − c) πL = a − qL − qL − cqL − F = n µ ¶ a − c − qL = qL − F n which leads to the optimal strategy: qL =

a−c 2

(1.8)

In this particular example the leader finds it optimal to commit to produce at the monopolistic level. As a consequence, each one of the followers will end up producing: µ ¶ a−c a−c q ,n = (1.9) 2 2n The total output becomes: ¶ µ 1 Q = (a − c) 1 − 2n and the equilibrium price is: µ ¶ a 1 p(n) = +c 1− 2n 2n

(1.10)

which again tends toward the marginal cost when the number of firms increases. The profits for the leader and for each follower are respectively: 2

πL (n) =

(a − c) − F, 4n

2

π(n) =

(a − c) −F 4n2

12

1. Competition, Leadership and Entry

Of course, entry of followers occurs if positive profits can be obtained.11 When this is the case, we expect that, at least in the medium or long run, followers will keep entering in the market until positive profits can be made. Since the profits of the followers are decreasing in the number of firms active in the market, the entry process will have a natural limit. We now move to the equilibrium in which entry occurs until all the profitable opportunities are exploited by the followers. As we will see, this equilibrium with endogenous entry is quite diﬀerent from the one analyzed here. 1.1.5 Stackelberg Equilibrium with Endogenous Entry Let us finally move to the last case, in which there is still a leader in the market, but this is facing endogenous entry of followers. Formally, following Etro (2006,a, pp. 147-8) consider the following sequence of moves: 1) in the first stage, the leader chooses its own output qL ; 2) in the second stage, after knowing the output of the leader, all potential entrants simultaneously decide “in” or “out”; 3) in the third stage, all the followers that have entered choose their own output qi (hence, the followers play Nash between themselves). In this case, the leader has to take into account how its own commitment aﬀects not only the strategy of the followers but also their entry decision. As we have already seen, in the last stage, if there are n ≥ 2 firms in the market and the leader produces qL , each follower produces: q(qL , n) =

a − qL − c n

This implies that the profits of each follower are: µ ¶2 a − c − qL π(qL , n) = −F n

(1.11)

which are clearly decreasing in the number of firms. This would imply that further entry or exit does not take place when π(qL , n+1) ≤ 0 and π(qL , n) ≥ 0. Moreover, no follower will find it optimal to enter in the market if π(qL , 2) ≤ 0, that is if not even a single follower can obtain positive profits given the output of the leader. This condition is equivalent to: √ qL ≥ a − c − 2 F Therefore when the leader adopts an aggressive strategy producing more than this cut-oﬀ level entry will be deterred, but when the leader produces 11

At least one follower has incentives to enter in the market if π(2) > 0 or F < (a − c)2 /16, otherwise the leader supplies its monopolistic production and no one else enters. In what follows we assume away this possibility (which corresponds to the case of a “natural monopoly”).

1.1 A Simple Model of Competition in Quantities

13

less than the above cut-oﬀ the number of entrants will be determined by a free entry condition. In this last case, ignoring the integer constraint on the number of firms,12 we can approximate the number of firms as a real number that satisfies π(qL , n) = 0. This implies: n=

a − c − qL √ F

(1.12)

When this is the endogenous number of firms, each one of the followers is producing: µ ¶ √ a − c − qL √ q qL , = F F which is independent from the strategy of the leader. Hence, the higher the production of the leader, the lower the number of entrants, while the production of each one of them will be the same. This would imply √ a constant level of total production Q = √ qL + (n − 1)q(qL , n) = a − c − F , and a constant price p = a − Q = c + F , which would be equivalent to the equilibrium price emerging under Marshall competition. After having derived the behavior of the followers, it is now time to move to the first stage and examine the behavior of the leader. First of all, let us remind ourselves that entry takes place only for a production level which is not too high. If this is the case, the profits of the leader must be: √ √ πL = pqL − cqL − F = qL F − F if qL < a − c − 2 F (1.13) In other words, when entry takes place, the market price is perceived as given from the leader, which is aware that any increase in production crowds out entry maintaining constant the equilibrium price. However, when the leader is producing enough to deter entry, its profits become: √ πL = qL (a − qL ) − cqL − F if qL ≥ a − c − 2 F (1.14) It can be immediately verified that the profit function linearly increases in √ the output of the leader for qL < a − c − 2 F and, after this cut oﬀ, it jumps upward and then decreases. Consequently the optimal strategy for the leader is to produce just enough to deter entry: √ qL = a − c − 2 F (1.15) which is equivalent to set the limit price: √ p=c+2 F 12

(1.16)

In the Appendix we oﬀer an analysis which takes this constraint into consideration

14

1. Competition, Leadership and Entry

The profits of the leader are then: √ ³ √ ´ πL = 2 F a − c − 2 F − F

(1.17)

One way to look at this result is by considering the role of the fixed cost of production. When this is zero, we are in the standard neoclassical situation where perfect competition takes place: the number of firms is indeterminate and the price must be equal to the marginal cost. However, whenever there is a small but positive fixed cost of production, the leader finds it optimal to produce enough to deter entry.13 Constant returns to scale (holding for F = 0) are not an minor approximation: a small departure from them leads to a radical change in the market structure. And when the fixed costs of production are high, the leader is able to obtain substantial profits.14 Another way to look at the result is to imagine that there are some potential entrants and we can establish a relation between their number and the market equilibrium: when the number of potential entrants is low enough (and the free entry condition is not binding) the market is characterized by all these firms being active. When there are many potential entrants (and entry is endogenized) there is just one firm in equilibrium, the leader. Furthermore, it is interesting to compare the free entry equilibrium with and without a leader. In the Stackelberg equilibrium with endogenous entry the limit price is higher than the equilibrium price √ √ in the Marshall equilibrium (the mark up p − c is doubled from F to 2 F ), consequently the consumer surplus is reduced. However, welfare as the sum of consumer surplus and profits is higher in the Stackelberg equilibrium with endogenous entry than in the Marshall equilibrium.15 13

14

15

This form of entry deterrence is radically diﬀerent from that emerging in the contestable markets theory of Baumol et al. (1982). First, they focused on price competition, which led to a limit price assigning zero profits to the leader, while our model of quantity competition leads to a limit price assigning positive profits to the leader. Second, their equilibrium was the same with exogenous or endogenous entry, while the role of the costs of production in endogenizing entry is crucial in our model. In the Appendix we will discuss how to endogenize the fixed costs. For instance, imagine that fixed costs are F = (a − c)2 /25. Then the profits of a leader facing endogenous entry can be calculated as πL = (a − c)2 /5. Compare these to the profits of a monopolist in the same market: its profits would be πM = (a−c)2 /4−F = 21(a−c)2 /100. It can be easily verified that the diﬀerence between the two is less than 5%. Welfare can be now calculated as: WS =

(a − c)2 Q2 + πL = − 3F 2 2

It can be verified that welfare is higher under Stackelberg competition with endogenous entry for any F < 4(a−c)2 /49, which always holds under our regularity

1.2 Increasing Marginal Costs and Product Diﬀerentiation

15

The extreme result on entry deterrence that we have just found holds under more general conditions. For instance, as we will see in Chapter 3, as long as goods are perfect substitutes, any kind of demand function will generate entry deterrence by the leader when entry of followers is endogenous. However, when the cost function departs from the linear version (that we used until now) and when imperfect substitutability between goods is introduced, entry deterrence may not be the optimal strategy anymore. Nevertheless, the leader will still play in a very aggressive way, producing always more than the followers when their entry is endogenous. To show this we will now turn to two related extensions of the basic model.

1.2 Increasing Marginal Costs and Product Diﬀerentiation The example adopted until now was extremely simple and stylized. Perfectly homogenous goods and marginal costs of production that are always constant are quite unrealistic features for many sectors. Most traditional markets are characterized by more complex shapes of the cost function and by substantial diﬀerentiation between products. Consider the market for cars. Companies like GM, Ford, Toyota, Nissan, VW, Porsche, Renault or FIAT oﬀer many diﬀerent models, sometimes under diﬀerent brands (for instance Alfa Romeo, Lancia, Maserati and Ferrari for FIAT), and always in multiple versions by engine size, color, varieties of optional tools, and so on: each product appeals to a diﬀerent class of customers and is sold at a diﬀerent price. Moreover, the production of each model has not a constant unitary cost: on one side, economies of scale can be reached at the plant level through large production, on the other, larger output levels may require additional investments in plants, employees, and other inputs. Generally speaking, for each model there is a level of production that minimizes average costs, and average costs have a U shape around this eﬃcient level. The simple model of competition in quantities studied in the previous section can be easily extended to take these realistic dimensions into account. For simplicity, we will consider the two issues separately. First, we will depart from the assumption of constant marginal costs assuming a U-shaped cost function, and then we will depart from the assumption of homogenous goods introducing imperfect substitutability between goods. assumption F < (a − c)2 /16 (which guarantees that the market is not a natural monopoly). Therefore antitrust authorities should punish the entry deterring strategy of the leader if they aim at maximizing consumer surplus, and they should not if they aim at maximizing total welfare.

16

1. Competition, Leadership and Entry

1.2.1 U-shaped Cost Functions In many markets, marginal costs of production are increasing at least beyond a certain level of output. Jointly with the presence of fixed costs of production, this leads to U-shaped average cost functions. Since technology often exhibits this pattern, it is important to analyze this case, and we will do it assuming a simple quadratic cost function. In particular, the general profit for firm i becomes: 

πi = qi a − qi −

n X

j=1,j6=i



qj  −

dqi2 −F 2

(1.18)

where d > 0 represents the degree of convexity of the cost function. When d = 0 we are back to the case of a constant marginal cost (zero in such a case). When d > 0 the average cost function is U-shaped. One can easily verify that the marginal cost is increasing and convex, and it crosses the average total cost at its bottom, that is at the eﬃcient scale of production: the one that minimizes average costs. This eﬃcient scale of production can be derived formally as: µ ¶ r dq F 2F qˆ = arg min + = 2 q d Let us look now at the diﬀerent forms of competition. Our four main equilibria can be derived as before. In particular, Nash competition would generate the individual output: q(n) =

a n+d+1

(1.19)

for each firm.16 Under Marshall competition each firm would produce: r 2F q= < qˆ (1.20) 2+d with a number of firms approximated by: r 2+d n=a −d−1 2F Notice that the equilibrium production level is below the cost minimizing level. This is not surprising since imperfect competition requires a price above 16

Amir (2005) shows that in this case industry profits have an inverse U shape with a maximum for n = 1 + 2d, while welfare always decreases with n. He generalizes this dimension in a number of ways and shows that with strong scale economies (d < 0) both industry profits and welfare can decrease with the number of firms.

1.2 Increasing Marginal Costs and Product Diﬀerentiation

17

marginal cost and free entry requires a price equal to the average cost and above the marginal cost. Since the average cost is always decreasing when it is higher than the marginal cost, it must be that individual output is smaller than the eﬃcient scale (von Weizsäcker, 1980). Under Stackelberg competition, the leader produces: qL (n) =

a(1 + d) [2(1 + d) + d(n + d)]

(1.21)

and each follower produces: q(n) =

a [1 + d + d(n + d)] [2(1 + d) + d(n + d)] (n + d)

(1.22)

Notice that, contrary to the basic linear case, here the leader produces less than a pure monopolist and its production diminishes with the number of entrants. Finally, consider Stackelberg competition with endogenous entry (Etro, 2008). In the last stage an entrant chooses q(qL , n) = (a − qL )/(n + d), but the zero profit condition for the followers delivers a number of firms: Ãr ! 2+d n = (a − qL ) −d 2F and each entrant produces: r 2F q= 2+d

(1.23)

which is the same output as with Marshall competition. Of course this happenspwhen there is eﬀective entry, that is when n ≥ 2 or qL < a − (2p + d) 2F/(2 + d). In such a case, total production is Q = a − (1 + d) 2F/(2 + d), and the price becomes: r 2F p = (1 + d) 2+d Both total production and the equilibrium price are independent from the leader’s production. The gross profit function of the leader in the first stage can be derived as: d 2 πL = pqL − qL −F = 2r d 2 2F = (1 + d) −F qL − qL 2+d 2 which is concave in qL . As long as d is large enough, we have an interior optimum and in equilibrium the leader allows other firms to enter in the market and produces:

18

1. Competition, Leadership and Entry

1+d qL = d

r

2F > qˆ 2+d

(1.24)

Notice that the leader is applying p a simple pricing rule which equates the price derived above p = (1 + d) 2F/(2 + d) to the marginal cost, which is dqL in this model. Of course, the leader can price at the marginal cost and obtain positive profits because its marginal cost of production is above its average cost. This can only happen in the region where the average total costs are increasing, which implies a production for the leader above the eﬃcient scale. Finally, the equilibrium number of firms is: r µ ¶ 2+d 1+d n=a − +d 2F d Total output and price are the same as in the Marshall equilibrium, therefore the consumer surplus is unchanged, but welfare must be higher since the leader makes positive profits.17 Notice that the leader is producing always more than each follower. While the followers produce below the eﬃcient scale, the leader produces above the eﬃcient scale. The intuition is as follows. Followers have to produce at a price where their marginal revenue equates their marginal cost, and free entry implies that the price has to be equal to the average cost. But marginal and average costs are the same at the eﬃcient scale, therefore the followers must be producing below this eﬃcient scale. Now, since the equilibrium price is determined by the endogenous entry condition, it represents the perceived marginal revenue for the leader, and the leader must produce where this perceived marginal revenue equates the marginal cost, which in this case must be above the eﬃcient scale for profits to be positive. 1.2.2 Product Diﬀerentiation We now move to another simple extension of the basic linear model introducing product diﬀerentiation and imperfect substitutability between the goods supplied by the firms. We retain the initial assumptions of constant marginal costs and competition in quantities. For simplicity, consider the inverse demand function for firm i: 17

In general, the profit of the leader in case of an interior solution is: πL =

F >0 d(2 + d)

In the alternative case of entry deterrence, the leader produces qL = a − (2 + d) 2F/ (2 + d). The profits of the leader are larger under entry deterrence when d is low enough or F is high enough.

1.2 Increasing Marginal Costs and Product Diﬀerentiation

pi = a − qi − b

X

qj

19

(1.25)

j6=i

where b ∈ (0, 1] is an index of substitutability between goods. Of course, for b = 0 goods are perfectly independent and each firm sells its own good as a pure monopolist, while for b = 1 we are back to the case of homogeneous goods. In this more general framework the profit function for firm i is:   n X πi = qi a − qi − b qj  − cqi − F (1.26) j=1,j6=i

The four main equilibria can be derived as usual. In particular a Nash equilibrium would generate the individual output: q(n) =

a−c 2 + b(n − 1)

for each firm. In the Marshall equilibrium each firm would produce: √ q= F

(1.27)

(1.28)

with a number of firms: a−c 2 n=1+ √ − b b F Under Stackelberg competition, the leader produces: qL =

(a − c)(2 − b) 2

(1.29)

and each follower produces: q(n) =

(a − c)[2 − b(2 − b)] 2[2 + b(n − 2)]

(1.30)

Finally, consider Stackelberg competition with endogenous entry. As long as substitutability between goods is limited enough (b is small) there are entrants producing q(qL , n) = (a − bqL − c)/[2 + b(n − 2)]. Setting their profits equal to zero, the endogenous number of firms results in: n=2+

a − bqL − c 2 √ − b b F

implying once again a constant production: √ q= F

(1.31)

for each follower. Plugging everything into the profit function of the leader, we have:

20

1. Competition, Leadership and Entry

πL = qL [a − qL − b(n − 1)q] − cqL − F = h i √ = qL (2 − b) F − (1 − b)qL − F

that is maximized when the leader produces: qL =

2−b √ F 2(1 − b)

(1.32)

which is always higher than the production of the followers. This strategy leaves space to the endogenous entry of firms so that the total number of firms in the market is: a−c 2 2−b n=2+ √ − − b 2(1 − b) b F Notice that the leader will oﬀer its good at a lower price than the followers, namely: µ ¶ √ b √ pL = c + 1 − F
1.3 A Simple Model of Competition in Prices In many markets, firms compete in prices rather than in quantities. The initial equilibrium concept for markets of this kind was the Bertrand equilibrium, which was initially applied to the case of homogenous goods (Bertrand, 1883). If goods are perfect substitutes, the marginal cost is constant and there are no fixed costs of production, the Bertrand equilibrium between two or more firms implies that anyone of them sells at a price equal to the marginal cost and obtains zero profits. If there are fixed costs of production, the theory 18

The profits of the leader are actually: πL =

b2 F >0 4(1 − b)

Again, this outcome emerges only if the degree of product diﬀerentiation is high enough. In the alternative case of entry deterrence, the production√of the leader √ is qL = (a − c − 2 F )/b and the limit price is pL = [c − (1 − b)a + 2 F ]/b. Entry deterrence is optimal for b or F large enough.

1.3 A Simple Model of Competition in Prices

21

of contestable markets associated with Baumol et al. (1982) shows that a single firm sets the price at a market clearing level which equates the average total costs and obtains zero profits again. With U-shaped cost functions, the Bertrand equilibrium boils down to a price equal to the minimum average cost for each firm, since any diﬀerent strategy either would leave space for profitable deviations, or would lead to losses.19 Things are not that simple when products are diﬀerentiated, the case to which we now turn. Competition in prices is crucial in markets where the products are highly diﬀerentiated. In this case, as we have already seen in the last section, each firm has a limited market power because it supplies a unique product which is only partially substitutable with the products of the other firms. Think of the fashion market, which is characterized by strong product diﬀerentiation, segmentation depending on the target customers, and competition in prices. Established luxury brands as Armani, Versace, D&G, Gucci, Etro, Yves Saint Laurent, Louis Vuitton and others oﬀer diﬀerent sophisticated clothes at predetermined prices in every season. Other companies which target wider markets, as Gap, Abercrombie, Benetton, Zara, H&M and so on, provide largely diﬀerentiated products and engage in analogous or even stronger forms of price competition.20 In this section, we will focus on the peculiarities of similar markets where goods are imperfect substitutes and firms choose their prices. In this introductory analysis of price competition, we will employ a model based on a simple form of the demand function, the so-called Logit demand. This is particularly interesting because it is simple but flexible enough to depict real world demand functions: not by chance it is widely used in econometric studies21 to estimate demand in various industries and in marketing analysis.22 The simplest form of the Logit demand is: N e−λpi i Di = hP n −λpj e j=1

(1.33)

where of course pi is the price of firm i, λ > 0 is a parameter governing the slope of the demand function, and N is a scale factor that can be thought of 19

20 21 22

It is immediate to verify that these equilibria correspond to a Stackelberg equilibrium in prices with endogenous entry in the case of homogenous goods. Therefore, the theory of Stackelberg competition with endogenous entry can be seen as a generalization of the theory of contestable markets to product diﬀerentiation, and to other forms of competition. For a recent analysis of the fashion industry see Dallocchio et al. (2006). See McFadden (1974). The classic reference on product diﬀerentiation and price competition is Anderson et al. (1992). See also Anderson and de Palma (1992) for the first analysis of Nash and Marshall equilibria within the Logit model of price competition.

22

1. Competition, Leadership and Entry

as the total income or the total number of agents expressing this aggregate demand. Since we focus on substitute goods, such a demand for firm i is decreasing in the price of the same firm i and increasing in the price of any other firm j. The general profit function for a firm facing this demand and producing with a constant marginal cost c and a fixed cost F < N/λ is: πi = Di (pi − c) − F =

N e−λpi (pi − c) Pn −λp −F j i=1 e

(1.34)

In a Nash equilibrium each firm chooses its own price taking as given the prices of the other firms. The first order condition for the optimal price of a single firm i is: Di − λ(pi − c)Di + λ(pi − c)Di2 /N = 0 which simplifies to: pi = c +

1 λ(1 − Di /N )

While this is an implicit expression (on the right hand side the demand of the firm i depends on the price of the same firm), it emphasizes quite clearly that the price is set above marginal cost. Moreover, since an increase in the price of any other firm j, pj , increases demand for firm i, Di , it also increases the optimal price of firm i: formally, ∂pi /∂pj > 0. This important property, which holds virtually in all realistic models of competition in prices, suggests that a higher price by one firm induces other firms to increase their prices as well. In other words, an accommodating behavior of one firm leads other firms to be accommodating too. To conclude our analysis of the Nash equilibrium, notice that in a symmetric situation with a price p for each firm, demand boils down to D = N/n and the equilibrium price is decreasing in the number of firms: p(n) = c +

1 λ (1 − 1/n)

(1.35)

In a Marshall equilibrium one can easily derive that the number of active firms is: n=1+

N λF

and each one of these sells its product at the price: p=c+

F 1 + λ N

(1.36)

Let us now move to models of price leadership. Of course it can be even harder for a firm to commit to a price rather than to a diﬀerent strategy (as

1.3 A Simple Model of Competition in Prices

23

the quantity of production). However, price commitments can be reasonable in the short run (for instance in seasonal markets), or when there are small menu costs of changing prices or it is costly to acquire the information needed to reoptimize on the price choice. In the next chapter we will deal with the commitment problem in a deeper way and we will suggest that there are realistic ways in which a strategic investment can be a good substitute for a commitment to a strategy. For now we will assume that a firm can simply commit to a pricing strategy and analyze the consequence of this. Concerning the Stackelberg equilibrium we do not have analytical solutions. However, it is important to understand the nature of the incentives of the firms, which is now rather diﬀerent from the model with competition in quantities. Here the leader is aware that an increase in its own price will lead the followers to increase their prices, which exerts a positive eﬀect on the profits of the leader. Accordingly, the commitment possibility is generally used adopting an accommodating strategy: the leader chooses a high price to induce its followers to choose high prices as well.23 The only case in which this does not happen is when the fixed costs of production are high enough and the leader finds it better to deter entry. This can only be done adopting a low enough price: therefore the leader can be aggressive only for exclusionary purposes. This standard result emphasizes a possible inconsistency within the model of price leadership, at least when applied to describe real markets. We have suggested that leaders are accommodating when the fixed costs of production (or entry) are small, because in such a case an exclusionary strategy would require to set a very low price and would be too costly. But these are exactly the conditions under which other firms may want to enter in the market: fixed costs are low and exclusionary strategies by incumbents are costly. Therefore, the assumption that the number of firms (and in particular of the number of followers) is fixed becomes quite unrealistic. Let us look at the Stackelberg equilibrium with endogenous entry. The solution in this case is slightly more complex, but it can be fully characterized. First of all, as usual, let us look at the stage in which the leader has already chosen its price pL and the followers enter and choose their prices. As before, their choice will follow the rule: 1 pi = c + λ(1 − Di /N ) where the demand on the right hand side depends on the price of the leader and all the other prices as well. However, under free entry we must have also that the markup of the followers exactly covers the fixed cost of production: Di (pi − c) = F 23

Nevertheless, the followers will have incentives to choose a lower price than the leader, and each one of them will then have a larger demand and profits than the leader: there is a second-mover advantage rather than a first-mover advantage.

24

1. Competition, Leadership and Entry

If the price of the leader is not too low or the fixed cost not to high, there is indeed entry in equilibrium and we can solve these two equations for the demand of the followers and their prices in the symmetric equilibrium: p=c+

1 F + , λ N

D=

λF N N + λF

(1.37)

Notice that neither one or the other endogenous factors depend on the price chosen by the leader. Therefore, it must be that the strategy of the leader is going to aﬀect only the number of followers entering in equilibrium, but not their prices or their equilibrium production. The leader is going to perceive this because its demand can now be calculated as: N e−λpL DL = Pn −λpj = Deλ(p−pL ) i=1 e

Since neither p or D depend on the price of the leader as we have seen before, the perceived demand by the leader is a simple function of its own price, and its profits can be derived as: πL = (pL − c)DL − F = = (pL − c)Deλ(p−pL ) − F where we could use our previous results to substitute for p or D. Profit maximization by the leader provides its equilibrium price: pL = c +

1 1 F
(1.38)

which is now lower than the price of the followers. Finally, the number of active firms can be derived as: n=2+

N − eλF/N λF

Rather than being accommodating as in the Stackelberg equilibrium, the behavior of the leader in a Stackelberg equilibrium with endogenous entry is radically diﬀerent. The leader is aggressive since it chooses a lower price, ends up selling more of its products, and obtains positive profits.24 Nevertheless, some followers enter in the market, and they have to choose a higher price than the leader without earning any profits. 24

The profits of the leader are equal to: πL =

F NeλF/N −F >0 N + λF

which is positive under the assumption that F < N/λ. Also in this case, if the fixed cost is high enough, it may be optimal for the leader to fully deter entry, choosing a price pL = c + 1/λ + F/N − (1/λ) log(N/λF ).

1.4 A Simple Model of Competition for the Market

25

1.4 A Simple Model of Competition for the Market The last example we are going to consider introduces us to a topic that we will encounter later on in the book in Chapter 4, the competition to innovate and therefore conquer a market with new or better products. In many high-tech sectors, this is becoming a main form of competition, since the life of a product is quite short and R&D investment strategies to conquer future markets are much more important than price or production strategies. Consider the pharmaceutical sector: in this market companies like Pfizer, Bayer, Merck, Hoﬀmann-La Roche, GlaxoSmithKline and many others invest a lot in R&D to develop, test and patent new drugs, while price competition over unpatented drugs plays a minor role.25 Competition for the market works as a sort of contest. Firms invest to innovate and to win the contest. It may be that the first innovator obtains a patent on the invention and exploits monopolistic profits for a while on its innovation. It may be that the same innovator just keeps it secret and exploits its leadership on the market until an imitator replaces it. In both ways the expected gain from an innovation is what drives firms to invest in R&D. In this framework we can also study alternative market structures depending on the timing of moves and on the entry conditions. Consider a simple contest between firms to obtain a drastic innovation which has an expected value V ∈ (0, 1) for the winner and generates no gains for the losers. Each contestant i invests resources zi ∈ [0, 1) to win the contest. This investment has a cost and, for simplicity, we will assume that the cost is quadratic, that is zi2 /2. The investment provides the contestant with the probability zi to innovate. The innovator wins the contest if no other contestant innovates, for instance because in the case of multiple winners competition between them would drive profits Qn away. Accordingly, the probability to win the contest is Pr(i wins) = zi j=1,j6=i [1 − zj ] , that is its probability to innovate multiplied by the probability that no one else innovates. In conclusion, the general profit function is:26

πi = zi

n Y

j=1,j6=i

[1 − zj ] V −

zi2 −F 2

(1.39)

Consider the Nash equilibrium. The first order condition for the optimal investment by a firm i is: 25

26

See Sutton (1998, Ch. 8) for a description of competition for the market in the pharmaceutical industry. √ We adopt a more restrictive assumption, V ∈ ( 2F , 1). This guarantees profitable entry for at least one firm. Indeed, a single firm would invest z = V < 1 expecting π = V 2 /2 − F > 0. Hence, investing z = 1 and innovating for sure can be profitable, but it is not optimal.

26

1. Competition, Leadership and Entry

zi =

n Y

j=1,j6=i

[1 − zj ] V

which shows that when the investment of a firm increases, the other firms have incentives to invest less: ∂zi /∂zj < 0. Each firm chooses its own investment without taking this externality into account, therefore competition for the market generates excessive investment from the firms point of view. For instance, in the case of two firms, each one would invest z = V /(1 + V ) in equilibrium, while collusion between them would reduce individual investment to the lower level z˜ = V /(1 + 2V ), which increases expected profits for each one of the two firms.27 This suggests that a joint venture between firms competing for a market may end up reducing aggregate investment. However, notice that we cannot evaluate these outcomes from a welfare point of view without expliciting the social value of the innovation: if the social value of the innovation is high enough, the investment is too low also in the Nash equilibrium, and R&D subsidies would be needed to restore social eﬃciency. Let us go back to the general case with n firms competing for the market. Now, the equilibrium investment is implicitly given by: z = (1 − z)n−1 V In the Marshall equilibrium we must also take into account the endogenous entry condition: z(1 − z)n−1 V − z 2 /2 = F and solving the system of the two conditions we have the number of agents: ³ √ ´ log V / 2F h i n=1+ √ log 1/(1 − 2F )

and the investment: √ z = 2F

(1.40)

The investment of each firm increases with the size of the fixed cost of R&D, while entry decreases in the fixed cost and increases with the value of the innovation. 27

Also in this case we can verify when collusion is sustainable by extending the model to an infinitely repeated game. Imagine that a deviation from collusion is punished with reversion to the Nash equilibrium. One can verify that the best deviation is zD = (1 + V )V /(1 + 2V ), and collusion is sustainable for a discount factor δ > (1 + V )2 /(2 + 4V + V 2 ): more valuable innovations make it harder to sustain collusion.

1.4 A Simple Model of Competition for the Market

27

Consider now a Stackelberg equilibrium. As already noticed, when the investment by one firm is increased, the other firms have incentives to invest less: then in a Stackelberg equilibrium the leader exploits its first mover advantage by investing more than the followers, so as to reduce their investment and increase its relative probability of winning. For instance, in a Stackelberg duopoly the leader invests zL = V (1 − V )/(1 − 2V 2 ) and the follower invests z = V (1 − V − V 2 )/(1 − 2V 2 ). In a Stackelberg equilibrium with endogenous entry, as long as the investment of the leader zL is small enough to allow entry of at least one firm, the first order conditions and the free entry conditions are: (1 − z)n−2 (1 − zL )V = z,

z(1 − z)n−2 (1 − zL )V = z 2 /2 + F

which deliver the√same investment choice by each entrant as in the Marshall equilibrium, z = 2F , and the number or firms: h √ i log (1 − zL )V / 2F h i n(zL ) = 2 + √ log 1/(1 − 2F ) Putting these two equations together and substituting in the profit function of the leader, we would have: z2 πL = zL (1 − z)n−1 V − L − F = 2 2 √ ´ zL zL √ ³ 2F 1 − 2F − −F = 1 − zL 2

(1.41)

which has not an interior optimum: indeed, it is always optimal for the leader to deter entry investing enough. This requires a slightly higher investment than the one for which the hequilibrium number of firms would be n = 2. √ i Since n(zL ) = 2 requires log (1 − zL )V / 2F = 0, we can conclude that the leader will invest: √ 2F z¯L = 1 − (1.42) V which is increasing in the value of innovations and decreasing in their fixed cost. Therefore, in a contest with a leader and free entry of participants, the leader invests enough to deter investment by the other firms and is the only possible winner of the contest. 1.4.1 The Arrow’s Paradox Until now we investigated a form of competition for the market where all firms were at the same level. Often times, competition for the market is between an

28

1. Competition, Leadership and Entry

incumbent leader that is already in the market with the leading edge technology (or with the best product) and outsiders trying to replace this leadership. In such a case the incentives to invest in innovation may be diﬀerent and it is important to understand how. Arrow (1962) was one of the first economists to examine this issue in a formal way. He found that incumbent monopolists have lower incentives than the outsiders to invest. His insight was simple but powerful: while the gains from an innovation for the incumbent monopolist are just the diﬀerence between profits obtained with the next innovation and those obtained with the current one, the gains for any outsider are the full profits from the next innovation. Consequently, the incumbent has lower incentives to invest in R&D. The expected gains of the incumbent are even diminished when the number of outsiders increases. When the latter is high enough the incumbent has no more incentives to participate to the competition, and, in particular, when entry in the competition for the market is free, the incumbent does not invest at all. Such a strong theoretical result is of course too drastic to be realistic. Many technological leaders invest a lot in R&D, try to maintain their leadership, and they often manage: persistent leadership is not that unusual: for this reason the theoretical finding of Arrow is considered a paradoxical outcome, the “Arrow’s paradox” indeed. Before oﬀering a theoretical solution for this paradox, however, we will extend our model to include an asymmetry between an incumbent monopolist and the outsiders. Imagine a two period extension of the model. In the first period an incumbent monopolist can exploit its technology to obtain profits K ∈ (0, V ]. We can think of K as the rents associated with an initial leading technology or some other exogenous advantage. If these rents are constrained by a competitive fringe of firms, we can also think that an increase in the intensity of competition reduces K. In the first period any firm can invest to innovate and conquer the gain V from the next innovation to be exploited in the second period. If no one innovates, the incumbent retains its profits K alsoQ in the second period. This happens with probability Pr(no innovation) = nj=1 [1 − zj ]. Then, assuming no discounting, the expected profits of the incumbent monopolist, that we now label with the index M , are: πM = K+zM

n Y

j=1,j6=M

[1 − zj ] V +(1−zM )

n Y

j=1,j6=M

[1 − zj ] K−

2 zM −F (1.43) 2

in case of positive investment in the contest, otherwise expected profits are given only by the current profits plus the expected value of the current profits when no one innovates. The profits of the other firms are the same as previously. Before analyzing alternative forms of competition, notice that when the monopolist is assumed alone in the research activity, its optimal investment is zM = V − K. Hence, an incumbent monopolist (with K > 0) has lower incentives to invest than a firm without current profits (with K = 0): the so-called Arrow eﬀect is in action. Moreover, if we think that the intensity

1.4 A Simple Model of Competition for the Market

29

of product market competition has a negative impact on the current profits K, while it has no impact on the value of the innovation (since this is drastic and the innovator will not be constrained by product market competitors), it clearly follows that an increase in the intensity of competition reduces K and increases the investment of the monopolist and the probability of innovation zM . Aghion and Griﬃth (2005) put a lot of emphasis on this eﬀect, which they label escape competition eﬀect: “competition reduces pre-innovation rents...but not their post innovation rents since by innovating these firms have escaped the fringe. This, in turn induces those firms to innovate in order to escape competition with the fringe.”28 Now, consider a Nash equilibrium with a general number of firms. If the incumbent does not invest, the equilibrium is the same of the symmetric model, but the expected profit of the monopolist π M (zM ) must be: √ √ 2F (1 − 2F )K πM (0) = K + V which is increasing in K (decreasing in the intensity of competition) and decreasing in the value of the innovation V (since this increases the incentives of other firms to innovate and replace the monopolist). If the monopolist is investing, however, the first order conditions for the monopolist and for the other firms in Nash equilibrium would be: z = (1 − z)n−2 (1 − zM )V ,

zM = (1 − z)n−1 V − (1 − z)n−1 K

which always imply a lower investment of the monopolist because of the Arrow eﬀect. For instance, with two firms we have: zM =

(1 − V )(V − K) 1 − V (V − K)

z=

(1 − V )(V − K) + K 1 − V (V − K)

(1.44)

It is interesting to verify what is the impact of an increase in the intensity of product market competition, which lowers current profits K without aﬀecting the value of the drastic innovation V : this increases the investment of the incumbent according to the escape competition eﬀect, but it decreases the investment of the outsider.29 28

29

See Aghion and Griﬃth (2005, pp. 55-56). An increase of the intensity of competition is associated with a lower price of the competitive fringe or with a higher probability of entry of equally eﬃcient firms. Of course, the Arrow eﬀect could be counterbalanced if we introduced a technological advantage for the incumbent (Barro and Sala-i-Martin, 1995) or absorptive capacity of the incumbent (Wiethaus, 2006,a,b), that is the ability to imitate the innovation of an outsider.

30

1. Competition, Leadership and Entry

When entry of firms is free, investors enter as long as the expected profits are positive, that is until the following zero profit condition holds: z(1 − zM )(1 − z)n−2 V = z 2 /2 + F

√ This implies that each one of the other firms invests again z = 2F , and we will now show that the incumbent monopolist prefers to withdraw from the contest and not invest in R&D. To see this, notice that the monopolist should invest less than the other firms, according to its optimality condition: √ √ zM (1 − zM ) = 2F (1 − 2F )(V − K)/V This implies that the optimal investment of the monopolist √ should decrease with K: from the same level as for the other firms zM = 2F when K = 0 toward zero investment zM = 0 when approaching K = V . The profits of the monopolist in case of positive investment would be: √ √ ¸ · z2 2F (1 − 2F ) (V − K)zM + K πM (zM ) = K + − M −F V 1 − zM 2 where zM should be at its optimal level derived above. Notice that for K = 0 these expected profits are −F , so the monopolist√prefers not √ to invest at all, and for K = V the expected profits tend to K + 2F (1 − 2F ) − F , which is again lower than the expected profits in case the monopolist does not invest at all. It can be verified that this is always the case for any K ∈ (0, V ),30 hence the monopolist always prefers not to invest and decides to give up to any chances of innovation. Finally, notice that the escape competition eﬀect disappears: an increase in the intensity of competition does not aﬀect the investment of any firm or the aggregate probability of innovation. Perfect competition for the market eliminates any impact of competition in the market on the investment in innovation.31 In this simple example, the lack of incentives to invest for the monopolist emerges quite clearly. On the basis of this theoretical result, it is often claimed that monopolistic markets or markets with a clear leadership are less innovative. In a neat article on this topic appeared on the The Economist (2004, “Slackers or Pace-setters? Monopolies may have more incentives to innovate than economists have thought”, Economic Focus, May 22) this issue has been explained quite clearly: 30

31

This immediate after comparing profits for the monopolist in case of zero and positive investment in Nash equilibrium as functions of K. Not by chance, Aghion and Griﬃth (2005) obtained the escape competition eﬀect in a model where the incumbent is exogenously the only investor. In the next section we present a model where the incumbent is endogenously the only investor to verify that both the Arrow eﬀect and the escape competition eﬀect disappear in that case.

1.4 A Simple Model of Competition for the Market

31

“By and large, oﬃcialdom these days continues to take a dim view of monopoly. Antitrust authorities in many countries do not shrink from picking fights with companies that they believe are too powerful. The biggest target in recent years, first in America and now in Europe, has been Microsoft, creator of the operating system that runs on some 95% of the world’s personal computers. One of the arguments against Microsoft is that its dominance of the desktop allows it to squeeze out smaller and (say the company’s critics) more innovative rivals. Despite this, compelling evidence that monopolists stifle innovation is harder to come by than simple theory suggests. Joseph Schumpeter, an Austrian economist, pointed out many years ago that established firms play a big role in innovation. In modern times, it appears that many product innovations, in industries from razor blades to software, are made by companies that have a dominant share of the market. Most mainstream economists, however, have had diﬃculty explaining why this might be so. Kenneth Arrow, a Nobel prize-winner, once posed the issue as a paradox. Economic theory says that a monopolist should have far less incentive to invest in creating innovations than a firm in a competitive environment: experience suggests otherwise. How can this be so? One possibility might be that the empirical connection between market share and innovation is spurious: might big firms innovate more simply because they are big, not because they are dominant? A paper32 published a few years ago by Richard Blundell, Rachel Griﬃth and John Van Reenen, of Britain’s Institute for Fiscal Studies, did much to resolve this empirical question. In a detailed analysis of British manufacturing firms, it found that higher market shares do go with higher investment in research and development, which in turn is likely to lead to greater innovation. Still, the question remains: why does it happen?” We now turn to this theoretical issue. 1.4.2 Innovation by Leaders In this section we will study innovation contests where a firm can act as a leader and commit to an investment level before the other firms (Etro, 2004). It is reasonable to imagine that the firm able to commit to an investment in R&D before the others is the same incumbent monopolist that has the leading edge technology. This will be our assumption. Consider Stackelberg competition where the incumbent monopolist is the first mover. The symmetric reaction of the other firms to the investment of 32

Blundell et al. (1999).

32

1. Competition, Leadership and Entry

the leader is still governed by their equilibrium first order condition z = (1 − z)n−2 (1−zL )V , where now zL is the investment of the leader, which is known at the time of the choice of the other firms. The above rule cannot be solved analytically, but it shows again that the investment of the outsider firms must be decreasing in the investment of the leader, ∂z/∂zL < 0: the higher the latter, the smaller the probability that no one innovates and therefore the expected gain from the investment of the followers is reduced. This implies that the leader has an incentive to choose a higher investment to strategically reduce the investment of the followers. However, the investment of the leader does not need to be higher than the investment of the other firms, because the Arrow eﬀect is still pushing in the opposite direction. For instance, with two firms we have: zL =

V K + (1 − V )(V − K) 1 − 2V (V − K)

z=

V K + (1 − V )V − V 3 1 − 2V (V − K)

(1.45)

and the Arrow eﬀect prevails on the Stackelberg eﬀect whenever K > V 3 /(1− V ). When entry is endogenous, things are simpler. As long as the investment of the leader is small enough to allow entry of at least one outsider, the free entry condition √ is z(1 − z)n−2 (1 − zL )V = z 2 /2 + F , which delivers again the investment z = 2F for each outsider. Putting together the two equilibrium conditions in the profit function of the leader, we would have: z2 πL = K + zL (1 − z)n−1 (V − K) − L − F = 2 √ ´ K√ ³ √ ´ z2 zL √ ³ 2F 1 − 2F + 2F 1 − 2F − L − F =K+ 1 − zL V 2

whose third element, the one associated with the current profits obtained in case no one innovates, is independent from the choice of the leader. Consequently, the choice of the leader is taken exactly as in our earlier model (with K = 0) and requires an investment: √ 2F z¯L = 1 − (1.46) V such that no other firm invests in innovation. Therefore, the profits of the leader can be calculated as a function of the value of the innovation π L = 2 K + z¯L V + (1 − z¯L ) K − z¯L /2 − F . Welfare comparisons are ambiguous: on one side the aggregate probability of innovation is lower under Stackelberg competition with free entry rather than in the Marshall equilibrium, on the other side expenditure in fixed and variable costs of research is lower in the first than in the second case.33 33

However, in a dynamic environment where the value of the innovation is endogenous, things would change. While without a leadership of the monopolist,

1.4 A Simple Model of Competition for the Market

33

Moreover, notice that when the monopolist is the leader in the competition for the innovation, the Arrow eﬀect disappears, because the choice of the monopolist is independent from the current profits. The leadership in the competition for the market radically changes the behavior of a monopolist: from zero investment to maximum investment. The cited article of The Economist (2004) has discussed the relation between this theory and innovation by monopolists in real world markets. When entry is endogenous: “a market leader has a greater incentive than any other firm to keep innovating and thus stay on top. Blessed with scale and market knowledge, it is better placed than potential rivals to commit itself to financing innovations. Oddly–paradoxically, if you like–in fighting to maintain its monopoly it acts more competitively than firms in markets in which there is no obviously dominant player. The most important requirement for this result is a lack of barriers to entry: these might include, for example, big capital outlays to fund the building of new laboratories, or regulatory or licensing restrictions that make it hard for new firms to threaten an incumbent. If there are no such barriers, a monopolist will have an excellent reason to innovate before any potential competitor comes up with the next new thing. It stands to lose its current, bloated profits if it does not; it stands to gain plenty from continued market dominance if it does. If the world works in the way Mr Etro supposes, the fact that a dominant firm remains on top might actually be strong evidence of vigorous competition. However, observers (including antitrust authorities) may well find it diﬃcult to work out whether a durable monopoly is the product of brilliant innovation or the deliberate strangulation of competitors. More confusing still, any half-awake monopolist will engage in some of the former in order to help bring about plenty of the latter. The very ease of entry, and the aggressiveness of the competitive environment, are what spur monopolists to innovate so fiercely. But what if there are barriers to entry? These tend to make the dominant firm less aggressive in investing in new technologies–in essence, because its monopoly with the existing technology is less likely to be challenged. Over time, however, other companies can innovate and gradually overcome the barriers... Meanwhile, the monopolist lives on marked time, burning oﬀ the fat of its past innovations. the value of innovation would be just the value of expected profits from this innovation (the innovator will not invest further), with a leadership by the monopolist, the value of innovation should take into account the option value of future leadership and future innovations: this would endogenously increase the value of being an innovator and would increase the aggregate incentives to invest. We will return on this important point in Chapter 4.

34

1. Competition, Leadership and Entry

So much for theorizing. What might the practical implications be? One is that antitrust authorities should be especially careful when trying to stamp out monopoly power in markets that are marked by technical innovation. It could still be that firms like Microsoft are capable of using their girth to squish their rivals; the point is that continued monopoly is not cast-iron evidence of bad behavior. There might be a further implication for patent policy. Patents, after all, are government-endorsed monopolies for a given technology for a specified period. Mr Blundell and his colleagues found that the pharmaceutical industry provided the strongest evidence of correlation between market share and innovation. Thus strong patents, despite their recent bad press, can be a source of innovation. Generally, though, when one company dominates a market, people should be careful in assuming that it is guilty of sloth. It may be fighting for its life.” The idea behind this discussion can be described in simpler terms as a derivation of two suﬃcient conditions under which monopolists have incentives to invest in R&D and to invest more than other firms: 1) leadership for the monopolist and 2) endogenous entry for the outsiders in the race to innovate. We will return on these issues in Chapter 4, and discuss their policy implications in Chapters 5 and 6. Finally, we confirm that, also when the incumbent monopolist endogenously invests in R&D, the escape competition eﬀect disappears: an increase in the intensity of product market competition as formalized by Aghion and Griﬃth (2005) does not aﬀect innovation when entry in the competition for the market is free. This may suggest that competition for the market could be a good substitute for competition in the market, another point on which we will return later in the book.

1.5 Conclusions In this chapter we developed some toy models to compare diﬀerent equilibria. Toy models can be quite suggestive and even provide many interesting insights, however they often hide very simplistic assumptions and it is hard to understand whether certain results hold in general or just under specific assumptions. That is why it is now time to generalize our models at a deeper level. The objective of the next chapters will be an investigation of the general properties of our four alternative equilibria. Moreover, in this chapter we developed examples in which firms compete strategically in a symmetric way, or in which a firm is a leader and has a first mover advantage in the choice of its strategy. Since a commitment to a strategy (especially a price strategy) can lack credibility (especially in the long run), it is important to verify whether alternative credible commitments

1.5 Conclusions

35

or strategic investments can sustain results similar to those derived here. In Chapter 2 we will approach this issue developing a general model of strategic commitments. Before moving to this task, however, it is important to summarize what we have learned with our toy models. First, we considered simple models of competition in quantities. We noticed that market leaders produce more output than each one of the other followers, both in the case of exogenous entry and in the case of endogenous entry. As we will see, this does not always hold with exogenous entry, but it always holds with endogenous entry. We also noticed that in certain situations (homogenous goods and constant marginal costs) leaders deter entry when entry is endogenous, while in other cases (U shaped average cost functions or imperfect substitutability between goods) they do not and allow entry. We also noticed that the behavior of market leaders under price competition was radically diﬀerent depending on the entry conditions. It is important to understand what drives these results, and we will explore this issue in Chapter 3. Finally, we looked at a simple model of competition for the market and obtained a surprising result. While incumbent monopolists do not have incentives to invest in R&D if the competition for innovating is free and symmetric between all firms, when these incumbents have a leadership in the competition for the market they also have strong incentives to invest and end up being the only investors. If this is the case, their leadership should be persistent over time and innovation and technological progress would be driven by market leaders. In Chapter 4 we will generalize the model of competition for the market in realistic ways and will try to evaluate these drastic results.

36

1. Competition, Leadership and Entry

1.6 Appendix 1. Taking Care of the Integer Constraint. In the derivation of the Stackelberg equilibrium with endogenous entry, homogenous goods and constant marginal costs of Section 1.1 we simplified things assuming that the number of firms was a real number. Here we verify that the equilibrium is exactly the same even if we consider, more realistically, that the number of firms in the market must be an integer. We provide a constructive proof since this is helpful to understand the general behavior of the profits of the leader in a more general version where the integer constraint on the number of firms is taken in consideration. Given the production of the leader qL and the number of firms n, the reaction function and the profits of each follower are the same as before. However, the number of firms is a step function of the output of the leader. In particular, the number of firms is given by the integer number n ≥ 2 when the output of the leader is between s(n) and s(n − 1), where these cut-oﬀs are defined as: √ s(n) ≡ a − c − (n + 1) F while only the leader can be profitably in the market (n = 1) when qL > s(1). Let us remember that for any exogenous number of firms the profits of the leader are maximized at the monopolistic output (a − c)/2, and therefore this profits are increasing before and decreasing after this output level. Given this, we can determine the behavior of the profits of the leader in function of its output distinguishing three regions. The high output region, emerges for a small √ enough number of firms n such that s(n) > (a − c)/2 or n < (a − c)/2 F − 1. In such a case, the profit of the leader is decreasing in its output and it must be that in any interval qL ∈ [s(n), s(n − 1)] profits are locally maximized for qL = s(n). In correspondence of this production, each one of the n followers must supply: µ ¶ a − s(n) − c n+1 √ q (s(n), n) = F = n n We can rewrite the profits of the leader as a function of the number of firms allowed to enter in the market: πL (n) = s(n) [a − s(n) − (n − 1)q(s(n), n)] − cs(n) − F = · µ ¸ ¶ ³ √ ´ √ n+1 √ = a − c − (n + 1) F (n + 1) F − (n − 1) F −F = n µ ¶ ³ √ ´ n+1 √ = a − c − (n + 1) F F −F = n µ ¶ 2 √ (n + 1) n+1 = (a − c) F − F −F n n

1.6 Appendix

37

It can be easily verified that π L (n) > π L (n + 1) for any number of firms active in this region, therefore it is optimal to choose a production that maximizes profits √ with n = 1, that is exactly the entry deterrence output s(1) = a − c − 2 F . This output delivers the profits: √ ³ √ ´ πL (1) = 2 F a − c − 2 F − F

The low output region emerges for any high enough number of firms n √ such that s(n − 1) < (a − c)/2, or n > (a − c)/2 F . This implies that the profits of the leader are always increasing in the output. Trivially, it is never optimal to produce less than the monopolistic output. The third case emerges for a number of firms such that s(n) < (a−c)/2 < s(n − 1), or: µ ¶ a−c a−c √ − 1; √ n∈ 2 F 2 F In the interval of production xL ∈ [s(n), s(n − 1)] it is optimal for the leader to choose the monopolistic output level, because (only) in this interval profits have an inverted U shape. In this interval, the leader produces (a − c)/2 and each one of the n−1 followers produces (a−c)/2n as in a standard Stackelberg model with an exogenous number of firms. The usual profits of the leader are then: 2

πL (n) =

(a − c) −F 4n

and we need to verify that these are always smaller than what the leader can obtain with the entry deterrence strategy. Since: πL (1) R π L (n)

⇔

(a − c)2 √ nR √ 8 F (a − c − 2 F )

the profit maximizing choice of the leader could be in this region if there is a number of firms n that belongs to the set derived above and that is lower than the cut-oﬀ√just obtained. However, this requires that this cut-oﬀ is larger than (a − c)/2 F − 1 and: a−c (a − c) (a − c)2 √ √ > √ − 1 iﬀ F > 16 8 F (a − c − 2 F ) 2 F

2

This is impossible because we assumed F < (a − c)2 /16 to exclude the case of natural monopolies. In conclusion, the global optimum for the leader is always entry deterrence.

38

1. Competition, Leadership and Entry

2. Endogenous Costs of Entry. The theory of Stackelberg competition with endogenous entry can also be seen as depicting the way a market leader can extract rents from a competitive market in the presence of fixed costs of entry. These costs can be interpreted as technological costs that are taken as given by the firms. However, they can also be endogenized imagining that they characterize the market and that the same leader can choose them in a preliminary stage. For instance, by investing in R&D or paying for an advertising campaign, or even by establishing certain barriers to entry associated with a cost of entry, the leader can set a sort of benchmark: all the other firms have to undertake the same investment, pay the same advertising campaign or face the same costs of entry to be able to compete in the market (Sutton, 1998). Imagine that the leader can choose the investment F . Consider for simplicity the linear example of competition in quantities of Section 1.1. The demand and cost characteristics of this market depend on this investment so that the parameters a(F ) and c(F ) are now functions of the endogenous investment. This will be chosen to maximize the expected profits of the leader: √ h √ i πL (F ) = 2 F a(F ) − c(F ) − 2 F − F

In general, the choice will imply a positive investment (otherwise the leader would expect zero profits). One can also show that from a welfare point of view, the leader will choose an excessive investment if this investment reduces its equilibrium production, but will choose a suboptimal investment in the opposite case.34 In other words, leaders tend to do too little of good things and too much of bad things. For instance, imagine that F serves no real purpose other than raising the cost of entry (a0 (F ) = c0 (F ) = 0). This is the case of what we usually call an artificial barrier to entry created by the dominant firm. The leader would maximize its expected profits choosing a positive barrier to entry: F∗ =

(a − c)2 25

which delivers the net profits: πL =

(a − c)2 5

In other words the leader would create a completely useless barrier associated with a fixed cost (born by the leader as well) just to profit ex post from its entry deterring strategy. Of course, in this case the welfare maximizing 34

This is an immediate consequence of the definition of welfare as a sum of consumer surplus and profits. When profits of the leader are maximized the investment is excessive if the consumer surplus is decreasing in the investment, that is if output is decreasing. Of course this is still a second best comparison.

1.6 Appendix

39

barrier would be F = 0, which would lead to complete rent dissipation and marginal cost pricing with zero profits for everybody. The moral of this story is that the priority in industrial policy should be to create the conditions for free entry and hence to fight against artificial barriers to entry, not to fight against leaders per se.

Index

Abreu, Dilip, 8 Absorptive capacity, 29 Abuse of dominance, 6, 171, 174, 195, 197, 200 Accommodating philosophy, 252 Acemoglu, Daron, 156 Ad valorem tax, 53, 57 Adobe, 210, 233 Adverse selection, 84 Advertising, 63, 70, 78, 249 Aerts, Kris, 159 Aggressive philosophy, 252 Aghion, Philippe, 29, 31, 34, 141, 148, 150, 155, 157, 160, 162, 164 Ahlborn, Christian, 176 Airbus, 66, 120 Aircraft industry, 66, 120 Airline industry, 244, 247 Akerlof, George, 84 Allen, Paul, 215 Amazon, 213 America Online, 219 America’s Cup, 251 American Express, 224 Amir, Rabah, 16, 52, 76 Anant, T.C.A., 155 Anderson, Simon, 21, 46, 55, 107, 113, 116, 123, 124 Apple, 131, 209—211, 215, 225, 228, 233 Application Programming Interfaces, 210 Areeda, Phillip, 198 Areeda-Turner rule, 198 Armani, 21

Armstrong, Mark, 78 Arrow’s paradox, 27, 31, 133, 137, 140, 146, 187, 228 Arrow, Kenneth, 28, 31, 133, 218 Article 81 of EU Treaty, 172 Article 82 of EU Treaty, 172, 195 Asymmetric information, 69, 84, 85, 177 Asymmetries between leaders and followers, 109 AT&T, 93, 220, 221 Atari, 215 Aumann, Robert, 8 Automobile industry, 15 Average Avoidable Cost, 200 Average Total Cost, 16, 199 Average Variable Cost, 198, 199, 201 Bain, Joe, 3, 93, 178 Ballmer, Steve, 218 Banking sector, 183, 244 Barriers to entry, 33, 108, 178, 186, 224, 244 Barro, Robert, 29, 155, 157, 223 Baumol, William, 3, 14, 21, 93, 105, 176, 179 Baxter, William, 213 Bayer, 25 Bayesian equilibrium, 2, 69, 84 Beath, John, 133 Becker, Gary, 70 Benetton, 21 Bergman, Mats, 245 Berry, Stephen, 248 Bertrand equilibrium, 86

276

Index

Bertrand, Joseph, 20, 46, 54, 56, 106, 162 Bessen, Jim, 151, 191 Bilbiie, Florin, 254 BlackBerry, 211, 215 Bloom, Nick, 150 Blundell, Richard, 31, 34, 134, 150, 156, 160 Boeing, 66 Boldrin, Michele, 156, 193, 194 Bonanno, Giacomo, 43, 82—84, 177, 185 Bonus-malus insurance, 85 Boone, Jan, 122 Bork, Robert, 79, 88, 119, 174, 179, 182 Boston Consulting Group, 186 Bowley model, 46 Boycko, Maxim, 123 Brander, James, 43, 72, 74, 120, 177 Brealey, Richard, 72 Bresnahan, Timothy, 219, 248 Brin, Sergey, 238 Bulow, Jeremy, 42, 68, 114, 177 Bundling, 43, 79, 185, 201, 205, 221, 230, 232, 234 Bush, George W., 221 Buxant, Martin, 237 Cable, John, 155 Caillaud, Bernard, 212 Cambini, Carlo, 63 Campari, 237 Capital-labour ratio, 115 Carlton, Dennis, 93 Cartels, 118, 150, 205 Cawley, John, 85 Cellophane fallacy, 200 CES demand, 55, 57, 107, 127 Chamberlin, Edward, 46 Champions League, 251 Chandler, Alfred, 132, 187 Chanel, 237 Chevalier, Judith, 75, 250 Chiappori, Pierre Andre, 85 Chicago school, 44, 79, 88, 119, 173, 174, 186, 204, 229, 230, 255

Clayton Act, 175 Clinton, Bill, 218 Coase, Ronald, 239 Coca-Cola, 237 Cohen, Wesley, 141 Collusion, 7, 26, 118, 148, 150 Competition for the market, 1, 25, 27, 31, 45, 108, 124, 131, 135, 142, 151, 159, 186, 189, 195, 196, 198, 203, 205, 229, 235, 246, 250 Competition in prices, 2, 20, 41, 44, 50, 54, 67, 71, 73, 79, 82, 84, 100, 106, 115, 121, 183, 212, 227, 246, 249, 252 Competition in quantities, 1, 4, 16, 18, 36, 41, 44, 50, 66, 70, 73, 76, 91, 100, 111, 115, 121, 180, 197, 227, 246, 248 Competitive strategy, 59, 252 Corporate finance, 43, 72 Cost reductions, 66 Cournot duopoly, 5, 111 Cournot, Augustin, 1, 52, 102 Court of First Instance, 172, 223 Cowell, Frank, 53 Cozzi, Guido, 154, 194 Credit cards, 78, 224 Cremer, Jacques, 77 Czarnizki, Dirk, 133, 149, 250 D’Aspremont Claude, 46 Darwinian selection eﬀect, 161 Dasgupta, Partha, 133, 136 Davidson, Carl, 87 Davis, Stephen, 231 De Bondt, Raymond, 67, 151 de Palma, Andrè, 21, 46, 55, 107, 116, 123, 124 Debt financing, 72, 150, 250 Deep pocket theory of predation, 76 Dell, 210, 216 Demsetz, Harold, 188 Deneckere, Raymond, 87 Denicolò, Vincenzo, 151, 154, 161, 162, 194 Department of Justice, U.S.A., 171, 218, 221

Index Diners Club, 224 Dinopoulos, Elias, 155 Director, Aaron, 174 Discover, 224 Distinct products test for bundling, 202 Dixit, Avinash, 2, 41, 55—57, 60, 91, 93, 127, 177 Dominance, 171, 174, 186, 196, 200 Dominant firm theory, 93 Dorfman, Robert, 71 Dorfman-Steiner condition, 71 Dosi, Giovanni, 208 Du Pont, 132, 200 Ducati, 121 Dynamic ineﬃciency, 159 Eaton, Jonathan, 120, 122 eBay, 213 Economides, Nicholas, 113, 227, 231 Economies of scope, 68 Eﬃciency defense, 196 Ellison, Glenn, 245 Ellison, Sarah, 245 Elzinga, Kenneth, 219 Encaoua, David, 116 Endogenous costs of entry, 38 Endogenous entry, 2, 3, 9, 12, 16, 17, 19, 22, 23, 26, 27, 30, 32, 36, 38, 42, 49, 53, 54, 57, 59, 63, 67, 71, 74, 77, 81, 83, 86, 88, 91, 97, 102, 107—109, 119, 121, 134, 138, 144, 146, 150, 178, 199, 224, 228, 232, 236, 243, 252 Endogenous leadership, 113 Engers, Maxim, 113 Entry deterrence, 3, 7, 13, 18, 20, 24, 27, 32, 36, 66, 69, 77, 79, 91, 98, 104, 108, 111, 177, 181, 197 Equity-Debt ratio, 72, 250 Erkal, Nisvan, 87, 104, 116, 117, 150, 151, 194 Erkal-Piccinin model, 88 Escape competition eﬀect, 29, 30, 34, 140, 143, 145, 148, 149, 159 Essential facility, 203

277

Etro, Federico, 12, 31, 33, 42, 53, 63, 74, 85, 92, 97, 111, 121, 122, 134, 138, 146, 150, 153, 154, 158, 159, 163, 178, 179, 191, 195, 200, 218 European Commission, 172, 195—197, 200, 201, 203, 204, 218, 221, 223, 235, 236, 240 European Court of Justice, 172, 223 European Parliament, 191 Evans, David, 176, 202, 207, 209, 212, 217, 219, 223, 228 Excel, 210, 217 Exclusive dealing, 83 Exclusive territories, 83 Export promoting policy, 120 Farrell, Joseph, 6 Fashion industry, 21 Fat cat strategy, 63, 72, 248 Favaro, Edgardo, 244 Federal Trade Commission, U.S.A., 171, 218 Ferrari, 15 FIAT, 15 Financial predation, 76 Financial structure, 72, 250 Firefox, 192, 233 First degree price discrimination, 84 Fisher, Franklin, 219, 226 Foncel, Jerome, 226, 227 Ford, 15 Formula 1, 251 Franchise fees, 82 Free Software Movement, 192 Friedman, James, 8 Front-loading eﬀect, 161 Fudenberg, Drew, 2, 8, 42, 60, 61, 63, 72, 96, 133, 177, 225 Fudenberg-Tirole taxonomy, 61 Gabszewicz, Jean, 46 Galbraith, John, 132, 187 Galilei, Galileo, 189 Gap, 21 Gates, Bill, 209, 210, 215

278

Index

Geanakoplos, John, 42, 68, 114, 177 General Motors, 15 General Public License, 192, 239 Ghironi, Fabio, 254 Gilbert, Richard, 111, 133, 140, 148 GlaxoSmithKline, 25 Goldfain, Katerina, 59 Google, 213, 218, 238 Goolsbee, Austan, 244 Green, Jerry, 56 Grieben, Wolf-Heimo, 159 Griﬃth, Rachel, 29, 31, 34, 134, 148, 150, 156, 160, 162, 164 Griliches, Zvi, 141, 156 Grossman, Gene, 120, 122 Gual, Jordi, 172, 173 Gucci, 21 H&M, 21 Hagiu, Andrei, 209, 217, 228 Hall, Brownin, 156 Hall, Chris, 227 Hall, Robert, 227 Hamilton, Jonathan, 113 Harley & Davidson, 121 Harrington, Joseph, 93 Harris, Christopher, 133 Harsanyi, John, 2 Hart, Oliver, 76 Hausman, Jerry, 156 Hellwig, Martin, 172, 173 Helpman, Elhanan, 120 Hewlett-Packard, 132, 192, 209, 210, 216 Hirshleifer, Jack, 69 Hoﬀmann-La Roche, 25 Holmstrom, Bengt, 76 Homogenous goods, 4, 16, 52, 101 Honda, 121 Horizontal diﬀerentiation, 45 Hotelling model, 45, 62 Hotelling, Harold, 45 Howitt, Peter, 141, 150, 155, 157, 160 Hughes, Danny, 188 Hyperbolic demand, 53, 102, 105

IBM, 132, 192, 193, 208, 212, 223, 228 Implications of the theory of market leaders for business administration, 252 Impullitti, Giammario, 159 Industrial revolution, 208 Information and Communication Technology, 207 Informative advertising, 70, 79 Insurance market, 84, 85 Intel, 66, 131, 132, 192, 206, 208 Interbrand competition, 82, 185, 249 International Chamber of Commerce, 195 Internet, 207, 218, 219 Interoperability, 43, 81, 204, 222, 235, 236, 240 Ionascu, Delia, 122 iPhone, 131, 193, 211, 215 iPod, 131, 211, 233 IPRs, 121, 151, 164, 187, 189, 192, 194, 203, 204, 223, 235, 236, 238—240, 244 Ivaldi, Mark, 226, 227 Java, 218 Jobs, Steve, 209 Jullien, Bruno, 212 Kadiyali, Vrinda, 248 Katsoulacos, Yannis, 133, 172, 186 Katz, Michael, 76 Keen, Michael, 53 Keun, Huh, 133, 246 Klein, Benjamin, 219 Klemperer, Paul, 42, 68, 114, 177 Klepper, Steven, 141 Kodak, 132, 248 Kortum, Samuel, 141, 156 Koski, Heli, 192 Kotler, Philip, 59, 70, 252 Koulovatianos, Christos, 159 Kovac, Eugen, 68, 122 Kraft, Kornelius, 133, 149, 250 Kreps, David, 177 Kroes, Neelie, 222

Index Krugman, Paul, 120, 220, 221 Laﬀont, Jean-Jacques, 62, 69 Lambin, Jean-Jacques, 70 Lambson, Eugen, 52 Lazzati, Natalia, 76 Leadership in prices, 23, 106, 107, 115, 122, 183 Leadership in quantities, 10, 12, 17, 19, 100, 102, 111, 115, 121, 180 Lean and hungry look, 63, 64, 248 Leapfrogging, 157, 254 Learning by doing, 43, 66 Lee, Tom, 133, 142 Lerner, Josh, 192, 225 Leverage buyouts, 75 Leverage theory of tied good sales, 79, 81 Levine, David, 156, 193, 194 Levinsohn, James, 248 Lewis, Tracy, 43, 72, 74, 177 Liberalizations, 123 Licenses, 238 Liebowitz, Stan, 217, 219, 239 Limit pricing, 3, 7, 13, 18, 20, 24, 36, 66, 69, 77, 91, 104, 177, 181, 197, 225 Linn, Joshua, 156 Linux, 192, 210, 216, 224, 225 Logit demand, 21, 54, 57, 107, 116, 127 Long-purse theory of predation, 76 Long-run Average Incremental Cost, 201 Loury, Glenn, 59, 133, 136 Maggi, Giovanni, 120 Malerba, Franco, 132, 250 Mankiw, Gregory, 103 Mann, Ronald, 191 Margolis, Stephen, 217, 219, 239 Marketing, 59, 252 Marketing mix 4 P’s model, 59, 249, 252 Marshall equilibrium, 2, 9, 16, 19, 22, 26, 30, 41, 49, 53, 54, 57, 59, 64, 138, 144, 149, 153, 166, 181

279

Marshall, Alfred, 2 Martin, Stephen, 243 Mas-Colell, Andreu, 56 Maskin, Eric, 8, 85, 151, 191 MasterCard, 224 McFadden, Daniel, 21 McGee, John, 175, 199 McKenzie, Richard, 224 Melitz, Marc, 254 Merchant guilds, 134 Merck, 25, 132 Mergers, 6, 43, 87, 171, 205 Merges, Robert, 191 Microsoft, 31, 34, 132, 207, 208, 210, 212, 215, 218, 223, 225, 228, 230, 235, 240 Microsoft Surface, 193, 229, 230 Microsoft vs. EU case, 221 Microsoft vs. US case, 218 Milgrom, Paul, 59, 69, 177 Miller, Merton, 72 Minniti, Antonio, 159 Modigliani, Franco, 3, 72, 93 Modigliani-Miller Theorem, 43, 72, 76 Monopolistic competition, 58 Monopoly, 5, 7, 53, 79, 118, 176, 185, 188, 189, 193, 223, 228, 251 Monti, Mario, 221 Moore’s Law, 131 Mosaic, 219 Most-favored-customer clause, 63 Motorola, 132, 210, 211 Motta, Massimo, 87, 171, 231 Mozilla, 192, 233 MP3 players, 131 Mueller, Dennis, 155 Mukherjee, Arijit, 87 Multi-homing, 79, 213, 225, 234 Multi-sided markets, 43, 76, 185, 198, 201, 202, 212, 217, 226 Multimarket competition, 68 Multiple leaders, 110 Multiple strategies, 114 Murphy, Kevin, 70, 231

280

Index

Myers, Stewart, 72 Myerson, Roger, 2 Myles, Gareth, 53 Nash equilibrium, 1, 8, 16, 19, 22, 25, 29, 41, 48, 52, 54, 57, 59, 61, 138, 143 Nash, John, 1 National Champions, 120 Netscape, 218, 219, 223, 231—233 Network eﬀects, 43, 76, 184, 188, 198, 201, 202, 210, 212, 217, 225, 226, 232, 234, 239 Newbery, David, 140, 148 Nichols, Albert, 219 Nintendo, 215 Nokia, 132, 211 Non-drastic innovations, 148 Nordhaus, WIlliam, 189 Novell, 192, 223, 224 Novshek, William, 2, 52 NTT, 212 Ogilvie, Sheilagh, 134 Open source software, 192, 193, 222, 229 Operating System, 192, 209, 210, 213, 215, 218, 221, 223, 225, 228—230, 238 Optimal export subsidy with price competition, 122 Optimal export subsidy with quantity competition, 121 Optimal protection of IPRs, 189, 190, 194, 196, 203, 235 Oracle, 192, 223 Orsenigo, Luigi, 132, 250 Padilla, Jorge, 176 Page, Larry, 238 Pakes, Ariel, 156, 248 Palm OS, 211 Panzar, John, 3, 14, 21, 93, 105, 176 Patent races, 133, 135, 142, 152, 155 Patentability of Computer Implemented Inventions, 191 Patents, 34, 151, 189, 191, 192, 194, 203, 204, 223, 235, 236, 238, 240, 244

PC industry, 207, 208, 210, 225 Peretto, Pietro, 157 Perloﬀ, Jeﬀrey, 93 Perrot, Anne, 172, 173 Persistence of leadership, 27, 29—32, 34, 66, 131, 135, 138, 142—144, 146, 148, 151—153, 155, 157—159, 162, 186, 189, 194, 195, 203, 205, 228, 235, 236, 250, 251 Pfizer, 25, 132 Pharmaceutical sector, 25, 190, 245 Philipson, Tomas, 85 Photographic film industry, 248 Piccinin, Daniel, 87, 104, 116, 117, 150 PlayStation, 210, 215, 218 Poisson process, 136 Political leadership, 254 Polo, Michele, 172, 173 Pooling equilibrium, 69, 84, 85 Porter, Michael, 59, 252 Posner, Richard, 79, 88, 119, 174, 175, 184, 220, 228, 229 post-Chicago approach, 69, 173, 176, 177, 186, 204, 227, 232, 253 PowerPoint, 217 Prantl, Susanne, 160 pre-Chicago approach, 174, 176 Predatory pricing, 7, 69, 175, 177, 183, 197, 205 Prescott, Edward, 113 Price discrimination, 43, 84, 185, 205 Principal-agent models, 59, 254 Privatizations, 123 Product diﬀerentiation, 18, 88, 104, 106, 181, 183, 246 Public enterprises, 123 Public production of private goods, 123 Public-private partnerships, 190 Puppy dog strategy, 62, 248 Quadratic utility function, 51, 116 Quality-price ratio, 115, 249 Quantity discounts, 82, 84 QWERTY, 240

Index Röller, Lars-Hendrick, 247 R&D Cartels, 26, 151 R&D investment, 25, 27, 31, 66, 131, 135, 142, 151, 159, 186, 189, 194, 203, 228, 235, 249, 250 R&D leadership, 26, 31, 66, 108, 131, 139, 144, 146, 150, 153, 157, 186, 235, 250 R&D subsidies, 26, 121, 159 RAND terms, 222, 238 Ready-to-eat cereal industry, 71, 246 Reagan, Ronald, 176 RealNetworks, 215, 221 Rebates, 82 Red Hat, 192, 224 Refusal to supply, 203 Reinganum, Jennifer, 133, 143, 145, 153 Reksulak, Michael, 190 Rent seeking, 45, 59, 254 Repeated games, 8 Resale price maintenance, 83 Research Joint Ventures, 151 Retailers, 82, 185, 249 Rey, Patrick, 43, 62, 77, 82, 84, 172, 173, 177, 185 Reynolds, Roberts, 87 Rhee, Ki-Eun, 171 Riley, John, 69, 85 Roberts, John, 59, 69, 177 Rochet, Jean-Charles, 78, 212 Rochet-Tirole rule, 78, 201, 214 Rockefeller, 175 Romer, Paul, 155, 220 Rothschild, Michael, 84, 85 Rothschild-Stiglitz model, 84 Rubinfeld, Daniel, 219, 226 Rudholm, Niklas, 245 Rule of reason, 175, 198, 201 Sala-i-Martin, Xavier, 155, 157 Salaniè, Bernard, 85 Salant, Stephen, 87, 149 Schelling, Thomas, 2 Scherer, Frederic, 133, 246

281

Schmalensee, Richard, 72, 207, 209, 217, 226, 228 Schmidt, Klaus, 172, 173 Schmidt, Tobias, 159 Schumpeter, Joseph, 31, 132, 135, 157, 187 Schumpeterian growth, 155, 158, 160, 166 Scotchmer, Suzanne, 151, 156, 159, 188, 239 Second degree price discrimination, 84 Sega, 215 Segerstrom, Paul, 155, 156, 159, 206, 236 Seinfeld, Jerry, 255 Selten, Reinhard, 2 Separating equilibrium, 69, 84, 85 Sequential innovations, 151, 152, 154, 187, 229, 235 Shakespeare, William, 63 Shapiro, Carl, 6, 76, 220 Shapley, Lloyd, 8 Sherman Act, 171 Shleifer, Andrei, 123 Showalter, Dean, 72, 74 Shubik demand, 117 Shubik, Martin, 116 Shughart II, William, 190 Sickles, Robin, 247 Siemens, 211 Signaling, 69 Slutsky, Steven, 113 Smart phones, 131, 211, 212 Software market, 191, 192, 207, 208, 210, 212, 215, 218, 223, 225, 228, 230, 235, 240 Software platforms, 212 Sony, 210, 211, 215, 218 Southwest Airlines, 244 Specific tax, 53 Spence, Michael, 55, 69, 91 Spencer, Barbara, 120 Spiller, Pablo, 244 SSNIP test, 200

282

Index

Stackelberg equilibrium, 2, 10, 17, 19, 23, 27, 31, 94, 100, 106, 108, 138, 144 Stackelberg equilibrium with endogenous entry, 3, 12, 17, 19, 21, 23, 27, 32, 36, 38, 91, 94, 97, 102, 105, 107—110, 113, 114, 121, 139, 146, 149, 153, 162, 167, 180, 183, 187, 241, 248, 252 Stackelberg, Heinrich von, 2, 52, 91, 100 Stallman, Richard, 192 Standard Oil Trust, 175 Standards, 238 State aids, 120, 205 Steiner, Peter, 71 Stenbacka, Rune, 172, 173 Sticky entry, 253 Stigler, George, 179 Stiglitz, Joseph, 2, 41, 43, 55—57, 74, 82, 84, 85, 127, 133, 136, 177, 185, 223 Strategic commitments, 23, 41, 42, 59, 61, 63, 118, 120, 123, 150, 184, 232, 249 Strategic complementarity, 42, 47, 49—52, 56, 60—63, 65, 68, 74, 81, 92, 96, 99, 106, 143 Strategic substitutability, 42, 47, 49—51, 59—63, 65, 66, 68, 74, 92, 96, 99, 102, 108 SubGame Perfect Equilibrium, 2, 10, 12, 63, 94, 97, 113 Sun Microsystems, 192, 219, 223 Sunk costs, 38, 179 Supergames, 8 Supermarkets vs retail business, 176 Sutton, John, 38, 66, 179, 209 Switzer, Sheldon, 87 Sylos Labini, Paolo, 3, 93 Symbian, 211, 218 Syverson, Chad, 244 Tax evasion, 53 Tax incidence, 53, 57 Tesoriere, Antonio, 111, 112, 114

Testing the theory of market leaders, 243 Theory of contestable markets, 3, 14, 21, 93, 105, 176 Third degree price discrimination, 85 Thisse, Jean Francois, 21, 46, 55, 107, 116, 123, 124 Thomas, Louis, 243, 246 Tirole, Jean, 2, 42, 60—63, 69, 70, 72, 76—78, 81, 83, 84, 96, 133, 177, 192, 212, 225 Tollison, Robert, 190 Top dog strategy, 62, 64, 79, 248 Torvalds, Linus, 192 Toyota, 15 Trade Policy, 120 Trade secrets, 236, 237 Tullock, Gordon, 59 Turner, Donald, 198 Tying, 79, 177, 185, 201, 219, 221, 230 U-shaped cost functions, 15, 16, 103, 181, 198 Ulph, David, 133, 186 US Patent and Trademark Oﬃce, 191 Valletti, Tommaso, 63 Van Reenen, John, 31, 134 Vandekerckhove, Jan, 67, 151 Venture capital financing, 150 Vernon, John, 93 Vertical diﬀerentiation, 71, 115 Vertical integration, 82 Vertical restraints, 43, 82, 185, 205, 249 VHS, 240 Vickers, John, 43, 82—84, 133, 163, 177, 185 Vickrey, William, 46 Videogame industry, 210, 215 Vinogradov, Viatcheslav, 68 Visa, 224 Viscusi, Kip, 93 Vishny, Robert, 123 Visscher, Michael, 113 Vives, Xavier, 95, 111, 113

Index Vodafone, 212 von Weizsacker, C.C., 2, 17

Webb-Pomerene Act, 120 Weiss, Andrew, 74 Welfare analysis, 14, 104, 108, 126, 127, 141, 148 Whinston, Michael, 43, 56, 79, 81, 83, 103, 177, 185, 232 Wiethaus, Lars, 29 Wikipedia, 193 Wilde, Louis, 133, 142 Williamson, Oliver E., 6 Willig, Robert, 3, 14, 21, 93, 105, 176 Wilson, Robert, 177

283

Windows, 210, 216, 218, 219, 221, 225, 229, 231 Windows MediaPlayer, 217, 221, 231 Word, 210, 217 World Trade Organization, 120 World Wide Web, 207, 218 Wozniak, Steve, 209 Xbox, 210, 215, 218 Yahoo, 213 Yves Saint Laurent, 21 Zanchettin, Piercarlo, 161, 162 Zara, 21 Zeira, Joseph, 157 Zigic, Kresimir, 67, 68, 122

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