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

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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