Marxism and the Labor Theory of Value

Jon Elster concluded his Making Sense of Marx with the claim that ‘It is not possible today, morally or intellectually, to be a Marxist in the traditional sense’ (1985, p.531). Acceptance of this statement depends, of course, on what is meant by traditional Marxism. Elster makes it clear that what he means by traditional Marxism is that ‘intellectually bankrupt’ and ‘non-scientific’ economic theory associated with the labor theory of value, the theory of the falling rate of profit, and ‘the most important part of historical materialism’, the ‘theory of productive forces and relations of production’ (1986, p.188-194). In place of these redundancies, Elster proposes a new Marxism founded upon logically consistent microfoundations (1982). To achieve this reconstruction, he explicitly favours the tools of neoclassical analysis; a ‘truly scientific’ methodology that posits the existence of economic institutions (for example, prices and markets), then attempts to show that they are compatible with the actions of individual agents who engage in rational calculated satisfaction-maximizing exchanges.

Defending a position very similar to Elster’s, Roemer (1989a, p.384) provides the following summary of Marx’s economic theory and its late twentieth century reconstruction:

Marx thought that the easiest way to explain how the surplus was produced was to assume a labor theory of value - that is, that prices of commodities were proportional to the amount of labor embodied in them. Exploitation took the form of workers producing goods embodying more of their labour than was embodied in the wage goods that they received in return, that surplus labour became monetized through the price system in a simple way because prices were assumed to be just proportional to the amounts of labor embodied in commodities. But it has long been known that equilibrium prices in a market economy are not proportional to the amount of labor embodied in goods; it was therefore necessary to ask whether the Marxist theory of accumulation could be made more precise even though the labor theory of value was wrong. This has been done during the last twenty years, by applying techniques of input-output analysis and general equilibrium theory, by Michio Morishima and others. It is, in my view, a winning point for Marxism that its theory of capitalist accumulation can be liberated from the false labor theory of value. Some Marxists, however, persist in viewing this reconstruction as heretical, dispensing as it does with the labor theory of value.

In considering the implications of these refutations of Marx’s value theory, it is important to recognize their origins in the ‘value controversy’. As Itoh recently suggested, the value controversy is more than an ‘internal debate among Marxians’ in so far as it involves a ‘three-way confrontation among neoclassical, neo-Ricardian and Marxian schools’ (1992, p.53). The controversy originated in the conceptual and mathematical framework set out by von Bortkiewicz and turned on the question of whether Marx’s two aggregate equalities - total profit and surplus value, and total price of production and value - could be made to determine prices simultaneously (Sweezy, 1966). Then, in the 1970’s, neoclassical theorists initiated a critique, showing that Marx’s values transform to prices only under unrealistic assumptions of zero surplus value, or a uniform organic composition of capital in all industries. Following this line, Morishima explored the implications of input-output analysis for mathematical understandings of the transformation problem, albeit at ‘some expense of its “historical” [labour theory] aspects’ (Morishima & Catephores, 1975, p.309). Finally, Sraffians entered the fray, with their claim that if equilibrium prices can be deduced from physical data of reproduction, Marx’s labour theory is in any case redundant as a price theory (Steedman, 1977). According to Itoh, these ‘criticisms had an unexpected effect among young Western scholars, who now realized that Marxian economic theory, no less than neoclassical or neo-Ricardian economics, might be worthy of mathematical analysis’ (1992, p.59).

In Itoh’s view, Sraffian theory acted on the value controversy like a ‘double-sided mirror’ reflecting inconsistencies in both neoclassical and Marxian economics: in this sense, ‘fundamental methodological differences among contemporary Marxian theorists arose from ‘their reactions to other perspectives within the triangle’ (1992, p.53). The views of the analytic school represent one contemporary reaction to the neoclassical/Sraffian critique, the assumptions of which are implicit in Roemer’s argument that the labour theory of value is either ‘false’ or imprecise or irrelevant, so Marxian theory would be all the better for mathematical reconstruction. An alternative reaction aims to refute the redundancy critique by stressing the principle virtue of Marxian theory: its focus on capitalist relations of production. According to this view, the labour theory of value - unlike the Sraffian and neo-classical approaches - is not a model for the determination of equilibrium prices, but a model designed to reveal the social relations based human labour that lies behind the phenomena of prices (Hunt, 1990; Lebowitz, 1988, 1994; Mandel & Freeman, 1984; Medio, 1972). If an explanatory principle underlies the task of economics as a social science, then far from being redundant, the labour theory of value is essential (Itoh,1992, p.60).: what is at stake is really a question of what the proper tasks of theory are: is the social content of the labour theory of value to be considered a virtue in its own right, apart from the issue of its logical correctness or consistency? This question is not amenable to a formal “scientific” solution, but it is not even admitted as a question within the narrowly limited methodological scope of neoclassical and neo-Ricardian theories.

At the heart of the contemporary defence of Marx’s value theory is a much older claim that methodology provides the ‘decisive difference’ between Marxism and ‘bourgeois social science’ (Lukacs, 1971). In a classic articulation of this position, Lukacs provided a definition of traditional Marxism entirely opposed to Elster’s version. According to Lukacs traditional Marxism ‘does not imply the uncritical acceptance of the results of Marx’s investigations. It is not the “belief” in this or that thesis, nor the exegesis of a “sacred” book. On the contrary, orthodoxy refers exclusively to method’ (ch. 27, p.1). The distinguishing feature of the Marxian method is its focus on the continuous dialectical interaction of the parts with the whole: this ‘point of view of totality’, this refusal to reduce analysis to the observation of the individual (or part) in isolation from the social context (or whole) was, for Lukacs, ‘the bearer of the principle of revolution in science’ (p.1).

The methodological stance adopted by the analytic school involves an explicit challenge to both traditional and contemporary concepts of Marxism as methodology. In his paper on the subject, Roemer wrote derisively that what constitutes a Marxian method is not even a ‘useful question to pose’ because ‘the techniques that ideological social science uses’ are not in themselves ideological; rather they may be usefully employed by ‘scientists of many different ideological persuasions’ (1989a p.377). He goes on to make the controversial argument that Marxism can develop ‘as a social science’ only when its central concepts are expressed as theorems, and elucidated in formalist models designed to prove derived postulates. In short: ‘Methodological individualism and the equilibrium method are essential to Marxian analysis’ (p.378). In the next two sections, I will try to articulate the ‘analytic’ position on methodology, and its practical implications for Marxian economics.

Methodological Individualism and Property Relations

In part, the analytic focus on consistency identified by Roemer comes from his stated objective to capture the Marxian ‘world view’ in ‘a rigorous and axiomatic fashion’ (Roemer, 1986c, p.200). This objective imposes certain requirements. The first of these requirements is a commitment to methodological individualism. As an epistemological position, methodological individualism upholds the categorical imperative that each individual possesses intrinsic properties that are essentially or ontologically prior to any particular society: ‘The parts have intrinsic properties, which they possess in isolation and which they lend to the whole’ (Levins & Lewontin, 1985, p.269; cited Lebowitz, 1988, p.194). Although it is possible to adopt methodological individualism without recourse to rationality, where ‘rational choice is not possible there is a fundamental indeterminacy in human behavior’ (Roemer, 1989a, p.379). In practice, economic theories based on the individualist premise almost always imply that each individual action is ‘a single instance of, a reflection of, the underlying uniformity of all actions as calculatedly rational efforts to optimize subject to constraints’ (Hunt, 1993, p.93). Thus, neoclassical analysis pre-supposes isolated individuals with exogenously given assets and skills; these individuals choose to enter into relations of exchange in order to satisfy exogenously given wants; and an economy is the sum total of their rationally chosen arrangements for exchange.

This is the overt position adopted by Elster (1985) who opened his Making Sense of Marx with the statement that: ‘all social phenomena - their structure and change - are in principle explicable in ways that only involve individuals - their properties, their goals, their beliefs, and their actions’. Thus, economic explanation begins with ‘a set of individuals all equipped with the same amount of labour power… but differently endowed with other factors of production’ (p.172). Faced by unequal endowments, individual agents have a single option open to them: exchange. They can exchange some of their assets (for example, labour power) for assets owned by other individuals. Alternatively, individuals can use their assets to exchange with nature: that is, to produce. As Hunt (1993) points out, Elster’s conceptual framework, is remarkably similar to that of neoclassical indifference and production functions, in that exchanges with other individuals (social relations) and exchanges with nature (technological relations) are analytically identical, embodying exogenously given preference orderings. In short, exchange is located by default at the center of economic theory because it provides ‘a mechanism, to open up the black box and show the nuts and bolts, the cogs and wheels, the desires and beliefs that generate the aggregate outcomes’ (Elster, 1985, p.5).

Roemer’s writings on method (1986c) make the centrality of exchange explicit, arguing that: ‘What Marxists must provide are explanations of mechanisms, at the micro-level, for the phenomena they claim come about for teleological reasons’ (p.192). Just as Elster rejects macro-level ‘supra-individual entities that are prior to individuals in the explanatory order’ (1985, p.6), so Roemer rejects all Marxian attempts to assign epistemological priority to the determination of structure within which the individual acts. He argues, for example, that the entities ‘capital’ and ‘capitalist class’ fail as explanatory concepts because the precise mechanism whereby the capitalist system influences individual action cannot be specified: ‘there is no agent who looks after the needs of capital’ (1986c, p191). His own theory departs unambiguously from micro-foundations to ‘explain’ economic phenomena ‘by deriving them from logically prior data’ defined as ‘differential ownership of the means of production, preferences and technology’: ‘Everything is driven by these data; class and exploitation are explained to be a consequence of initial property relations’ (1986b, p.178).

Roemer’s methodological position leads him to the controversial claim that his ‘property relations’ approach is superior to Marx’s ‘surplus value’ approach. Roemer’s argument is essentially this: the labour theory of value has no place in economic explanation, because (1) collective categories of ‘labour’ and ‘capital’ are analytically non-existent, and (2) theorems of ‘exploitation’ and ‘class’ can be deduced mathematically from data without recourse to a value theory. Two conclusions follow: firstly that ‘the fundamental feature of capitalist exploitation is not what happens in the labour process, but the differential ownership of productive assets’ (1982a, pp.94-95); and secondly, that exploitation is independent of the historical specificity of productive relations: ‘The historical process which gives rise to the initial endowments where my model begins is not the subject of my analysis. That is a topic for an historian’ (1986b, p.138). A topic for an economist posits a pre-existing economic institution - either a labour market or a credit market - and proceeds to analyse constraints faced by atomistic maximizers who have differential endowments of assets. This is what Roemer does in a work rightly considered by proponents and opponents alike as the centrepiece of analytic Marxism.

Roemer’s Theorems of Exploitation and Class

Discussing A General Theory of Exploitation and Class, Elster argued that Roemer’s ‘pathbreaking’ achievement was precisely in ‘generating class relations and the capital relationship from exchanges between differently endowed individuals in a competitive setting…. The overwhelmingly strong argument for this procedure is that it allows one to demonstrate as theorems what would otherwise be unsubstantiated postulates’ (1985, p.7). In other words, Elster considers Roemer’s genius to be his reformulation of Marxian concepts within the conventional methods of economic methodology - a reformulation based on assumptions of individual utility maximization, where equilibrium is a logical requirement (Roemer, 1989a, pp.380-381):

An equilibrium is a vector of actions, one for each individual, satisfying two conditions: that (1) for each individual i, the action that it takes is feasible for it, given the actions of the other units, and (2) that the outcome for society of the vector of actions is socially feasible…. Should an equilibrium of a model not exist, then the model cannot be a reasonable model of a social system… Thus, checking for the existence of an equilibrium is the first check for the consistency of the model, which is a necessary condition for its being a possible model of society.

Accordingly, Roemer begins his analysis of class and exploitation with a general equilibrium model of an economy in which an economic agent is defined as having ‘a utility function, an endowment of labour power and alienable productive assets’ (Roemer, 1989a, p.390). He then specifies class formation as the logical consequence of a process in which individuals - facing differential endowments of assets - optimize subject to their particular wealth constraints. In his model economy ‘agents choose their own class position: it is the optimal pattern for them, facing the prices and resource constraints that hold’ (1989a:390). Thus, pure capitalists, will realize an optimal solution by operating productive enterprises entirely with hired labour; pure proletarians will derive all of their income by selling their labour on the market. In the middle are other categories: small capitalists who hire labour, but also contribute labour themselves; petit bourgeois or self-employed labourers; and mixed proletarians who, in addition to working for themselves also hire themselves out as labourers.

The ‘strong’ argument comes when Roemer introduces a labour market into his model of rational economic agents facing wealth constraints. The model postulates that, as a consequence of optimizing behaviour, those individuals with low endowments will exercise autonomous preferences by selling labour-power; that is, they will be ‘exploited’ in the classical Marxian sense that the labour they contribute to society’s productive process will exceed the labour embodied in the commodity bundle they consume. By contrast, those who have high initial endowments will hire labour-power and will be ‘exploiters’; that is, the labour embodied in their consumption commodity bundle will be less than the labour they contributed to the social process. To relate these two decompositions of society - the class decomposition and the exploitation decomposition - Roemer introduces his Class-Exploitation Correspondence Principle (CECP). On the basis of this principle he derives a mathematical proof of the central proposition of Marxian economic theory - the selling of labour power is associated with exploitation.

Nevertheless, as Lebowitz (1988) points out, Roemer does not arrive at the same conclusion as Marx. In Roemer’s model, as in neoclassical theory, the individual’s economic choice is over income and leisure. Key points of difference with classical Marxian theory arize as a result: (1) the labour market transaction as a criteria for determining class emerges after the fact, as a consequence of an individual’s optimizing behaviour facing competitive commodity markets; and (2) an exploited agent is not defined as one who is compelled to sell labour power, but an individual who chooses to expend more labour in production than is embodied in the commodity bundles that he or she can purchase with the wages so obtained. Thus, ‘relations between exploitation and class that were taken as definitional in the original Marxian formulation emerge in this model as theorems deduced from more primitive characterizations of agents’ (Roemer, 1989a, p.390). Exploitation and class are derivatives of the model, and depend crucially upon the unequal distribution of productive assets, and the assumption of simultaneous market clearing. Proof of the CECP depends, for example, on the definition of labour values after equilibrium prices are known. In a classic inversion of Marxian logic, labour values come to depend on price (1989b, p.92):

Suppose that there is enough endowment in aggregate so that, were it divided equally among the people, each person could produce his subsistence needs in six hours. In the private ownership economy, prices established in a market for commodities allow agents to trade inputs… and to trade outputs [in accordance with a production plan that is subject to a wealth constraint]… A price vector p is an equilibrium for this economy if, when each agent chooses his optimal production plan subject to p, the market for production inputs clears, and the market for trade in produced commodities after production clears: each agent ends up with his desired subsistence bundle. It can be proved that at an equilibrium, some agents (the ones whose initial endowments are small) work more than six hours, and others (the ones whose initial endowments are large) work less than six hours. Exploitation in the unequal exchange sense, occurs although there is no labor exchange of any kind; the labor transfer occurs entirely through the trade of produced commodities.

The first implication of Roemer’s inversion of the classic Marxian postulate of equal exchange under unequal relations of production, is the conclusion that the sources of exploitation are to be found not at the point of production, but in the realm of commodity circulation ‘if there is trade from an unequal initial distribution’ (1989b, p.305). The controversial proof comes to fruition where Roemer substitutes a credit market for a labour market, arriving at a functionally equivalent result: those with low endowments hire capital to produce and are exploited since their labour (in the form of rent) buys commodity bundles for those who do not themselves labour productively; exploitation exists even where labourers control the production process and own the output produced. On this basis Roemer introduces his ‘isomorphism theorem’: ‘truly it does not matter whether labour hires capital or capital hires labour: the poor are exploited and the rich exploit in either case’ (Roemer, 1982a, p.93).

From this theorem, Roemer derives the ‘heretical’ proposition that ‘the fundamental feature of capitalist exploitation is not what happens in the labour process, but the differential ownership of productive assets’ (94-95). In essence, the exploitation of a ‘coalition of agents’ (S) by its compliment (S`) is given as a function, not of production, but distribution (1982b, p.285):

(1) If S were to withdraw from society, endowed with its per capita share of society’s alienable property (that is, produced and non-produced goods), and with its own labor and skills, then S would be better off (in terms of income and leisure) than it is at the present allocation; (2) If S were to withdraw under the same conditions, then S` would be worse off (in terms of income and leisure) than it is at present; (3) If S were to withdraw from society with its own endowments (not its per capita share), then S` would be worse off than at present.

The objective of this distributional measure of exploitation is to ‘compare how well a coalition is doing with how well it would be doing in a counterfactual situation where differential ownership of the alienable means of production is abolished’ (1982b, p.213). The counterfactual in Roemer’s property relations approach is intended to generalize the Marxian theory of exploitation beyond the specifics of the capitalist labour process to account for all modes of production in which there is an unequal endowment of productive assets and a factor market. The demonstration of universality is provided in A General Theory of Exploitation and Class (1982a), where Roemer makes clever use of counterfactual property relations to specify socialist, feudal, neoclassical and status exploitation. In all cases, exploitation is arrived at in a game theoretic way, by specifying the payoffs available to coalitions under different counterfactual regimes. In all cases, for exploitation to hold, one coalition must be gaining at the expense of another in accordance with the specified functions. Given these specified functions, comparison of exploitative relations under alternative property regimes is made possible.

Roemer’s derivation of exploitation from property relations alone, can be compared with Marxian exploitation, considered to be inherent in any society where one class possesses the means of production and utilizes the labour of a subordinate class, who do not possess the means of production. In this view, exploitation is linked into the labour process through the proposition that labour is the origin of value. Briefly, Marx argued that workers are coerced through capitalist control of the productive process to produce surplus value which is expropriated by the capitalist class. Surplus value is extracted either by extending the hours that must be worked over and above the time required to produce the worker’s socially necessary subsistence bundle (embodied in the wage), or by intensifying the labour process through capital investment in technology. Exploitation is therefore unavoidable under the capitalist mode of production. Even if workers receive their ‘marginal product’, they are still exploited, and capitalists are the exploiters, never the exploited.

Roemer’s rejection of classical Marxian exploitation theory is based on the logical conclusions of a market in perfect symmetry: (1) through exchange all commodities are exploited (they yield up exchange-value in excess of an original value), so the exploitation of labour power under capitalism cannot explain profits and accumulation; (2) workers and machinery are indistinguishable, since both have the properties of being commodities, and both expend activity in production; and (3) property relations precede exploitation, so exploitation is a derivative that cannot be legitimately used to explain property relations (Roemer, 1985). In so far as Roemer’s ‘distributive’ definition of exploitation is based on an inversion of classical Marxian determination with respect to value, his conclusions are logically valid. But, what happens to the Marxian theory of exploitation once the particularities of capitalist production have been obliterated in favour of a universal formalism pertaining to all societies in which there are unequal distributions of wealth?

Characteristically, it is Elster who most succinctly draws out the implications of the analytic Marxist argument: ‘Roemer’s argument is an irrefutable objection to the “fundamentalist” view that exploitation must be mediated by domination in the labour process’ (1985, p.181). Since exploitation is not inherent in the structural features of capitalist production, the property relations approach ‘demonstrates, I think conclusively, that exploitation is not inherently wrong’ (Elster, 1986, p.98). By ‘inherently wrong’ it must be assumed that Elster refers to a normative judgement that he attributes to the ‘fundamentalist’ view of exploitation as associated with expropriation, domination, and alienation. By contrast, analytic Marxists are said to judge exploitation unjust, only because ‘exploitation has almost always had a thoroughly unclean causal origin, in violence, coercion, or unequal opportunities’ (p.99). It follows that ‘exploitation is legitimate when the unequal capital endowments have a “clean” causal history’ (p.99).

So, when is exploitation just? Roemer maintains that ‘we require knowledge of the justice of property relations to pass judgement’ (1989b, p.93). He posits two individuals, Karl and Adam, who have equal initial endowments of productive assets, but different preferences over leisure and income: Karl prefers a commodity bundle containing more of the former and Adam prefers a commodity bundle containing more of the latter. As a result, Adam works hard in period one, while Karl expends his capital stock. In period two, Adam hires Karl to work for him. Is Karl unjustly exploited?

Answering the question, Roemer makes it clear that he no longer considers the post-withdrawal welfare of coalition S to be an adequate measure of exploitation; rather, the judgement of exploitation rests upon the ‘moral status’ of the original property relations that give rise to conditions of unequal exchange: ‘if Karl knew what the consequences of his leisure-taking in period one would be, and if his preferences were autonomously formed under conditions of equal opportunity… we cannot call this outcome exploitative…(1989b, p.94). In what may be considered an ingenious application of Rawlsian theory, Roemer views Adam’s purchase of Karl’s labour power as fair, given the ‘justice [equality] of the initial distribution and the autonomous formation of preferences’ (1989b, p.94; my italics). Hence, exploitation reduces to the contingent character of original accumulation, where the key question is whether property rights were unfairly violated.

In distinguishing his mature ‘property relations’ approach from his earlier ‘unequal exchange approach’ Roemer affects a shift away from the technicalities of exchange, towards issues of abstract justice. In the mature theory, exploitation is derived in terms of ‘the distributional consequences of an unjust inequality in the distribution of productive assets and resources’ (1985, p.65). In affecting this shift, Roemer becomes increasingly aware that, ‘the lines drawn between contemporary analytic Marxism and contemporary left-liberal political philosophy are fuzzy’; indeed, ‘it is not at all clear how analytic Marxists will differ from non-Marxist philosophers like Ronald Dworkin, John Rawls, and Amartya Sen’ (Roemer, 1986c, pp.199-200). Given the questions that interest analytic Marxists, Roemer candidly admits that he cannot say ‘what is Marxist and what is not’ (Roemer, 1989a, p.377). Predictably, critics have responded by challenging analytic Marxists to explain their appropriation of the term ‘Marxist’ in their efforts to reduce Marxian definitions to non-Marxian theorems? More importantly, do the resulting theorems in any way generate insights or propositions relevant to a Marxian analysis of contemporary capitalism (Hunt, 1993; Lebowitz, 1988, 1994)?

The Critique of Method, and the Method of Critique

In that view all class societies are characterized by the expropriation of a surplus from a large class of direct producers by a small class of property holders. The bourgeois view of history is, in contrast, that each factor earns its appropriate return. Each view represents, I think, a possible world, and hence I think consistent models can be constructed to formalize the insights of each view. For that reason, it is not useful to criticize neoclassical economics for its possible inconsistency (which is what the so-called Cambridge controversy was about); the criticism must be, more fundamentally, of the view of history which neoclassical models reinforce… I think one’s view of history implies the models one builds, and if the models are good, they will clarify the ethics whose root lies in the actual history.

The first difficulty for Roemer is that Marxists are unlikely to accept his bizarre definition of Marxism as ‘belief’ in the injustice of capitalism, or a product of historical curiosity divorced from ‘economics’. As Itoh (1992) explicitly argues, classical Marxists reject any claim to the ethical superiority of Marxian theory; on the contrary, they almost unanimously favour a methodological distinction between Marxian political economy and its rivals. Moreover, Marx refuted the views of theorists such as Proudhon, who argued that the capitalist system would be fair and just if prices were set in proportion to embodied labour quantities. By showing that exploitation did not arize through the exchange process, even in the unlikely event that equilibrium prices are proportional to values, Marx debunked the notion of distributive justice embodied in utopian socialist thinking.

The second difficulty pertains to the hypocrisy of Roemer’s view on ‘consistency’: it is one thing to level a charge of inconsistency against Marx’s value theory, and quite another thing to claim that ‘it is not useful’ to criticize the inconsistency of neoclassical utility and production functions - particularly when those inconsistencies are part and parcel of Roemer’s own approach. The whole question of consistency is, in fact, far more complex than Roemer’s focus on formal logic allows. In its broadest conception, consistency refers not only to the logical relationship of theorems to postulates, but also to the question of whether a particular theoretical structure provides acceptable solutions for the tasks set for it. That is, the definition of consistency must be extended beyond the question of the internal coherence of a theory’s constructs, questions, methods and answers, to account for the external relevance and realism of the theory. According to Avenell (1983, p.9):

The question of the relevance and realism of a theoretical structure… requires judgement with regard to the adequacy of the propositions in question in dealing with the processes of the actual economy. That is, critical assessment of the consistency of the theory in question with the object of investigation. In sum, discussion on the level of relevance and realism turns on whether the right questions have been asked and whether the correct methods and view of the economy are employed. Judgements in this area consequently require the application of criteria external to the theory per se.

Avenell suggests that the question of relevance and realism differs from, and goes beyond a simple comparison of theories in methodological terms. Whereas comparison of one theory in terms of another theory implies, at best, the falsification of one set of propositions with reference to another set of propositions, criticism of relevance and realism ‘requires substantial and continual reference to the underlying epistemological and ontological view being taken, however it is perceived’ (1983, p.10). Epistemology - how we construct knowledge of the world - has obvious implications for ontology - what we understand as material and social ‘reality’. With respect to epistemology, there are several important differences between Marx and Roemer, including simple differences in the meaning of common terms, and crucial differences in methodology. These differences manifest ontologically in three closely related areas: the delineation of historical periods, the role of production in historical change, and the importance of value theory in economic explanation.

While a discussion of what does (or does not) constitute Marxian epistemology is important and relevant to a full evaluation of the analytic school, the task is well beyond the limited objective of this paper. Rather, in applying Avenell’s criteria of relevance and realism, I am concerned with a more modest end: to direct attention to Roemer’s stated aim to construct a formal model consistent with the ‘insights’ of a Marxian view of historical reality and the operation of the economy. The key questions: (1) does Roemer succeed in justifying his claim that methodological individualism and equilibrium analysis are essential to the elucidation of a specifically Marxian vision, and (2) are the central concerns of Marxian economics adequately addressed using the analytic tools favoured by Roemer?

Conceptualizing Reality: The Limits to Individuals

In Making Sense of Marx, Elster himself specifies the ‘social contradiction’ of methodological individualism by referring to the nature of inference that proceeds from the individual to the whole. He states the ‘paradox’ as follows: all social action is considered to be the outcome of individual actions, yet generalising from what is true for any single agent or coalition of agents to what is true for all agents necessarily involves a ‘fallacy of composition’ (1985, pp. 44-45). This is so because ‘economic agents tend to generalize locally valid views into invalid global statements; that is, individuals fail to perceive that causal relations that obtain ceteris paribus may not hold unrestrictedly’ (1985, p.19). In short, when individuals act on the basis of mutually invalidating beliefs, unintended consequences result. Elster labels these unintended consequences ‘counterfinality’. Essentially, counterfinality is the observable substance of the fallacy of composition.

It is quite clear, from Elster’s own statements, that he considers the ‘social contradictions’ of counterfinality and the fallacy of composition to be important in any adequate appraisal of economic methodology. He declares the ‘extremely powerful’ idea of ‘social contradiction’ to be ‘Marx’s central contribution to the methodology of social science’; at least in so far as he (Marx) demonstrated ‘that in a decentralised economy there spontaneously arises a fallacy of composition with consequences for theory as well as for practice’ (1985, p.19). Yet, implicit in Elster’s own concept of the fallacy of composition is the existence of a priori constraints on individual action; and these constraints imply methodological limits on the individual as a primary unit of analysis: ‘Insofar as the fallacy of composition revolves around the non-universality of a given property, a specific limit to universality is obviously a presuppositon. However, the refusal of Analytic Marxism to entertain supra-individual entities means that such limits are revealed only ex post facto as counterfinality’ (Lebowitz, 1994, p.167).

In demonstrating the non-universality of a given property, Lebowitz refers to Cohen’s Structure of Proletarian Unfreedom. In Cohen’s classic example of collective unfreedom, ten people are locked in a room, and there is a single key on the floor. Since any one individual may pick up the key and leave the room, for each individual the property ‘freedom’ obtains. If we then impose the condition that only that person may leave the room, the individual property - freedom - fails to obtain universally. Lebowitz interprets this outcome as a limitation placed by ‘global constraints’, that precede the action of any one individual (1994, p.167):

Significantly, in this [Cohen’s] example, we have prior knowledge that the relevant property (freedom to leave the room) is ‘non-universalizable’. Knowledge of the specific whole in this case is prior in the explanatory order to understanding the conditional and contingent state of the individuals within this whole. More is involved than simply a question of epistemology; it is also an ontological question: the true properties of the individuals are only given by the characteristics of the whole.

Ironically, it is in the much vaunted theory of exploitation that the fallacy of composition implicit in analytic methodology most clearly obtains. Consider Roemer’s ‘social withdrawal’ criterion for exploitation. A coalition of individuals withdraw from society with their ‘share’ of society’s scarce commodities and resources: if each individual’s income and leisure hypothetically increases, while the assets of the members of the opposite coalition hypothetically decrease, the withdrawing coalition were exploited; if not then they were not exploited. To make any sense of this criterion of exploitation we must first know how an individual’s inalienable ‘share’ in the social capital is to be measured: ‘How much could a worker produce if she or he had never been trained, socialized and educated in a capitalist system? If she or he had none of the values, emotions, and passions that the current system has generated?’ (Hunt, 1993, p.100). Embedded in the social functioning of an economic system, such assets are not the inalienable properties of individuals, but have meaning and value only in relation to participation.

Hence, the central measures of Romerian exploitation - ‘income’ and ‘leisure’ and ‘capital’, as well as the notions of ‘justice’ that sustain them - cannot be derived from the properties of individuals alone. Rather, these categories constitute the cultural artefacts of philosophical and economic analysis, their meanings implicit in a particular view of science, and a particular view of socio-economic reality, at a given point in historical time. The idea that ‘economic knowledge’ constitutes a psychological orientation to economic experience is exemplified in Geertz’s ideational definition of culture as a symbolic regulatory system of ‘plans, recipes, rules, instructions - for the governing of behavior’ (1975, p.44). Applying this definition, knowledge production within American academia may be thought of as contingent upon conventional understandings of what economics is: ‘Man is precisely the animal most desperately dependent upon such extragenetic, outside-the-skin control mechanisms… for ordering behaviour’ (p.44). Or, as Popper would have it, the rational economic individual is not the precondition of society, but a product ‘created by the effort which life in an open, and partially abstract society continually demands from us’ (1973, Vol. 2, p.176).

Popper rejected methodological individualism: firstly, on philosophical grounds that the presumption of rationality is an outcome of socio-economic life, rather than a presupposition; and secondly, on practical grounds that the presumption of rationality is inessential to a falsificationist reference to external reality. Marx set his own method in opposition to both analytic ‘idealism’ and positivist ‘objectivity’. By contrast with the analytic focus on ‘an imagined activity of imagined subjects’ and the empiricist obsession with ‘dead facts’, the premises of Marxian science ‘are real men, not in any fantastic isolation or abstract definition, but in their actual, empirically perceptible process of development under definite conditions’ (1983, p.170). For Marx, a true science of human activity in society must elucidate the constraining conditions, through analysis of the profound interconnectedness of the part and the whole:

The social structure and the state are continually evolving out of the life process of definite individuals, but of individuals not as they may appear in their own or other people’s imagination, but as they really are; i.e. as they are effective, produce materially, and are active under definite material limits, presuppositions and conditions independent of their will (p.169).

Committed to the Cartesian priority of the part over the whole, analytic Marxism reduces Marx’s concern with the interconnections between individual action and social change to ‘part of the exogenous data for the maximization problems’ of individuals (Hunt, 1993, p.96). On the basis of the presuppositions of methodological individualism, economic ‘reality’ becomes nothing other than an abstract stage for the elucidation of outcomes arizing from infinite wants, under an implicit ceteris paribus assumption that psychological states of ‘rationality’ remain, in some way, eternally unchanging. In this way, distributional states may be taxonomically specified with reference to ‘counterfactual’ opposites, without reference to the generative processes of change. Certainly, Roemer’s analysis does not preclude speculation as to the counterfinality that might result if every individual in a Romerian exploited coalition ‘rationally’ withdrew from society. Yet, it is precisely where abstract ‘speculation ends - in real life - that real, positive science begins: the representation of the practical process of development of men’ (Marx, 1983, p.170).

In reality, the ‘absurdity of the idea’ that individuals might withdraw from economic activity as a practical prescription for working class action in a real capitalist economy is so ‘transparent’ as to leave no doubt whatsoever as to the ‘strictly mental and hypothetical nature of the analysis’ (Hunt, 1993, p.100). If economic knowledge is perceived to be scientific only insofar as it has implications for real human action in the real world, then Roemer’s formal solution to the problem of exploitation ‘is not science, but science fiction’ (Hunt, 1993, p.100).

Conceptualizing Change: The Limits to Equilibrium

Specifically, Marx was concerned with the ‘inner divisions’ of the capitalist system into production, circulation and exchange. To explore these inner divisions, the labour theory of value is an indispensable tool, enabling a distinction between labour and labour-power. Under Capitalism, labour-power is a ‘factor of production’ - the worker’s inalienable capacity to work - sold on the market like any other commodity; and the ‘price’ paid for labour-power (the wage) is ‘fair’ in so far as it is determined in accordance with the principles of supply and demand. Labour - the performance of a specified number of hours of work - can be sold only in an embodied form, in produced commodities. Crucially, the distinction between labour and labour-power - between spheres of production and exchange - implies that while labour is the determinant of surplus-value, that surplus is realizable only in exchange. This inner division, inherent in the concept of capital, appears in exchange where it ‘determines both the sum total of the exchange which can take place and the proportions in which each of these capitals must both exchange and produce’ (Marx, 1973, p.443).

For Marx, crises result from an inability to realise the surplus value of produced commodities in the sphere of exchange. This ‘contradiction’ in the proportions produced and exchanged (overproduction) can exist in conjunction with a competitive market only because it comes out of the fact that ‘workers are important for the market as buyers of commodities. But as sellers of their commodity - labour power - capitalist society has the tendency to restrict them to their minimum price’ (1978, p.391n). In other words, the continuous drive to increase the rate of surplus value (productivity increases above the real wage rate) in the sphere of production produces a ‘barrier to the sphere of exchange’ because the consumption of workers ‘does not grow correspondingly with the productivity of labour’. As a result the production and exchange of commodities do not necessarily correspond simultaneously in specific and restricted proportions.

Lebowitz (1994) points out an evident fallacy of composition in the counterfinality of overproduction. Any individual capitalist can alter the technological composition of his or her capital, lower costs of production, and realise the additional surplus values thereby generated. Nevertheless, if we generalize from this locally valid statement to all capitalists, it becomes clear that limits to the rate of surplus value are given by totalities: the level of expenditures on means of production and consumption. Marx’s point about the logical priority of the whole is precisely that consideration of supra-individual entities is crucial to the revelation of constraints on individual autonomy, where the form of competition among individual capitals produces an inherent tendency to violate the proportional equalities of production and exchange: the ‘necessary balance and interdependence of the various spheres of production and the proportions between them’ is achieved ‘through the constant neutralisation of a constant disharmony’ (Marx, 1968, p.529).

For Marx, recurrent crises of overproduction are the visible manifestations of a conflictual relationship between these separate, and yet interdependent spheres of production and exchange: ‘there would be no crisis without this inner unity of factors that are apparently indifferent to each other’ (1968, p.500). At an ontological level, Cartesian commitments to equilibrium analysis do not permit articulation of the relationships among the ‘unity of factors’ that most concerned Marx. On the contrary, General Equilibrium Theory’s singular vision of ‘economy’ as the result of individual exchanges of sellers and buyers, confines interrelationships to the simultaneous resolution of competing desires in hypothetical environments where vector prices allow no excess of supply. By adding time preferences, Debreu’s proof of Walrasian theory provides a unique equilibrium where markets clear in all present and possible futures. The significance for more practical supporters of the theory is that it shows (contra Marx) that the only possible market clearing process in a market is that of perfect competition.

Yet, paradoxically, the logical consistency of Walrasian theory results from a rigour that ‘dictates the axiomatic form of analysis’ in complete disregard for ‘the dynamics of convergence of an economy to Walrasian equilibrium’ (Wientraub and Mirowski, 1994, http). In other words, Debreu rendered the model logically consistent, at the expense of consistency in relation to the actual functioning of an economy. Rather than model reality, Debreu’s mathematical formalism destroyed the ‘illusion’ of Walrasian correspondence to exchange economies by demonstrating ‘once and for all, the disconnectedness of the Walrasian structure from its interpretations’ (Wientraub and Mirowski, 1994, http):

The issue [of the actual motion of market economies] could not be avoided forever, however, and there was a long interval in the postwar period in which “dynamics” were redefined to mean “stability” within the mathematical economics community (Weintraub, 1991). In that context, the question was posed by Hugo Sonneschein whether the basic “structure” of Walrasian general equilibrium models placed any substantial restrictions upon the uniqueness and stability of the resulting equilibria, and he proposed the startling answer: no, outside of some trivial and unavailing global restrictions.

For Weintraub and Mirowski, the importance of Debreu’s theory of value is precisely that ‘it illustrates the intersection of technical, philosophical and historical concerns when it comes to telling what happens when the sublimity of pure mathematics (the music of reason, as Dieudonne calls it) meets the impurity of scientific discourse, a confrontation which can only be postponed but never altogether prevented’ (1994, http). Whatever the analytic Marxists may think, the economic activities of individuals (including their own mathematical activities) are social activities, and therefore impure. Since ‘reflection on the impure involves reflection of the relationship of order to disorder’, equilibrium analysis provides, at best, an inadequate and reified understanding of the determinations of exchange in actual economies. In his earlier work, Roemer seemed to be aware of these shortcomings, adding a ‘caveat on the lineage’ of his equilibrium model (1980, p.524):

Certain aspects of capitalist production are captured here, but perhaps not those aspects most important to Marx… the capitalist labor process is eclipsed in the present model: there is no theory of what determines technology, the real wage, and the organization of production.

Lebowitz (1994) goes further, arguing that Roemer’s treatment of property relations as analytically separate from relations of production introduces profound ‘distortions and intolerances’ into Marxian theory. Specifically, his treatment of production as no more than a set of technical relations obliterates the critical distinction between labour and labour power; and so necessarily circumvents a full analysis of the origins of profit, the coordination of production, and the forces that promote technological change. Adhering to tools of Walrasian equilibrium, analytic Marxists are unable to address the key interest of the dynamism of capitalism in producing constant revolutions in the processes of production.. Instead, they aim to tidy up the scope of Marxism by removing the study of disorder - and therefore the study of change - from the agenda.

Lebowitz’s critique brings into full focus our line of inquiry: why should Marxists accept the agenda? Why should the individualist principle hold, given the fallacy of composition, admitted in principle by Elster? Why should the abstract and historically contingent preferences of the Walrasian framework be taken as the ‘essential’ structure from which all mathematical work in Marxian economics (indeed all economics) must necessarily depart?

Hegemony and Critique

Nowhere are the generally agreed upon facts more clearly in evidence than in Roemer’s statements on the labour theory of value: this theory is ‘false’, and that is all there is to it. The claim plays an extremely important role in the theory and practice of analytical Marxism. Given that Marxian value theory is ‘false’, ‘trivial’, ‘obscure’, and ‘virtually devoid of content’, Marxian economics can be safely declared ‘intellectually dead’, without ever engaging the classical critique (Elster, 1985, pp.161-5; 1986, pp.60, 192). At the same time, the validity of the original conclusion is placed beyond question, mediated by standards of ‘rigor and clarity’ that form the ‘common sense’ substance of neoclassical methodology. This method of criticism amounts to a ‘preemptive methodological strike’ foreclosing debate on the ontological question of the origin of value (Lebowitz, 1994).

The ontological question is one of determination. In justifying his preference for equilibrium analysis, Roemer remarks that analytic Marxists ‘choose models to make the CECP true’ (1982c, p.285). If Marxian theory must be inverted - if values must come to depend on prices in order to make the principle hold - then so be it. The actual correspondence to economic reality of Roemer’s value theory is beside the point since his derived theorems are consistent with the simultaneous solutions given by his axiomatic models. These simultaneous solutions then become the tablet of stone through which all of Marxian economics is interpreted. The ‘falsity’ of Marx’s value theory as a price theory is given a priori by its failure to permit Walrasian equilibrium-type solutions to Marxian equalities.

Fine points out that this so-called ‘transformation problem’ has ‘invariably proved to be the grounds on which bourgeois economics has dismissed Marxism, preoccupied as this economics is with the precise calculation of prices, for which a labour theory of value is irrelevant’ (Fine, 1988, p.333). According to Fine, the criteria of ‘bourgeois’ judgement is itself irrelevant. For Marx, the determinants of value are located not in axiomatic models of market exchange, but in real chronological time and expressed in a description of the circuit of capital through successive cycles of production and exchange. The value of a commodity, determined in the process of production, has no implications for the relation of value to price in the current circuit: today price may exceed value by $10, and tomorrow fall below it by $20 - so what? Likewise, inputs and outputs cannot be determined simultaneously, and to attempt to do so merely invents an illusionary correspondence of value to price. Marx attributed this illusion to the ‘vulgar’ economists (1978, p.186):

… ‘value’ says Bailey, … ‘is a relation between contemporary commodities…’ This derives from his general misunderstanding, according to which exchange-value equals value… He does not in the least suspect, therefore, that value functions as capital only in so far as it remains identical with itself and is compared with itself in the different phases of the circuit, which are in no way ‘contemporary’, but rather occur in succession (my italics).

Successivist determination is so central to a Marxian explanation of the genesis, growth and crisis of capitalism that it is difficult to see how anyone could judge the labour theory of value ‘false’ on the criteria that Marxian equalities fail to hold simultaneously. Yet, this is exactly what Elster does, declaring categorically that ‘Marx certainly intended the labor theory of value to be a theory of prices and profits’ (1978, p.70). The same assumption operates in Roemer’s claim that ‘Marx thought… surplus values became monetized through the price system in a simple way because prices were assumed to be just proportional to the amounts of labor embodied in commodities’ (1989a, p.384). This argument is completely untenable, and nowhere substantiated. While Marx certainly assumed that commodities are ‘the material depositories of exchange-values’, he also perceived the central contradiction of capitalism to be precisely its inability to enable the realization of surplus-values in the realm of exchange.

The analytic Marxist claim that Marx intended his values to explain prices is seriously misplaced. It is, if I may, a vulgar bourgeois misreading of Marx. Freeman (1996) agrees, arguing that the ‘transformation problem’ originates not in Marx, but in Bortkiewicz (an early admirer of general equilibrium theory), who appears to have deemed it his mission to ‘free modern economics’ from the ‘successivist prejudice’ associated with Marx. Freeman provides an excellent account of the distortions that Bortkiewicz’s simultaneous approach introduced into a century of academic debate on the labour theory of value. His conclusion: the ‘death of value’ is inherent not in Marx’s method but, on the contrary, in the logic of ‘Walrasian Marxism’.

Freeman’s crucial point is that the ‘falsity’ of the labour theory of value rests solely upon academic acceptance of equilibrium analysis and positivist methodology as ‘appropriate’ methods for doing ‘economics’. These methodological conventions exercise hegemony in so far as they dictate the ‘common sense’ view of what constitutes good ‘economics’ and good ‘science’; they are ideological in so far as they are concerned with the imposition of meanings. In the work of the analytic Marxists, parameters of meaning are defined by exclusion - through reference to professional specialization. Consider, for example, Roemer’s exclusion of Marxian political economy from the field of ‘economics’ on the grounds that its subject matter is more rightly fitted to the study of ‘history’!

Intolerance of alternative methods and meanings is the hallmark of ideological hegemony, a powerful rational behind the century-long search for ‘appropriate’ micro-mechanisms to correct Marx’s mistakes towards the neoclassical system. A less ideological agenda is surely that of Steedman (1977) who fully recognizes the differences and incompatibilities between economic methodologies. Although Roemer appears less willing than Steedman to break entirely with Marx, his anti-value polemic is directed to the same effect; only with less honesty in its representation of the alternative view.

Conclusion

In this respect, analytic Marxism, represents less a ‘modern’ approach to economic science, than a restatement of the 17th century view of the universe as rationally ordered, and empirically understandable. In contrast, Marxism as a body of economic knowledge, is founded upon a conception of ever-changing material and social realities, and a view of the economic world as a place in which money and labour are real commodities defining social relations of power. In seeking out the generative mechanisms that underlie the social relations of power, Marxism is committed to a process of holistic explanation in which there are no a priori assumptions concerning individual behaviour, or market clearing, or the simultaneous equation of value to price. Failures of understanding at this level of ontology explain why Elster makes non-sense of Marx, why Roemer believes that his model is consistent with Marxism, why both of them regard any defence of the labour theory of value as ‘fundamentalist’, and why their own contributions to economic thought are motivated by an arrogant and unsubstantiated dismissal of a method of critique founded precisely on the critique of method.

Ironically, in replacing the method of critique with the tools of a hegemonic economic theory, the analytic school have effectively deprived themselves of any opportunity to influence Marxian thinking. Within the conceptual framework set down by methodological individualism and neoclassical general equilibrium, ‘unequal endowments’ are privileged as the core of an idealized world of agents seeking equilibrium in an idealized market untainted by monetary influences. In such a market, the correspondence between exploitation and class is reduced to the role of a postulate, directing attention away from the study of disorder and crisis, and towards theoretic models that allow the principles to hold. In short, Roemer’s models violate the essential Marxian requirement that science move beyond reductionist interpretations of the world defined by fixed states, where determination exists without time.

In evaluating the contribution of analytic Marxism on criteria of relevance and realism, the conclusion is rather obvious: the simplifying - in fact, stultifying - assumptions which analytic Marxists have grafted onto Marx’s concepts are not only inconsistent with the aims of Marxian political economy, they are unrealistic; and therefore, irrelevant. Quite simply, analytic Marxists are unable to pose any of the questions that interested Marx.