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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 RelationsWhat do the adherents of analytic Marxism identify as the constituent elements of their value-free methodology? For Wright, the central intellectual thread is the ?systematic interrogation and clarification of basic [Marxian] concepts and their reconstruction into a more coherent theoretical structure? (1985, p.2). Similarly, Elster names ?standards of rigour and clarity? (1985, p.xiv) as the underlying principles of his ?search for microfoundations?. A more focused description comes from Roemer: ?analytically sophisticated Marxism? takes ?central organizing categories? from Marx and explores them with ?contemporary tools of logic, mathematics and model building?; it is marked by a ?commitment to the necessity for abstraction? and ?methods of analytic philosophy and positivist social science?(1986a, pp.1-2). In reformulating Marxian categories, ?the tools par excellence are rational choice models: general equilibrium theory, game theory, and the arsenal of modelling techniques developed by neoclassical economics? (1986c, p192). Analytic Marxism is defined by a ?non-dogmatic approach to Marxism? that rejects classical Marxism?s ?deep anchor in a certain view of history?; ?what matters? is not history, but ?the coherence of the idea?(1986a, p.1).

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 ClassThe heritage of Marxism, as an idea, is a set of powerful descriptive insights. These descriptions must not be assumed to be true, but rather shown to emerge as theorems in models whose postulates are elementary and compelling (Roemer, 1986c, p.201).

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.

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