Reduction, Rationality and Game Theory in Marxian Economics (Routledge Frontiers of Political Economy)

Reduction, Rationality and Game Theory in Marxian Economics

Beneath the exterior, what is the nature of capitalism? In this volume it is argued that capitalism remains exploitative and can be crisisprone. Moreover, Marxian economics is still an approach that can yield significant insight into how class antagonisms operate and endure in capitalist economies. This book develops Marx’s analysis of class conflict and the competitive process in light of the emergence, since the late 1970s, of analytical Marxism. However, the approach of analytical Marxism is criticised because of the problematic methodological approaches to social science endorsed by leading practitioners. Contra analytical Marxism, this book argues that it is essential to relocate game-theoretic Marxism in a methodological structure that gives primacy to class, rather than individual agents, in the process of generating social scientific explanations. In the first part of the book, methodological individualism is subjected to criticism and it is suggested that alternative levels of social scientific investigation can be considered, to provide insight into the nature of capitalism. Game theory may be used to explore how capitalist economies function, but the individual human actor will often not be the relevant unit for investigation. The second part of the book explores value and exploitation in Marxian economics, surveying a number of approaches to the former before evaluating Roemer ’s game-theoretic contributions to exploitation and class. The importance of the notion of surplus labour time is made clear in the context of conflict over the length of the working day, before considering working class ‘preferences’ for hours. Finally, the paradox of the ‘falling rate of profit’ controversy is reconsidered in the light of prior arguments. Of interest to economists and specialists in Marxist theory, Philp’s book advances this key critical area. Bruce Philp is Lecturer in Economics at Nottingham Trent University. He is the author of several articles on Marxism and game theory.

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Reduction, Rationality and Game Theory in Marxian Economics Bruce Philp

Reduction, Rationality and Game Theory in Marxian Economics

Bruce Philp

First published 2005 by Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN Simultaneously published in the USA and Canada by Routledge 270 Madison Avenue, New York, NY 10016 Routledge is an imprint of the Taylor & Francis Group This edition published in the Taylor and Francis e-Library, 2005. “To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.” © 2005 Bruce Philp All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging in Publication Data A catalog record for this publication has been requested ISBN 0-203-33722-0 Master e-book ISBN

ISBN 0–415–28765–0 (Print Edition)

Contents

ix

Contents

List of figures and tables Acknowledgements

xi xiii

1

Introduction

1

2

Methodology of reduction

11

3

Marxism and the foundations of collective action

29

4

Value, price and exploitation

41

5

Marxian theories of exploitation and class

63

6

Class conflict and working hours

85

7

Reduction, rationality and the rate of profit

99

8

Conclusion

117

Notes References Index

123 131 139

x

Contents

Figures and tables

Figures 3.1 3.2 4.1 6.1

Time line for divide and rule Divide and rule Wage–profit frontier Exploitation-hours curves with variation in the wage rate

36 37 53 91

Tables 4.1 4.2 4.3 4.4 4.5 5.1 5.2

Value categories in Marx’s Capital Durability of constant capital and cost price Commodity price and price/value divergence Value categories in the new solution Prices of production in the new solution Roemer’s class structure with a market for labour power Roemer’s class structure with a credit market

43 44 44 57 58 71 72

Acknowledgements

I am grateful to a number of people who have contributed to the ideas which this book represents. While I was a postgraduate and undergraduate student, David Young (as PhD supervisor), Pat Devine, Keith Gibbard and John Kemp provided excellent supervision and teaching. John King provided constructive suggestions and extensive advice. During my time working at Manchester Metropolitan University and Nottingham Trent University, I have been privileged to work in inclusive intellectual environments. As colleagues, David Harvie, Gary Slater, Ian Steedman and George Zis contributed to the development of the ideas contained in this book. I would also like to thank Gary Mongiovi, Stephen Parsons, Frank Thompson, Alex Wharton and Mike Williams for comments on specific chapters. Finally, I’d like to express thanks to my parents for their encouragement and support throughout my studies. Parts of Chapters 2 and 3 draw heavily upon articles previously published and I thank the Journal of Interdisciplinary Economics for permission to reproduce parts of them here. Chapter 2: Anti-Reductionism, Methodological Individualism and Analytical Marxism. Journal of Interdisciplinary Economics 7(4), pp. 237–53, December 1996. Chapter 3: Game Theory, Marxism and the Foundations of Collective Action. Journal of Interdisciplinary Economics 11(1), pp 77–94, January 2000.

1

Introduction

Contemporary issues in Marxian economics Without wishing to begin in an unduly negative way, it is important to recognise that there are a number of difficulties which confront the future development of Marxian economics. Theoretical problems associated with value, the falling rate of profit and surplus-value require investigation, and these are discussed in detail in this book. The nature, mechanisms and structures advocated as an alternative to capitalist/market systems require parallel elaboration, in particular in the light of the failures of the political and economic systems which prevailed in Eastern Europe throughout much of the twentieth century. The failure of ‘Communism’ in Eastern Europe and the former Soviet Union, the continued dominance of dictatorial politics in China, the apparent failure of the central allocation of resources, and the incentive problems which arise as a consequence of these factors all warrant explanation from Marxists wishing to develop a sound materialist alternative to capitalism. However, in recognising the failure of Communism in Eastern Europe one should not be distracted from developing a modern, alternative understanding of the functioning and dynamics of capitalist economies, to that which is proposed by neoclassical economists. And while Marx provided many valuable theoretical, historical and methodological insights, capitalist economies have evolved and developed since his death. Moreover, Marx’s theory of capitalism was incomplete when he died. There have been noteworthy developments in Marxian economics in the intervening period. But the task of developing Marx’s work has not been completed, and theoretical work is required to render convincing the case for replacing capitalism with a democratic socialist alternative.

2

Introduction

There are compelling reasons for seeking an alternative to capitalism. The existence of positive profits, necessary to enable capitalism to persist, requires the exploitation of workers. Workers are alienated and work for longer than is necessary to produce what they themselves consume. It is desirable that some in society work surplus labour time to provide for those unable to satisfactorily provide for their own needs. However, under capitalism the social surplus, the product of surplus labour time, is in principle appropriated on the basis of property. Thus, the existence of capitalism presupposes exploitation. Other problems facing the world’s population in the late twentieth century include a global environmental threat which governments seem unable to control, and famines and war which leave large proportions of the population of this planet under continual threat. Dictatorial politics are not confined to Communist states, and western democracies tolerate and trade arms with dictatorships. Such ‘democracies’ also have distinctly anti-democratic forces working within them. Agents’ preferences (for commodities and policies) are systematically manipulated through advertising and mass media, and this serves to stifle serious, fundamental debate about the functioning and ethics of capitalism itself. Elsewhere, the fall of the Soviet Union has given rise to civil wars, rising crime and extortion. Moreover, we can observe concentration of ownership of large, formerly state-owned assets, in the hands of a few very wealthy individuals – primitive accumulation for the modern era. In recognising these problems, this does not represent a desire to return to the Communism of the Soviet Union before the fall. Rather resolution of these ills require political and economic structures other than those adopted in western capitalist economies. This book will focus on a small subset of these problems – namely exploitation and the process of competition in capitalist economies. These involve strategic interaction between agents and so one approach which is explored is the use of game theory. It is therefore possible to identify two key issues which Marxist economists should endeavour to address: ‘What are the forces which determine pricing, development and distribution in capitalist economies?’ Secondly: ‘What alternative form(s) of political and economic arrangements might overcome these difficulties and provide universal and equal opportunities for self-realisation and welfare?’ Whilst there is a clear connection between these issues, it is principally the first question which is examined in this book.

Introduction

3

There are further issues to be resolved in that much has been written in recent years concerning the method of Marxian social science. In particular, the suggestion offered by a number of analytical Marxists, that a microfoundations approach may constitute the most appropriate method by which to investigate/model capitalist economies, is challenged. This challenge to traditional Marxian ‘holistic’ approaches represents a fundamental departure since it suggests individual agents be our units for analysis. Traditionally, one distinguishing feature of Marxian analysis has been the emphasis on classes as important explanatory units. However analytical Marxists have modelled classes as emerging out of individual optimising decisions made by individual agents. Such an approach is inadequate. Nevertheless, rejection of microfoundations approaches does not entail that all methods and tools used within neoclassical economics need be rejected. One suggestion made here is that game theory may be used to either provide insight into aspects of Marxian economics, or to communicate some of the insights of Marxian economics to a broader audience. But to use game theory in a Marxian setting requires more that simply adopting the tools and methods of non-cooperative game theory, root and branch. One of the features of the application of non-cooperative game theory in neoclassical economics has been the adoption of methodological individualism which Marxists (other than analytical Marxists) are generally hostile to. Therefore, an important precursor to applying game theory to Marxian economics, if we reject the microfoundations approach often adopted by analytical Marxists, is to extract those aspects of strategic interaction pertinent to Marxian analyses of capitalism, from the underlying, and deeply problematic assumptions of neoclassical theory.1 This work begins from the premise that Marxian analyses of capitalism can still provide powerful insights into the functioning, dynamics and ethics of capitalist economies. Moreover, these insights are likely to be more profound than those offered by competing schools of economic thought. In Capital, Marx sought to develop a theory of the dynamics of capitalist economies and to provide a historical account of the emergence and functioning of capitalism. Such approaches remain crucial in understanding how the world works, as economies and cultures are assimilated into the global capitalist system while injustice, exploitation and crisis pervade contemporary society. In such a climate, one might expect interest in Marx, and Marxian work, to be

4

Introduction

considerable. However, in the field of economics this is not the case as neoclassical economics and its variants have occupied an increasingly dominant position, and attempts to offer serious immanent critiques of capitalism are ignored in the mainstream literature. Marx was critical of the ideological role of bourgeois political economists; so neoclassical economists today play a similar role as the hired prize-fighters of the ruling class. What passes for academic research either seeks to demonstrate the efficiency of market systems, or how interventionist measures can bring about improvements. But there is no serious attempt to examine, fundamentally, the limits, injustices and contradictions of capitalism. Intellectual resources are not channelled to address these questions, of course, because it is not in the interest of policy makers and business to raise such problematic issues. The case for developing further a truly critical analysis of capitalism is thus overwhelming, whatever the historical and contemporary problems faced. This book is concerned with the determinants and dynamics of exploitation, mediated through the competitive process. The approach is inspired by the work of Marx and the challenge posed by analytical Marxism. The latter work has sought to defend important elements of Marx’s theory using the tools and methods of mainstream social science. This book, in the process of examining Marx’s work, rejects certain elements, most significantly a labour theory of exchange-value. However, a labour theory of exploitation is regarded to be of utmost importance for understanding the functioning and inequality of capitalism. The reductionist pretensions of a number of analytical Marxists are rejected although not, perhaps, for the same reasons as given by orthodox Marxists. In each of these fundamental theoretical and methodological respects, this book can neither be considered orthodox nor analytical in its approach to Marxism. However labelled, it is nevertheless hoped the reader is convinced that the issues raised here are important, and concurs with the view that capitalism need not and should not represent the pinnacle of economic development.

Neoclassicism, Marxism and methodology The development of theory and pursuit of empirical research implicitly or explicitly involves adopting a methodological position. While some social scientists may see overt interest in methodology as peripheral, such considerations have benefits that are likely to

Introduction

5

contribute constructively to the development of human understanding. Explicit reflection on how social science is to be pursued has the advantage of aiding the researcher in developing a consistent approach. This should not be taken as implying methodological conformity is desirable amongst social scientists; indeed there is considerable merit in maintaining a plurality of methodological approaches. However, it is likely to yield further development and more constructive debate if a given social scientist states what they regard to be fundamental to their scientific approach. Methodology is not important solely for identifying the approach of an individual researcher. Schools of economic thought are each methodologically distinct and identification of these differences is important. It is also important to note that such classification may lead to over-simplification and there are all too frequently exceptions which make hard and fast distinctions, at the least, problematic. But it is useful to identify some common characteristics to render debate and comparison between different paradigms practical. Neoclassical economics represents the dominant orthodoxy in economics. Whilst the term ‘neoclassical’ may not reflect the diversity of modern mainstream economics, the use of the term is sufficiently widespread to make its use convenient. Here the term ‘neoclassical economics’ is taken to refer to that body of work which assumes: (i) agents are instrumentally rational, maximising utility in a world of scarcity using marginal calculus; (ii) individual optimising agents are our units for analysis, and methodological individualism the appropriate philosophy of science; (iii) equilibrium is the dominant modelling tool and general equilibrium modelling is an extension intended to reflect the interaction of agents and markets in a macro economy. In empirical work neoclassical economists test predictions of behaviour based on these rationality postulates and compare these with the empirical evidence from gathered data. In the modern economic literature there is the frequent use of econometric methods. Indeed this is consistent with Friedman’s approach, where he suggests: ‘the only relevant test of the validity of a hypothesis is comparison of its predictions with experience’ (1953, p.8). Neoclassical economics can take different forms, from research which uses simple utility functions to look at particular markets, to the work of those who focus on the interaction of markets in computable general equilibrium models. Underpinning these are the optimisation techniques referred to above, and while there are some exceptions, this definition of neoclassical economics captures

6

Introduction

what are generally held to be the essential characteristics of that body of work. Marxian economics is distinct in that it identifies capitalism, or a market system, as one of a number of modes of production (feudalism, capitalism, socialism, communism), whereas neoclassical economics focuses exclusively on capitalist economies (with the possibility, of course, of some government intervention). Even Marxist economists who have flirted with aspects of neoclassical methodology have nevertheless identified capitalism as one of a number of economic systems (e.g. Roemer 1982a, 1982b, 1986b). This makes it possible for Marxist economists to challenge, not only particular market outcomes, but the ethics of capitalism as a system as a whole. As Roemer suggests, Marxism maintains ‘a belief in the injustice of capitalism, and the transience of it, which flows from a historical world view, based on the evolution of forms of property’ (1986c). At the heart of Marx’s analysis of capitalism lies the concept of surplus-value, or capitalist exploitation. In this book the Fundamental Marxian Theorem (FMT) – the claim that capitalist exploitation is necessary and sufficient for the production of positive profit – is taken to be the key to understanding the injustice of capitalist economies. However, Marxist economists also see the invisible hand floundering as capitalism is crisis prone. In common with the optimisation assumption of neoclassical economists, Marxists generally hold that capitalists seek to maximise profits, achieved through extracting as much surplus labour time as possible. But in seeking to maximise profits, by introducing new techniques, Marx maintained that this would result in a fall in the general rate of profit. Such a structure is not necessarily at odds with some of the outcomes generated by neoclassical economists. Paradoxical examples such as the prisoners’ dilemma and public good provision are studied intensively by neoclassical economists and these are formally not dissimilar outcomes. In addition to Marxists beginning with the economic structure, and regarding ethical concerns as fundamental to the analysis of capitalism, there are other elements which distinguish their methodology. One particular element concerns the boundaries between economic and broader social scientific explanations of phenomena. The ceteris paribus assumption is frequently invoked by neoclassical economists. This may be done as a modelling assumption to facilitate investigation of causal processes individually, because of the complexity of examining many factors all at once. This is not dissimilar to the traditional approaches adopted to the study of certain issues, such as the

Introduction

7

analysis of the falling rate of profit as a consequence of technical change, which tends to hold other factors, such as respective class power, constant in order to focus on a particular issue. However, neoclassical economists are also prone to use the ceteris paribus assumption to render non-economic causes/factors exogenous in the process of investigation. Thus instrumental rationality presupposes exogenously determined preferences, precluding any investigation of how desires might be cultivated or false needs induced. There have been suggestions recently that neoclassical economics should cultivate its relationship with other social sciences (e.g. Lazear 2000), but the presumption from within neoclassical economics is that the appropriate methodology is that which is employed within mainstream economics, and the relationship should be one of economics imperialism. Marxist economists, in contrast, may be taken by some to be a misnomer, since it implies the possibility of there being a distinct branch of Marxian investigation separate from a broader social scientific understanding of political, social and economic systems. While this book will focus on quite narrowly defined economic aspects, non-economic causes are not precluded, a priori, in the process of investigation.

Structure of argument In considering class conflict, three broad economic themes emerge. In Marx’s analysis, competition between the capitalist and working class in the labour market is modelled in terms of surplus-value. This presupposes the capitalist class has a monopoly over the means of production. Secondly, competition among groups of workers is often analysed in terms of ‘divide and rule’ models, suggesting a need for an analysis of class consciousness and collective action. Finally, theories of competition between capitalists are more diverse. Considerations include the equalisation of the rate of profit, the tendency for the rate of profit to fall, and more general theories of crises. This is a considerable body of work and therefore, to make analysis tractable, this book will primarily examine unrestricted competitive capitalism where product markets are not characterised by monopoly. The recent development of analytical Marxism and contemporaneous developments in orthodox Marxism raise important methodological issues that are discussed in Chapters 2 and 3. The issues surrounding alternative methodologies of explanation are of extreme importance in all areas of social science that apply any form of aggregate

8

Introduction

analysis. Chapter 2 assesses a number of alternative positions that have emerged in recent years in debates surrounding the development of analytical Marxism. The issue of reduction in the philosophy of science is considered, and it is claimed that reduction, which is often interpreted as an ontological claim is, in reality, a claim about the possibility of explanation. In Chapter 2, the ‘reductionism versus holism’ oversimplification is rejected and it is claimed that there are at least four methodologies of explanation: atomism, methodological individualism, anti-reductionism and radical holism. The latter two reject reductionism. The work of three analytical Marxists – Wright, Levine and Sober – is the reference point for this discussion. Their work is particularly pertinent since they do not advocate methodological individualism, which typifies the approach of other analytical Marxists, such as Roemer and Elster. Finally, the relevance of this debate to a theme of central importance in Marxism – class analysis – is considered, and the reductionist approach is questioned. In Chapter 3, the philosophical foundations of game-theoretic Marxism are discussed. Initially the reductionist pretensions of analytical Marxism, which has practised game-theoretic Marxism, are considered and rejected. After advancing an anti-reductionist game-theoretic formulation of Marx’s theory of surplus-value, in terms of bilateral monopoly, problems of collective action are examined. In Chapter 4, the most significant problems facing Marxian economic theory in the last hundred years, namely value, price and distribution are discussed. After framing the problem in Marx’s own terms from the third volume of Capital, Böhm-Bawerk’s subsequent critique is outlined. Thereafter a number of solutions to the transformation problem are considered. Proposed solutions – such as the approach of Morishima, Roemer’s ‘Walrasian’ general equilibrium model, and Dumenil, Levy, Foley and Lipietz’s ‘new solution’ – are introduced before discussing recent developments in the Marxian theory of exploitation and class in Chapter 5. After discussing Marx’s original formulation of surplus-value, Roemer’s game-theoretic general theory of exploitation and class is considered. The limits of Roemer’s microfoundations model of class formation are highlighted, before discussion of the relationship between property relations (PR) and unequal exchange (UE) definitions of exploitation. It is noted that Roemer does retreat somewhat from his original view, advocating a PR-UE hybrid. This, it is suggested, is similar to Marx’s own position. Moreover, conceiving exploitation in terms of labour time allows

Introduction

9

consideration of the relationship between class exploitation in the market sector, and other forms of exploitation. Chapter 6 elaborates on the Marxian theory of exploitation. Having established that this should be considered in terms of property rights and working time, this chapter analyses class conflict over the length of the working day, utilising a particular interpretation of Marx’s theory of surplus-value. Marx’s theory is represented in terms of the ratio of surplus to necessary labour time, thus giving epistemological priority to labour time in examining conflict over distribution and conditions of work. Thereafter, the effects of redistributing work from the employed to the unemployed are considered (incorporating a basic taxation system), with an interesting outcome. Before concluding, Chapter 7 considers a number of theoretical themes in Marxian theories of competition between capitalists. Initially, Marx’s theory of the falling rate of profit is outlined, before providing a formal treatment of the Okishio theorem, which states that rational profit-maximising capitalists will not, ceteris paribus, introduce techniques which lower the rate of profit. The motivation of agents is considered in the light of the investigation of Chapter 3. Two proposals for what Laibman (1992) describes as class struggle neutrality are considered (constant real wage and constant rate of exploitation), and it is shown that rational capitalists can introduce techniques which ultimately lead to a fall in the rate of profit through a prisoners’-dilemma-type structure. In concluding, it is suggested that the central tenets of Marxian economics – that capitalist economies are exploitative and/or unjust, and that outcomes and allocation are contradictory and can be crisis prone – are elaborated upon in this book. It is suggested that some insight can be provided by extracting some developments in mainstream/neoclassical economics; however, the uncritical acceptance of neoclassical methods is not likely to enhance the development of a sound materialist alternative understanding of the ethics and dynamics of capitalist economies.

2

Methodology of reduction

Introduction What is the relevant unit for social scientific analysis? On occasion in mainstream game theory we find that an individual human being is our unit for analysis. On other occasions game theorists focus on the firm or, in the case of a monopolist bargaining over conditions with a union closed-shop, we have bilateral monopolists. In other words, game theory need not entail that the individual asocial agent is our unit for analysis – there can be a number of levels at which social scientific investigation can be conducted. The claim that Marxian analysis should be robust by the standards of contemporary philosophy of science is not antithetical to Marx’s work. Indeed, Marx’s commitment to the analysis of class and revolutionary socialism and their development through the application of sound scientific method, was unambiguous in his mature work. In the preface to the only volume of Capital which Marx himself edited, he clearly stated: I welcome every opinion based on scientific criticism. As to the prejudices of so-called public opinion, to which I have never made concessions, now, as ever my maxim is that of the great Florentine: ‘Sergui il tuo corso, e lascia dir le genti.’ [‘Go on your way, and let the people talk.’] (Marx 1976, p.93) In recent years there has been a debate in Marxism concerning the relationship between human individuals, social groups and the whole socio-economy. This debate has followed the development of analytical Marxism, whose practitioners claim to reinvigorate Marxism through

12

Methodology of reduction

applying the methods of conventional social science. In the field of economics this has led to the consideration of game theory and general equilibrium as approaches which might be used to enhance the Marxian analysis of capitalism. Criticism has however been forthcoming from orthodox Marxists, who have sought to defend the central theoretical and methodological corpus of Marx’s work. The analysis of individual-level intentional explanations has been controversial in debates surrounding analytical Marxism since, previously in Marxian social science, it has often been the case that groups or structures have been the basis for many explanations. In this context Marxism has been portrayed as frequently advancing macro-explanations of social phenomena, in which the relevant unit of investigation is a large-scale feature of society and the explanans a description of some other macro-phenomena (Little 1991). This approach has attracted criticism from some, who claim that this is methodologically dubious from the perspective of modern philosophy of science. In the field of social science, Marxian economists have often sought to discover and explain large-scale patterns of development based on features of the capitalist economic structure; Marxist political scientists have sought to explain the role of the state in terms of the needs of the capitalist economic structure; and Marxist sociologists have frequently examined class activity in terms of the objective interests of that class (Little 1991, pp.195–6). While this generalises somewhat, this pattern is sufficiently common such that it can be considered a useful fiction. In the face of the concentration upon groups and social structures, characteristic of orthodox Marxism, the focus on the individual by analytical Marxists has aroused debate among those with an interest in methodology and the philosophy of science. At times a number of theorists have presented the differences between analytical and orthodox Marxism as a tension between methodological individualism and methodological holism.1 This view is an over-simplification, and the work of three analytical Marxists – Erik Olin Wright, Andrew Levine and Elliott Sober – will be used to demonstrate this. The significance of their work is that they seek to advance a methodology of science which advocates individual-level explanations of certain events, but suggests that such an approach may not be possible in seeking explanation of other phenomena. The implications of this crucial debate are of the utmost importance if Marxism is to continue to adhere to the belief that class is a relevant unit of analysis and cannot simply be reduced to individual-level explanations.

Methodology of reduction

13

In this chapter, the contribution of Wright, Levine and Sober (1992) is discussed. The following section outlines the reduction issue, and introduces some basic terms used in the philosophy of science. This is necessary so that we can have an understanding of what Wright et al. propose to reject. Thereafter the validity of methodological individualism, advanced by a number of analytical Marxists, is examined alongside the specific proposition of anti-reductionism that Wright et al. advocate. In the conclusion, the relevance of this debate for Marxian social science, and class analysis in particular, is considered.

Reduction in the philosophy of science Reductionism is usually presented as a position in the philosophy of science concerning the relations between adjacent areas of scientific interest. Frequently, reductionist claims are stated in the form that something ‘just is’ something else. One may claim, for example, that a social system, organism or mental state is simply a physical thing: this is physicalism. However, reductionism frequently implies something stronger than physicalism. Reductionism can be considered on a disciplinary or a theoretical level. Between disciplines, predicate reduction implies that the terms employed within ‘higher-level’ theories, such as sociology or economics, can ultimately be defined in terms employed within more basic sciences such as chemistry or physics. A stronger reductionist claim is that the laws of higher-level theories can be explained in terms of those of some lower-level theory. For example we may be able to substitute laws of psychology for those of economics, thus reducing one discipline to another. Accepting this stronger claim, known as law reductionism, implies acceptance of the weaker agenda of predicate reduction. The reduction issue is therefore intimately connected with an agenda in the philosophy of science outlined by Oppenheim and Putnam (1991) – the unity of science as a working hypothesis. In their work, Oppenheim and Putnam identified a number of different levels which form the basis for reduction. These, they suggest, are the basis for micro-reduction, that is, the claim that a certain object can be explained as the sum of the parts. The six reductive levels identified are: 1. Social groups 2. (Multicellular) living things 3. Cells

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Methodology of reduction 4. Molecules 5. Atoms 6. Elementary particles.

Microreduction implies that the laws of higher-level theories – those concerning social groups – can be reduced to the laws of lower-level theories. In the case of economics and sociology this implies explaining the activities of social groups (level 1) in terms of the actions of human individuals (level 2). A reduction is said to occur between two theories (X and Y) when: the vocabulary of X contains terms not in Y; any observed data explained by X can be explained by Y; and X is at least as well systematised as Y. Given this definition, it becomes apparent that reduction, which is on the face of it an ontological question, is really a question about the possibility of explanation (Garfinkel 1991, p.443).2 It does not necessarily follow, from this definition of the relationship between X and Y, that the reduction that occurs must be a micro-reduction. However, Oppenheim and Putnam claim that ‘the only method of attaining unitary science that appears to be seriously available at present is micro-reduction’ (1991, p.408). In support of this assertion they cite the case of psychology and physics. On the one hand, it may be plausible to reduce psychological states to the workings of the atoms which constitute the brain. That is, psychology is reducible to physics. However, it appears implausible to assert that the converse is the case; one cannot plausibly suggest that the behaviour of inorganic matter can be explained with reference to psychological laws. It is in this sense that Oppenheim and Putnam advocate micro-reduction. One pre-eminent analytical Marxist who has advocated micro-reduction is Elster, who has suggested that ‘reduction is both feasible (in principle) and desirable’ (1989, p.195). Its desirability stems from three arguments. First, according to Elster, it allows us to see the mechanism by which a given macro-phenomenon actually works. This, secondly, improves the confidence in our proposed explanation; that is, our belief about the explanation of our macro-state does not rest on a spurious non-explanatory connection. Finally, Elster asserts that ‘reduction to lower levels is necessary to understand the stability and change of aggregates’ (1989, p.196). This final element can, however, be criticised from the perspective of the philosophy of science. The a priori assumption that micro-reduction is the ‘correct method’ to apply in scientific investigation has been challenged by Garfinkel, who has elucidated a predator–prey model, claiming that under certain circumstances macro-explanations may

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be superior to micro-explanations. Consider the example of two populations: foxes and rabbits. Suppose, following Garfinkel (1991, pp.445–9), that there are two basic variables: the level of the fox population in a given period (Xt ), and the level of the rabbit population (Yt ). The main influence on the levels of the two populations is the frequency with which foxes encounter rabbits. The frequency of encounter appears as a positive contribution to Xt and a negative contribution to Yt . If we take Xt Yt as an estimate of the frequency of encounter we can represent fox population dynamics by the following equation: dY =aXY −bX (2.1) dt And the dynamics of the rabbit population can be given by: dY =cY −eXY dt

(2.2)

Taken together, equations (2.1) and (2.2) provide us with the information concerning the population dynamics for foxes and rabbits. Suppose, given these equations, we wish to know why a rabbit gets eaten by a fox. One possibility is a macro-explanation: the cause of the death of the rabbit was the size of the fox population. Alternatively, we could advance a micro-explanation. That is, the given rabbit was eaten because it passed into the capture space of a given fox at a given place and time. This explanation provides us with a wealth of information. However, it ‘contains much that is irrelevant to why the rabbit got eaten and does not really answer that question at all’ (Garfinkel 1991, p.447). In this example the macro-explanation provides the explanation that we are seeking, and the micro-explanation is really answering a different question entirely. In this sense, dispensing with macro-explanations is not straightforward. Further practical problems concerning reduction arise. Recalling Oppenheim and Putnam’s (1991) six reductive levels, the claim of analytical Marxists is that level 1 should be reduced to level 2, i.e. social groups should be explained in terms of individual human beings. However, the unity of science as a hypothesis would suggest that further reduction is desirable, such that social groups should be explained in terms of actions and reactions at the cellular level. As noted by Howard and King such a reductionist programme becomes continuous: ‘Reduction will always be an unending procedure because any element of the material world is capable of further decomposition’ (1992,

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p.341). If analytical Marxists were to claim that reduction to the level of individual agents was sufficient, this in itself would violate the principles of reductionism. It is difficult to see where a reductionist programme would end, and the complexity and practicality of such a programme suggests it to be implausible. As argued by Sturrock: Everything that is not by its nature indivisible can be shown to have a structure, to be a complex whole capable of analysis into its constituent elements, these elements themselves being related to each other according to rules also to be discovered. It may be the dream of certain sciences to discover ultimately simple entities incapable of further division, but the search for them, as in theoretical physics, is strikingly unsuccessful, since each simple entity that physicists discover turns out on closer acquaintance to be an unsuspected complex one. The indivisible atom of old has failed to be replaced by anything smaller as the presumed ‘building-block’ of matter. (Sturrock, 1986, p.vii) Thus it is difficult to see how the reductionist pretensions of analytical Marxism can be fruitfully achieved and indeed the notion of reductionism that they employ seems itself to be only partial.

Anti-reductionism In Reconstructing Marxism, Wright, Levine and Sober examine a number of alternative approaches to explanatory reduction. They contrast their anti-reductionist stance with three alternative explanatory methodologies: atomism, methodological individualism and radical holism. The essential differences between these alternative approaches are summarised in Table 2.1, adapted from Wright, Levine and Sober (1992, p.124). The proposition of atomism is defined by Wright, Levine and Sober as ‘a methodological stance that denies that relations are ever genuinely explanatory, whether those relations are between individuals or between social entities’ (1992, p.109). However, the non-explanatory status of relations between individuals is not synonymous with interaction being unimportant: If the concept of ‘relation’ is equated with ‘interaction’, then plainly, no theorist could deny the explanatory relevance of relations.

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Even a radical atomist would acknowledge that the interactions [sic] of a parent with a child is consequential for the child. What is being claimed by atomists, ... is not that interactions have no consequences, but that interactions are governed entirely by mechanisms located within the atomistically constituted entities engaged in the interaction. (1992, p.110, n.5) The methodological position of atomism can be contrasted with that of methodological individualism, which has been defended by a number of leading analytical Marxists.3 Methodological individualism comprises a number of distinct theses. Specifically, there is a claim concerning matter (ontological thesis), a claim over the meaning of social concepts (meaning thesis), and, finally, a claim concerning explanation (explanatory thesis). The ontological claim of methodological individualism states that ‘all social entities are reducible without remainder to logical compounds of individuals’ (Little 1991, p.183, emphasis added). The meaning thesis states that social concepts must be definable in terms of concepts that refer to individuals, their relations and behaviour; however, difficulties arise for this analysis. Consider the example cited by Little (1991), in which an agent (Albert) behaves in a manner that can be described in the following ways: Albert waves his hands; Albert gestures to Fred; Albert insults Fred; Albert breaches diplomatic protocol. These different descriptions of the action vary in terms of the social knowledge which we use in order to interpret the observed behaviour. The meaning thesis requires us to rely upon only those facts which refer to individuals and their psychological properties. However, Little suggests: ‘there is no reason to think that such a reduction is possible’ (1991, p.185). Thus the meaning thesis of methodological individualism is problematic. In the form of methodological individualism advocated by some analytical Marxists it is not the weak ontological form of methodological individualism that is defended. Rather it is a form that implies meaning reduction and explanatory reduction. Elster has suggested that methodological individualism is based upon the premise that social phenomena can be explained in terms of individual behaviour. This does not imply that social processes are monadic, since certain individual properties are inherently relational and require reference to others. Instead, methodological individualism proposes that relations among individuals are explanatory, whereas relations

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among, for example, classes, are only explained as a product of the individuals who compose that class, together with relations between those individuals. It is sometimes the case that Marxists distrust methodological individualism because of the belief that it is synonymous with political individualism. This is a claim rejected by Elster (1989, p.201), who identifies two forms of political individualism. First there are those who praise freedom, and suggest that, specifically, free-market competition unrestrained by state intervention is the most effective way of maximising economic welfare (however this might be defined). Alternatively, there are those who suggest that freedom is a value in itself; political individualism is defined in this case as ‘a political program in which the preservation of individual liberty is made the touchstone of government action’ (Blaug 1980, p.49). Elster suggests that the former view is in some sense value-neutral, in that it is intended as a view about ends–means relationships. Therefore, according to Elster, political individualism in not necessarily a normative approach. In any event, acceptance of political individualism does imply acceptance of methodological individualism, which can be summarised as a methodological outlook in which social institutions are explained purely in terms of individuals, who exist prior to any macro-social categories. The essential unit upon which theories of methodological individualism are founded is the individual human being; social institutions are aggregates of individuals and their relationships. The dual of methodological individualism is radical holism (methodological collectivism), a position vigorously attacked by all analytical Marxists. Wright et al. suggest that radical holism is more extreme than simple holism. Rather than suggesting that the whole is more than the sum of the parts, radical holists claim that in any explanation the individual elements are causally preceded by the whole; macro-phenomena precede micro-phenomena in the explanatory order. This entails a rejection of the claim that relations among individuals are explanatory, and macro-social categories, including class and the state, are, by assumption, not explained by micro-level categories. Elster has used the term ‘methodological collectivism’ to describe radical holism, explaining that: Methodological collectivism – as an end in itself – assumes that there are supraindividual entities that are prior to individuals in the explanatory order. Explanation proceeds from the laws either

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of self-regulation or of development of these larger entities, while individual actions are obtained from the aggregate pattern. (Elster 1985, p.6, emphasis added) It is suggested by Wright, Levine and Sober that holistic teleologies are prevalent in accounts of history that see the trajectory of social change directed to an ultimate state which exists independently of the goals and actions of human individuals (1992, p.113). And Elster (1985) has attacked such functional explanations within Marxism, claiming that they generally reflect teleological thinking about the nature of society and history, and ignore the importance of micro-level mechanisms. The anti-reductionist methodology advanced by Wright, Levine and Sober acknowledges the importance of micro-level accounts in explaining social phenomena, but allows for the irreducibility of macro-level accounts. For methodological individualists, reduction only becomes a problem when there is inadequate knowledge or cognitive limitation. In contrast, in their version of anti-reductionism Wright, Levine and Sober do not prejudge whether macro-level explanations can be finally reduced (in principle) to micro-level accounts. To understand why this may not be theoretically possible, Wright, Levine and Sober introduce a distinction between types and tokens drawn from the philosophy of science. They define these thus: ‘Tokens’ are particular instances: for example, a particular strike by a group of workers in a particular factory or an idea in the head of a particular individual. ‘Types’ are characteristics that tokens may have in common. Thus a particular strike – a token event – can be subsumed under a variety of possible ‘types’: strikes, class struggles, social conflicts, etc. (1992, p.116) In this case the explanatory status of type concepts is the issue on which methodological individualism can be distinguished from anti-reductionism. The methodological individualist would suggest that type concepts can be reduced to an explanation which refers only to individuals. The methodological individualist would further suggest that token reductionism is, a priori, possible. The anti-reductionist would concur with the latter of these claims, but not with the former. Thus ‘[t]he methodological individualist would be committed

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to micro-reducibility of both the token event and the social type. Our quarrel is not with the first of these claims, but with the second’ (Wright, Levine and Sober 1992, pp.117–18). Consider the case of mental states: For any kind of mental state – for example, the belief that snow is white, the intention to buy a chocolate bar, the feeling of pain – there are in principle many, perhaps infinitely many, physical states that could realise the mental state in question. This relationship is referred to as one of multiple realizability: mental states can be multiply realized by many different brain states. Similarly for social phenomena: many distributions of properties of individuals – their beliefs, desires, resources, interrelationships – can realize the same social type. In the case of multiply realized properties and relations, type–type reductionism will not be possible. (Wright, Levine and Sober 1992, p.118) The phenomenon of multiple realisability therefore leads to the potential irreducibility of social types. Thus it may not be theoretically possible to explain a social type phenomenon in terms of individual actions. One example cited by Wright, Levine and Sober is the case of firm survival under capitalism. They suggest that for each token instance of economic survival we can identify a set of decisions made by individuals (with exogenously given beliefs, information and resources) that explains that instance of survival at a particular point in time. However ‘there need not be anything in common at the micro-level between the mechanisms that enable firm X to survive and the mechanisms that enable Y or Z to survive’ (Wright, Levine and Sober 1992, p.119). One firm may survive because the workers in that firm were passive and complied with management demands. Another firm may survive because, although workers were militant, the management were ruthless. Alternatively, a third firm may survive because the management were innovative. Thus the type concept, firm survival under capitalism, can be multiply realised from a vast array of possible micro-mechanisms. The view that it may not be possible to reduce type phenomena is one that many Marxists may find acceptable. Wright, Levine and Sober maintain that the proposition that it is theoretically possible to reduce token events is one that most Marxists would agree with, since most Marxists are materialists. Since materialism, in this context, is the claim that all tokens are ‘made’ of matter, ‘[t]o oppose materialism would

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be to accord ontological status to (putatively) non-material entities (like disembodied minds or élans vitals)’ (1992, p.117, n.16). On the face of it, this analysis suggests that token-reductionism is intended as an ontological claim. However, in the work of Wright, Levine and Sober, token-reductionism is also intended as an explanatory claim. They suggest that, ‘if current views about the relation between human beings’ minds and brains are correct, Marxists ... would concede that a particular mental state of that individual can be explained by describing the brain of that individual at that moment in time’. Furthermore, ‘for social phenomena, particular instances can be explained by appeal to the activities, properties and relations of the particular individuals who collectively comprise the phenomenon’ (1992, p.117). It becomes apparent, therefore, that Wright, Levine and Sober are not just advocating token reductionism in a weak ontological sense. Rather they intend token reductionism as an explanatory claim. More explicitly, Wright, Levine and Sober suggest that ‘science will have two sorts of explanatory projects: it will seek to explain why token events occur and also to explain the nature of the types that fall within its domain’ (1992, p.118). While the ontological claim is not in dispute here, token-reductionism as an explanatory claim is considerably more problematic. The relationship between the ontological and the explanatory thesis is frequently stated as the latter following logically from the former. If B is constituted by things of sort A, then the behaviour of B is wholly determined by the properties of things of sort A. This is, however, not a valid inference. To illustrate this point, consider the example of a car stopped at a set of traffic lights, cited by Garfinkel (1991). In visualising this event in terms of the properties of the underlying physics, we have a steady, stable distribution of mass and energy. A small perturbation in the distribution of energy manifests itself as a change in the light from red to green. The driver recognises this as a sign to proceed, and this gives rise to a large mass (the car) being set into motion. We can therefore write this explanation as:

 red stops light→car (2.3) green goes The relationship between the light and the car is stable along all of its parameters, with the exception of the red–green boundary. Varying the height of the traffic light, or intensity of the light, will not cause the car to proceed. It is only a change in the electric current from the

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red to the green bulb that will cause the car to proceed. On the face of it this explanation is satisfactory. However, as Garfinkel suggests: ‘The fact that there is such instability means that we cannot simply cite the underlying physics as the explanation for the cars’ stopping or going’ (1991, p.543). Neither the colour of the traffic light, nor the action of the car, nor the chemical state of the brain ‘explains’ why the red–green boundary is the source of instability. As Garfinkel comments: ‘what is necessary for a true explanation is an account of how the underlying space is partitioned into basins of irrelevant differences, separated by ridge lines of critical points’ (1991, p.452). A purely mechanical explanation therefore misses the point, in that it fails to explain the source of instabilities, which is imposed on the underlying substratum rather than emerging from it. Therefore, Elster’s claim that ‘reduction to lower levels is necessary to understand the stability and change of aggregates’ (1989, p.196) cannot be considered a universal truth. Consider now the case of firm survival under capitalism cited by Wright, Levine and Sober. In their example, one firm survived because of the passivity of workers, each with a given brain state. From a materialist viewpoint no explanatory power is accorded to non-material entities. Nevertheless, to provide an economic explanation of that firm’s survival we must supply additional information concerning how and why the instabilities concerning passivity and impassivity arise. In the case of the survival of our given firm we can postulate the underlying physics as:

 passive survives workforce→firm (2.4) impassive does not survive That is, the unstable parameter that determines the survival of this given firm is the boundary between a passive and an impassive workforce. However, what this explanation does not tell us is why this instability occurs. In their example Wright, Levine and Sober take agents with given beliefs, preferences, information and resources. These are the elements which determine whether the workforce is passive or not; we cannot simply cite the underlying observed physical reactions as the basis for explanation. This is not the only problem that we can point to in the framework suggested by Wright, Levine and Sober. We might ask what the purpose of investigating type concepts is. One possibility is that ‘science has

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explanatory projects beyond the explanation of token events’. In the context of survival, they suggest, ‘Besides asking why this organism or that firm survived, we also want to explain what various objects and processes have in common’ (1992, p.120). Consider the example of capitalism. There are many forms of capitalism in the world, and as social scientists we might seek to investigate, for example, capitalism in the United Kingdom in 2004. However, it is also insightful for the social scientist to have some understanding of what capitalism is: that is, an understanding of what the type concept ‘capitalism’ means. Precisely what these ‘insights’ may be is something we may speculate upon. Consider, for example, social scientists who investigate capitalism in a number of different periods and times, and who develop a type model of capitalism. Suppose they then encounter an economy and wish to define its socio-economic structure. The type framework contains certain elements which together define a capitalist socio-economy. But, beyond this sense in which the type concepts are useful for definitional purposes, we could conceive of circumstances in which the framework is useful. It may be that our knowledge of this ‘new’ economy is limited, but we can infer the missing information from our type model. In summary, type frameworks have practical applications, which social scientists may usefully employ. Therefore, a given social scientist entertains beliefs about type concepts since they believe that such categories are, in some sense, useful in explaining the observed phenomena in the real world. If not, there is no point investigating the type/token distinction and the proposition of anti-reductionism is a chimera – an unfounded conception. It follows that, if some people entertain beliefs about irreducible social categories (types), our explanation of token events in which the actions of such individuals play some role should refer to these irreducible social categories as a component part. And, if a significant number of social scientists adhere to the belief that type concepts are insightful, it may well be the case that agents generally believe some insight can be found from a consideration of irreducible social categories, albeit implicitly. Therefore, explanation of such token events contains elements that are irreducible. This is one argument which Elster has dismissively considered, claiming that ‘if people entertain notions about aggregates with beliefs and goals of their own, they are irrational’ (1989, p.194). In contrast to Elster, it is suggested here that this perhaps gives an opportunity to refine and elaborate the

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notion of rationality employed within the social sciences, rather than dismissing irreducible elements by assumption because they don’t ‘fit’ with our unjustified preconceptions.

Microfoundational analysis Debate over explanatory reduction and questions of whether the individual agent or irreducible macro-social entity should serve as the unit for analysis has implications for the elaboration of micro-foundations, where we derive aggregate behaviour as a consequence of the actions of human individuals. Roemer has asserted that traditionally Marxist social science is conceived of in terms of class, so that individual human agents can only be understood in the context of their class location. In contrast to such an orthodox Marxist approach, Roemer has modelled both class formation and exploitation in terms of cooperative game theory, where individual agents are optimising and rational. Anticipating potential criticism of his method, Roemer has sought to distinguish approaches which preclude one another, and those approaches which are not mutually exclusive or may be complementary. Thus: Marx has claimed that although people exist organically as individuals, we can conclude that they act as members of classes ... it is not antithetical to Marxian theory to produce models using the micro-foundations approach. In particular, I suggest that one theorem of Marxism is a ‘micro-foundations of class’ analysis. (Roemer, 1981, p.8) Roemer here indicates his agreement with Marx on the question of ontological reductionism. In a physical sense individuals do, in terms of ‘matter’, comprise societies. However, what has been at issue in this chapter is whether such a physical claim entails the possibility of explanatory and predicate reductionism. It has been contended that these issues are, in principle, separable. Analytical Marxists – whether anti-reductionist in the sense of Wright, Levine, and Sober, or methodological individualists, in the sense of Elster, Roemer and Van Parijs – have all expressed a commitment to the micro-foundations approach. For example, Roemer has made the ‘search for foundations’ an element of his definition of analytical Marxism (Roemer, 1986a, p.3). However, while there is apparent

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unanimity on the merits of the micro-foundational approach, the two positions of anti-reductionism and methodological individualism posit different degrees of commitment to, and belief in, the robustness of this agenda.4 The view of Elster and Roemer is that micro-foundations are necessary, and failure to elaborate such foundations is, very much, second best. In contrast, Wright, Levine and Sober have argued that in the case of token events elaboration of micro-foundations is desirable, but that certain social scientific categories may not be reducible due to the possibility of multiple-realisability. That is, elaboration of micro-foundations for certain macro categories is impossible, and not just as a result of cognitive limitations. Elster has advocated the micro-foundations approach on two grounds. He suggests that on a practical level the specification of micro-mechanisms is indispensable for establishing the credibility of macro-relationships; moreover, the micro-foundations approach shows the mechanisms by which a given social phenomenon ‘actually works’ in terms of the individual actions which generate the social result (Elster, 1985, p.5). Similarly Van Parijs claims that ‘the specification of micro-foundations offers the only promising path towards theoretical integration’ (1983, p.120). The advantage of the micro-foundations approach, for Van Parijs, is that by explicitly outlining micro-mechanisms we can fix a wide array of disconnected explanations into a unified environment. One notable example of the micro-foundations approach is that of Roemer which is discussed in Chapter 5. Roemer has utilised the language and tools of the theory of games and neo-Walrasian general equilibrium theory to provide a general theory of exploitation and class. However, the results obtained by Roemer are sensitive to the assumptions made, and such models do not incorporate elements that cannot be formalised. Ironically one of the attractions of the Marxian paradigm has been that it provides a scientific, political and ethical system (Weizsäcker, 1973, p.1245). Orthodox Marxism offers a ‘grand narrative’ or comprehensive system of thought, founded on the alchemy of the Hegelian–Marxian dialectic. In comparing orthodox and analytical Marxism it would be incorrect to suggest that analytical Marxism is integrated or unified in the same systematic manner as orthodox Marxism. Analytical Marxism has tended to produce ‘particularistic’ models, and the nature of the axiomatic method of modelling has tended to produce results which are specific to abstract narrowly defined environments. Although

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recognising this should not be taken to imply that the analytical Marxist ‘critique’ is incorrect, there are reasons to be sceptical of the coherence and theoretical integration of analytical Marxism.

Conclusion The development of analytical Marxism has stimulated a constructive debate concerning the methods employed by Marxian social scientists. This has implications for the method employed within social science generally, since there is merit in the cross-fertilisation of ideas between Marxian and orthodox social science. This provides Marxian economists, sociologists and other social scientists with new methods with which they can elaborate theories. Furthermore, if there is a project within Marxism which involves the dissemination of ideas to a broader audience, such action is necessary. This chapter has examined one crucial question that has emerged in debates over the status of analytical Marxism – the question of reduction. This debate has been useful for orthodox Marxism, in that the danger of teleological and functionalist arguments has been highlighted. This challenge can only lead to improvements in the theories and models employed within Marxist social science. Similarly, a number of analytical Marxists have begun to appreciate the profound problems with methodological individualism. Wright, Levine and Sober, in particular, have acknowledged some of the problems associated with methodological individualism and discarded it entirely in favour of the approach of anti-reductionism. This methodological framework accepts that some macro-social categories may be irreducible because of the possibility of multiply-realised social elements. Elements of the work of Wright, Levine and Sober have been criticised here, in particular their portrayal of token-reductionism as an explanatory claim. Their approach suggests that, because Marxists are materialists, token reductionism is a worthwhile theoretical project. This can be challenged in two ways. First, it is suggested here that, in seeking a ‘complete’ explanation of a token event, it is necessary to explain how a given brain state arose. Secondly, it was claimed that it is possible that agents entertain beliefs about type concepts. In this sense the explanation of the token event requires reference to irreducible social aggregates if a complete explanation of that event is to be forthcoming. A word of caution is necessary, since claims for

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complete explanations suggest an unrealistic research agenda in the social sciences. However, the criticism intended in this book is confined to the philosophical and theoretical difficulties of providing a complete explanation, as opposed to the empirical problems. Quite clearly, this debate has profound implications for one of the crucial elements of Marxian analysis – that is, the use of class as an explanatory element in the analysis of capitalism and other modes of production. The approach of methodological individualism takes the individual as the starting point of any social scientific investigation. However, Marxism has traditionally taken class as an explanatory element. In one sense, not only is a class composed of human individuals (that is an ontological reduction), but also the class location of individuals determines their actions, at least in part. Hence providing an explanatory micro-reduction is problematic. The approach of anti-reductionism can give us a solution to this dilemma, in that type concepts (the capitalist class, the proletarian class, the petty-bourgeoisie) can be multiply-realised on a vast array of micro-mechanisms. In this sense ‘class’ retains an explanatory role separate from the actions of individuals. And, if individuals entertain beliefs about class (in particular in situations of imperfect information) this clearly impinges upon our analysis of token events. In this sense we can provide a scientific basis for the use of class as a unit for analysis. Certain phenomena may be partially explained using a rationalchoice micro-foundational approach. Nevertheless, the limits of such an approach should be taken seriously if analytical Marxism is to maintain its intellectual integrity as a new school of progressive thought. The work of Wright, Levine and Sober represents a valuable contribution to this ongoing discussion, and, if Marxism is to be considered a school of social scientific analysis, serious consideration of the methodology of reduction must be brought to the fore as an area of debate.

3

Marxism and the foundations of collective action

Introduction Classical and Marxian political economy were both concerned with the distribution of income in class terms. While Marx criticised classical political economy, it was a tradition with which he sought intellectual engagement. Engagement with other schools of thought is a worthy and productive activity. A quarter of a century ago, Morishima noted: ‘It is our great misfortune that economists have for a long time been divided between the “orthodox” and Marxian camps as a result of cliquishness ... They are at daggers drawn and describe each other as a society for reactionaries and a society for economists with lower I.Q.s’ (1973, p.1). There are, of course, exceptions, such as analytical Marxism, whose practitioners have engaged with modern mainstream theorists. Analytical Marxists have applied the tools and methodology of analytical philosophy and ‘positivist’ social science to issues of theoretical interest to Marxian scholars. The essential thrust of analytical Marxism is that Marxian social scientific methodology is deficient, and it is Marx’s theoretical insights which are more profound. In this chapter, following from the previous, it is claimed that wholesale rejection of holistic arguments in favour of reductionism is problematic. One of the features of Marxian social science is that analysis can be, and is, conducted on a number of different ‘levels’ (including at the level of classes) and such an approach can be put to theoretical use. Indeed, it is also suggested that this is an approach which mainstream social science would do well to explore, where it has not already done so. As a preliminary to discussion of the application of game theory to Marxism it may be useful to explain how game theory is interpreted

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Marxism and the foundations of collective action

in this chapter, and to indicate the potential benefit of such an approach to Marxian social science. Game theory offers an approach to social science in which individual agents or institutions are assumed to interact strategically. More specifically, game theory provides a language and format (i.e. strategic and extensive form taxonomies) for communicating ideas and unifying theories. This language offers a number of solution techniques, which agents can adopt. These are useful if it is the theorist’s belief that the nature of agents’ rationality, or the method through which institutions act, conforms to that which underpins the given solution concept.1 Marxian game theory may employ such solution techniques and taxonomies differently from their application in neoclassical economics. It is argued that game theory need not be reductionist and the application of game theory is considered in relation to the discussion of reduction in Chapter 2. Then an anti-reductionist model of class conflict and surplus-value production, based on the principle of bilateral monopoly, is outlined. Subsequently particular attention is paid to cases in which self-interest (as a Nash equilibrium outcome) is self-defeating (in aggregate). This is discussed through a ‘divide and rule’ model in which two groups (or coalitions) of workers are set in opposition to one another through the imposition of a detrimental structure for pay bargaining. In Chapter 4 the idea of ‘exploitation’, in a game-theoretic sense, is explored in more detail. It is by separating and challenging each of these elements of game theory, as it has been practised within neoclassical economics and analytical Marxism, that a truly distinctive Marxist view of game theory can be developed which will enhance attempts to advance a materialist account of economic evolution and progress.

Game theory and reductionism It is predominately analytical Marxists who have explored applying the language and techniques of game theory to Marxian social science (for example Roemer 1982a, 1994a; Elster 1982, 1985).2 Game-theoretic Marxism, as it has been practised, has therefore often accepted many of the premises of neoclassical economics, such as methodological individualism and instrumental rationality, leaving what are in principle separable philosophical positions conflated.3 Individual scholars have advocated a Marxist approach to game theory which is anti-reductionist. For example, Maarek (1979) has sought to use the theory of games to illuminate Marx’s theory

Marxism and the foundations of collective action

31

of surplus-value while rejecting the principle of methodological individualism. In addition, Lebowitz (1988) has argued that Marx’s approach is inherently game-theoretic, although it is a collective game theory that Marxists should seek to develop, with classes rather than individuals as the unit for analysis. Such approaches are not antithetical to game theory, as it has been practised. While the field of non-cooperative game theory does assume that groups or coalitions are only formed as the outcome of optimising decisions on the part of individual human agents, the less-developed field of cooperative game theory allows agents to make binding agreements, hence groups or coalitions may be the players in games of strategic interaction. This raises philosophical questions concerning explanations, which have been considered in debates between analytical and orthodox Marxists. The former, such as Van Parijs (1983) and Elster (1985), have generally asserted the primacy of explanations based on microfoundational analysis. In contrast the latter, such as Lebowitz (1988, 1994), reaffirm Marx’s claim that individuals should be understood as an outcome of social processes, and that units of analysis other than individual human beings are indispensable for examining socio-economic evolution. Stated in terms of neoclassical economics, orthodox Marxist approaches to social science emphasise how the actions of individual agents are influenced by structural factors (some of which may not be observable), which not only affect constraints but also influence the preferences of agents. Thus societies create individuals who then reproduce and transform those societies. This poses a problem for those social scientists who wish to explain why and how classes function. Moreover, it is relevant to the theory of preference formation. Assume, as does Roemer (1986c), that agents’ preferences are products of both past preferences (specific to the individual) and social formation. It follows if the latter is historically more significant than the former, as we return further back ‘dating’ preferences and seeking an explanation, so individual-level ‘causes’ diminish, and social factors predominate. The individual is no longer autonomous, but is rather a product of social factors; that is, individuals’ actions are a consequence of the society in which they exist. Stated thus it is the circumstances and not the passions or reason of agents that lie at the heart of generating social scientific explanations. Such an argument is also teleological, in that the direction of evolution and change is determined independently of the goals and aspirations of individual agents. One way to overcome the problem of

32

Marxism and the foundations of collective action

teleology is to adopt methodological individualism as a social scientific method (Elster, 1985). However, for reasons outlined in Chapter 2 this is problematic. Indeed, many philosophers regard methodological individualism as an inappropriate methodological assumption, hence an alternative approach is desirable (e.g. Bhaskar, 1989; Garfinkel, 1991). The alternative approach to explanation adopted here involves recognition that social scientific explanation can be conducted on a number of different levels, and using classes as our units for analysis is legitimate.

Surplus-value: a game-theoretic formulation It is possible to represent a number of Marx’s theories, such as that of surplus-value, in game-theoretic terms.4 Maarek, for example, takes two agents which we shall, in this chapter, recast as classes and whom we label C and W (the capitalist and working class).5 Following Maarek (1979, pp.125–34), assume that coalition W possesses no capital and coalition C has a stock of food. This stock will facilitate subsistence for two days for coalition C, or for one day for all members of society (i.e. coalition C plus coalition W ). Coalition C also possesses the tools necessary for production. It is important to note that Maarek formulated the following problem in terms of the size of the relative consumption bundles for the two classes. In contrast to Maarek, we will recast the model to formulate the problem of distribution and bargaining in terms of the working day, thus adopting the notion of necessary and surplus labour time, familiar from Marx’s Capital.6 Assume that the daily subsistence required by coalition C and W is B for each, and that during the course of the working day 2B can be produced using the tools plus the labour of one class. It is apparent that coalition W requires B to subsist during the first day, and that use of the tools is required in order to produce the required subsistence for the next day. Since all coalition W has to exchange is labour power, the question arises, for what proportion of the working day will the working class agree to work on behalf of the capitalist class, in exchange for the use of the means of subsistence and production? What will be the magnitude of surplus labour?7 Taking a working day (L), and a consumption bundle (B) which is necessary for the survival of each class, we assume that the two classes negotiate to enable coalition W to survive, while both classes seek to minimise their own labour input. The model becomes one of

Marxism and the foundations of collective action

33

bilateral monopoly. The payoffs are denoted SW for the workers and SC for the capitalists, and are determined in this case by whether each class possesses the necessary consumption goods to survive, and by the number of hours in the working day which members of each class are compelled to work, denoted h(0≤h≤L) where performing labour causes disutility. The payoff to agents is thus: S =f (B,h)

(3.1)

 The disagreement point (SW ,SC ) is the payoff to each if no agreed ∗ bargain can be struck, and the equilibrium payoff is SW to the workers ∗ and SC to the capitalists. The gains (GW ,GC ), in equilibrium, are given by: Gi∗ =Si∗ −Si (3.2)

If disagreement is the outcome, this implies that coalition W is unable to produce enough to consume; that is BW =0 for each worker. We shall assume that this is the worst possible payoff for the workers,  giving a payoff of SW =−∞. Likewise, death is the ultimate sacrifice for the capitalists, yielding a payoff of −∞. However, disagreement for coalition C does not imply death; rather each capitalist will be compelled to perform half a day’s labour each day to produce their own means of subsistence, if no agreement can be reached. Assuming, for simplicity, that the number of workers (w) is the same as the number of capitalists (c), and c+w=n, the following holds, where half a day’s labour is required for the subsistence of each person: hww+hc c=

Ln 2

(3.3)

In Maarek’s model four conditions are necessary to produce a negotiated outcome in a model of bilateral monopoly. In the formulation offered in this chapter Maarek’s conditions are equivalent to: ∗ >−∞, otherwise the workers would rather die of hunger. 1. SW 2. GC∗ ≥0, otherwise the capitalists would perform their own work. ∗ 3. GW maximises the gain to the working class, given SC∗ , otherwise the workers would adopt a different strategy. That is, the equilibrium outcome for coalition W is strategically stable. ∗ 4. GC∗ maximises the gain to the capitalists, given SW , otherwise coalition would adopt a different strategy. That is, the equilibrium outcome for the capitalists is strategically stable.

34

Marxism and the foundations of collective action

These conditions give a range of average values for the workers of hw where (0.5L≤hw ≤L) and for the capitalists of hC where (0≤hC ≤ 0.5L). But, other than predicting that the outcome will be in this range, bilateral monopoly theory can tell us little more.8 We know that the capitalists will be better off, relative to their disagreement point, if they can get the workers to work anything greater than half a day. The workers will be better off if they do not die, and they would be willing to work up to a full day to guarantee this subsistence. The outcome cannot be uniquely determined in such a framework. This model, in which each class labour-minimises and ends up receiving the same quantity of goods is, of course, highly abstract. However, let us use this simple model to consider the relative strengths of the two classes. Workers can threaten to perform no labour for the capitalists, above the half-day they would have to work with the capitalists’ equipment to produce their own means of subsistence. If coalition C refuses to comply, the outcome for the workers is death. The capitalists, knowing that coalition W ’s threat to perform no labour for them is not credible, will refuse to allow the workers to work anything less than the full day. Capitalists can threaten to use the equipment to produce their own subsistence, and leave the workers to die. This is a more credible threat since such an outcome does not entail that the capitalists die, as is the case for the workers. Accordingly, coalition C can use this threat to force the workers to labour for the whole day, while the capitalist class perform no labour. A credible threat and the disagreement point together combine to make this a plausible outcome within this model. Essentially, because of the economic power which the capitalist class possesses, given private property rights, capitalists are able to secure decisions which favour their interests. The essential point is that under competitive capitalism, workers do not possess the means to bargain from a position of equality relative to the capitalists.9 The act of exchange is unequal. If we assume that workers are labour-minimisers, i.e. workers wish to work as few hours as possible to obtain a fixed income, it follows that the existence of surplus labour-time implies that the workers are working for longer than is socially necessary for their reproduction. Alternatively, if we assume the workers to be wage-maximisers, in the sense that they wish to maximise income for a given period of labour, it follows that the workers are not receiving, in terms of goods, the full equivalent of what their labour produces.

Marxism and the foundations of collective action

35

Thus far we have considered this model using class as the unit of analysis, taking the capitalist and working class to be the foundation of our system. However, problems of class cohesion may exist when mechanisms are established which cause coalition dissolution. That is, collective action may be hampered when ‘divide and rule’ characterises the organisation of workers. In the next section we consider how a coalition can be divided in such a way as to benefit the capitalist, when groups of workers are assumed to act in their own individual self-interest.

Divide and rule In order to focus discussion, let us consider a specific example intended to show one possible approach to ‘divide and rule’ in cases of collective action. The notion of ‘divide and rule’ seeks to place the interest of different groups of workers in conflict, to the benefit of the capitalist class. This is socially divisive and places barriers in the way of workers who might otherwise seek political, economic and social union. Coordination, which would be to the mutual economic advantage of workers, is thus prevented. One implication of the following example is that the chronology of bargaining is shown to be significant in generating paradoxical outcomes, where ‘paradoxical’ implies each coalition could secure a higher payoff were cooperation guaranteed. However, self-interest on the part of coalitions produces a lower payoff than that which would have been provided had agents adopted a collaborative strategy. Assume that there are two coalitions of workers, A and B, who bargain over pay and conditions sequentially. It was assumed previously that the payoff, or well-being of workers, is determined by two factors: the number of hours they work and the payment they receive (i.e. their real wage in this model). This was given before as S =f (B,h). Long working hours and/or low wages render dissatisfaction. In capitalism the real wage and hours worked are determined as a result of a process of bargaining or conflict. In our model we shall now assume that workers in a particular bargaining cycle are only bargaining over pay (hence for the moment hours of work are given). In this situation the payoff to each respective group will be the hourly wage rate (measured in euros, Ł). We assume the chronology of bargaining is set by the capitalist and that it is as that outlined using a time-line in Figure 3.1. Note that group A negotiates wages first and group B negotiates second.

36

Marxism and the foundations of collective action 1

Workers A decide on whether to adopt a hostile (H) or passive (P) bargaining strategy.

2

Workers B decide whether to support (S) or not support (S´) the action of workers A. (ii) Workers B decide whether to adopt a hostile (H ) or passive (P ) bargaining strategy. (i)

3

Workers A decide whether to support (S) or not support (S´) workers B.

Figure 3.1 Time line for divide and rule

Payoffs are depicted in Figure 3.2. These are determined by whether each group of workers adopts a hostile (H ) or passive (P) bargaining strategy with respect to the capitalist, and are also determined by the degree of support received from other workers during an industrial dispute. For industrial action to be successful, support (S) is required from other workers. However, support is not costless and some income is forgone in refusing to cross picket lines etc. Hence a material incentive is created for groups of workers, in one-off situations, to refuse to lend support to other workers, or to scab (S  ). Hence the highest payoff to workers is obtained when they strike, and are supported by the other group, but do not lend support themselves in any dispute. We shall assume in our game that this will give a payoff of Ł10/hour to the successful strikers. Of course, the worst possible situation is to strike and not receive support yourselves, whilst having lent support to the others. We shall assume this yields a payoff of Ł6/hour. If workers support the other group, but do not strike themselves, their payoff is Ł7/hour. If neither group strike, the payoff to each is Ł8/hour. Finally, if mutual support occurs and both groups of workers act militantly, a payoff equivalent to Ł9/hour can be secured. The payoff structure is outlined in Figure 3.2 (with the first payoff being to group A, and the second payoff to group B). What strategy should the respective groups of workers adopt? Consider this using backward induction, where the terminal nodes are considered first. Even if a promise to act collaboratively by the coalition who is bargaining first has been struck with the coalition bargaining second, this promise may not be credible in that, if they have already received a payoff in terms of higher pay, the coalition bargaining first has no material incentive to now render support to the coalition bargaining second. Hence at each terminal decision node,

Marxism and the foundations of collective action BSH BSP

AS

(€9, €9)

A S´

(€10, €6)

B S ´H

AH

AS AS´

B S ´P

37

(€10, €7) (€6, €10) (€7, €7)

AP

AS BH

A S´ BP

(€7, €8) (€7, €10) (€8, €7) (€8, €8)

Figure 3.2 Divide and rule

where A has a choice between supporting (S) and not supporting (S  ), they are materially better-off through not supporting. The payoff to A is always Ł1 greater through not supporting B at each terminal node. Hence the Nash equilibrium in each of these subgames involves A not supporting B’s industrial action. Recognising this, we can proceed to consider other subgames in Figure 3.2 – specifically those where B chooses whether or not to support A (if the latter has chosen a hostile strategy), and that where A has chosen a passive strategy. In the event A is hostile, given the outcome of the subgames outlined above, the optimal strategy for B is to adopt a passive role and, additionally, to not support A’s industrial action. Given this, we can identify the subgame perfect Nash equilibrium as involving both A and B adopting a passive approach to bargaining – leading to a payoff of Ł8 each. Had both sets of workers been able to guarantee reciprocity in the form of support for their industrial action, they would have been able to force a wage of Ł9/hour. In this sense we can see that timing of action is important, and the format of extensive form games helps us understand the nature of the problem. Chronology of bargaining matters, and we can see how timing can be manipulated to serve the ends of capitalists. In the case we have proposed we have shown that if the capitalist can manipulate a particular chronology, workers can be divided. However, capitalists

38

Marxism and the foundations of collective action

may also adopt other strategies to divide workers, such as fostering racism, religious or gender discrimination by workers, or division on the basis of sexual orientation etc. Using wage differentials, piece-wages or locating plants in different regions or countries are other strategies which may be used to foster divisions and undermine collective action. These areas have traditionally occupied the attention of Marxist economists. The suggestion here is that representing such struggles in extensive form can illuminate the process through which such problems arise, and provide an indication as to how these problems can be overcome. Marx recognised the nature of the problem: Competition separates individuals from one another, not only the bourgeois but still more the workers, in spite of the fact that it brings them together. Hence it is a long time before these individuals can unite ... Hence any organised power standing over and against these isolated individuals, who live in conditions daily reproducing this isolation, can be overcome only after long struggles. To demand the opposite would be tantamount to demanding that competition should not exist in this definite epoch of history, or that individuals should banish from their minds conditions over which in their isolation they have no control. (Marx 1976, p.75) We can therefore, in this game, identify a dichotomy between the optimal response for the working class as a whole and the rational response of separate groups. However, ‘divide and rule’ may not just emerge as an unintended beneficial consequence of the actions of capitalists – it may be created and fostered by them. Edel (1979) is one economist who has suggested that game theory may illuminate our understanding of collective action. Some collective action games are similar to prisoners’ dilemmas for example. And given structures such as that outlined in Figure 3.2 it may be that groups of workers move towards collaborative solutions as games are repeated. Thus ‘solidarity is not irrational – it is one of the rational responses possible in any repeated prisoners’ dilemma game’ (Edel 1979, p.758). As noted by Edel, empirical evidence does suggest that repeated prisoners’ dilemma games tend to generate more collaborative responses than do one-shot games (the game outlined in Figure 3.2 has been treated as a one-shot game). However, if such games

Marxism and the foundations of collective action

39

are repeated finitely then the rigid assumption of rationality still predicts mutual defection. Although Edel suggests that the collaborative response is rational, we should note it is not rational in the sense implied by instrumental rationality. Edel observes the possibility of ‘individual and collective rationalities’, but acknowledging the possibility of the latter implies something other than instrumental rationality on the part of individual agents. In this sense attempts to unify Marxian and neoclassical notions of agency are problematic, and the prisoners’ dilemma makes explicit this contradiction. As Booth suggests, ‘solidarity of action based on non-neoclassical assumptions must also be considered in explanations of large group collective behaviour’ (1979, p.762).

Conclusion It is possible to observe, in the real world, instances in which interaction between groups or individual agents involves strategic planning. Wright (1994) has argued that, if it is accepted that in some important social contexts (a) individuals or social groups make conscious decisions, (b) when they make choices they take into account the expected consequences of those actions, and (c) in formulating their expectations of the consequences of their actions they take the actions of others into account, then it follows that game theory may contribute to the development, clarification and dissemination of the theories of Marxian social science. In this chapter an example has been constructed which relates Marx’s theory of surplus-value to the case of bilateral monopoly, and it is suggested that the notion of ‘credibility of threats’ provides an insight into how the respective power of each class influences the outcome. The approach adopted took exogenously given classes as our units for analysis and cast the problem of distribution in terms of surplus and necessary labour time. Thereafter the rationality of collective action was investigated using a game-theoretic example of divide and rule. There are potential gains from the development of a game-theoretic Marxism. In formulating and understanding the process of class conflict, game theory gives us a methodology from which to understand how classes and agents within capitalism could or do act strategically. It offers a taxonomy for formalising Marxian theories and for understanding the limits of narrow notions of rationality. Not only are these useful developments for contemporary Marxists wishing to

40

Marxism and the foundations of collective action

understand the functioning of capitalist socio-economies, they also provide a language through which the theories of Marx and Marxian economics can be communicated to a broader audience. Of course, to appropriate game theory means more than simply adopting it. Rationality, as interpreted thus far, is not a trans-historical fact of human nature, and moral and historical evolution is possible. Alternative ‘levels’ of analysis are possible in which classes, rather than isolated human individuals, can serve as useful units of analysis in the process of social scientific investigation. Accepting such caveats does not however involve rejecting a distinctly game-theoretic Marxism; at a particular moment in time when an individual agent, or a class acts in unison, and does so strategically, such an approach is inherently game-theoretic. Game theory has shown us that in some circumstances self-interest can fetter economic development and, from a neoclassical perspective, generate inefficient outcomes. Recognising this serves as a useful starting-point for further social scientific investigation. Neoclassical economists, anxious to account for these problems, have focused upon the philosophical problems of knowledge and beliefs, assuming that there may exist ‘irrational’ or altruistic players. In this chapter the basis for self-interest has come under scrutiny, and it is suggested that if Marxian economics is to develop and utilise the tools of game theory, it should first separate the formal logic from the a priori assumption that human agents are individually rational. Indeed, this is a necessity since two things game theory has shown us are the normative limits and the experimental inadequacy of such an assumption.

4

Value, price and exploitation

Introduction Problems associated with pricing have plagued Marxian economic theory since the critiques of Marx’s theory commenced soon after the publication of the third volume of Capital in 1894. The problem of explaining prices in Marxian economics relates to the question of methodology. The distinction between essence and appearance is significant since, traditionally, Marxists claim that while prices are what we observe in the course of exchange, underlying these are values which somehow determine these prices. Moreover profit is determined, in part, by the rate of surplus-value.1 In order to focus discussion we shall outline the basic problem before discussing a number of proposed solutions. In particular, it is suggested here that value theory is not useful as a theory of price in capitalist economies, but it captures what Marxists regard as exploitation. In this sense a labour theory of exchange value is rejected, while a labour theory of exploitation is retained. We outline the transformation problem before presenting a linear solution to Marx’s problem. Then we consider a Walrasian general equilibrium approach to price, as proposed by Roemer. Thereafter we consider the ‘new solution’, an approach which has received growing attention since its independent discovery by a number of economists. In the case of each approach the perceived shortcomings are identified. No solution presents itself as an obvious alternative along the lines suggested by Marx, but the approach of Morishma (1973), it is suggested, is the most likely to provide a robust foundation for development.

42

Value, price and exploitation

The transformation problem The transformation problem has produced a considerable literature with an array of solutions proposed. As a preliminary to considering such solutions it is useful to consider the original problem as formulated by Marx in Chapter 9 of the third volume of Capital. The rate of surplus-value is determined by the ratio of surplus-value to variable capital. Surplus-value comprises the profit, interest and rent produced and variable capital is that portion of total capital used to pay the wages of labour. Denoting the rate of surplus-value e, surplus-value s, and variable capital v, it follows that:2 s (4.1) e= v According to Marx the rate of profit for a particular commodity (ri ), is the ratio of surplus-value to the total capital outlay, i.e. constant plus variable capital. Where c is constant capital (comprising fixed and circulating elements), we may write the value rate of profit for particular commodities as: si ri = (4.2) ci +vi Expanding (4.2) gives: ri =

si /vi ( cvii +1)

(4.3)

It is an implication of the assumption of atomistic competition that, where capital movements are unrestricted, capital will flow from sectors yielding a low rate of profit to sectors yielding a high rate of profit. This suggests that there will be the formation of an average rate of profit, r, and in the sphere of circulation there would be a redistribution of surplus-value such that profit realised by capitalists would be equalised in the sense that it will correspond to their capital outlay. To understand why this is necessary, consider the following: if we define cvii as the organic composition of capital, and the rate of surplus-value is assumed to be equal between industries, equalisation of the rate of profit between two industries, I and II, implies that: eII eI rI = cI = cII =rII (4.4) +1 vI vII +1

However, (4.4) will not generally hold given an equal rate of surplus-value and divergent organic compositions of capital. Explaining

Value, price and exploitation

43

Table 4.1 Value categories in Marx’s Capital

Industry c v I 80 20 II 70 30 III 60 40 IV 85 15 V 95 5 Source Marx 1981: 255

e=s/v 100% 100% 100% 100% 100%

s 20 30 40 15 5

c+v+s 120 130 140 115 105

ri 20% 30% 40% 15% 5%

the formation of an equal profit rate, consistent with an equal rate of surplus value, is thus not simple. Further, the connection between value and price warrants explanation. Marx fully recognised this but believed that prices diverge systematically from labour values. In the transformation of values into prices Marx simultaneously transforms surplus-values into profits and this is illustrated in the third volume of Capital. Consider the case of five industries in Table 4.1. The total of constant plus variable capital applied in each industry is equal. By assumption, the rate of surplus-value is equal, giving rise to varying organic compositions of capital and differing rates of profit in each sector. The individual rate of profit is highest in the industry with the lowest organic composition of capital. The implication, as suggested in equation (4.4), is that varying the organic compositions of capital gives rise to divergent rates of profit. Thus, in Table 4.1 the individual  rate ofprofit varies from 5 per cent to 40 per cent. In aggregate, c=390, v=110, and the average rate of profit r=22 per cent. Divergence in the rate of profit, as a consequence of varying organic compositions of capital is, as predicted in equation (4.4), manifest in Marx’s numerical example. However, this contradicts the assumption that the free mobility of capital from one industry to another leads to equalisation of the rate of profit. This lies at the heart of the transformation problem. Marx elaborates on this problem by referring to an example in which constant capital varies in durability such that not all of c that is applied is consumed in the process of production. Constant capital, which is actually consumed, is given as c∗ in Table 4.2. It is c∗ which forms the cost of constant capital in the cost price. Thus we can obtain the value c∗ +v+s (in terms of consumed constant capital) and the cost price c∗ +v of commodities.

44

Value, price and exploitation

Table 4.2 Durability of constant capital and cost price

Industry e=s/v I 100% II 100% III 100% IV 100% V 100% Source Marx 1981: 255

s 20 30 40 15 5

ri 20% 30% 40% 15% 5%

c∗ 50 51 51 40 10

c∗ +v+s 90 111 131 70 20

c∗ +v 70 81 91 55 15

Table 4.3 Commodity price and price/value divergence

c∗ +v+s

c∗ +v

p

r

I 20 90 II 30 111 III 40 131 IV 15 70 V 5 20 Source Marx 1981: 256

70 81 91 55 15

92 103 113 77 37

22% 22% 22% 22% 22%

Industry

s

Price/value divergence +2 −8 −18 +7 +17

Marx maintained that we could use the information in Tables 4.1 and 4.2, together with the average rate of profit (r), to derive the commodity prices, depicted in Table 4.3. The commodity price is equal to the cost price plus the average rate of profit. Note that aggregate prices and values are equal and that the sum of price/value deviations is zero. Also the total profit and total surplus-value are equal. In summary, Marx derives the individual profit rates on the basis of equation (4.2), but given divergent organic compositions of capital these will differ from one another. Therefore Marx transforms from values to prices of production, which comprise average profit on the costs of production r(c∗ +v), added to cost price (c∗ +v), i.e. p=(c∗ +v)(1+r)

(4.5)

Marx maintains that surplus-value is redistributed between industries with a high organic composition of capital, to industries with a low organic composition of capital, to bring about a situation in which individual capitalists will receive a return on their capital r, rather than ri ; i.e. ‘the profit that is added to … cost price, is governed not by the mass of profit that is produced by this specific capital in its specific

Value, price and exploitation

45

sphere of production, but by the mass of profit that falls on average to each capital invested’ (Marx, 1981, p.258). The precise mechanism of redistribution is not explicitly stated in Marx’s Capital, but the process is predicated on the assumption that the sum of values is equal to the sum of prices and the sum of surplus-value is equal to the sum of profit (see Marx, 1981, p.273 for an explicit statement to this effect).3 Marx’s approach, elaborated in the third volume of Capital, received criticism shortly after being published. Böhm-Bawerk’s (1975) critique was published in German in 1896, before being published in English in 1898. The problem is reconciling the ‘law of value’ with an explanation of the prices of production. In this context Böhm-Bawerk states: I cannot help myself; I see here no explanation and reconciliation of a contradiction, but the bare contradiction itself. Marx’s third volume contradicts the first. The theory of the average rate of profit and the prices of production cannot be reconciled with the theory of value. (Böhm-Bawerk, 1975, p.30) A number of arguments could be advanced in favour of the law of value, and Böhm-Bawerk systematically criticises them. Marxists might argue that while individual commodities may be sold above or below their values, the total of the prices of production remains equal to the sum of their values. Böhm-Bawerk’s objection to such a claim is that this does not give any explanation of divergences of the relative prices within this whole. Indeed: ‘In the case of prices of production which deviate from the “values”, it is not a question of fluctuations, but of necessary and permanent divergences’ (Böhm-Bawerk, 1975, p.39). Moreover, the belief that the sum of prices of production are equal to the sum of values, and that deviations mutually cancel each other out, provides no systematic account of individual prices. A second defence of Marx’s approach, which Böhm-Bawerk speculates upon, concerns the suggestion that increasing or reducing working time will cause the prices of production to rise or fall. When working time necessary for the production of the commodities decreases, ceteris paribus, prices also fall. And, when working time necessary for the production of commodities increases, ceteris paribus, prices rise. Böhm-Bawerk maintains this is over-simplistic because such movements will change the organic composition of capital. Moreover, Böhm-Bawerk suggests that the claim that changes in labour expended

46

Value, price and exploitation

determine relative price movements would be analogous to making such an assertion about ‘capital’ (i.e. constant capital). Such an argument might take the form: ‘prices rise or fall when, other conditions remaining equal, the length of time during which the capital is invested increases or decreases’ (1975, p.40). Böhm-Bawerk maintains that such a claim concerning capital is absurd, as is the Marxist claim that the amount of labour expended is the sole determinant of relative price movements. Another Marxist defence runs as follows: the law of value governs the exchange of commodities in certain ‘primary’ stages in which the change from values into prices of production has not yet been accomplished. Beginning with a condition of society in which capitalist production is not yet prevalent, Marx claims that prices will be exclusively determined by their values. But Böhm-Bawerk suggests that the length of time from the act of expending labour, to the time when that labour receives the remuneration for that activity, also influences the remuneration. If workers were paid at the end of the production process, would a worker engaged in a production process that takes a year to complete be prepared to be paid at the same daily rate as a worker who completes their production process in day? Böhm-Bawerk describes Marx’s thesis to be, even in pre-capitalist societies, ‘inherently improbable’ (1975, p.47). The final Marxian argument that Böhm-Bawerk seeks to refute concerns the suggestion that, in a complicated economic system, the law of value regulates the prices of production indirectly. Because the total value of commodities (determined by the law of value) determines total surplus-value, and this in turn regulates the average rate of profit, there is an indirect link between values and prices. Böhm-Bawerk criticises Marx on the following grounds. Marxists claim that the law of value regulates the prices of production. Prices of production are determined in part by the quantity of labour expended and also by the wages paid to that labour. The former is compatible with the law of value, but variation in the latter is not. Thus Böhm-Bawerk suggests: The ‘aggregate surplus-value’ would have to co-operate with a completely foreign element, the mass of social capital, in determining the average rate of profit; and, finally, the latter would have to co-operate with a partially foreign element, expended wages, in determining the accruing total profit. (1975, p.60)

Value, price and exploitation

47

For Böhm-Bawerk, the ‘law of value’ is only one of the determinants of prices of production. And ‘Marx passes silently over’ (Böhm-Bawerk 1975, p.60) these other determinants in formulating his theory of value and price. In the wake of Böhm-Bawerk’s critique, a number of Marxists have sought to defend Marx’s theory from the collected criticism of neoclassical theory. Bortkiewicz (1952) outlined a solution to the so-called ‘transformation problem’, and in recent years the number of solutions have multiplied. Criticisms that echo those formulated by Böhm-Bawerk continue. For example Samuelson remarked of Marx’s approach to value and price: ‘Contemplate two alternative and discordant systems. Write one down. Now transform by taking an eraser and rubbing it out. Then fill in the other one! Voila! You have completed your transformation algorithm’ (1971, p.400). Such criticism concurs with the objection raised by Böhm-Bawerk. Relatively recent views include those advanced by Morishima (1973) and Steedman’s (Sraffa-inspired) suggested reformulation (1977).4 The latter claims that ‘Marx’s value magnitude reasoning should be abandoned by those seeking to develop a materialist account of the capitalist economy’ (p.27). At the heart of the problem is the recognition by Marx’s critics that the rate of profit in a competitive capitalist economy is not equal to the ratio of surplus-value to the sum of constant and variable capital. And since, following Sraffa (1960), the rate of profit can be determined without any reference to value magnitudes, ‘the “transformation problem” is a pseudo-problem, a chimera: there is no problem of deriving profits from surplus-value and production prices from value to be solved’ (Steedman 1977, p.15). The central thrust of this approach is therefore that Marx’s value reasoning should be abandoned, to be replaced by a ‘consistent’ reformulation of price such as that of Sraffa. This should not be taken to imply a rejection of a broader surplus approach since Sraffa’s approach was just that. Moreover, Sraffa’s (1960) work had the explicit purpose of laying the foundations for a logical-deductive critique of economic theories which were based on the ‘existence of a “factor of production”, capital, conceived as a given aggregate value’ (Steedman, 1981, p.12). Marx suggested that, in capitalist economies, the rate of profit is given by S/(C +V ). Steedman defines S, C and V as the aggregate amounts of labour required (directly and indirectly) to produce the bundle of commodities going to the capitalists divided by the bundle

48

Value, price and exploitation

of commodities required to replace used-up means of production plus those which go to the workers as wages. To obtain the rate of profit in money terms it is essential to ‘value’ the three elements of the rate of profit in terms of prices and then divide profit by total capital. Steedman’s critique then proceeds thus: [Marx] used this expression for the rate of profit, to show ... that commodity prices will not be proportional, except by fluke, to the quantities of labour required for their production. But if prices are not proportional to labour contents then the ratio S/(C +V ), in which both the surplus product and the total capital advanced are ‘valued’ in terms of their labour contents, will not be equal ... to the ratio of surplus product to total capital advanced, where both are ‘valued’ in terms of prices. This latter ratio is, however, precisely what is meant by the rate of profit. Thus S/(C +V ) is not the rate of profit. (1981, p.14) We therefore have two ratios, one in value terms, S/(C +V ), and one in money terms, and they will only coincide by pure chance. If we are to generate explanations of the functioning of the capitalist economy as an outcome of profit maximisation on the part of individual capitalists (since Marx asserted that capitalists do not reason in ‘value’ magnitudes), the question becomes ‘which rate will the capitalist seek to maximise?’ Plainly, given such criteria capitalists will seek to maximise the money rate of profit, and value magnitudes are irrelevant. Moreover, the problem, for Marx, according to Steedman, is that he sought to determine first the rate of profit then subsequently the normal prices of production. In contrast to this approach, Steedman maintains that the profit rate and prices of production should be treated as simultaneously determined. In place of the labour values, suppose we take as given the bundle of goods comprising the real wage, the physical quantities of output and input, and labour-time in each industry. Given this it is possible to demonstrate: (i) there is a determined rate of profit and prices of production; (ii) the rate of profit depends on real wages; (iii) quantities of embodied labour play no role in determining the rate of profit and the prices of production. Shaikh has challenged such a view, claiming that: In the real process ... social labour time really regulates exchange. The physical data are then a conceptual summary of the real

Value, price and exploitation

49

determination, and if we then use the data to conceptually calculate values, we only capture in thought their real magnitudes. Such a calculation no more determines these values than does the calculation of the mass of the Earth determine either the Earth or its mass. It merely recognises what already exists. Thus it is a fundamental point in a materialist view of the world, and the eighty-year failure of the neo-Ricardians to distinguish between real and conceptual determination reveals their long attachment to the idealist method. (Shaikh, 1981, p.281) Shaikh has criticised the Sraffian interpretation, claiming that the value rate of profit, denoted s/(c+v), is a monotonically increasing function of the rate of surplus-value, as is the money rate of profit. Where v+s is the value of living labour, d the length of the working day, and n the number of workers employed, it follows that L=dn=v+s. Taking the expression for the value rate of profit, s/(c+v), dividing the numerator and denominator by v, substituting (c/L)(L/v) for (c/v), and writing the ratio of dead to living labour as k =(c/L), we may write: rv =

e k(1+e)+1

(4.6)

Because k depends upon the technology (c) and the average length of the working day when the conditions of the labour process are given, r v will vary directly with the rate of surplus-value. Hence the value and money rates of profit are monotonically increasing functions of the rate of surplus-value and ‘the transformed rate of profit appears as a displaced image of the value rate of profit’ (Shaikh, 1981, p.290). In this sense Shaikh maintains a connection between the value and money rates of profit and deems that value categories are a useful first approximation from which equilibrium prices can be derived using an iterative process.5 Analytical Marxists are in broad agreement that there is a serious problem with Marx’s ‘value’ reasoning. Elster has argued that the labour theory of value is ‘useless at best, harmful and misleading at its most infrequent worst’ (1985, p.120). Cohen (1981) suggests that ‘it has been proved that Marx’s value reasoning is often internally inconsistent, completely failing to provide the explanation which Marx sought for certain features of the capitalist economy (p.206). And Roemer, in reformulating Marx’s theory in terms of general equilibrium, has

50

Value, price and exploitation

suggested that the labour theory of value is ‘no real loss’ (1981, p.201). Analytical Marxists therefore reject this major component of Marx’s economics, although this does not imply that they are unanimous in their support for Roemer’s ‘Walrasian’ alternative.

Value and exploitation In seeking to reconstruct Marxian economic theory, Morishima’s Marx’s Economics: A Dual Theory of Value and Growth (1973) sought to demonstrate that exploitation was necessary for the existence of profits in a capitalist economy. Essentially, Morishima offered a labour theory of exploitation while rejecting the principle of the labour theory of value. The result was derived rigorously, and Morishima indicated that the method was inspired by developments in mainstream mathematical economics. Morishima’s theory of pricing and exploitation underpins the examination of conflict over the length of the working day in Chapter 6. Thus, to provide theoretical foundations for subsequent chapters, and to aid understanding of current debate over the labour theory of value, Morishima’s work warrants examination. Initially, based on Roemer (1988, pp.36–42) we shall begin with a simple model in which there is a single non-labour commodity which enters as an input and is combined with labour to produce a commodity output. The commodity input and output are the same (e.g. corn) and only circulating capital is used. Thereafter we shall extend the model to incorporate commodities. Roemer (1988) takes a single commodity, such as corn, which can be produced using a single technique. This commodity is used as an input and combined with a labour input (L) to produce an output. Assume that p is the price of the commodity, w is the wage, and a is the quantity of commodity input required to produce one unit of the commodity net (since a is constant and fixed, this assumes constant returns to scale). In such a single-commodity system, price is determined by the costs of production, on which a profit (r) is added: p=(1+r)(pa+wL)

(4.7)

Assume a subsistence wage where b is the real wage, or subsistence commodity bundle. This need not be a biologically determined minimum and may be at a ‘socially determined’ level. Thus in money terms:

Value, price and exploitation w=pb

51 (4.8)

In a single-commodity system the rate of profit is given by: r=

p−(pa+wL) pa+wL

(4.9)

In order to obtain the embodied labour in our single commodity system, let the gross output be given by x, and the commodity input required to produce this be ax (assume 0
1 (1−a)

(4.11)

If L is the quantity of labour required to produce one gross unit of the good, this implies that the quantity of the good required to produce one net unit of the good will be Lx. This gives us the labour required to produce 1 unit of the good plus the labour required to produce the commodity ‘used-up’ in the process of production: Lx=

L ≡λ (1−a)

(4.12)

In equation (4.12) λ is defined as the labour embodied in producing one unit of corn. Equation (4.8) assumes a subsistence wage. In Roemer’s representation the labour embodied in the production of the subsistence bundle will be given byλb, where this is termed socially necessary labour time. And, where the length of the working day is denoted by T , the rate of surplus-value, or rate of exploitation, is given as: e=

T −λb λb

(4.13)

If labour time is measured in terms of the length of the working day, where this is constant, we can normalise T =1 and e is given by: e=

1−λb λb

(4.14)

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Value, price and exploitation

Thus a rate of exploitation, consistent with a system of relative prices which is logically robust, has been demonstrated. Given (4.8) we can substitute into (4.7) to give: p=(1+r)p(a+bL)

(4.15)

If we divide through (4.15) by p this gives: 1=(1+r)(a+bL)

(4.16)

1 =(1+r) a+bL

(4.17)

By rearrangement:

If this is a corn model, a is the quantity of corn used to yield one unit of corn. The second term of the denominator on the left-hand side of (4.17) is the quantity of corn that must be fed to the workers to yield one unit of corn. Hence, from a physical point of view, if there are to be any profits, the following inequality must hold: a+bL<1

(4.18)

In order for there to be a positive rate of exploitation, the length of the working day must be greater than socially necessary labour time. That is: λb<1 (4.19) Substituting (4.19) into the equation for labour embodied, (4.12), gives: bL <1 (4.20) (1−a) Which is, by rearrangement: a+bL<1

(4.21)

The conditions for positive profit and positive exploitation, equations (4.18) and (4.21) respectively, are the same. Thus the existence of positive exploitation is necessary and sufficient for the existence of positive profit. Let us now consider a numerical example from which we can derive a wage–profit frontier. If we were to assume that 0.5 units of corn and 1 unit of labour was required to produce a net output of one unit of

Value, price and exploitation

53

Rate of profit (r)

1 0.8 0.6 0.4 0.2 0 0

0.1

0.2

0.3

0.4

0.5

Real wage (w) Figure 4.1 Wage–profit frontier

corn (i.e. a=0.5 and L=1), w, r and p are unknown. Setting p=1 (to render the system determinate) we can derive an inverse wage–profit function as in Figure 4.1. Thus far we have considered a particularly abstract model in which there is a single produced commodity. For this commodity, the organic composition of capital is the same as the average organic composition of capital. Hence, there is no transformation problem to be solved. It is therefore necessary to extend our analysis to consider an n-commodity system, taking a system {A,L} in which A is an n×n input matrix of commodities, L is a 1×n vector of direct labour inputs, and p is a 1×n commodity price vector. The rate of profit is written r and, in equilibrium, prices satisfy: p=(1+r)(pA+L)

(4.22)

Thus, price is determined by adding the unit costs of production plus a mark-up, where we continue to assume no fixed capital. If b is a n×1 subsistence vector of commodities and the wage is just sufficient for subsistence to be affordable then pb=1. Assuming the unit of time which defines L is a working day of fixed duration, we may write: p=(1+r)p(A+bL)

(4.23)

The 1×n vector of labour values, denoted by %, is defined as: %=% A+L

(4.24)

which, if indecomposable and productive, may be written: %=L(1−A)−1 >0

(4.25)

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Value, price and exploitation

Labour time embodied in the subsistence bundle is therefore %b. Assume the length of the working day to be T , which in this instance is normalised. It therefore follows that surplus labour time is given by 1−%b and e is: 1−%b (4.26) e= %b In a commodity system comprising n commodities (1,2, . . . ,i, . . . n) the rate of profit for commodity i can be expressed as: ri =

pi −(p1a1i +p2a2i+. . . +pi aii +. . . +pnani +wLi ) p1a1i +p2a2i+. . . +pi aii +. . . +pnani +wLi

(4.27)

And, as before, Morishima’s Fundamental Marxian Theorem holds. That is, exploitation of labour is necessary and sufficient for the existence of positive profit (see Roemer, 1981, pp.16–17). Moreover, this system is consistent with the individual capitalist adopting a programme of profit maximisation.

Walrasian Marxism Roemer’s models of general equilibrium draw upon one of the major neoclassical research projects of the 1950s. The approaches of Morishima (1973) and Roemer (1980, 1981) are distinct from one another in that the latter allows for the possibility of continuous substitution of factors of production. While Roemer accepts the critique of Marx’s analysis advanced by Steedman (1977), he seeks to offer an alternative solution to that proposed by Morishima. While Morishima suggests a linear equilibrium input–output model, Roemer proposes models of capitalist reproduction in which capitalists face convex production sets: ‘exploitation is the key concept in these economies, as it provides a necessary and sufficient condition for the existence of non-trivial equilibria’ (1980, p.524). The use of individual labour values of produced commodities ‘falls by the wayside’, and the Marxian theory of exploitation can be derived ‘independently of microdenominated individual labour values’ (1981, p.36). It follows that social surplus-value need not be aggregated from individual surplus values. Of particular importance to Roemer is the explicit specification of the microfoundations which generate an equal-rate-of-profit price vector as an outcome of profit maximisation on the part of individual capitalists. In Roemer’s basic convex model each capitalist faces a given

Value, price and exploitation

55

production possibility set. Production involves transformation of direct labour and commodity inputs into commodity outputs. He assumes both that producing zero output is possible for each capitalist and that the production possibility set is closed and convex. Moreover, labour is not itself a producible commodity and labour is necessary for any productive activity. All non-labour commodities are producible and any non-negative net outputs can be produced. A distinction between inputs and outputs must be made, since time enters into our reckoning. Capitalists must pay for inputs before production commences and they must not violate their budget constraint, or initial capital endowment, to fulfil this task. In the basic model, capitalists cannot borrow; however, Roemer (1981) develops this to incorporate a capital market. Given a capital market, Roemer defines the labour value of a subsistence commodity bundle as the minimum amount of direct labour needed to produce it as a net output of social production. The time required to produce this commodity bundle is necessary labour-time. Surplus labour-time is the time worked in the production period beyond necessary labour-time. A given capitalist has an initial capital endowment in a given period. Faced with prices in that period the capitalists’ objective is to maximise their expected endowment in the subsequent period. The capital endowment in the subsequent period comprises output from the present period together with unused commodity inputs carried over from the present period. The capitalist seeks to maximise the expected value of tomorrow’s endowment subject to the budget constraint that expenditure cannot exceed present capital. Roemer (1981, pp.41–4) offers an existence proof such that the economy is reproducible, and the equilibrium solution is socially feasible based upon the principles of profit maximisation and a subsistence wage.6 Criticisms of Roemer’s approach have been made, e.g. Dymski and Elliott have suggested that: ‘Roemer ignores Marx’s own rich textual argument and imports into Marx’s dynamic and historical system the narrow methodology of Walrasian general equilibrium’ (1988, p.30).7 Since criticisms are not made of the formal logic of Roemer’s work, Dymski and Elliott’s criticism could be thus levelled at any the proposed solutions to problems of value, price and exploitation presented in this chapter.

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Value, price and exploitation

The new solution The ‘new solution’ is identified with Duménil (1980), Duménil and Lévy (1983), together with its independent discovery by Foley (1982) and Lipietz (1982). A useful introductory survey concerning the new solution has been offered by Mohun (1994). At the outset Mohun considers the claim that Marxian theories of value and price are contradictory. Mohun suggests that there are different types of contradiction in social science and that to describe a contradiction does not necessarily entail the social scientist has logically committed one (1994, pp.392–3). The dialectical methodology of Marx recognises three aspects to the theorising of such contradictions. First, it is necessary to reproduce in thought contradictions which are evident or underlie a class-divided society. Second, these oppositions should then be elaborated. Finally, Marx sought to distinguish between ‘essence’ and ‘appearance’ and maintained that the underlying structures and dynamics generate mystifying forms of appearance. The new solution, which Mohun advocates, seeks to connect the form of appearance (price) with the underlying structure (value). The new solution has, perhaps, been most clearly stated by Foley (1986, p.95), who takes a system of production in which the following inputs of steel (S), wheat (W ) and direct labour (L) are used: 0.25S +1L→1W

(4.28)

0.5S +1L→1S

(4.29)

The direct and indirect labour input in the production of steel is thus: λs =1+0.5λs (4.30) λw =1+0.25λs

(4.31)

Rearranging (4.30) gives λs =2, and substituting the labour value of steel into the equation giving the labour value of wheat, we can derive λw =1.5. If the value of money is equal to unity, that is, if £1 is the value created by one unit of labour, then under conditions of ‘equal exchange’ it follows that ps =£2 and Pw=£1.50. If we assume that the exogenously given wage (m) is £0.50 and the value created by one unit of labour is, as before £1, Foley (1986) derives Table 4.4, where the output of steel and wheat is 10,000 of each commodity. Foley assumes that the sum of values of the net product is equal to the sum of prices of the net product. Howard and King (1992) contrast

Value, price and exploitation Table 4.4 Value categories in the new solution c v s (c+v+s) s/v Wheat 5,000 5,000 5,000 15,000 100% Steel 10,000 5,000 5,000 20,000 100% Total or 15,000 10,000 10,000 35,000 100% average Source Foley 1986: 97

r 50.0% 33.3% 40.0%

57

p £1.50 £2.00

this to the approach of Marx and Bortkiewicz, both of whom applied an invariance condition between the sum of values and prices with respect to the gross product. Howard and King identify a second difference between Foley and Marx, in that the former defines the value of labour power as the value of money multiplied by the money wage, whereas Marx defined the value of labour power as the labour embodied in the means of subsistence consumed by the worker. Having outlined the value accounting system in the new solution, let us now consider the prices of production. These are derived by taking the previous input–output relationships, and incorporating prices and an equal rate of profit condition (Foley 1986, p.97). Taking equations (4.28) and (4.29) and writing in terms of the prices of production, we derive: (0.25ps +0.5)(1+r)=pw (4.32) (0.5ps +0.5)(1+r)=ps

(4.33)

By assumption the sum of the prices of the net output is equal to the sum of the net value created (the total of v+s in Table 4.4). Thus, with an output of 10,000 for each commodity: 10,000(pw −0.25ps +10,000(ps −0.5ps )=20,000

(4.34)

In order to derive equilibrium prices and the rate of profit, take equations (4.32) and (4.33), isolate (1+r), and rearrange to give: pw =

ps (0.25ps +0.5) 0.5ps +0.5)

(4.35)

Substitute into (4.34) and rearrange to give the following quadratic equation: 0.75p2s −0.75ps −2=0 (4.36) Solving gives ps =2.208 or ps =−1.208. Assuming non-negative price, we can substitute ps =2.208 into (4.33) to obtain the rate of profit

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Value, price and exploitation

Table 4.5 Prices of production in the new solution c Wheat 5,520 Steel 11,040 Total or 16,656 average Foley 1986: 99

v 5,000 5,000 10,000

Π

3,960 6,040 10,000

r 37.66% 37.66% 37.66%

p 1.448 2.208

r=37.66%. Substituting the rate of profit and ps into equation (4.32) gives the price of wheat, pw =1.448. Given this we can write the rate (r) and sum (Π) of profit, and the prices of production, as in Table 4.5. The new solution provides a system in which the sum of surplus-value is equal to the sum of profit, although the system differs from that of Marx since the sum of the net product is equal in value and price terms, rather than the gross product, as in the work of Marx and Bortkiewicz. One result, given Foley’s assumptions, is that the value of gross output is less than the price of gross output. Second, the transformation process has involved an increase in the real wage, since the price of wheat is lower in Table 4.5 than in Table 4.4. The new solution approach does give an equilibrium model in which we can consistently maintain a link between values and prices, but, as noted by Howard and King (1992, p.278), this task is accomplished in a single-process model in which joint production, fixed capital and choice of technique are absent. As argued by Steedman (1992), in the ‘empirically relevant’ (p.123) case of joint production, there is the possibility of non-uniqueness of the profit rate for a given real wage. Thus, while some advocates of the new solution suggest that there is really no transformation problem to be solved, since prices can be interpreted in value terms (e.g. Duménil and Lévy, 1991), Steedman maintains ‘the “new solution” certainly is not a solution to the transformation problem, as traditionally understood, in the real world case of joint production’ (1992, p.126). Thus, Samuelson’s assertion that value and price represent alternative and discordant systems is not fully refuted by the logic of the new solution.

Exploitation and class in Marxian economics The inspiration of Marxian exploitation theory derives from Marx’s theory of surplus-value embodied in his account of capitalist exploitation. This theory can be considered both normatively and

Value, price and exploitation

59

positively. In dividing the working day between surplus and necessary labour-time it is possible to make the normative claim that workers are working for longer than necessary to produce their means of subsistence and production in a labour-minimisation model. Alternatively, we may suggest workers are not receiving the equivalent of what they themselves produce (in an income-maximisation model). Marx’s model of surplus-value also has positive content, in that surplus-value was deemed to explain the rate of profit. In recent years this notion, known as the Okishio–Morishima Fundamental Marxian Theorem (FMT), has been rigorously proved in a number of alternative contexts (see in particular Morishima, 1973, and Roemer, 1980, 1981). However, while Morishima’s account of exploitation provides an excellent treatment inspired by Marx’s account of absolute surplus-value production, and Roemer (1980, 1981) expresses the rate of exploitation as a function of technology, neither sought to unify Marx’s theories of absolute and relative surplus-value.9 Roemer’s contribution to Marxian exploitation theory is significant for three reasons. First, Roemer advances a theory of exploitation independently of a labour theory of value. Secondly, he emphasises the foundational role of property rights in giving rise to exploitation. While Roemer is not correct to suggest the differential ownership of productive assets (DOPA) is more significant than the institution of the labour market, he nevertheless correctly emphasises, as Marx had done, the role of property-rights (this is discussed in Chapter 5). Finally, Roemer’s general theory of exploitation and class is sufficiently universal that exploitation in alternative modes of production can be considered. While these elements do not comprise the totality of Roemer’s contribution they are nevertheless significant so that his contribution should be regarded as worthwhile. In recent years, the work of Roemer on exploitation and class has occupied the attention of scholars within different branches of Marxism. The institution of private ownership of the means of production is subject to hostility from Marxists on the basis of both efficiency and equity considerations. Roemer suggests that Marxian criticism on the basis of efficiency rests on the claim that there is some alternative system that would be better for all (1988, p.3). However, such a claim is problematic, since Marxists would usually view the efficiency of a system in terms of the development of the productive forces, and whether the production relations fetter further development of those productive forces. The notion that this will be universally beneficial for all is not uncontroversial. Indeed, Roemer’s notion of 8

60

Value, price and exploitation

efficiency, in this context, corresponds to the Pareto welfare criteria familiar from neoclassical economics (see Varian, 1992). The central emphasis of Roemer’s criticisms of capitalism is not on the basis of efficiency. Rather Roemer emphasises capitalism’s inequity since ‘it is perceptions and ideas about justice that are at the root of people’s support for or opposition to an economic system’ (1988, p.3). Therefore, what is at issue is the ethical basis of distribution in alternative economic systems. Capitalist property relations can be somewhat obscured in developed capitalism. Moreover, other forms of exploitation, such as by gender, pervade, complicate and confuse examination of exploitation and the ethics of distribution in the capitalist system. Advocating Marxian, class-based, analyses of distribution does not involve a denial that other approaches can be insightful. Marxists tend to focus on exploitation of the working class by the capitalist class. But this does not deny the validity of considering other notions of exploitation. Indeed, ‘The history of capitalism may be a history of struggle among exploiters ... [or] it may be a history of struggle among women, nations, races or religious groups’ (Przeworski, 1985, p.227). Furthermore, capitalism also demonstrates a capacity to generate struggle amongst the exploited. Does the capitalist woman exploit the working man? Was the Irish worker exploited by the English labourer in nineteenth-century England? In the colloquial sense, where ‘exploitation’ is taken to mean ‘to take unfair advantage’ we can recognise that an individual may exploit a second individual in one sense while the latter may exploit the former in a different sense. Of course, Marxists would maintain that class-based technically defined exploitation is generally the most relevant for understanding the ethical inadequacy of capitalism, but this does not involve a denial that other emancipatory projects are worthwhile. Methodological parallels may be drawn between the problems of value and price in Marxian economics and the neoclassical search for the existence, stability and uniqueness of a general equilibrium, in that each are based upon atomistic competition between agents. However, as Maarek (1979) has insightfully observed, capitalism is also typified by conflict between classes, and the nature of this conflict is more similar to an anti-reductionist class-based opposition, as in a model of bilateral monopoly, than to Roemer’s model involving individualist competition. Thus, analysis of the functioning and dynamics of the socio-economy can be conducted at a number of different levels. This methodological

Value, price and exploitation

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realisation, discussed in Chapters 2 and 3, is regarded in this book as being of particular significance.

Conclusion Recently, several attempts to resolve the transformation problem have been offered, and these differ in the extent to which they seek to preserve Marx’s original formulation. In this chapter, ‘equilibrium’ treatments of value, price and exploitation have been considered. This approach would be greeted with condemnation from some quarters of Marxian economics, for example from the practitioners of the sequential non-dualist approach, also known as the temporal single system approach (see Freeman and Carchedi, 1996). Critics of ‘equilibrium’ modelling sometimes misconstrue the nature of the approach. Equilibrium is not intended to describe reality, but is rather a modelling tool intended to simplify analysis of interrelationships, which are inherently more complex. Naples’s claim that Sraffian methodology is deficient because of the assertion that ‘equilibrium and a uniform rate of profit are possible in capitalism’ (1996, p.95) thus misconstrues the purpose of making such assumptions. As noted by Laibman (2000), ‘equilibrium paths are the necessary ground for the study of disequilibrium dynamics’ (p.329). Thus: ‘Capitalism is inherently crisis-prone, and its accumulation path does not behave like the steady-state, tranquil models of neoclassical growth theory. It also, however, maintains a certain coherence over time. The homeostatic aspects must be balanced against the transformative, crisis provoking ones’ (Laibman 2000, p.329). Roemer has also considered the notion of equilibrium, rejecting the view that equilibrium entails stationarity, and interpreting it as a requirement that a model be internally logically consistent (1989a). Thus, it is maintained here, there is a clear place for modelling aspects of pricing and exploitation in equilibrium terms. Among equilibrium approaches, the new solution and Morishima’s formulation remain dominant. The former maintains a role for value in the process of price determination, whereas the latter abandons the relationship between value and price. The assumptions of the new solution are problematic and the economic rationale for the assumptions regarding value and price are not self-evident. Therefore, the most appropriate foundation for future development of Marxian theory should, on the basis of theory presently known, be in the

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direction indicated by Morishima. A labour theory of value is problematic, but a labour theory of exploitation remains an insightful way to comprehend what Marxists would maintain are the injustices of capitalism. Roemer (1982a, 1994a) has also played a valuable role in emphasising the concept of exploitation under capitalism and has also considered the relationship between such exploitation and that under alternative modes of production. This is discussed in more detail in Chapter 5. The underlying approach adopted in this work is one sympathetic to the political aspirations of Marx, together with the belief that social scientists should explore the epistemological priority which Marx gave to time. That is not to suggest that relative price is determined by relative quantities of labour expended in the production of commodities. Rather the emphasis is upon the time workers are required to labour, and the proportion of the ‘fruits’ of their labour which they receive. Marx’s theory of value is problematic; however, the theory of exploitation is empirically insightful and ethically illuminating.

5

Marxian theories of exploitation and class

Introduction In recent years the Marxian theory of exploitation has received new impetus, in particular, from the work of Roemer, who has sought to develop a game-theoretic general theory of exploitation and class which is logically robust and more general than that provided by Marx. In particular, in elaborating on his general theory, Roemer attempted to make explicit the link between property and exploitation in a Marxian sense. Roemer’s work attracted criticism from within Marxism, in particular because some felt it a departure from Marx’s approach. There raises a question of method, and the role of theory in Marxian economics. The incongruence between orthodox Marxists’ use of surplus-value and Roemer’s proposed reformulation may be seen to indicate a profound underlying methodological tension. The criterion for ‘truth’ within Roemer’s work is based upon the requirement that a model be internally logically consistent, using a formal method. In contrast, Marx, in the first volume of Capital, provided historical foundations for his theories. These foundations are considered in the following section. Attention is paid to Marx’s account of primitive accumulation, since this represents his historical account of the evolution of capitalist property relations. Thereafter, we consider Marx’s theory of surplus-value. We examine the evolution of Roemer’s thought from Roemer (1982a), to subsequent work published and debated in leading academic journals (reprinted in Roemer 1994a). In particular, Roemer’s Class Exploitation Correspondence Principle is outlined. The relationship between a property relations (PR) definition of exploitation (based upon the differential ownership of productive

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assets) and what Roemer describes as an unequal exchange (UE) definition of exploitation is elaborated on.1 Thereafter the principles of feudal, capitalist, socialist and bureaucratic exploitation are outlined.2 Finally, we evaluate the respective approaches of Roemer and Marx, suggesting similarities and tensions. In addition the ‘game-theoretic’ aspect of Roemer’s thought will be evaluated, suggesting that the strategic element of the analysis is deficient.

Marx’s account of capitalist exploitation In order to assess the ethical basis of income distribution between respective classes, it is insightful to consider the emergence, historically, of capitalist property rights. This is what Marx does in the first volume of Capital, and there is a contrast between this approach and that of Roemer, who takes agents’ initial endowments as given prior to formulating his theory of capitalist exploitation. Marx sought to provide an account of the evolution of capitalist property relations through his examination of primitive accumulation. Marx discusses the relationship between exploitation and property rights thus: We have seen how money is transformed into capital; how surplus-value is made through capital, and how more capital is made through surplus-value. But the accumulation of capital presupposes surplus-value; surplus-value presupposes capitalist production; capitalist production presupposes the availability of considerable masses of capital and labour-power in the hands of commodity producers. The whole movement, therefore, seems to turn around in a never-ending circle, which we can only get out of by assuming a primitive accumulation ... which precedes capitalist accumulation; an accumulation which is not the result of the capitalist mode of production but its point of departure. (1976, p.873) Furthermore: This primitive accumulation plays approximately the same role in political economy as original sin does in theology. Adam bit the apple, and thereupon sin fell on the human race. Its origin is supposed to be explained when it is told as an anecdote about the past. Long, long ago there were two sorts of people; one, the diligent, intelligent and above all feudal elite; the other, lazy rascals,

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spending their substance, and more, in riotous living . . . Thus it came to pass that the former sort accumulated wealth, and the latter sort finally had nothing to sell but their own skins ... Such insipid childishness is everyday preached to us in the defence of property. (Marx, 1976, pp.873–4) Thus Marx suggested that the process which created the capital–labour relation was nothing other than the process which divorced the producer from the means of production. That is, private ownership of the means of production created the conditions through which exploitation could take place. In England, serfdom had disappeared in practice by the latter part of the fourteenth century, and although feudal trappings remained, the majority of the population were free peasant proprietors. With the dissolution of the bands of feudal retainers at the turn of the sixteenth century, many were forced to seek other employment. Debate in economic history has tended to emphasise that before the advent of parliamentary enclosure there had been much ‘voluntary’ enclosure. This process did, however, have a profound effect on the majority of the rural population who could show no legal or customary rights to the commons (Perkin, 1985). Marx claimed that this process was even more antagonistic: ‘In actual history, it is a notorious fact that conquest, enslavement, robbery, murder, in short, force, played the greatest part’; thus ‘the methods of primitive accumulation are anything but idyllic’ (Marx, 1976, p.874). With the Reformation the property owned by the Catholic church was appropriated by the monarch and his loyal followers. In addition, the law served to hasten the process of enclosure as two notable bursts of parliamentary enclosure occurred in 1760–80 and 1790–1815. According to Marx: ‘With the “setting free” of a part of agricultural population, therefore, their former means of nourishment were also set free’ (1976, p.908). The majority of what had been free peasant proprietors now became workers for capitalist farmers and industrialists, and the majority of the population were transformed into material elements of variable capital. The process of primitive accumulation, in implementation and effect, was more extreme in the Celtic fringes than in the rest of the British Isles (see Prebble, 1963 and Perelman, 2000). In the highland clearances in Scotland, customary rights were abandoned as the lairds ceased to act as heads in a traditional feudal structure, and began to raise rents as landlords. Some classical economists

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such as Smith emphasised free exchange and voluntarism, whereas Steuart justified raising rents in Scotland on the grounds that the surplus of the farmer becomes the subsistence for others. Perelman (2000) demonstrates the hostility of the classical economists to the self-sufficient peasantry, described as ‘superfluous mouths’ by Steuart. The fundamental determinants of the social division of labour were, for Steuart, political and were not market-driven. This division was to be achieved through ‘voluntary subordination’ whereby more and more people would have no choice but to accept wage labour. The subsequent neglect of Steuart, contra Smith, can be attributed to a number of factors. Perelman suggests of Steuart: ‘His sophisticated application of the classical theory of primitive accumulation made his work an embarrassment to the mainstream political economists who pretended that capitalist development was a voluntary affair’ (2000, p.158). This emphasis on political power was what Marx developed in his account of the emergence of capitalist property rights. Surplus-value is created through the labour and valorisation processes (for a discussion of these see Marx, 1976, pp.283–306). Marx views labour as a process between people and nature, and people appropriate the materials of nature and adapted them to their own needs. The simple elements of the labour process comprise a ‘purposeful will’ directed toward work, an object on which work is to performed, and the instruments of that labour. The labour process involves purposeful activity aimed at the production of use-values. Under capitalist property relations the instruments of labour, raw materials and labour power are bought by the capitalist; thus production ‘is a process between things the capitalist has purchased, things which belong to him [or her]’ (Marx 1976, p. 292). And the product is a use-value which is the property of that capitalist. The purpose of capitalist production is to produce an exchange-value greater than the value of labour power plus the means of production consumed during the labour process. The process of valorisation is summarised thus: The fact that half a day’s labour is necessary to keep the worker alive during 24 hours does not in any way prevent him from working a whole day. Therefore the value of labour-power, and the value which that labour-power valorizes (verwertet) in the labour process, are two entirely different magnitudes; and this difference was what the capitalist had in mind when he [or she] was purchasing the labour-power ... What was really decisive for him [or her] was the

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specific use-value which this commodity possesses of being a source not only of value, but of more value than it has itself. (Marx 1976, pp.300–1) The valorisation process serves as the foundation for Marx’s account of exploitation under capitalism since the daily sustenance of labour power requires less than a full day’s labour (as assumed in Chapter 3). However, the capitalist has purchased the labour power, which can remain effective for the full working day.3 For Marx, capital (C) is made up of money laid out on the means of production, or constant capital (c), and that portion of capital expended on labour power, that is, variable capital (v), i.e. C =c+v. During production under capitalism there occurs a valorisation process such that capital is augmented and a ‘surplus-value’ is produced. Thus after production has occurred capital becomes C  =(c+v)+s. The augmentation of capital is purely the result of an alteration in the value of variable capital. In the process of surplus-value production, Marx claims constant capital does not contribute to the production of surplus-value: At first sight it appears strange to equate the constant capital to zero. But we do this every day. If, for example, we want to calculate the amount of profit gained by England from the cotton industry, we first of all deduct the sums paid for cotton to the United States, India, Egypt and various other countries, i.e. we posit the value of the capital that merely re-appears in the value of the product as a zero magnitude. (Marx, 1976, p.323) Marx suggests that assuming c=0 in the process of surplus-value production is analogous to the chemist ignoring retorts and other vessels necessary in a chemical process when they undertake analysis of the results. In addition to expressing the constituent parts of the rate of surplus-value in terms of surplus-value and variable capital, Marx also sought to express the equivalent of these components in terms of time. The portion of the working day during which the worker produces what is necessary for their reproduction is described by Marx as necessary labour-time: ‘necessary for the worker, because independent of the particular social form of his [or her] labour; necessary for capital and the capitalist world, because the continued existence of the worker is

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the basis of that world’ (1976, p.325). This necessary labour-time is the time in which the worker produces the value of their labour power, which is equivalent to the variable capital advanced. During the second part of the working day, or period of the labour process, the worker is no longer engaging in necessary labour. It is during this portion that the worker engages in surplus labour-time, which is equivalent to surplus-value. Thus for Marx: It is just as important for a correct understanding of surplus-value to conceive it as merely a congealed quantity of surplus labour-time, as nothing but objectified surplus labour, as it is for a proper comprehension of value in general to conceive it as merely a congealed quantity of so many hours of labour, as nothing but objectified labour. What distinguishes the various economic formations of society – the distinction between for example a society based on slave-labour and a society based on wage-labour – is the form in which this surplus labour is in each case extorted from the immediate producer, the worker. (1976, p.325) It follows that the rate of surplus-value, or exploitation, is given by the ratio of surplus-value to variable capital, or its equivalent, the ratio of surplus to necessary labour-time. This expression, normatively, represents the extent to which the capitalist exploits the worker. The latter formulation is of particular importance owing to its significance in examining conflict over the length of the working day, discussed in Chapter 6, and conflict over the intensity and productivity of labour, embodied in Marx’s account of relative surplus-value production.

Roemer’s general theory of exploitation and class Analytical Marxists such as Roemer endorse specifying microfoundations. Such an approach can be contrasted with Marx’s ‘historical’ approach. This raises questions concerning the relevant unit for analysis in social science. Marxism has traditionally maintained that class is both a relevant unit for analysis and indispensable for understanding the motivation and actions of human individuals. In contrast to such a traditional approach, Roemer (1982a, 1986b) has sought to model class formation as an outcome of a constrained optimisation programme, and in so doing he has developed a theory of endogenous class formation. In formal models Roemer (1986b)

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considers three institutional structures: an economy with neither a market for labour power nor credit, an economy with a market for labour power and no credit market, and an economy with a credit market and no market for labour power. Consider the first institutional structure, in which there is only a market for produced goods, and producers are assumed to minimise labour to obtain a fixed subsistence bundle. In such subsistence models, rationality implies labour minimisation, in this context minimisation of labour-time, in order to obtain a fixed commodity bundle. Since the institution of a market for labour power is absent, Roemer (1986b, p.84) describes this model as one of a pre-capitalist economy. Formally, as in Chapter 4, A is an n×n input matrix of commodities, L is the 1×n vector of direct labour inputs, b is the n×1 vector of subsistence vector of commodities, and p is a 1×n price vector for produced goods. Assume $v is the n×1 vector of produced endowments of the vth producer, and xv is the activity-level vector for the vth producer. Roemer (1986b, p.85) suggests that producer v, facing a price vector p, adopts an activity vector to minimise labour-time, that is: minLxv |xv ∈Rn

(5.1)

p(1−A)xv ≥pb

(5.2)

pAxv ≤p$v

(5.3)

Lxv ≤1

(5.4)

xv ≥0

(5.5)

Subject to:

Equations (5.2)–(5.4) imply that producer v can feasibly realise their subsistence bundle when faced with a capital and labour constraint. In this model, in which there is a social division of labour, traders exchange their endowments of produced goods in order to facilitate productive activity. Moreover, at the end of the period agents return to the market to obtain their subsistence needs. However, it is important to note first that there is no market for labour power and second that agents choose different processes, which require different amounts of time to operate.

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The vector of labour values, %, is defined in equation (4.24). In this institutional structure Roemer defines a solution as egalitarian if each producer works exactly %b (average socially necessary labour-time). Where some agents work more, and some less than %b, the solution is inegalitarian. This outcome occurs even when there is no institution for labour exchange, as exploitation can be mediated through markets for produced commodities. Consider now the case of exploitation with a market for labour power, where the wage rate is w. Roemer considers a structure in which agents trade commodities, including labour power. It follows that labour power can be utilised in the following ways: (i) agents may utilise capital using their own labour (the quantity of such labour is given by xv); (ii) agents may utilise capital using labour power which has been hired (yv ); and (iii) labour power may be sold, using the capital of the agent employing them (zv ). Of course, labour which is sold by   one agent is also hired by another, hence yv = zv . Roemer (1986b, p.87) assumes labour minimisation to obtain a fixed subsistence bundle, accordingly agents with given initial endowments choose: (xv,yv ,zv ) min (Lxv +zv )

(5.6)

This is subject to the following constraints: p(1−A)xv +(p−(pA+wL))yv +wzv ≥pb

(5.7)

pAxv +pAyv ≤p$v

(5.8)

Lxv +zv ≤1

(5.9)

Equation (5.7) requires that agent v can earn enough income to purchase their subsistence commodity bundle. Equation (5.8) is the capital constraint faced by agents, where the cost of operating capital which is self-employed plus the cost of operating capital with hired labour, is no greater than the monetary value of the initial capital endowment; and (5.9) is the condition requiring agents not to use more labour (either labour sold, or self-employed) than they possess. Reproducibility in this economy requires that production input demand must be feasible from the existing stock of capital; total output is sufficient to meet consumption demand; and the market for labour power is in equilibrium in that there is a unique wage, w, which is market clearing.

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Table 5.1 Roemer’s class structure with a market for labour power

Class Capitalist Small capitalist Petit bourgeois Mixed proletarian Proletarian

xv 0 + + + 0

yv + + 0 0 0

zv 0 0 0 + +

If aggregate socially necessary labour-time is N %b, an egalitarian solution implies that each agent works precisely %b. An inegalitarian solution implies that some agents work more than average socially necessary labour-time, and others less. The former are characterised as exploited and the latter exploiters. Roemer (1986b) advances two theorems based upon this analysis. The first is that the richest, in terms of initial wealth, will become pure capitalists, and the poorest proletarians. Thus class emerges endogenously as a consequence of an individual agent’s initial wealth endowment, and the possible decomposition is given in Table 5.1. The decomposition into classes in Table 5.1 reflects the fact that agents will not, given labour homogeneity, simultaneously hire and sell labour power. Hence, in Table 5.1 the small capitalist is required to perform labour for themself, but also hires labour power on the market for labour power. The mixed proletarians perform some work on their own behalf, but cannot sustain their existence working their own capital, and must therefore supplement income through selling labour power on the market for labour power. It is in this sense that decomposition into five, rather than three classes, is possible. The second theorem that emerges from Roemer’s analysis is the Class-Exploitation Correspondence Principle (CECP). The CECP relates the decomposition of society into the exploited and exploiters to the decomposition of society into classes. It states that every agent who belongs to a labour-hiring class is an exploiter and every agent who belongs to a labour-selling class is exploited. Roemer formally derives this result. Given this Roemer then attempts to demonstrate that it is not only through the sale of labour power that exploitation can emerge. Indeed, he attempts to show that exploitation based upon endowments of financial capital is ‘functionally equivalent’ to the exploitation of labour (Roemer, 1982a, p.104).

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Table 5.2 Roemer’s class structure with a credit market

Class Big lender Mixed lender Neither borrower nor lender Mixed borrower Pure borrower

xv 0 + + + 0

yv + + 0 0 0

zv 0 0 0 + +

In order to demonstrate this claim, suppose we have a subsistence model with markets in produced goods plus a credit market. There is by assumption no market for labour power. Assume that there is an initial capital endowment for each agent and that agents borrow and lend their capital endowment to one another with a rate of return on such lending. An equilibrium price vector consists of commodity prices and an interest rate such that markets clear. As in the model incorporating a market for labour power, total labour-time is N %b. An egalitarian solution is one in which all agents work precisely average socially necessary labour-time, %b. In an inegalitarian solution some members of the society work more than socially necessary labour-time (the exploited) and some work less than socially necessary labour-time. Thus class emerges endogenously according to the wealth constraint of the members of this society, and the CECP holds in this model. The possible decomposition into classes is given in Table 5.2. Any member of the lending class is necessarily an exploiter, and any member of the borrowing class exploited. This exercise, according to Roemer, is far from trivial. Assuming agents in these two environments (the one without a market for labour power and the one without a credit market) to be identical, then the only difference between the two environments is in the institution through which exploitation originates and is mediated. The basic point is that the existence of a market for labour power is sufficient but not necessary for the emergence of an inegalitarian outcome. Roemer suggests that ‘a misplaced emphasis on the labor process can lead to faulty, or at least non-materialist, analysis’ (1982a, p.104). Such a position can be criticised in that, while it is logically correct that exploitation can be conceived of in terms of credit, Marxists select exploitation of labour because at other levels of analysis only labour is involved. As noted by Laibman ‘one can readily concede that, formally, any basic commodity other than labor can serve as the substance of value, but we choose to put labor into this role because of

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the other levels of the theory at which only labor is involved’ (1992, p.57; emphasis original). The decomposition into classes in Table 5.2 reflects the fact that agents will not simultaneously borrow and lend capital. Hence in Table 5.2 the mixed lender is required to work some of their own capital in addition to lending on the credit market. Mixed borrowers work some of their own capital, but cannot sustain their existence working their own capital, and must therefore supplement income through borrowing on the credit market. The CECP holds and decomposition into five classes is possible. Roemer maintains such a framework is analogous to that of exploitation on the market for labour power, as above. Thus a market for labour power is sufficient but not necessary for exploitation to occur. Other critiques of the traditional approach to exploitation can be brought to bear which pose further problems for Marxian analyses in general, and for Roemer’s theorems in particular. Elster (1986, p.98) gives the example of interaction between two individuals, both of whom possess capital. One is rich in terms of capital endowment and the other is poor. The rich agent enjoys prodigious consumption while the poor agent enjoys his leisure time, foregoing full utilisation of his capital endowment. Suppose that the rich agent employs her own capital, using her own labour power, and then sells her labour power to the poor agent, whose income is supplemented. The poor agent (who enjoys leisure) hires, and the rich agent sells her labour power; thus the poor agent is exploiting the rich agent. For Elster such an example ‘demonstrates ... conclusively that exploitation is not inherently wrong’ (1986, p.98).4 In this chapter, this is interpreted as implying, for Elster, the extraction of surplus labour time is not necessarily morally wrong. Elster’s example relates to the two theorems of Roemer’s ‘market for labour power’ model. The CECP holds, since the rich agent sells her labour power and is exploited while the poor agent hires the rich agent’s labour power and is, as a consequence, an exploiter. However, Roemer’s second theorem, which relates the decomposition of agents into classes according to their initial endowment, does not hold. In Roemer’s typology, represented in Table 5.1, the poor agent becomes a capitalist (or a small capitalist), while the rich agent becomes a mixed proletarian, using her own labour to work her capital endowment while also selling her labour power to the poor agent to supplement her income from self-employment alone.

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Faced with such a counter-example, Roemer responded: ‘If the exploitation of the worker seems unfair it is because one thinks the initial distribution of the capital stock which gives rise to it, is unfair’ (1988, p.54). This result is important since it implies that exploitation under capitalism can be conceived of in terms of unequal initial endowments, rather than in terms of surplus-value. In contrast, Marx maintained that clearly defined and legally enforceable property rights are necessary for exploitation, conceived of in terms of surplus labour time. This manifests itself as interest, profit and rent.

Property, labour and exploitation One of the features of Marxian social science is that class is considered the basis for exploitation in different social systems. Marx’s approach to class consists of three elements: historical, theoretical and political. In contrast, a characteristic practice of the work of a number of analytical Marxists, including Roemer, is to employ a methodology in which logical arguments are presented shorn from actual historical events. This is not the only abstraction that Roemer makes. Wright (1994) and Przeworski (1985) also suggest that Roemer’s definition of class is too narrow, in that it fails to incorporate certain political considerations which are significant.5 Roemer’s interest in developing Marx’s theory of exploitation stems from his efforts to explain developments in the second half of the twentieth century. As he suggests: ‘How can one understand the formation of inequality, strata and classes, and perhaps exploitation, in socialist society?’ (1982b, p.87). Roemer not only attempted to bring Marx’s theory of exploitation into the late twentieth century, he also rejected a labour theory of exploitation. This was replaced with a property relations (PR) definition, thus ‘the Marxian concept of exploitation, defined as the extraction of surplus labor at the point of production, should be replaced by a definition which gives priority to property relations’ (1994a, p.13). Roemer rejected the central role of ‘time’ encapsulated in Marx’s mature analysis and replaced it with an emphasis on PR, characteristic of the initial endowments presupposed by neoclassical general equilibrium theory. Roemer (1994a, p.104) paid attention to a PR definition of exploitation and directly compared it with his unequal exchange (UE) definition of exploitation, where the latter may be summarised as follows: 1. There is an economy in which the coalition S and the complement S  produce some net product. Labour embodied in the net product

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is equal, by definition, to the total labour expended by S and its complement S  . 2. S is said to be exploited if the share of the net product that it receives embodies less labour than its members expended in production. 3. This is equivalent to saying that S  receives a share of the net product embodying more labour than its members expended. Discussion of this definition is given in Roemer (1989b). This can be compared with a PR definition of exploitation which is specified by Roemer (1982b, p.89) as a case in which a coalition S, in a larger society N , is exploited if and only if: 1. There is a hypothetically feasible alternative (in terms of the distribution of alienable and inalienable assets) under which S would be better off. 2. Under this alternative the complement of S, N −S =S  , would be worse off if this hypothetically feasible alternative were realised. 3. S  is in a relationship of dominance to S. Roemer suggests that for most practical purposes 1 and 2 together are a satisfactory definition of exploitation. And, given this clear PR definition of exploitation, it becomes possible to identify a number of forms of exploitation, two of which are familiar artefacts of classical Marxian analysis, and two of which enable us to enquire into the nature of exploitation in the former socialist economies of Eastern Europe. In Roemer’s system, exploitation is defined in terms of the hypothetically feasible alternative under which coalitions would be better off. Thus exploitation, as defined in each economic system, is compared with a counterfactual; the test being to consider whether an alternative set of arrangements for economic activity can eradicate such exploitation. Under feudalism he makes the ‘cavalier assumption’ that the serf’s family plot was part of their initial endowment (1982b, p.93). The serfs are considered feudally exploited if by withdrawing from the economy with their share of endowments they would be made better off, assuming that they had the same access to the means of production (and did not have to provide labour for the demesne or corvée). A second form of exploitation defined by Roemer is capitalist exploitation. The withdrawal criterion in this case is stated as one in which a coalition can withdraw with its per capita share of alienable, non-human property, and its own endowment of inalienable assets, or skills. This precise definition allows us to also consider a distinction

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within the class of capitalists, which is between entrepreneurs and coupon-clippers. According to Roemer ‘entrepreneurs presumably earn a high return to their inalienable endowments, while coupon-clippers earn a return only to their alienable endowments’ (1982b, p.96). This distinction is particularly important when we begin to debate the hypothetical feasible alternatives to capitalism, and the disincentive to entrepreneurship, which critics of socialism suggest automatically follows. According to the PR definition (Roemer 1994a, p.40) capitalist exploitation is defined thus: 1. If S were to withdraw from the society, endowed with its per capita share of society’s alienable property (that is, produced and non-produced goods), and with its own labour and skills, then S would be better off (in terms of income and leisure) than it is at the present location. 2. If S  were to withdraw under the same conditions, then S  would be worse off (in terms of income and leisure) than it is at present. 3. If S were to withdraw from society with its own endowments (not its per capita share), then S  would be worse off than at present. In comparing the notions of PR and UE exploitation, Roemer proposes a number of examples which he claims demonstrate the superiority of the former notion. It is relevant to elaborate a number of these examples. Consider first an economy in which there is one commodity, corn, which can be produced using two technologies, the farm or factory. Roemer assumes a subsistence economy in which each agent requires b units of corn per day to subsist. Using the farm technology, 16 hours of labour are required to produce b, whereas the factory method only requires 8 hours of labour. It is also assumed that the factory method requires seed-corn as an input (in addition to labour power), whereas the farm technology only requires labour power. Throughout Roemer’s examples, he assumes that the economy only has enough seed corn to produce corn for half the population using the factory method. Therefore, for society to reproduce itself an average of 12 hours labour power per person is socially necessary, since half the economy’s output must be produced by the farm method. Roemer’s first example considers the case in which the seed-corn (necessary for the factory method) is distributed equally across the economy. In this situation the simplest arrangement is for each worker to work for 4 hours in the factory, producing 12 b, and for 8 hours on the

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In this example, there is plainly no exploitation by farm, producing the PR definition of exploitation since the original distribution of assets is already egalitarian. Let us, however, consider a second example in which a social division of labour has taken place and one group of agents, called coalition H , is going to hire another coalition S. Suppose we have an agent in S, called Smith, who initially works her own capital using the factory technology for 4 hours, obtaining 12 b. Thereafter Smith goes to work for another agent, Jones, who belongs to the labour-hiring coalition (H ). Smith works for 4 hours before going to work for another agent, Kaplan, for 4 hours. Each of the labour-hiring agents will pay Smith 41 b as a wage and retain 41 b as profit on their capital. The labour-hiring agents will also have to perform 12 hours labour on the farm to produce the other 43 b required for subsistence, hence each agent in the economy will work precisely 12 hours. No agent is worse off under these arrangements than in the case of example 1, and ‘if there are savings from the social division of labor (such as lost time in commuting from the farm to the factory), then the equilibrium in example 2 can be arranged so that everyone works less time than in example 1’ (Roemer, 1994a, p.43). The crucial question of interest here is whether any agent is exploited under these market arrangements. According to Roemer: 1 2 b.

Certainly H is profiting from S’s labor; by the Marxian labor-theory-of-value definition, H appears to be exploiting S ... But I claim it is incorrect, intuitively, to view S as exploited by H for the outcome of each producer working twelve hours is identical to example 1, where clearly there is no exploitation. The initial distribution is egalitarian and the outcome is egalitarian – how can there be exploitation? (1994a, pp.43–4) According to Roemer, the answer lies in recognising that the essence of exploitation is in PR rather than in the institution of the market for labour power: interest should be focused on PR as opposed to what he describes as UE. And, as becomes apparent, we move to a situation in which the central issue concerns PR, and the orthodox Marxian labour theory of exploitation can be considered secondary. Such an approach can be contrasted with that of Bowles and Gintis (1986) who emphasise contested exchange as a fundamental

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aspect of Marxian analysis. Furthermore, Bowles (1985) has pointed to power and conflict in the process of production as typifying Marxian, as opposed to Walrasian, accounts of the production process. It would seem that Roemer’s account is somewhat closer to Bowles’s characterisation of the Walrasian production process than to the Marxian. In elaborating Roemer’s theory of exploitation let us now consider the definition which he proposes for exploitation in post-capitalist societies. Perhaps the most controversial notion of exploitation advanced by Roemer is the notion of socialist exploitation. Consider agents who have equal access to alienable assets, but have unequal endowments of inalienable assets, that is skills. Under market arrangements, those with scarce skills will be better off than the unskilled. This inequality is not capitalist exploitation since all have equal access to alienable property. However, were the unskilled coalition to withdraw from the economy with its share of alienable and inalienable assets, quite clearly it would be better off and, using Roemer’s general PR definition of exploitation, this coalition can be considered exploited. This notion is controversial since it is difficult to see the circumstances under which this conditionally feasible alternative can be brought about. Roemer suggests: ‘although the potential realisation of the alternative is problematical, as a hypothetical test it can be specified’ (1982b, p.98). In doing this, Roemer argues, we can then distribute the property rights to one person’s skills among all, hence eradicating socialist exploitation. It may be argued that to characterise a socialist state as exploitative, from a Marxist perspective, is counter-intuitive. However, as Wright suggests: ‘Given Roemer’s formal criteria for exploitation, this would be a reasonable way of characterising the distributional outcomes of skill inequalities in socialist societies’ (1994, p.66). A final notion of exploitation suggested by Roemer is status exploitation. Roemer states that there was inequality in socialist countries which comes about by virtue of status, such as Communist Party membership. While it may be the case that status is itself a ‘competitive’ remuneration of skill, Roemer suggests that ‘not all (or even most) of the remuneration to status can be explained by remuneration to skill’ (1982b, p.102). According to Roemer, from a formal point of view, this form of exploitation is identical to feudal exploitation, and therefore it should not detain us. Before proceeding it should be noted that what is formally equivalent to feudal exploitation need not be confined to pre-capitalist modes of production.

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In the face of criticism of his innovative approach, Roemer reconsidered the relationship between the PR and UE definitions of exploitation. He suggests: ‘This variation was an attempt, never entirely satisfactory, to deal with pathological counter-examples’ (1994a, p.13). The ‘withdrawal’ criterion considers whether one can conceive of economic arrangements which are free from exploitation. The counter-examples are significant because it is also important that our notion of exploitation implies the existence of an injustice. The result was that Roemer recognised a role for labour power in the theory of exploitation. The revision of his theory of exploitation was an attempt to accommodate the criticisms of a number of commentators, such as that from Elster (1986) cited above. Recall the rich and poor agents who exhibit different preferences for leisure and income respectively. The poor agent prefers leisure while the rich agent wishes to consume prodigiously. In the example the rich agent works all her capital stock and wishes to consume more, so she pays the poor agent so she can work his capital stock. According to Roemer’s UE theory of exploitation, the rich agent is exploited and the poor agent is the exploiter. Roemer suggests this example seems counter-intuitive when we accept that agents possess different preferences. Therefore, Roemer proposes to replace clause 3 of the PR definition to give us a hybrid definition of exploitation. Roemer’s hybrid PR/UE definition recognises the importance of labour power in defining exploitation, thus conceding ground to the original definition of Marx. The property clause still remains, but we should point out that Marx recognised the role of property rights in creating the conditions for the exploitation of labour (see Marx, 1976, Part VIII). Thus Roemer (1994a, p.110) proposes replacing clause 3 of the PR definition with a new clause: I propose as a definition of exploitation, in a situation where neither S nor S  enjoy or suffer consumption externalities by virtue of the consumption or behaviour of the other, that S is exploited and S  is exploiting if and only if: (A) the members of S would gain, and the members of S  would lose, by virtue of a redistribution of alienable assets so that each owned his per capita share, or the PR definition (clauses [1]–[2]); and (B) S  gains by virtue of the labor of S.

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Thus Roemer has gravitated towards a position in which both property rights and labour play a role in capitalist exploitation.

Marx and Roemer on Exploitation Opinion regarding Roemer’s work on exploitation and class differs.6 It is probably true to say that most advocates of Roemer’s approach do so because of the formal rigour and clarity of his argument, as evidenced by broad support from other analytical Marxists. Roemer has attracted criticism because his views have changed as time has gone by. This is not fair, since this demonstrates that Roemer reflects upon, and is responsive to, certain criticisms which have been levelled against his work. Of course, Roemer has not really added an empirical/historical element to his work, but he has modified his approach in response to some of the counter-examples given with regard to the logic of it. It thus remains the case that one common criticism of Roemer’s approach, that is it is ahistorical, remains. In Marx’s historical analysis, the distinction between exploitation and achievement models can be observed in his account of primitive accumulation.7 Logically, exploitation is a class-relational concept which is dependent upon property relations. In divorcing the peasantry from the means of production this created a market for labour power in which the dispossessed were forced to sell their labour power out of economic necessity. Accordingly, Marx’s account of surplus-value, that is, his theory of exploitation, should be thought of in terms of the evolution of the capitalist mode of production embodied in his theory of primitive accumulation. Assessing the morality (or otherwise) of a system necessitates a theory of the evolution of that system. Such historical detail is absent in Roemer’s analysis, since he starts his examination of capitalist exploitation with given property rights, hence limiting its relevance.8 Roemer does come to a conclusion not dissimilar to Marx’s, in suggesting that these two elements are the basis of capitalist exploitation. Marx also provides rich historical detail relating to how the ratio of surplus to necessary labour time might change. Prolongation of the working day, and changes in technology affecting the labour process, are both key influences in the dynamics of exploitation. The former, in particular, is discussed in the next chapter. What then does Roemer’s approach therefore offer Marxian economics? First, we are presented with clear, formal definitions of the terms in use. Further, Roemer offers clear formal relationships

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between economic variables in a framework underpinned by a logically consistent theory of price. Finally, the notions of socialist and bureaucratic exploitation help provide insight into the basis of some of the inequality which was observed in the supposed ‘Communist’ economies in the Soviet Union and Eastern Europe. What is missing, however, is a detailed elaboration relating these definitions and formal relationship to periods and actual historical contexts. Aside from the issue of ahistoricism, a number of Marxists have been particularly sceptical of his use of game theory to elaborate Marxian arguments. The use of game theory, usually identified with neoclassical economics, is controversial among Marxists since some claim it is a tool used to justify the prevailing (neoclassical) ideology. Some orthodox Marxists are less hostile, suggesting that game theory is not necessarily antithetical to the approach of Marx. For example, Lebowitz has suggested, ‘not only may we speculate that Marx would have been quick to explore its techniques but we can go further and suggest that Marx’s analysis was inherently a “game-theoretic” perspective’ (1988, p.197). Game theory provides a language and tools for analysing strategic interaction between either individual agents or irreducible groups. However, as argued previously, game theory is frequently a formal and abstract approach, and as such it is frequently disconnected from historical processes which give rise to socio-economic systems. But, this consideration limits, though does not invalidate, Roemer’s formalisation of capitalist exploitation, even though his ethical position concerning the morality of that system abstracts from actual history. There are other issues which need to be considered in evaluating Roemer’s use of game theory. In his approach Roemer starts with individual agents who are each possessed of an initial endowment. Acts of individual exchange are conducted which define agents’ class position. But these are (Walrasian) competitive exchanges in which no agent has the power to influence the market. In this sense, class formation occurs prior to any strategic interaction and in discussing ‘withdrawal’ no strategic analysis is offered. Friedman (1991) has elaborated on the relationship between Walrasian competitive exchange equilibrium, and the theory of games, suggesting: A pillar of competitive economics – indeed, the element defining the term competitive – is that the actions of one agent have no effect on the opportunities facing any other agent. In a pure trade model . . . [such as Walrasian competitive exchange equilibrium] having no

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Marxian theories of exploitation and class effect on the opportunities of others means that (a) the endowment of a consumer is fixed, independently of the actions of others, and (b) no single agents can affect prices. Thus, the player interactions that generally take place in noncooperative games, which many regard as a distinguishing characteristic of such games, are absent. (Friedman 1991, p.97)

Thus, the first stage of Roemer’s theory of exploitation and class, the point at which classes are formed, is not game-theoretic in a ‘strategically interactive’ sense. Since our interest here is in game theory as a metaphor for strategic interaction, this form of game is not relevant to the process of class conflict, other than it may be of some use for definitional purposes. Subsequently, Roemer takes these classes and assumes the agents are bound (with no theory of how class cohesion is brought about – i.e. with no theory of agency) and proceeds to consider whether it is in their class interest to withdraw from the economy. How does this cooperation come about? The composition of the class is determined by the initial endowments of agents, but no explanation for why they come to act as members of a class is given. This seems to run contra to Roemer’s own emphasis on micro-founded explanations. Roemer may formulate a reason why a coalition (or class) should withdraw from an economy, but he does not provide us with understanding of how they can withdraw from the economy. This raises another question in that there is a divide in game theory between cooperative and non-cooperative games. This is a sharp formal divide, but it is not replicated in reality, where there are often degrees of cooperation which may be broken at particular moments. It may be that we could examine what Lebowitz (1988) has called a ‘collective game’, in which classes are atoms of the system. But there are forces which may operate to divide such classes, and this is something which game theory can illuminate, as was the case in Chapter 3. In other words, interactions between sub-groups of a class may provide interesting scenarios which illuminate the process of class conflict. There may be good reasons to posit why members of a class may act as one, but to assume that they do runs contra to methodological individualism and the microfoundations approach. The only way to invalidate such criticisms of Roemer’s approach is, therefore, to accept that there are alternative levels of investigation and to accept that we cannot, a priori, suggest that one has more explanatory importance than another.

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Conclusion This chapter has sought to outline Marx’s theory of exploitation, comparing it with the recent contribution of Roemer. Since Marx regarded his theory of surplus-value to be his main theoretical discovery, this is a debate of paramount importance. The Marxian theory of exploitation has not been subject to as much substantive evaluation from neoclassical, heterodox and Marxian economists in recent years, since greater emphasis has been placed on controversy over the labour theory of value. This has been because of the mistaken belief that the Marxian theory of exploitation relies upon a labour theory of value. Accordingly, the contribution of Roemer is especially welcome. One theme which has been developed throughout this chapter has been that of the role played by labour values in a Marxian theory of exploitation. Plainly, this was one purpose of Marx’s own labour theory of value. However, the problems posed by that theory have rendered such a formulation problematic, to say the least. Other problems present themselves, including joint production and labour heterogeneity. Nevertheless, Roemer’s early work (1980) and the evolution of his theories of exploitation (1982a, 1988, 1994a) have drawn further attention to the role of property rights in creating the conditions necessary for exploitation, a theme which is outlined at length by Marx in Part VIII of the first volume of Capital. Further, faced with pathological counter-examples, Roemer has conceded that the concept of labour-time cannot be dropped from Marxian theory without further counter-intuitive dilemmas emerging. Roemer may have adopted an ahistorical approach. But one cannot expect an individual researcher to develop every avenue of inquiry – Roemer’s particular contribution is in the logical-deduction. It may be for others to develop, and evaluate, Roemer’s work in historical context. Problems do, however, remain. Roemer’s approach does not explain why classes come to act as classes. Nor is there a theory of strategic interaction in his general theory of exploitation and class. It may be that alterative explanations, some microfounded and others not, may be offered. But to suggest, as Roemer does, that microfounded explanations are the only satisfactory ones, is problematic, and contradicts his principle of ‘withdrawal’ in his theory of exploitation and class. Roemer’s contribution is insightful, for definitional purposes, but it is not game-theoretic in the sense of having ‘strategic’ agents, be they classes or individuals.

6

Class conflict and working hours

Introduction Marx extended his theory of exploitation through examining the conflict over working hours, the organisation and intensity of labour. The theories of absolute and relative surplus-value are the extension of this theory, and the former serves as the starting point for the theoretical investigation in this chapter. In Volume II of Capital, Marx also identified the ‘preferences’ of workers for leisure as a source of conflict. In the early phases of the implementation of the factory system in England, for a given hourly wage rate, workers exhibited a preference for fewer hours with lower wages. Aside, therefore, from a distributional conflict over surplus and necessary labour time, there was also a conflict between capitalists and workers over hours for a given hourly wage. Thus class conflict can be theoretically divided between what we describe here as ‘class struggle’ (over the rate of exploitation) and ‘class preference’ (over the ‘normal’ hours of work, with a given hourly wage rate). As a preliminary, it will be useful to indicate why these issues are of contemporary importance. Marx considered the conflict over the length of the working day against the backdrop of the adverse health effects which went along with excessive working hours. Such concerns are not irrelevant in modern industrialised economies. For example, Buell and Breslow (1960) found that men working more than 48 hours per week had double the incidence of coronary heart disease compared with those working less than this. While this study is now dated, it was nevertheless based upon a large sample, and the findings are relevant to the present discussion. Barton and Folkard (1993) investigated the effects of shift work on health, discovering that shift workers working, on

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average, in excess of 48 hours per week, suffered a greater incidence of mental and physical health problems, including anxiety, cardiovascular and digestive problems, and neuroticism. The problems of working long hours are also acute in Japan where workers work on average approximately an hour longer each week than United States workers, and 250 hours a year longer than their British counterparts (Crafts, 1997). In Japanese the word karoshi is used to describe death from overwork, and Shimomitsu and Levi (1992) suggest this is becoming a major social problem in Japan. In the context of debate over a 48-hour working week, the extensive meta-analysis conducted by Sparks et al. (1997) offers support for a link between long working hours and ill-health. In spite of the fact that on average workers work fewer hours than they did during the mid-nineteenth century, there is still compelling evidence that some workers are suffering health symptoms, and Marx’s contention that workers are being ‘consumed irrationally’ is still relevant. Marx was especially interested in how the State, through legislation, came to restrict working hours. This, too, has modern relevance, in that the European Union have gone some way to legislating against long working hours in recent years, as part of a policy to improve health and safety at work (see Philp, 2001). This recognition, together with the previous evidence on the adverse health effects of long working hours, suggests a modern Marxist analysis might be a fruitful source of insight. In this chapter, we begin by outlining the theory of surplus-value, showing how increases in working hours increase the rate of exploitation. Thereafter, for a given level of exploitation, conflict between the preferences of the capitalist and working class is discussed. Before concluding, there is a consideration of the role of working hour reduction as a strategy to reduce unemployment. Some of the distributional effects of redistributing work from the employed to the unemployed are explored. It is shown that it may be in the interest of the capitalist class, and against the interest of the working class, to redistribute work thus when we measure ‘interests’ solely in terms of net aggregate income to each respective class.

Preferences, class struggle and working hours In order to look at absolute surplus-value production, Marx initially held other factors determining the rate of surplus-value (such as

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real wages and the intensity of labour) constant. Effectively, Marx was making a ceteris paribus assumption. Some, such as Carchedi (1996), have been critical of the use of the ceteris paribus condition in neoclassical economics; in the case of supply and demand, Carchedi suggests that: ‘People do not react to a variation in a certain price by assuming the ceteris paribus condition. Rather they react by taking into account the highest possible number of variables influencing their decisions, like price changes of other goods, forecast future income, employment, and so on’ (1996, p.166). However, while there may be many inherent weaknesses in the supply and demand approach, it is not the ceteris paribus condition per se which is at fault. Indeed, in this chapter and the next the assumption of ‘class struggle neutrality’ is used to isolate and identify different factors determining the length of the working day and the rate of profit. The notion of ‘class struggle neutrality’ is taken from Laibman (1992, pp.121–4). This essentially involves holding the rate of exploitation constant and then looking at the relationships between other variables. In looking at technical change, Laibman argues ‘it has been thought necessary to hold in abeyance the other broad set of forces determining the rate of profit: namely the class struggle over the wage bargain and working conditions’ (1992, p.121). This he does by assuming a constant rate of exploitation, thereby formally isolating the relationship between technical change and the rate of profit. The purpose is to isolate changes in the rate of profit as a consequence of technical change, from changes in the rate of profit as a consequence of changes in the balance of class forces. In the context of the rate of profit, this is discussed in Chapter 7. Here, however, we propose an interesting use for the assumption of class struggle neutrality, namely, to provide insight into conflict over the length of the working day. The question posed initially is this: In the absence of class struggle over the ratio of surplus to necessary labour time (or exploitation), can there still be conflict over working hours? In this section we make a number of assumptions: 1. Assume a single-commodity system in which there are two classes: the capitalist and the working class. 2. The working class are divided into the employed (workers) and the unemployed. 3. We assume, initially, that the unemployed receive no income (this is relaxed in the third section). 4. Assume that output, and the number of hours worked in the

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Class conflict and working hours economy is fixed, and that there are enough workers such that the capitalist class can find enough labour. 5. We assume the hourly wage is constant and annual income is related proportionately to the number of hours worked.

In Capital there are three alternative definitions of the rate of surplus-value (Marx 1976, p.671) – the ratio of surplus-value to the value of labour power, the ratio of unpaid to paid labour, and the ratio of surplus to necessary labour time.1 The formal equivalence of these ratios is demonstrated by Morishima (1973, pp.46–51). The starting point of Marx’s theory of surplus-value involves the recognition that what workers consume only takes part of the working day to produce. However, workers labour for the whole of a ‘normal’ working day. If the duration of the latter is greater than that of the former, this was considered exploitative by Marx. The time required to produce the daily means of subsistence is called necessary labour time, and the existence of surplus labour time presupposes that the length of the working day exceeds this time. It should be noted that in Marx’s analysis the daily means of subsistence are socially rather than biologically determined. Surplus labour time is defined as the additional time the worker works during a given day beyond the time required to reproduce their own means of subsistence and production. The rate of exploitation, or surplus-value, is therefore given by the ratio of surplus to necessary labour time. In this chapter, surplus-value is defined as the average rate for those in employment in the economy. As has already been noted, two programmes can be adopted to increase the rate of surplus-value. Relative surplus-value production involves reducing the period of necessary labour time, for a working day of given duration. This can be achieved through making workers work more intensively or through changing production methods (e.g. increasing the division of labour or introducing machinery). Absolute surplus-value, which is related to the content of this chapter, involves increasing the rate of surplus-value through increasing the length of the working day. If necessary labour-time is of a fixed duration, increasing the length of the working day increases the period of surplus labour time. The ratio of surplus to necessary labour time thus increases, increasing the rate of surplus-value. In equation (4.14) the length of the working day was normalised. Prior to this the rate of surplus-value was defined in (4.13) thus:

Class conflict and working hours e=

T −λb λb

89

(4.13)

As the length of the working day increases, so it follows that the rate of exploitation increases for given levels of λb (i.e. with given levels of productivity and subsistence). Hence we can rewrite (4.13), conceiving of it in terms of ‘average rates’ in our one-commodity system as: e=−1+

1 T λb

(6.1)

This positive relationship between exploitation and working hours in equation (6.1) is also shown in the upper portion of Figure 6.1. Here exploitation–hour curves for different real wage levels (b1, b2 and b3) are represented. Each of these trade-offs – e(b1,T ), e(b2,T ) and e(b3,T ) – are somewhat similar to the conflict which emerges in bilateral monopoly, i.e. with a single seller and a single buyer, with respective classes being our units for analysis (see Chapter 3). In neoclassical economics, increases in the length of the working day tend to be analysed assuming corresponding increases in the daily wage rate, on the grounds that they would reflect changing ‘preferences’ of workers in favour of increased income as opposed to leisure. Accordingly, the hours people work reflect personal choices and vary because workers’ labour and leisure preferences vary (West, 1983, p.266). In contrast, Marxian analyses emphasise the role of class power in determining the ‘normal’ hours of work and there are reasons to suppose that these may not coincide with those that would be chosen in a neoclassical labour–leisure preference framework. Normal hours tend not to be chosen by individuals and depend upon the work practices in a given industry or manufacturing process, together with legislation setting limits on working hours. Thus Marx suggests ‘the establishment of a norm for the working day presents itself as a struggle over the limits of that day, a struggle between collective capital, i.e. the class of capitalists, and collective labour, i.e. the working class’ (1976, p.344; emphasis added). Of course, even though there may be a normal working day, a centre of gravity around which hours of work fluctuate, we may well expect to observe exceptions which may deviate most extremely from this norm, just as we do with wage and profit rates. The extent to which capitalists can extend the length of the working day depends on a number of factors including the extent of unionisation, the level of unemployment (or size of the ‘reserve army’ of

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the unemployed), the legal security of employment, legislation aimed at curbing excesses, and the extent and conditions attached to social security (in bargaining-type games, the ‘disagreement point’ matters). It is important to recognise all of these important factors which contribute to the determination of working hours in actual economies. However, let us initially focus on the relationship between working hours and wages, in an environment which assumes a particular form of class struggle neutrality. Both working hours and wages are matters of conflict between respective classes, and Marx himself tended to isolate variations in the wage by assuming a (socially-determined) subsistence wage level. He could then elaborate on the process of absolute surplus-value production (the equivalent of a ‘given’ b in our mathematical notation). Here, instead, we shall begin by adopting a notion of ‘class struggle neutrality’ which will yield a trade-off between wages and working hours, which presupposes a given level of class struggle. We isolate this, as Laibman (1992) does in the context of the Marxian theory of the falling rate of profit, by assuming a given rate of exploitation. The intention is to separate the variations in working hours as a consequence of class conflict, from the other factors which influence them. Given the frontier identified in the lower part of Figure 6.1, we can suggest that there is a point on this frontier which is optimal for workers as a whole. Suppose this point is at N, corresponding to (b2,T2). These are not preferences in a ‘neoclassical’ sense, but are rather the norms sought, or aspirations of the working class, which prevail at a particular point in time. This is an interesting suggestion because it is possible that, not only will the material welfare of classes be set in opposition, with given technology, but the ‘preferences’ of workers and the capitalist class may also be set in opposition. In using the assumption of class struggle neutrality we can isolate conflict over the rate of exploitation from this conflict over our position on the wage–hours frontier depicted in the lower part of Figure 6.1. Thus we can separate ‘class-struggle’ conflict over working hours from ‘class-preference’ conflict. This may also, of course, be the case in a system with technological change. Marx suggests that, when workers forego increases in consumption in favour of improving their condition through reduced working hours, this is greeted with an outcry from capitalists who are fearful, not only of the effect in the workplace, but also of the impact on the demand for their commodities. In one of the last manuscripts added to Capital II, Marx cited an article by Drummond in 1879 which suggested:

e

e(b1,T)

e(b2,T) e(b3,T)

TMAX

T

A C

bMAX b3 b2

N

N´

b1

0

T1

T2

T3

TMAX

T

Figure 6.1 Exploitation-hours curves with variation in the wage rate

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Class conflict and working hours The working-people have not kept up in culture with the growth of invention, and they have had things showered on them which they do not know how to use and thus make no market for ... The problem remains, how to raise him as a consumer by rational and healthful processes, not an easy one, as his ambition does not go beyond a diminution of his hours of labour, the demagogues rather inciting him to this than to raising his condition by the improvement of his mental and moral powers. (Drummond, cited in Marx, 1978, p.591)

Marx’s response highlights the impact of long working hours upon the condition of the working class: Long hours of labour seem to be the secret of these ‘rational and healthful processes’, which are to raise the condition of the worker by improving his ‘mental and moral powers’ and making a rational consumer out of him. In order to become a rational consumer of the capitalists’ commodities, he must before all else – but the demagogues prevent him – begin by letting his own labour-power be consumed irrationally and in a way contrary to his own health, by the capitalist who employs him. (Marx, 1978, pp.591–2) A number of points are noteworthy here. First, technical change causes our trade-off between wages and working hours to pivot. In Drummond’s terms, the ‘growth of invention’ gives workers the opportunity to ‘have things showered on them’. But the problem for factory owners is that workers’ ambition ‘does not go beyond a diminution of … hours of labour’. If in Figure 6.1 the wage–hours trade-off pivots from 0C to 0A (as a consequence of technical change) workers preferences will, in this case, move from N to N , i.e. they will forego any wage increase (in the absence of class struggle) in favour of reduced working hours. There may not be a problem of labour supply if there is a substantial reserve army of the unemployed, but if the economy is at or near full-employment level this can impede growth in production. Moreover, since workers demand no more goods (and workers tend to consume a greater proportion of their income than do capitalists), this creates the possibility of crisis. We see that the preferences of workers for leisure and consumption goods connect with aggregate demand. The suggestion of conflict on the basis of ‘class

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preference’ over working hours may be one which is not antithetical to Marx’s own approach. It is perhaps also worth reminding ourselves of other factors which may influence, or distort the class preferences of workers, such that they may deviate from what would otherwise be their true preferences. Advertising plays a key role in distorting the aspirations of workers toward commodities and away from leisure. As noted by Baran and Sweezy: ‘The strategy of the advertiser is to hammer into the heads of people the unquestioned desirability, indeed the imperative necessity, of owning the newest product that comes on the market’ (1966, p.132). The connection to working hours has been drawn by Cohen: No ads say: WHEN YOUR UNION NEGOTIATES, MAKE IT GO FOR SHORTER HOURS, NOT MORE PAY. ELECTRIC CARVING KNIVES ARE FINE, BUT NOTHING BEATS FREEDOM. There are no ‘leisure ads’ because firms have no interest in financing them, nor in paying for public reminders of the unpleasant side of the labour which buys the goods. (1978, p.318) As an unintended beneficial consequence of advertising their own products, the impact of advertising as a whole on the working class is to influence their preferences, and as a consequence the class preference, toward increased wages as opposed to reduced working hours. In the absence of technical change, why might capitalists prefer workers to work longer, rather than fewer hours with more employed? One reason might be that this will have the effect of increasing, or maintaining at a high level, the ‘reserve army of the unemployed’. As already suggested, one of the factors which contributes to relative strength in the process of class struggle over the length of the working day is the unemployment level. Thus the class preference of capitalists may well be for long working hours, with fewer workers (such as point C on Figure 6.1) because they anticipate this will change the balance of class forces, thus facilitating increased exploitation because of the existence of a larger reserve army of the unemployed. The motivation giving rise to such an occurrence would require elaboration however; it may be that such an outcome would be an unintended beneficial consequence rather than a result of rational deliberation by individual capitalists or the capitalist class. Nevertheless, it is useful to separate, logically, hour determination on the basis of class preference, from hour

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determination on the basis of class struggle (i.e. struggle over the ratio of surplus to necessary labour time). But plainly in reality the two are interconnected as the example just outlined demonstrates. In the model outlined so far we have assumed capitalists seek to obtain a given aggregate amount of labour-time, and we have implicitly assumed that the unemployed (those members of the working class who are not workers) have no source of income. Since policy-makers in different European countries have suggested that reductions in working hours may be a way of reducing unemployment, this would seem to run counter to the suggestion that the State is being used to reinforce the interests of the capitalist class. This may be true. However, in the next section we shall introduce a tax on income into our price system and show how capitalists may benefit from redistributing work from the employed to the unemployed.

Reducing hours as an employment policy In legally enforcing the hours people work there emerges a key issue concerning distribution of income. At stake in the debate over restricting hours is whether the weekly wages (or indeed monthly or annual salary) or the hourly rate of workers is to remain constant. If it were the latter, legally restricting working time would, ceteris paribus, have the effect of redistributing labour from the employed to the unemployed working class. This will reduce the ‘reserve army of the unemployed’ but the working class could, on average, receive lower annual incomes. There are social and health benefits to workers from reduced working hours and the purpose of this section is not to suggest this is a bad thing. Rather, it is important to consider the implications of such policies for the distribution of income between classes. Possible distributional effects can be illustrated using a simple model. Assume we have a single good (e.g. corn) which can be combined with labour to produce a surplus. Assume also that a given level of output is being produced in this economy, and we will look at the costs and incomes associated with the production of a particular unit of this fixed level of output. If r is the rate of profit, w the hourly wage rate, Le the number of workers initially employed in producing a unit of output, h the number of hours worked by each employed worker, and p the price of the commodity, we may rewrite equation (4.7) as: p=(1+r)(pa+wLe h)

(6.2)

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We shall now introduce a basic social security system to allow consideration of distribution of income between classes when working hours change. Assume now that there is a ‘reserve army of the unemployed’ whom we label Lu, such that the working class comprise L=Le +Lu. This is expressed in terms of per unit of output. Social security benefit is raised, we shall assume, through taxation on the income of capitalists and the employed, and in this model we shall assume no government surplus or deficit. Enough tax per unit output (T ) must therefore be raised to cover the benefit paid (s) to each unemployed worker. That is: T =sLu

(6.3)

The income taxation rate t (assuming0≤t <1) is levied on all incomes from production such that revenue raised will satisfy (6.3). That is taxation is levied on profit (r(pa+wLe h) and on wages for those in employment (wLe h): T =t(r(pa+wLe h)+wLe h)

(6.4)

Marx adopted a number of definitions of the rate of surplus-value, including the ratio of unpaid to paid labour, the ratio of surplus to necessary labour time, and the ratio of surplus-value to variable capital (1976, p.617). Adhering to the latter definition (while recognising that this simple model does not incorporate interest and rent), we can define the rate of surplus-value as: e=

r(pa+wLe h) wLe h

(6.5)

Suppose now that government introduces a policy aimed at reducing unemployment and they adopt a rule to restrict hours to the level at which unemployment would be eradicated. That is, the government would adopt a policy rule restricting working hours for the employed to h∗ at which: Le h=Lh∗

(6.6)

This implies (6.3) is equal to zero and the taxation rate will be zero. The result of such a policy is that capitalists receive a net (i.e. after-tax) income which is greater than that previously since: r(pa+wLh∗ )>tr(pa+wLe h)

(6.7)

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And, for our given output level, workers as a whole receive an income that is less than previous wages plus benefits, i.e.: wLh∗
(6.8)

Within the model, workers as a whole are, in a Marxian sense, as exploited as before since: e=

r(pa+wLe h) r(pa+wLh∗ ) ∗ = =e wLe h wLh∗

(6.9)

The redistribution of work from the employed to the unemployed, with the associated reduction in the taxation rate, implies that capitalists received a higher net (i.e. after-tax) income. Workers who were previously in employment also benefit from the reduction of taxation; however, this gain is less than the weekly income lost through reduced working hours at a constant hourly wage rate. The implication, within this model, is that a government policy aimed at reducing unemployment by reducing the working hours of the employed, through legal mechanisms, will benefit the capitalist class in conflict over the distribution of income. The analysis of the previous section has shown that workers may have a preference for fewer hours. Long working hours contribute to ill-health and dysfunctional families. But, if reduced working hours is seriously proposed as a method for reducing unemployment, there can be no question of this redistribution being conducted on the basis of a constant hourly wage. Because of the reduced incidence of taxation on the capitalist class, it is their class who will ultimately benefit since it is they who will increase realised income per unit of output.

Conclusion This chapter has not provided a comprehensive analysis of the determinants and dynamics of working hours. What it has done, however, is to suggest a number of factors which can be explored in looking at exploitation, working hours and (potentially) technical change. The logical extensions of the arguments have not been fully worked out. It is nevertheless suggested that the account provided here may be a useful place to start, to impart new impetus into the Marxian theory of exploitation and conflict over the length of the working day. In particular, it is suggested that the distinction between conflict over ‘class preference’ and ‘class struggle’, for different working

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hours, is useful. Laibman’s notion of ‘class-struggle neutrality’ is also helpful in this regard. Furthermore, it is important to consider the cost of maintaining a ‘reserve army of the unemployed’, through a social security system. By looking at after-tax profits and wages, in an environment in which we assume a constant rate of exploitation, we can see interesting distributional outcomes which suggest a countervailing tendency which has a negative effect on the capitalists’ preferences for long working hours. These avenues for exploration are interesting, and it may be that they can be connected, usefully, to theories of crisis and under-consumption.

7

Reduction, rationality and the rate of profit

Introduction The relationship between class struggle and technical progress was of the utmost importance in Marx’s Capital, as was the relationship between these factors and the rate of profit. A consequence of competition is that there is a tendency for wage and profit rates to equalise. The rate of profit is the most general indicator of the ‘efficiency’ (from the perspective of the capitalist class) of a given capitalist economy and consideration of this is relevant to understanding Marxian theories of crisis. Marxists have traditionally claimed that there is a long-run tendency for the rate of profit to fall through time, since the organic composition of capital has a tendency to rise with technological progress. This, of course, was only one cause of crisis identified by Marx. This particular view was founded on the belief that the competitive forces compel capitalists to introduce techniques which raise the organic composition of capital, but this would cause a crisis in the capitalist economy as a whole owing to its effect on the rate of profit. Thus: ‘The challenge posed by the classical Marxist theory is to explain the behaviour of the powerful, cutting-edge capitals – the prisoners’ dilemma that turns their individual rational actions into a systematic contradiction’ (Laibman, 2001, p.92). Marx’s theory of the falling rate of profit has been subject to criticism, in particular since the work of Okishio (1961) cast doubt – based on the assumption of a constant real wage – on whether one could demonstrate a prevailing tendency for the rate of profit to fall as a consequence of technical change, when the motivation of individual capitalists is to maximise profit. This chapter investigates how alternative assumptions of class struggle neutrality (such as that of

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the constant real wage adopted by Okishio) may give rise to different effects of technical change on the rate of profit. The difficulties surrounding value and price, discussed in Chapter 4, are reflected in Marx’s theory of the falling rate of profit, to be discussed presently. It was in the late 1920s and 1930s that the notion of the falling rate of profit came to occupy a pivotal role at the core of the Marxist theory of crisis (see Van Parijs, 1980). In that period, the work of Grossmann (1992) and Dobb (1972) brought the theory to the forefront of Marxist debate. Contemporaries of Grossman and Dobb, such as Moszkowska (1935), Sweezy (1970) and Robinson (1976; first edition 1942) sought to challenge the validity of the traditional Marxist interpretation. More recent work has sought to terminate the debate over the falling rate of profit. Notably, Okishio’s influential work has provided the basis for many of those who have sought to discard this element of Marx’s theory (Okishio, 1961, 1963, 1977). Subsequent critiques along the lines of Okishio’s have been forthcoming from Morishima (1973), Steedman (1977), Van Parijs (1980) and Roemer (1981). Others have sought to defend, reinterpret and revise Marx’s analysis while retaining the role played by the falling rate of profit in the Marxian theory of crisis. Examples of the latter include Shaikh (1978, 1987), Nakatani (1979), Alberro and Persky (1979), Ernst (1982), Laibman (1982, 1992), Freeman (1996) and Kliman (1996). The alternatives proposed by advocates of the falling rate of profit thesis are by no means unified and it is important to distinguish approaches that suggest the rate of profit can fall as a consequence of the capitalist intending to maximise profit from those which suggest that the long-run secular tendency is for the rate of profit to fall through time, as a consequence of technical change. Nakatani (1979) and Shaikh (1987) both argue that intense competition among capitalists leads to price reductions. Firms adopt techniques that maximise profit rates when prices decline to some minimum acceptable level, rather than assuming that current equilibrium prices hold. This can lead to the adoption of sub-optimal techniques, which can in turn lead to a falling rate of profit. Alberro and Persky (1979) focus upon the unexpected appearance of new techniques. These can yield a higher potential stream of returns than existing techniques, which can lead to a falling rate of profit since capitalists overestimate the returns from introducing new techniques. In this approach, as Kliman (1996) has observed, it is not mechanisation per se which leads to a falling rate of profit, but systematic forecasting

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errors by capitalists. In contrast, Ernst (1982) and Freeman (1996) seek to root the tendency for the rate of profit to fall in mechanisation. The approach of Laibman (1982, 1992) is given particular attention in this chapter, since he demonstrates that the rate of profit can fall if we assume a constant rate of exploitation. The underlying assumption of class struggle neutrality outlined in Chapter 6 is thus relevant once more.

Methodological considerations This chapter focuses upon theoretical discussion, and two specific considerations are addressed. First, it is argued that it must be shown that any tendency for the rate of profit to fall is consistent with the rational capitalist intending to maximise profit. Secondly, in order to demonstrate the tendency for the rate of profit to fall as a consequence of the process of technical change, we have to hold other factors governing the rate of profit, such as the length of the working day, constant. In this book, an anti-reductionist position has been advocated and the dangers of teleology and functionalist argument have been highlighted. This is relevant to the falling rate of profit, since the assumption of capitalist profit maximisation presupposes instrumental rationality on their part (in the sense in which the term ‘instrumental rationality’ is used by Sugden 1991 and Varoufakis 1993). Moreover, we seek to explain the tendency for the rate of profit to fall as a consequence of technological change, assuming rational decision making by individual capitalists. Thus we are making a micro-founded argument which is not inconsistent with an explanation based on methodological individualism. This prompts the question: ‘Is there a contradiction between such a position and the previous criticism of methodological individualism?’ In Chapter 2, it was suggested that certain phenomena may be partially explained using a rational-choice microfoundational approach. It is important to recognise that a ‘complete’ explanation of the determinants of the profit rate and the distribution of income is not being proposed. Rather the intention is to examine the relationship between technological change and the rate of profit. Such a micro-founded argument is desirable, since the orthodox Marxian claim that the rate of profit will tend to fall is founded on this being an unintended consequence of intentional capitalist profit-maximising behaviour.1

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Marx’s theory of the falling rate of profit Marx defined the rate of profit as the ratio of surplus-value to constant plus variable capital. This can be expressed as the ratio of the rate of surplus-value to the organic composition of capital plus one (see Chapter 4). Given this conception of the rate of profit, it follows that, as the level of constant capital increases, the organic composition of capital rises and, ceteris paribus, there is a fall in the rate of profit. Marx asserts that: it has been shown to be a law of the capitalist mode of production that its development does in fact involve a relative decline in the relation of variable capital to constant, and hence also to the total capital set in motion. This simply means that the same number of workers or the same quantity of labour-power that is made available by a variable capital of a given value, as a result of the specific methods of production that develop within capitalist production, sets in motion, works-up, and productively consumes, within the same period, an ever-growing mass of means of labour, machinery and fixed capital of all kinds, and raw and ancillary materials – in other words, the same number of workers operate with a constant capital of ever-growing scale. (Marx, 1981, p.318) A rising organic composition of capital leads to a falling rate of profit, and ultimately, to crisis in capitalism. It should be noted that Marx did maintain that there would be counteracting factors at work. For example, an increased exploitation of labour stemming from relative and absolute surplus-value production, and the appropriation of supplementary labour (women and children), may have an opposite effect. In addition, Marx notes that it may be possible to reduce wages below their value, and although in Marx’s models he assumes that commodities exchange at their value he does not reject the empirical possibility that this counteracting factor operates. One further element which affects the determination of the rate of profit is the cheapening of the elements of constant capital and this, together with the devaluation of existing capital, may counteract the downward pressure on the rate of profit from technical change. Finally, Marx suggests that increasing foreign trade leads to a cheapening of the elements of constant capital and this, together with the access to new markets, may temporarily stem or reverse the downward pressure on the rate of profit. In sum,

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Marx’s argument can be reduced to the claim that, when the rate of exploitation is constant, the rate of profit falls as capital per worker increases. There are countervailing tendencies, but these are limited such that the prevailing tendency is for a fall in the rate of profit through time. Problems with Marx’s approach to the falling rate of profit are now well known. Joan Robinson, an early critic, suggested that one could not simultaneously maintain that the rate of exploitation and the real wage are constant in the face of productivity increase: ‘if the rate of exploitation is constant, real wages tend to rise as productivity increases. Labour receives a constant proportion of an increasing total. Marx can only demonstrate a falling tendency in profits by abandoning his argument that real wages tend to be constant’ (Robinson, 1976, p.36).2 Another problem identified by Robinson concerns the countervailing tendencies. Marx did argue that there are limits to the effects of these countervailing tendencies such that they cannot be sufficiently strong to offset the tendency for the rate of profit to fall as a consequence of technical change. The counteracting tendencies, for Marx, are limited, whereas the process of technical change is not (except insofar as it will eventually lead to crisis in capitalism). While accepting there are limits to the length of the working day, and the intensity with which labour could be worked through time, Robinson challenged the view that all countervailing tendencies were limited: To these tendencies, which all help to raise the rate of exploitation, there are obvious limits, and Marx argues that they cannot be sufficiently strong to offset the falling tendency of the rate of profit ... But the rise in the rate of exploitation which comes about through a rise in productivity, with constant hours and intensity of work, and constant real wages, is not limited in the same way. (Robinson, 1976, pp.38–9) That is, while it may be accepted that absolute surplus-value is limited by the number of hours in the day and the physiology of workers, relative surplus value production is not so limited. Others have more recently criticised Marx’s conception of the falling rate of profit thesis (see Okishio 1961, Steedman 1977, Van Parijs 1980). Therefore in the following section we consider Okishio’s critique before examining Laibman’s suggested reformulation of Marx’s thesis.

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The Okishio theorem Okishio summarised the classical Marxian argument in the following way: competition among capitalists forces them to introduce new techniques which raise the productivity of labour; production techniques which raise the productivity of labour usually increase the organic composition of capital; it follows that, if the rate of surplus-value remains constant, the rate of profit decreases as the organic composition of capital rises. Thus there is a tendency for the rate of profit to fall as a consequence of technical change. Okishio observes that, in the classical Marxian argument, it is suggested that this process is partially offset by the recognition that production techniques which raise the productivity of labour in wage–good industries increase the rate of surplus-value. However: ‘in spite of this offsetting effect the rate of profit has the tendency to fall owing to continuous introduction of new techniques which increase the organic composition of capital’ (Okishio 1961, p.85). This is the position which Okishio sought to challenge, claiming that the falling rate of profit hypothesis is not a ‘corner-stone’ upon which a Marxian system can be built. Instead, movement in the rate of profit is determined by the struggle between conflicting classes (p.96). Thus it is important to separate changes in the rate of profit stemming from class conflict from those which arise from the process of technical change. Okishio (1961) proposed that class struggle should be isolated by assuming a constant real wage. To simplify discussion, we outline and develop Okishio’s theorem based upon, and expanding, Laibman’s (1992) formalisation, since this will facilitate comparison between the Okishio theorem, based on the assumption of a constant real wage, and Laibman’s re-examination of the falling rate of profit, assuming a constant rate of exploitation. Assume, following Laibman, that there is a two-good economy incorporating a capital (good 1) and consumption sector (good 2). The capital good plus direct labour enter as inputs into the production of both goods, and the consumption good is an input in neither sector. The quantity of the capital good used as an input in the production of the capital good is denoted by a1 and the quantity of the capital good used in the production of the consumption good is denoted by a2. The direct labour input for the production of each good is given as l1 for good 1 and l2 for good 2. The rate of profit is written r. To reduce the complexity of equations, following Laibman (1992, p.105), we define R≡(1+r). Since

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105

we assume perfect capital mobility, in equilibrium there can only exist one uniform rate of profit. For simplicity, assume that wages, given by w, are paid at the end of the production period. The wage is a money wage rate expressed in terms of the consumer good, which is the numeraire. Hence, in Laibman’s model, the real wage coincides with the money wage rate. Taking the price of the consumption good as the numeraire, p is the price of the capital good expressed in terms of the consumption good. The equal profit rate equilibrium combination of prices for this economy are given as follows: p=R(pa1)+wl1

(7.1)

1=R(pa2)+wl2

(7.2)

By rearrangement of equation (7.2) we may write: p=

1−wl2 a2 R

(7.3)

If we substitute (7.3) into (7.1) and rearrange this gives: R=

1−wl2 a1 +w(a2l1 −a1l2)

(7.4)

And the equilibrium price of the capital good is: p=

a1 +w(a2l1 −a1l2) a2

(7.5)

Technical coefficients and the rate of profit Now we elaborate on Laibman’s analysis and consider the relationship between technical progress and the rate of profit using calculus. Consider the partial differentials of the equilibrium profit rate given in (7.4). As we would expect, R varies inversely with w. Applying the quotient rule and partially differentiating R with respect to wages gives: −a2l1 ∂R = ∂w (a1 +wa2l1 −wa1l2)2

(7.6)

By assumption, the capital good is required in the production of the consumer good; therefore a2 >0. Furthermore, labour is required in the

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production of the capital good, so that l1 >0. It therefore follows that in (7.6) there is an inverse relationship between R and w. It is also the case that R varies inversely with each of the four technical coefficients a1, a2, l1 and l2. For a1: ∂R −(1−wl2 )2 = ∂ a1 (a1 +wa2 l1 −wa1 l2 )2

(7.7)

Since the numerator is negative and the denominator is, as before, positive, as a1 increases the rate of profit falls. Ceteris paribus, using more capital input to produce capital goods reduces the rate of profit. For a2: ∂R −wl1(1−wl2) = (7.8) ∂ l2 (a1 +wa2 l1 −wa1 l2 )2 Since 1−wl2 >0, and the denominator of (7.8) is also greater than zero, it follows that (7.8) is negative; that is, the rate of profit falls as the quantity of the capital good used in the production of the consumer good rises. For l1: ∂R −wa2(1−wl2) = (7.9) ∂ l1 (a1 +wa2 l1 −wa1 l2 )2 As before, since 1−wl2 >0 and wa2 is positive, ceteris paribus, as the quantity of labour required to produce the capital good increases, so the rate of profit falls. Finally, for l2: ∂R −w2 a2 l1 = ∂ l2 (a1 +wa2 l1 −wa1 l2 )2

(7.10)

Since w, a2 and l1 are positive, and the denominator of equation (7.10) is negative, as the quantity of labour required to produce the consumption good falls the rate of profit rises. Laibman’s approach to viability Laibman (1992) develops his analysis by considering the micro-rationality of individual capitalists, asking whether they would or would not plausibly introduce new technologies which would result in the rate of profit falling. For capitalists to consider a new technique (ai ,li ) to be superior to the old technique (ai ,li )

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we assume that the new technique costs less to operate, per unit of output, at the existing prices and profit rate. This condition is formally equivalent to assuming that capitalists will only introduce this technique if the innovator’s profit rate is higher than the existing equilibrium profit rate. This is elaborated by Laibman (1992, p.106), who writes these conditions as follows. Viability of the new technique in the capital goods sector implies that: Rpa1 +wl 1
(7.11)

And viability for an innovation in the consumption good sector implies that: Rpa2 +wl 2 <1

(7.12)

In order to ascertain whether it is possible for the rational optimising capitalist to introduce a technique which will, ceteris paribus, lower the rate of profit, we will assume that capitalists in one sector are unable to calculate the effect of their technological innovation upon the vector of prices or the general rate of profit once equilibrium is re-established. This is the assumption of atomistic, unrestrained competition among individual capitalists. Given the criteria for viability above, we now formulate the falling rate of profit condition. In so doing we can identify whether a technique which is viable for a particular sector can lead to a reduced general rate of profit once price equilibrium is re-established. The rate of profit was previously given in (7.4), but now assume that the old technique remains in the capital goods sector, while technological change occurs in sector 2, such that labour and capital good inputs are now given by a2 and l2 . The falling rate of profit thesis suggests this does, or can, give rise to a new rate of profit lower than the initial rate of profit. That is: R =

1−wl 2
(7.13)

By rearrangement of the right-hand side of (7.13) we can derive the following inequality consistent with a falling rate of profit: 

l2 >

Rl 1  1 a − w 1−Ra1 2

(7.14)

However, viability of technical change in the consumption goods sector implies that inequality (7.12) holds, which, by rearrangement, implies that:

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l2 <

1 pR  − a w w 2

(7.15)

Equation (7.1) can be rewritten to give: Rl1 pR = w 1−Ra1

(7.16)

Since we assume the technical coefficients in the capital goods sector to be unchanged, we can substitute (7.16) into (7.15) to give: 

l2 <

Rl 1  1 a − w 1−Ra1 2

(7.17)

The condition consistent with a falling rate of profit given in inequality (7.14) is found not to be consistent with the inequality indicating a new technique is viable (7.17). Technological change in the consumption good sector which ultimately reduces the rate of profit will not, ceteris paribus, be viable. To rigorously demonstrate the Okishio result, now consider the effect on the rate of profit of technical change in the capital goods sector. Viability of technical change in the capital goods sector, by rearrangement of (7.11), implies that: 

l1 <

p pR  − a w w 1

(7.18)

Substituting technology (l1a1) for (l1 , a1) implies that the condition for the falling rate of profit is: R =

1−wl2
(7.19)

Rearranging (7.2) and multiplying both sides by wl1 gives: wl1 wl1 a2 = pR 1−wl2

(7.20)

Using (7.20) we can rewrite (7.19) as: 

l1 >

p pR  − a w w 1

(7.21)

The condition for viability of technical change based upon atomistic competition, given in inequality (7.18), contradicts inequality (7.21)

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derived from the falling rate of profit condition given in (7.19). As Laibman demonstrates, techniques which result in a falling rate of profit are not viable, given the assumptions outlined in this model, and in this sense the Okishio critique is logically robust. Viability using differential calculus In order to demonstrate that the Okishio theorem holds, given a constant real wage, let us now, using calculus, consider the approach of individual capitalists. The capitalist uses data on price and costs which is currently available to assess the viability of introducing a new technique which will reduce either the labour or capital input coefficient. That is, we assume that capitalists make decisions about production techniques assuming that current prices and costs will continue, unaffected and independently of their own particular business decisions. From the perspective of the capitalist in the capital good industry, R in equation (7.1) can be written: R=

p−wl1 pa1

(7.22)

The effect of economies in the use of the capital good used in the capital good industry will be: ∂R −p+ l1 w = a21 p ∂ a1

(7.23)

Viability of a new technique of production in the capital good industry implies that the price of the capital good is greater than the labour input used in the production of the capital good; hence (7.23) is negative. As capitalists perceive it, the effect of capital-saving in the capital good industry is to increase the rate of profit. The effect of economies in the use of labour as an input in the capital good industry will be: ∂R −w = ∂ l1 a1 p

(7.24)

Since w, a1 and p are positive, the rate of profit is inversely related to the quantity of labour used in the production of the capital good. The capitalist will therefore introduce such labour-saving techniques. For the capitalist in the consumption good sector, R is perceived as:

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1−wl2 pa2

(7.25)

The effect of economies in the use of the capital good in the consumption good sector is: ∂R −1+ l2 w = a21 p ∂ a2

(7.26)

Since the consumption good is the numeraire, viability implies that l2w<1. Hence (7.26) will be negative, suggesting that, from the perspective of the capitalist, economies in the use of the capital good imply an increase in the rate of profit. Finally, from the perspective of the capitalist in the consumption good industry, the ceteris paribus effect of introducing techniques which change the labour input is: ∂R −w = ∂ l2 a2 p

(7.27)

Since w, a2 and p are positive, the capitalist assumes an inverse relationship between the rate of profit and the labour input in the consumption good sector so that labour saving in the consumption good industry implies an increase in the rate of profit. These are the effects of changes in the technical coefficients, viewed from the perspective of the capitalists operating those sectors. The full effects in the present framework were examined in section ‘Technical Coefficients and the Rate of Profit’. In the next section, we change the assumption of a constant real wage in the global model while continuing to assume that the capitalists’ perception of the effect of changes in the technical coefficients is, as outlined here, partial. The implication of this analysis is that the Okishio theorem, on its own terms, is correct. However, in the following sections we turn our attention to the trajectory of the rate of profit when the notion of class struggle neutrality is modified. If it can be found that there are circumstances when an intentionally profit-maximising capitalist will introduce a technique which will result in a long-term fall in the general rate of profit, there is still scope for advancing a Marxian theory of crisis which has its origins in technical change.3

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Constant rate of exploitation Okishio assumes a constant real wage. Given this assumption, he demonstrates that there is not a tendency for the rate of profit to fall as a consequence of technical change, thus Marxists should look elsewhere for a theory of the falling rate of profit. The candidate Okishio proposes is the conflict between capital and labour: ‘Thus the movement of the rate of profit is determined by the struggle between conflicting classes’ (1961, p.96). One reason to assume a constant real wage is to separate out possible changes in the rate of profit stemming from the class struggle between the working and capitalist class from changes in the rate of profit resulting from technical change. However, if technical change raises the productivity of labour while the real wage is constant, it follows, ceteris paribus, that the capitalist class is capturing a larger share of the product. It would appear, in this sense, that the notion of class struggle neutrality adopted by Okishio should be set against other notions which might be adopted. It is also important to recognise that working hours change, and this emerges as an additional source of class conflict. The assumption of a constant real wage becomes ambiguous when we consider the possibility of absolute surplus-value production or, relatedly, reductions in working hours stemming from legislation or changes in the balance of class forces. In this sense, as argued in Chapters 5 and 6, the rate of exploitation is a more satisfactory indicator of the balance of class forces than is the wage rate. Thus Laibman’s reconstruction of the falling rate of profit thesis, with its assumption of a constant rate of exploitation, is both interesting and relevant to the debate concerning the determination of the rate of profit. Reframing the previous argument in terms of the rate of exploitation, or the value wage rate, necessarily complicates the model. Laibman defines the value wage rate as the ratio of necessary labour time to the length of the working day (i.e. surplus plus necessary labour time). Recalling the single commodity and n-commodity cases in Chapter 4, we can express the amount of labour required, directly and indirectly, for the production of the capital good as: λ1 a1 + l1 = λ1 By rearrangement, the unit value for the capital good is:   1 λ1 = l1 1−a1

(7.28)

(7.29)

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The labour required, directly and indirectly, for the production of the consumer good is given by: λ1 a2 + l2 = λ2

(7.30)

Substituting (7.29) into (7.30) and rearranging gives the unit value for the consumer good:   l1 a2 (7.31) λ2 = l2 + 1−a1 The rate of surplus-value is given by the ratio of surplus-value to variable capital, or alternatively the ratio of surplus to necessary labour time. The value wage rate is the ratio of necessary labour time to surplus plus necessary labour time. Thus, following Laibman (1992, p.110), the value wage rate (w∗ ) is given by the real wage (w) multiplied by the time taken to produce those goods consumed (λ2). Using (7.31) we can write: w∗ =w λ2 =wl2 +

wl1 a2 1−a1

(7.32)

And instead of holding the real wage constant, Laibman holds the value wage rate constant, implying a constant rate of exploitation. Rearranging (7.32) gives: w=

w∗ (1−a1) l2(1−a1)+ l1 a2

(7.33)

Expressing the real wage in terms of the value wage rate, using (7.33), we can rewrite the wage–profit frontier in (7.4) to give: R=

l2(1−a1)(1−w∗ )+ l1 a2 a1[l2(1−a1)(1−w∗ )+ l1 a2]+(1−a1)w∗ l1 a2

(7.34)

As in the case of the proof of the Okishio theorem above (‘Laibman’s approach to viability’), it is possible for us to build on Laibman’s model and use differential calculus (as in ‘Viability using differential calculus’) to examine the relationship between the effect upon the rate of profit consequent upon a change in the value wage rate, or consequent upon a change in the technical coefficients. Thus the effect of a change in the value wage rate on the rate of profit is: (−1+a1)a2 l1(a2 l1 + l2 −a1 l2) ∂R = ∂w (a21 l2(−1+w∗ )−a1(a2 l1 + l2)(−1+w∗ )+a2 l1 w∗ )2

(7.35)

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Since the capital good sector is productive, −1+a1 <0 and l2 >a1l2. Therefore the denominator of (7.35) is negative, implying an inverse effect on the rate of profit from a change in the value wage rate. The effect of changes in the technical coefficients is the same as in the Okishio class struggle neutrality assumption for a1, a2 and l1. Thus, for a1: ∂R (a22 l12 −2(−1+a1)a2 l1 l2 −(−1+a1 )2 l22(−1+w∗ ))(−1+w∗ ) = ∂ a1 (a21 l2(−1+w∗ )−a1(a2 l1 + l2)(−1+w∗ )+a2 l1 w∗ )2

(7.36)

For a2: ∂R (−1+a1 )2 l1 l2(−1+w∗ )w∗ = 2 ∂ a2 (a1 l2(−1+w∗ )−a1(a2 l1 + l2)(−1+w∗ )+a2 l1 w∗ )2

(7.37)

When surplus-value is produced, (−1+w∗ )<1, this implies an inverse relationship between a2 and the rate of profit. That is, economy in the use of the capital good in the consumption good sector leads to an increase in the rate of profit. For l1: ∂R (−1+a1 )2 a2 l2(−1+w∗ )w∗ = 2 ∂ l1 (a1 l2(−1+w∗ )−a1(a2 l1 + l2)(−1+w∗ )+a2 l1 w∗ )2

(7.38)

As before, since (−1+w∗ )<1, it follows that labour-saving in the capital good industry has a positive effect on the rate of profit. However, the effect of labour-saving in the consumption good sector is not the same. For l2: ∂R −(−1+a1 )2 a2 l1(−1+w∗ )w∗ = 2 ∂ l2 (a1 l2(−1+w∗ )−a1(a2 l1 + l2)(−1+w∗ )+a2 l1 w∗ )2

(7.39)

The conditions for the falling rate of profit imply that where a new technique is introduced the new rate of profit will be lower than that previously. This implies, for new technique (l2 , a2): R =

l2 (1−a1)(1−w∗ )+ l1 a2
(7.40)

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Since the existence of exploitation implies that (−1+w∗ )<1 and we assume the capital goods industry to be productive, i.e. (−1+a1)<0, labour-saving in the consumption good industry has a negative effect on the rate of profit if we assume a constant rate of exploitation. The issue is: would a rational capitalist introduce such a technology? As has been shown above, the assumption of atomistic competition suggests that this will indeed be the case and so, assuming a constant value wage rate, rational capitalists may introduce techniques which will result in reductions in the rate of profit. If distributive shares, expressed in terms of exploitation, are maintained at pre-change levels, the rate of profit can fall as a result of technical change. It has been contended in this book that an appropriately defined measure of exploitation is a useful indicator of class struggle. Given this assertion, Laibman’s assumption of class struggle neutrality is a useful alternative to the criterion proposed by Okishio and it provides interesting results elaborated upon here.

Conclusion In recent years there has been a productive debate concerning the falling rate of profit controversy. The Okishio theorem, in terms of its internal logic, is not in dispute. But the assumptions from which Okishio begins have been subject to criticism. It is important to isolate changes in the rate of profit due to technical change from other factors which influence the trajectory of the profit rate. The balance of forces in the class struggle, influenced by many elements, plays a part in the determination of the rate of profit. Factors also might include legal restrictions on firms and workers, trade union strength, the right to unimpeded political organisation, the cultural and social homogeneity of workers, the extent of organisation by employers, and the mobility of capital and workers. This raises the issue of how to isolate changes in the rate of profit stemming from changes in the balance of such class forces, from changes as a consequence of technical change. The approach adopted by Okishio is founded upon the assumption of a constant real wage for workers. In this chapter, this approach has been questioned as a measure of class struggle neutrality, since one can think of examples where technical change leads to a rise in the real wage and the rate of profit, while the share of output workers’ gain diminishes. According to the criterion of class struggle neutrality offered by Okishio, this implies that the workers are being

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made better off; however in distributive terms the converse is the case. The Okishio theorem also uses a comparative static framework, adopting the assumption of equilibrium. Laibman (1992) also uses this framework; however he employs an alternative assumption of class struggle neutrality, in which a constant rate of exploitation is assumed. As has been asserted in this chapter and Chapter 6, this alternative notion of class struggle neutrality provides a broader notion of ‘constancy’ in the balance of class forces. The result, thus, is not that the rate of profit will fall as a result of technical change. The result is somewhat weaker; the rate of profit can fall as a consequence of technical change. In this weak form, a Marxist theory of the falling rate of profit founded on technical change, may endure.

8

Conclusion

Summary of results Marxian social science is a diverse and considerable body of work. This presents problems for a study such as this and it has been important to demarcate clear boundaries and to identify specific themes. This work has sought to consider a number of themes in Marxian economics in the light of the debates between analytical and orthodox Marxists. Both these traditions have adopted an approach that embraces mathematical formalism. However, analytical Marxists are hostile to a labour theory of value, whereas orthodox Marxists regard value theory as useful, if problematic. The units for analysis in social scientific investigation warrant consideration, and these were investigated in Chapters 2 and 3. This is important, since Marxian approaches to social scientific investigation have frequently been constructed in terms of class conflict as opposed to conflict between atomistic agents. The relationship between macro and microeconomics has been subject to consideration within and on the periphery of mainstream theory. Hicks (1979, pp.vii–viii), for example, has suggested that the question of the relationship between macro and microeconomics is problematic. In particular, Hicks questioned what the grounds were for believing that microeconomics was a more solid foundation for economic investigation than macroeconomics. The relationship between macro and microeconomic theory in Marxian economics is somewhat different from that in neoclassical theory. The latter more frequently (although not always) maintains strict disciplinary boundaries, whereas in Marxian theory social, political and historical aspects are considered useful and even indispensable. In particular, explanations involving classes, defined

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in terms of the source and nature of agents’ revenue (i.e. profits, interest, rent or wages), as in the classical and Marxian tradition, cannot be regarded as complete without a social, political and historical context. Thus, in Chapter 2, the relationship between macro and microexplanations is not regarded in the purely economic sense of neoclassicism, but rather in a broader social science context. The issues here relate to problems of reduction and multiple-realisability. The thrust of Chapter 2 is a critique of explanatory reduction, although it should be noted that there are also problems of predicate reduction as outlined by Little (1991). In neoclassical economics such problems are usually avoided by treating non-economic fluctuations as exogenous, for example by assuming the preferences of agents are given. However, while this makes such neoclassical analyses tractable, it cannot be satisfactory if the most significant explananda are treated as beyond the scope of analysis. In addition, it is deemed unreasonable for neoclassical theory and for other approaches, such as analytical Marxism, to maintain that a microfoundations approach is the only satisfactory method for conducting social scientific investigation. There are further problems for microfoundational approaches, such as those of methodological individualism and atomism. Not only are there issues of irreducibility in explaining class conflict, for example, but there is also a problem of how individual action is perceived and modelled in micro-theory. There are reasons to be sceptical of rational-choice accounts based on the machinations of individual agents. This has particular implications for those seeking to apply game theory to Marxism. Analytical Marxists have sought to apply the theory of games to illuminate Marxian questions. However, this approach has simultaneously advocated microfoundational analysis and (frequently) instrumentalism (in the sense used by Sugden 1991 and Varoufakis 1993). The question of the motivation for agents, and behaviour when faced with collective action problems, warrants consideration and this lies at the heart of choice-theoretic models. In Chapter 3, it was shown that capitalist competition frequently coerces agents into adopting instrumental rationality. However, one should not confuse the rationality agents are forced to adopt in competitive capitalism with human nature. Indeed overcoming particular problems, such as the prisoners’ dilemma, involves seeing through such structures and abandoning instrumental rationality in favour of some other guide to action. Lebowitz (1988) has argued that game theory can be used to illuminate Marxian theory, but methodological individualism should be abandoned and a collective game of class conflict accurately

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captures the essence of class antagonism in capitalism. It may be that abandoning methodological individualism would have the effect of rendering game-theoretic Marxism, along the lines suggested by Lebowitz, unrecognisable by neoclassical economists. It has been questioned whether any fresh insights will be forthcoming. In Chapter 3, game theory was used to model surplus-value and a ‘divide and rule’ approach to conflict within the working class. But this merely stated, in game-theoretic terms, ideas which were already well known within Marxian economics. Accepted arguments have also been restated in game-theoretic terms in neoclassical theory. The work on oligopoly by Cournot (1960) and Bertrand (1997) in the nineteenth century had been formulated long before the development of game theory embodied in the work of Neumann and Morgenstern (1944). Other examples of early work which implicitly adopted what has become known as game theory, are contained in Dimand and Dimand (1997). In a similar vein Marxian game theory may not, as such, yield startling new results. However, in stating Marxian theory in such terms this body of work may be communicated to a mainstream economic audience, and this is a beneficial consequence. Moreover, in developing game theory in Marxist economics one must explicitly consider the motivation of agents and the level of analysis to be adopted. In specifically addressing such questions, the critique of neoclassical economics, and its instrumental approach to preferences, may be refined. Value, price and exploitation were considered in Chapter 4. The transformation problem was outlined, using the original work of Marx and Böhm-Bawerk. Contributions to the value controversy in the last three decades were surveyed, with the linear approach of Morishima, the new solution, and Walrasian Marxism being discussed. This controversy has detracted attention from other valuable lines of Marxist inquiry. However, a number of logical solutions now present themselves. In Chapter 6, it was claimed that it is possible to separate the labour theory of value from a labour theory of exploitation, i.e. the latter need not rely on the former. This, it was suggested, is likely to be the most productive position to adopt in order to facilitate the development of Marxian economics. And accepting this point will allow Marxists to concentrate on formulating theories, and developing empirical work, which demonstrates the exploitative nature of capitalism. The question of microfoundations is significant when seeking to model class conflict and exploitation, and this was discussed in Chapter 5. Marx’s theory of surplus-value has encountered theoretical problems

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as a result of its close connection with the labour theory of value. In this model exploitation is conceived of in terms of working time, where the capitalist is able to extract surplus labour as a consequence of the ownership of productive assets. Marx’s framework developed this in the context of the historical account of primitive accumulation. Roemer, a leading analytical Marxist, has sought to develop a game-theoretic theory of exploitation and class which has rigorous microfoundations and which is based on logical deduction as opposed to an empirical or historical account. Roemer has received recognition from both Marxian and neoclassical economists. Roemer’s appeal to neoclassical economists is clear, since he has published in journals that are not generally regarded suitable for publication of Marxian work (e.g. the Economic Journal and Econometrica). Indeed, the impact of Roemer’s analysis of exploitation and class is likely to have repercussions for the future development of Marxism, as a focal point for analytical Marxist research and as a basis for methodological critique from orthodox Marxists. As was made clear in Chapter 5, in evolving and recognising the significance of the comments of his critics, in particular concerning a property-relations definition of exploitation, Roemer has strengthened his general theory. Roemer has come to acknowledge the role of an unequal exchange aspect of exploitation. In spite of such concessions, however, there are reasons why a labour theory of exploitation remains more insightful than Roemer indicates. For example, conflict over remuneration, intensity and duration of work can readily be examined using a labour theory of exploitation. In Chapter 6, Marx’s theory of absolute surplus-value was revised to take account of value-theoretic problems raised by Morishima. Defining the rate of surplus-value in aggregate, the conflict between classes was presented in terms of a conflict between collective capital and collective labour. Such an approach is also consistent with the approach to surplus-value adopted in Chapter 4. In neoclassical economics, the foundation of the theory of working hours is a rational-choice labour–leisure individual preference model. In this book it has been maintained that such a choice-theoretic model is unsatisfactory, since working hours are determined as an outcome of class conflict in which the normal and accepted hours of work are established. In the same sense as subsets of the working class may be divided (for example in the divide and rule model of Chapter 3), so, in the process of competition, capitalists have both divided and shared interests. In orthodox Marxian economics, the process of technical change raises

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the organic composition of capital, reducing the rate of profit. Although there may be offsetting factors, there is an underlying tendency for the rate of profit to fall as capitalism develops. In Chapter 7 this process was examined in the light of Okishio’s critique of Marx’s analysis. It is important to distinguish changes in the rate of profit as a consequence of technical change from changes in the rate of profit resulting from a change in the balance of class forces. Okishio (1961) did maintain that it was possible for the rate of profit to fall as a consequence of class conflict. Thus Laibman emphasises the role of a form of class struggle neutrality in establishing the Okishio theorem. The Okishio theorem presupposes that class conflict is exogenous; hence one impediment to reduction of the argument is removed. However, Okishio distinguishes changes in the rate of profit as a consequence of technical change from those caused by changes in the balance of class forces by assuming a constant real wage. With rising output as a consequence of increased productivity, this would imply a reduced wage share in national income. It would be counter-intuitive to suppose that, in such circumstances, the rate of profit would fall. However, as a method of isolating class struggle, such an approach is unsatisfactory, and Laibman’s proposal to isolate class struggle by assuming a constant rate of exploitation is preferable. Given this assumption, it follows that the rate of profit can fall as a consequence of technical change that is labour-saving in the consumption good industry. An alternative proof of Laibman’s thesis is offered, using calculus. The result does not refute the Okishio theorem, but does give an indication of circumstances that may cause the rate of profit to fall in the face of technical change.

The future development of Marxism This work has examined the relationship between reduction, rationality and game theory in Marxian economics, in the light of the critique offered by analytical Marxism. Important questions have been raised regarding explanation, units for analysis and the motivation of agents. This discussion has been prompted by the development of analytical Marxism, and it is this that has served as the reference point for this discussion. Wright has suggested that, ‘One of the hallmarks of contemporary Marxism has been the dedicated attack on dogmatism’ (1994, p.154). This attack on dogmatism by the practitioners of analytical Marxism is no doubt a worthy motivation, in that critical appraisal is likely to lead to theoretical development. Nevertheless,

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methodologically and theoretically there are serious and profound problems with the approaches adopted by analytical Marxists, and the critique of orthodox Marxism offered by analytical Marxists may yet have a more enduring effect on the future development of Marxism than the method and theory which analytical Marxists propose instead. Having rejected the assertion that methodological individualism is a universally appropriate approach to explanation, the Marxian theory of class, exploitation and the rate of profit were investigated. Three elements may be identified as being of particular significance in Marxian microeconomic theory. Marx’s labour theory of value has been rejected in favour of Morishima’s reformulation of pricing. The theory of surplus-value, or exploitation, has also benefited from Morishima’s theoretical work, and this was used to consider conflict over working hours. The relationship between property and unequal exchange was considered before finally addressing the relationship between technical change and the rate of profit. These remain theoretical questions of considerable importance in developing our understanding of the functioning of capitalist socio-economies. A non-dogmatic approach to such theoretical questions can yield fresh insights and contribute progressively to the political debate surrounding the future for capitalism and socialism. Marx’s work has much merit. However, the challenge facing Marxists is to critically assess and develop this legacy.

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Notes

1 Introduction 1

The analogy between class conflict and ‘games’ has been made in other contexts. For example the games manufacturer Avalon-Hill produced Class Struggle in the 1970s. To give a flavour of the content, the game rules state: ‘Class struggle reflects the real struggle between classes in our society. The object of the game is to win the revolution … ultimately’. In the Karl Marx House in Trier, some years ago, I also came across a game which Marx himself made to play with his children – the game was called Strike. The analogy between games and class conflict is not, thus, solely confined to the narrow, technical sphere, of Marxian economic theory.

2 Methodology of reduction 1 2

3

4

Examples of such approaches can be found among both analytical Marxists (Elster, 1989) and orthodox Marxists (Lebowitz, 1988, 1994). For an introduction to analytical Marxism see Roemer (1994b). The practicality and verification of a given reduction may also be problematic. For example, Garfinkel has suggested that the syntax of the vocabularies of A and B may not be identical. Further, this positivist approach relies upon observation, and ‘[e]ven if theory B explains all the observation sentences that theory A does, its status as a reduction would be in doubt unless it could also explain the mechanisms and postulated unobservables, the explaining entities, of theory A’ (1991, p.445). Reduction as an issue is therefore not without its practical difficulties. Statements concerning methodological individualism are commonplace in the work of many analytical Marxists. Clear statements can be found in the work of Elster (1985, 1989), Roemer (1981, 1989a) and Van Parijs (1983). Elster has suggested that the micro-foundations approach is synonymous with methodological individualism (1986, p.23). This view is incorrect if we acknowledge the existence of the anti-reductionist methodology of Wright, Levine and Sober.

124 Notes

3 Marxism and the foundations of collective action 1 2

3

4

5

6

An excellent introduction to game theory is provided by Kreps (1990). Alternatively, for a rigorous introduction see Rasmusen (1994), and for a philosophical discussion see Hargreaves Heap and Varoufakis (1995). A useful discussion of the different terms used to describe analytical Marxism, including game-theoretic Marxism, neoclassical Marxism, and rational-choice Marxism, is offered by Carling (1986). In contrast to Carling, in this chapter the term ‘game-theoretic Marxism’ is taken to refer not to the work of analytical Marxists, but rather to any attempt to apply the language and techniques of game theory to Marxian economics. Thus the game-theoretic work of analytical Marxists is a subset of this more universal body of work, which does not necessarily presuppose methodological individualism. Roemer’s position on this matter is unclear. In Roemer (1982a) class location is modelled endogenously as an outcome of instrumental optimising behaviour by individual, economically motivated, agents. Elsewhere Roemer suggests that the claim that ‘individuals act as a member of a class, rather than individuals, should be taken as a theorem in Marxian economics, not a postulate. Marx’s point is that despite the capitalist’s incarnation as a human being they are forced by the system to act as an agent for the self-expansion of capital. Workers, similarly, may have their individual yearnings and habits, but conditions of life force them to acquire a class consciousness and to act, at times, as agents of the working class as a whole and not as their own agent’ (1981, p.7; emphasis added). The notion of surplus-value will be explored in more depth in Chapter 5 and, in particular, Chapter 6. The essential purpose of the following model is to provide an example of an anti-reductionist model of class conflict, in game-theoretic terms. It is important to note that such a framework presupposes the existence and enforcement of property rights based upon power and force. The emergence of such property rights, embodied in Marx’s account of primitive accumulation, is discussed in Chapter 6. Of note is the fact that Marx was hostile to historical accounts of the emergence of clearly defined property rights based on voluntarism. Lebowitz has suggested that game theory may be a useful tool for analysing relations between classes. However, it is a ‘collective’ game that should be examined (1988, p.197). In contrast, Elster has claimed: ‘Cooperative games are logically secondary to non-cooperative games. This is not an assertion about the motivation of agents, only a restatement of the principle of methodological individualism’ (1986, p.207). Elster’s view is rejected in this book, in part on the basis of the argument in Chapter 2. This raises epistemological questions concerning time. In framing the question of distribution in terms of the time the labourer works, we can readily extend the investigation to consider conflict over the length of the working day and the intensity of labour. Theoretical problems arise if we seek to provide micro-denominated labour values, since conventionally defined labour values may sometimes be negative in systems of joint production where profits are positive (Steedman, 1977). Hence it is necessary to define surplus labour in aggregate terms for the

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economy as a whole. In such circumstances, the claim that positive profits are possible without positive surplus labour time is counter-intuitive. As King suggests: ‘if the labour force spends less time at work than is required to produce its own means of subsistence, even what Marx termed the “simple reproduction” of the economic system should be impossible, and there should be no question of maintaining a nonproducing class’ (1994, p.396). We shall assume the existence of private property rights. Marx’s analysis of the production process under capitalism takes labour power as a commodity, which the capitalist purchases and consumes productively. Thus, the labour-time of the worker belongs to the capitalist under whose control they work, and the product of the worker’s labour is accordingly the property of the capitalist. Marx’s analysis of the labour process, technically and socially, concerns ‘a process between things the capitalist has purchased, things which belong to him’ (Marx, 1976, p.292). This brings to mind the contract curve, familiar in the Edgeworthian approach to general equilibrium. Weintraub (1979) suggests that the Edgeworthian approach to general equilibrium is inherently gametheoretic. The problem of indeterminacy, as occurs in bilateral monopoly, would be fundamental to general equilibrium theory. Neo-Edgeworthian general equilibrium theorists overcome such problems of indeterminacy by appealing to the notion of the ‘shrinking core’; i.e. the range of possible final settlements (i.e. equilibrium outcomes) shrinks as the number of traders grows (for a discussion of recontracting see Negishi, 1989). Adam Smith recognised that capitalists possessed power over workers in determining the agreement over remuneration: ‘What are the common wages of labour, depends everywhere upon the contract usually made between those two parties, whose interests are by no means the same ... It is not difficult to foresee which of the two parties must, upon all ordinary occasions, have the advantage in the dispute, and force the other into compliance with their terms ... A landlord, a farmer, a master manufacturer, or merchant, though they did not employ a single workman, could generally live a year or two upon the stocks which they have already. Many workmen could not subsist a week, few could subsist a month and scarce any a year without employment’ (1970, p.169). While Smith is to be credited for this insight, it is important to note that he framed this conflict in terms of remuneration, and this does not lend itself to consideration of conflict over the length of the working day or intensity of labour, in the same way as Marx’s framework does. The ‘Ricardian socialists’ did get further than Smith in that they emphasised the role of force, fraud and political power in creating the conditions under which property incomes could result. As noted by Howard and King (1985), the Ricardian socialists also identified surplus labour as the source of profits and rent.

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4 Value, price and exploitation 1

2 3 4

5

6

7 8

The distinction between essence (Wesen) and appearance (Erscheinung) adhered to in this book, and in Marx’s method, is derived from Hegel. This has been subject to criticism by Elster (1985, p.125) who has suggested that Marx misinterprets Hegel, in that ‘appearance’ has two different antonyms. On the one hand the opposite of ‘appearance’ may be ‘hidden’, or accessible only by thought. It is in this sense that Marx used the distinction. In contrast, Elster suggests Hegel intended ‘appearance’ in the sense of the local character of appearance, and Hegel’s use of the term ‘essence’ implies the totality of interrelated appearances, not something that is behind and of a different ontological order. Throughout this work the terms ‘rate of exploitation’ and ‘rate of surplusvalue’ will be used interchangeably. We might speculate that the equalisation of the rate of surplus-value would be brought about by mobility of labour. Carling has indicated that these two pieces of work are significant for the development of analytical Marxism in the sense that it is now possible to see a range of writers, including Elster, Przeworski, Roemer, Van Parijs and Wright, who have ‘bobbed about in the wake of Michio Morishima and Ian Steedman’ (1986, p.25). The critical re-evaluation of Marx’s work and its relationship to the development of Marxian economics in the context of the ‘value controversy’ both mirrors and is connected with the development of analytical Marxism. Both Morishima and Steedman do not burden their work with textual exegesis from Marx’s writings, a feature in common with the approach of analytical Marxism. However, Morishima has produced a considerable body of work, only some of which may be considered Marxist. Moreover, Steedman’s research has predominantly been critical, building on the contribution of Sraffa. In this sense, while analytical Marxist economic theory has adopted the same standards of rigour as Morishima and Steedman, much of their work is not, as such, Marxist. In addition Morishima (1973) and Steedman (1977) do not explain their theories of price in terms of intentional explanation, rather they emphasise structural determinants in terms of input–output coefficients. Roemer has criticised Shaikh’s approach suggesting ‘it is difficult to see what the purpose of such an exercise is … Such “determination” of prices from values appears entirely formal and lacking in interesting economic content’ (1986d, p.34). Such a criticism is similar to that of Steedman by Shaikh, but Roemer does not elaborate on the detail of Shaikh’s approach. This raises an issue that warrants note. Namely, being Walrasian such an approach to pricing treats money as neutral. That said, such a criticism could also be made of some linear input–output approaches to exploitation and price. Similar criticisms have been outlined by Devine and Dymski (1989, 1992). For a defence of his approach see Roemer (1992). The positive–normative distinction is adopted here for the purpose of clarification. However, this is not intended to indicate that it is possible clearly to separate these approaches in practice. For example, in neoclassical general equilibrium theory the ethical basis for initial

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endowments is frequently left unchallenged (a notable exception being Bergson, 1938). It is, of course, as value-laden not to challenge initial endowments as it is to do so. Although neither Morishima nor Roemer adopt the same definition of exploitation as Marx, their respective treatments bear close enough resemblance to his to warrant their description as Marxian. Moreover, their approaches do not simultaneously elaborate on Marx’s treatment of absolute and relative surplus-value. But Morishima, in viewing exploitation as a function of the length of the working day, is to be credited with rigorously developing a theory of exploitation with similar intent to that outlined by Marx (1976, pp.320–416). Roemer, in viewing exploitation as a function of technology, provides a modern rigorous analysis concerned with similar issues to those raised by Marx (1976, pp.429–639). Both these treatments differ from that of Marx in that they are solely formal as opposed to historical. In addition, neither endorses a labour theory of value.

5 Marxian theories of exploitation and class 1

2

3

Roemer uses the term ‘unequal exchange’ to describe a situation in which an agent expends more labour in production than is embodied in the goods they can purchase with their revenue from production (see Roemer 1994a, p.97). In the case of capitalism this implies workers work longer than necessary labour time. Thus this acknowledges the valorisation process and the distinction between labour and labour power. By this definition, Marx’s theory of surplus-value is also an example of unequal exchange. Roemer’s work has evolved in response to criticism since publication of Roemer (1982a). This has led Houston to suggest: ‘This ongoing modification of his analysis, while leading to improvements, makes it hard to know what is fundamental’ (1989, p.175). This is unconvincing, since Roemer’s adherence to a logical-deductive method and his emphasis on property rights can be regarded as continuing and fundamental since publication of Roemer (1982a). This raises the question of Marx’s view on justice. In his account of the valorisation process Marx suggests that, since the capitalist has purchased the labour power of the worker, they have the right to consume that labour power as they wish. Geras (1985, 1992) has claimed that although Marx did not think he criticised capitalism on the grounds of justice, implicitly, he actually did: ‘Marx, as is well known, was quite impatient and dismissive of overt theoretical reflection about normative questions, condescending only rarely to engage in it himself. He was hostile, not neutral, towards the explicit elaboration of socialist ethical theory, disdained in this area the kind of rigorous examination of problems and concepts he so insisted upon elsewhere. At the same time, and despite this, like just about everyone else he was given to the use of moral judgment’ (Geras, 1985, p.62). Geras’s view can be contrasted with that of Wood who suggests that a critique of capitalism in the name of justice would enable the revolutionary ‘to deliver the keynote address at the next Democrat Convention’ (1980, p.30). Rather than criticising

128 Notes

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7

8

capitalism because of its inefficient or contradictory nature, which would require capitalism be abolished, a critique in the name of justice is indicative of capitalism being open to reform. For this reason, Wood is sceptical of critiques of capitalism in the name of justice. The claim to a conclusive result is problematic. If the poor agent has a greater initial capital endowment than they wish to employ with their own labour, why should the rich agent be required to pay to use a resource which would, otherwise, not be utilised? In addition to considering the morality of initial endowments, society as a whole may also place value on the leisure pursuits enjoyed by agents. One general area on which Roemer and Wright disagree concerns the nature of exploitation. According to Wright: ‘Exploitation models of income inequality regard the income distribution process as fundamentally relational’ (1994, p.27, emphasis added). Roemer contradicts this thesis: ‘It is important to note that exploitation is not defined relationally. The statement “A exploits B” is not defined, but rather “A is an exploiter” and “B is exploited.” Exploitation, as I conceive it, refers to the relationship between a person and society as a whole as measured by the transfer of the person’s labor to the society, and the reverse transfer of society’s labor to the person, as embodied in goods the person claims’ (Roemer, 1994a, p.66). Roemer’s claim is problematic in that, while he defines exploitation as a relationship to society as a whole, the latter is a closed set. Obtaining a subset excluding those who are (purely) self-employed (i.e. the petty bourgeois in Table 6.1), the complement of the exploiters are the exploited. In this sense exploitation is an inescapably relational property. Wright describes Roemer’s work as ‘one of the few genuinely novel contributions to the Marxist theory of exploitation and class to be produced in recent years’ (1994, p.71). In contrast, Dymski and Elliott, in evaluating Marx and Roemer’s alternative perspective on exploitation, have suggested that: ‘Roemer ignores Marx’s own rich textual argument and imports into Marx’s dynamic and historical system the narrow methodology of Walrasian general equilibrium’ (1988, p.30). According to Wright (1994, p.21) the basis for inequality in material welfare can be explored in terms of two broad conceptualisations: achievement models and exploitation models. An achievement model views income distribution as a process of agents acquiring wealth as a return to their own efforts. In contrast, exploitation models, which lie at the theoretical heart of the orthodox Marxist critique of capitalist economies, view the income distribution process under capitalism as fundamentally exploitative in some way. One other criticism of Roemer, and indeed analytical Marxism generally, concerns the neglect of other emancipatory projects such as those which seek to remove exploitation by gender or ethnicity. Carling has suggested: ‘there is a remarkable – seemingly total – omission of reference either to feminist theory or to the general topic of sexual difference’ (1986, p.56). We might therefore suggest that Roemer’s theory is not a general theory of exploitation and class, but rather a general theory of class exploitation.

Notes

129

6 Class conflict and working hours 1

One should note that ‘unpaid labour’ does not, in Marx’s analysis, refer to labour performed in the non-market (household) sphere of the economy. However, framing questions of distribution in the market (capitalist) sphere of the economy in terms of time does give a plausible route to integrating theories of capitalist exploitation, with those concerning labour which is unpaid in the household sector (see Laibman, 1992, pp.55–70).

7 Reduction, rationality and the rate of profit 1

2

3

This point is stressed by Laibman, who suggests that ‘the Okishio theorem assumes an environment of atomistic, unrestrained competition among individual capitals. This is the strong assumption of the capitalist process in its fullest development, and is clearly the correct basis on which to settle the issue of the falling rate of profit’ (1992, p.106). One should note that atomistic competition does not entail perfect competition, as defined in neoclassical economics. Atomistic competition implies each commodity is supplied by a large number of producers, acting individualistically, bound together neither by open collusion nor unconscious class loyalty; it entails that any capitalist is free to enter any line of activity they choose. This raises the problem of Marx’s theory of wages. The presumption that Marx maintained that real wages tend to be constant is contentious. Mandel has argued that Marx’s critics confuse the value of labour-power with the category of real wages (Mandel, 1976, p.70). It is important to recognise that standards of living are not at a biologically determined level in Marx’s Capital, and are, in part, determined by habit and custom, which form a ‘moral-historical’ component of the value of labour-power (p.68). Accepting such a historical component implies that the assumption of a historical tendency for constant real wages is unwarranted. Of course there are other Marxian theories of crisis. For example, economic growth may change the balance of class forces in favour of the working class, resulting in an increase in real wages. Also, it may be that the capitalist class will be unable to realise surplus-value owing to underconsumption. Finally, disproportionality between sectors arising from the atomistic and uncoordinated nature of capitalist markets, may represent a further cause of failure to realise surplus-value, resulting in crisis.

130 Notes

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131

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138 References

Index

139

Index

Alberro, J. 100 agency 39, 82 anti-reductionism 8, 11, 13, 16, 19–27, 30, 32n4, 60, 101 atomism 8, 16–7, 118 Baran, P. 93 Barton, J. 85 Bergson, A. 59n8 Bertrand, J. 119 Bhaskar, R. 32 Blaug, M. 18 Böhm-Bawerk, E. 8, 45–7, 119 Booth, D. 39 Bortkiewicz, L. von. 47, 57–8 Bowles, S. 77, 78 Breslow, L. 85 Buell, P. 85 capital: constant capital 42–6, 67, 102; fixed capital 42, 53, 58, 102; market for capital 55; total capital 42, 48, 102; variable capital 42–3, 47, 65–68, 95, 102, 112 Capitalism 1–6, 12, 20–3, 27, 32n7, 34–5, 39, 60–2, 64n1, 67, 74, 76, 80n7, 102–3, 119–22 capitalist: class 7, 27, 30n3, 32–5, 60, 85–97, 99, 110n3, 111, 120; economy 47–50, 99; individual 6–9, 30n3, 32n7, 34n9, 35–8, 42, 44, 48, 54–5, 66–8, 92–3, 99–115, 120

Carchedi, G. 61, 87 Carling, A. 30n2, 47n4, 80n8 class formation 68–74 class conflict: over intensity of labour 32n6, 34n9, 68, 85, 87, 103, 120; over wages and profits 34n9, 35, 38, 48, 85, 87, 90, 92–7, 103, 105–6, 118; over working hours 8, 33–5, 49, 50–4, 59n9, 66, 68, 76, 77, 85–97, 101, 103, 111, 120, 122. Cohen, G. 49, 93 collective action 7–8, 29–40, 118 contradictions: of capitalism 4, 99 (see also falling rate of profit and divide and rule); game theoretic 30, 39, 99 (see also prisoners’ dilemma), in Marx 42–50, 56 Cooper, C. 86 Cournot, A. 119 Crafts, N. 86 Devine, J. 55n7 divide and rule 35–40 Dimand, M. 119 Dimand, R. 119 Dobb, M. 100 Duménil, G. 8, 56, 58 Dymski, G. 55, 80n6 economics: discipline 7, 11–14, Marxian 1–9, 11–12, 30, 40–1, 47n4, 50, 58, 60–1, 63, 80–1,

140 Index 117–121; neoclassical 3–7, 30–1, 50, 59–60, 81, 87, 89, 101n1, 117–120 Edel, M. 38–39 Elliott, J. 55, 80n6 Elster, J. 8, 12n1, 14, 17–19, 22–5, 30–2, 41n1, 47n4, 49, 73, 79 equilibrium: general equilibrium 5, 8, 12, 25, 34n8, 41, 49, 50, 54–5, 59n8, 60, 74, 80n6; Nash equilibrium 30, 37; outcomes 33, 49, 53, 57–8, 61, 70, 72, 77, 100, 105, 107, 115; use and criticism of 5, 8, 61 Ernst, J. 100–1 exploitation 41–83; bureaucratic exploitation 81 (see also status exploitation); feudal exploitation 75, 78; and the Fundamental Marxian Theorem 6, 54, 59; socialist exploitation 75, 78; status exploitation 78 Foley, D. 8, 56–8 Folkard, S. 85 Freeman, A. 61, 100–1 Fried, Y. 86 Friedman, J. 81–2 Friedman, M. 5 game theory 2–3, 8, 11–12, 24, 29–40, 64, 81–3, 118–19, 121; collective games 32n5, 82; cooperative games 31, 32n5, 82; non-cooperative games 3, 31, 32n5, 82 Garfinkel, A. 14–15, 21–2, 32 Geras, N. 67n3 Grossman, H. 100 Gintis, H. 77 Hargreaves Heap, S. 30n1 Hicks, J. 117 holism 8; methodological holism 8; radical holism 8, 16, 18 hours of work: see class conflict over working hours Houston, D. 64n2 Howard, M. 15, 34n9, 56–8

individualism: methodological 3, 5, 8, 12–13, 16–18, 25–7, 30–2, 82, 101, 118–19, 122; political 18 intensity of work: see class conflict over intensity of work joint production 58, 83, 30n3 King, J. 15, 32n6, 34n9, 56–8 Kliman, A. 100 Kreps, D. 30n1 labour time: necessary labour time 9, 39, 51–5, 59, 64n1, 67–72, 80, 86–8, 94–5, 111–12; surplus labour time 2, 6, 32–4, 54–5, 68, 73–4, 88, 120; see also class conflict over working hours Laibman, D. 9, 61, 72–3, 87, 88n1, 90, 97, 99–115, 121 Lazear, E. 7 Lebowitz, M. 12n1, 31, 32n5, 81–2, 118–19 levels of analysis: class as a level of analysis 29; individual-level explanations 12, 18–19, 22, 31, 40; and unity of science 13–16 Levi, L. 86 Levine, A. 8, 12–13, 16–27 Lévy, D. 8, 56, 58 Lipietz, A. 8, 56 Little, D. 12, 17, 118 Maarek, G. 30, 32–3, 60 Mandel, E. 103n2 market: for labour power 7, 59, 69–73, 77, 80; credit market 69, 72–3 Marx, K. 1, 3–4, 6–9, 11–12, 24, 29–32, 34n9, 38–50, 54–68, 74, 80–1, 83–90, 92–3, 95, 99–100, 102–4, 119–22 Marxism: analytical Marxism 3–4, 7–8, 11–18, 24–7, 29–31, 47n4, 49–50, 68, 74, 80, 117–120; game-theoretic 8, 30–5, 39–40, 63–4, 81–3, 119–20; orthodox Marxism 4–5, 7, 12, 24–6, 29, 31, 63, 77, 80n7, 81, 101, 117, 120, 122

Index materialism 20–1 microfoundations 3, 8, 11–27, 31, 54, 67–8, 82, 101, 117–20 mode of production: capitalist 64, 80, 102; communism 1–2, 6; feudalism 6, 64, 65, 75, 78; socialism 1, 6, 11, 64, 74–6, 78, 81, 122 Mohun, S. 56 monopoly 7; bilateral monopoly 8, 30, 33, 34, 39, 60, 89; over means of production 7 (see also property, private) Morgenstern, O. 119 Morishima, M. 8, 29, 47, 50, 54, 59, 61–2, 88, 100, 119–20, 122 Moszkowska, N. 100 Nakatani, N. 100 Naples, M. 61 Negishi, T. 34n8 Neumann, J. von. 119 Okishio, N. 9, 59, 99–115, 121 Oppenheim, P. 13–5 organic composition of capital 42–5, 53, 99, 102, 104, 121 Perelman, M. 65–6 Perkin, H. 65 Persky, J. 100 Philp, B. 86 Prebble, J. 65 preferences 2, 7, 22, 31, 79, 85–94, 97, 118 prices: equilibrium 49, 53, 57, 72, 100, 105; price vector 53–4, 69, 72, 107; of production 44–8, 57–8; relative 45, 52 primitive accumulation 2, 32n4, 63–6, 80, 120 prisoners’ dilemma 6, 9, 38–9, 99, 118 profit rate: equalisation 7, 42–3, 54–5, 57, 99, 105; falling 1, 7, 9, 90, 99–115 property: emergence of property rights 3, 32n4, 64, 66 (see also primitive accumulation);

141

private 34, 32n7; relations 8, 60, 63–6, 74–80, 120 Przeworksi, A. 47n4, 60, 74 Putnam, H. 13–5 Rasmusen, E. 30n1 rational choice 27, 30n2, 101, 118, 120 rationality 5, 7, 24, 30, 39–40, 69, 101, 106, 118, 121 reductionism 8, 11–27, 29–32; token and type reductionism 19–27 (see also antireductionism) Robinson, J. 100, 103 Roemer, J. 6, 8, 12n1, 17n3, 24–5, 30–1, 41, 47n4, 49–51, 54–5, 59–64, 68–83, 100, 120 Samuelson, P. 47, 58 Shaikh, A. 48–9, 100 Sharom, A. 86 Shimomitsu, T. 86 Smith, A. 34n9, 66 Sober, E. 8, 12–13, 16–27 Sparks, K. 86 Sraffa, P. 47 Steedman, I. 32n6, 47–8, 49n5, 54, 58, 100, 103 Sturrock, J. 16 Sugden, R. 101, 118 surplus-value 1, 6–9, 30–5, 39, 41–68, 74, 80, 83, 86–90, 95, 102–4, 110n3, 111–13, 119–122 (see also exploitation); absolute surplus-value 59, 85–97, 102–3, 111, 120; relative surplus-value 59, 68, 85, 88 Sweezy, P. 93, 100 transformation problem 8, 41–62, 119 values 1, 8, 41–62, 66–9, 72–3, 77, 83, 117, 119–22 (see also surplus-value): exchange value 4, 41, 66, (see also prices); use value 66–67; vector of labour values 53, 70

142 Index Van Parijs, P. 17n3, 24–5, 31, 47n4, 100, 103 Varoufakis, Y. 30n1, 101, 118 wages: hourly wage 35, 85, 88, 94, 96; money wage 57, 105; piece wages 38; real wage 9, 35, 48, 50, 53, 58, 87, 89, 99–112, 121; salaries 94; value wage 111–14; weekly wage 94

Weintraub, E. 34n8 Weizsäcker, C. von. 25 West, E. 89 Wood, A. 67n3 working class 7, 30n3, 32–38, 60, 86–95, 110n3, 119–120 (see also class formation and divide and rule) Wright, E. 8, 12–13, 16–27, 39, 47n3, 74, 78, 80, 121