[T]hat different lines of industry have different rates of profit, which correspond to differences in the organic composition of their capitals... [that] ... capitals of equal magnitude yield equal profits in equal periods, applies only to capitals of the same organic composition, even with the same rate of surplus-value. These statements hold good on the assumption which has been the basis of all our analyses so far, namely that the commodities are sold at their values. There is no doubt, on the other hand, that aside from unessential, incidental and mutually compensating distinctions, differences in the average rate of profit in the various branches of industry do not exist in reality, and could not exist without abolishing the entire system of capitalist production. It would seem, therefore, that here the theory of value is incompatible with the actual process, incompatible with the real phenomena of production, and that for this reason any attempt to understand these phenomena should be given up. (Marx, 1974 : 153)
In what follows, I consider what has come to be known as the 'transformation problem', which Marx discusses in Capital Volume III and elsewhere (Marx 1974 : 154-- 172). This article has four parts. In Part 1, I make some preliminary remarks about Marx's version of the labour theory of value, on the assumption that this is necessary for an understanding of the discussion of his views regarding the transformation problem. In Part 2,1 examine one way of thinking about Marx's understanding of the transformation problem, which is associated with a certain interpretation of the labour theory of value. On this view, what Marx says about the transformation problem is a contribution to a theory of prices, not values. This traditional reading is commonly held in the secondary literature and does have support from the primary sources. Indeed, it is dominant in Marx's own reflections on the subject.
In Part 3, I question the assumptions on which the traditional understanding of the transformation problem is based and suggest that if we attribute to Marx a different set of assumptions then the transformation problem, as it has been traditionally understood, does not arise. I also propose an alternative reading of Marx, according to which his reflections on the transformation problem are best seen as a contribution to a theory of value, not prices. They amount to a more detailed exposition of the labour theory of value, which Marx introduces to his readers in Capital Volume I, and of the notion of 'socially necessary labour-time'. Finally, in Part 4,1 point out some of the methodological issues which are raised by this alternative reading of Marx.
Marx and the labour theory of value
Central to the labour theory of value, as Marx understands it, is the notion of 'social necessity'. When discussing this issue in Capital Volume I, Marx states that the value of a commodity is determined by the amount of 'socially necessary labour time' which goes into its production. This is, he says, the labour-time 'required to produce an article under the normal conditions of production, and with the average degree of skill and intensity of labour prevalent at the time in a given society' (Marx 1958 [1898/1865]: 422, 1974 : 46-47). In the case of the cotton industry, Marx (1989 [1861-1863]) states in his Economic Manuscript of1861-1863 that 'the quantity of labour by which, for example, [the value of] a yard of cotton is determined' is again 'not the quantity of labour it [actually] contains, the quantity the manufacturer expended upon it', but rather 'the average quantity with which all the cotton-manufacturers produce one yard of cotton for the market' (p. 428). It matters a great deal, therefore, what Marx means when he talks about average conditions of production.
Marx accepts that the amount of labour-time which actually goes into the production of a particular commodity could in principle differ from this average. Whether or not it differs, in fact, depends on the productivity of the labour which produces it, which in turn depends on the level of technological development of the machinery which is employed by the labourer. In short, it depends on what Marx (1974 ) refers to as the 'organic composition of capital', understood in the technical rather than the value sense of that term (p. 574; also pp. 582-583). The distinction that Marx (1974 ) makes between the 'individual value' of a commodity and its 'social value' is important here (pp. 301, 383). I shall say more about this later.
When Marx introduces the labour theory of value in Capital Volume I, he makes three simplifying assumptions, two of which are implicit and the other explicit. The first of these is the implicit assumption that the organic composition of capital in all units of production is the same. Paul Sweezy (1942) has rightly pointed out that 'throughout Volume I Marx develops his analysis as though the law of value were directly controlling for the prices of all commodities', a procedure which is 'legitimate so long as it is assumed that in every branch of production the organic composition of capital is the same' (p. 109). Thus, complications associated with the existence of different organic compositions of capital do not arise in Volume I. Such complications arise only later, in Capital Volume III, when this first assumption is relaxed.
The second simplifying assumption which Marx makes in Capital Volume I, as he explicitly informs his readers in Volumes II and III, is that commodities sell at their values. For example, at one point in Volume III, Marx (1974) states that 'these statements hold good on the assumption which has been the basis of all our analyses so far, namely that the commodities are sold at their values' (p. 153; also pp. 150, 178, 193, 195). And in Capital Volume II, Marx (1977 (1893 )) notes that, as in the case of Capital Volume I, it is 'taken for granted here that the commodities are sold at their values' (p. 26). It is only in Volume III of Capital, when discussing the transformation problem, that Marx abandons this second assumption.
The third simplifying assumption which Marx makes in Capital Volume I, although implicitly rather than explicitly, is a logical corollary of the first two. It is that, quantitatively speaking, the socially necessary labour-time and the actual labour-time required to produce a commodity are one and the same. According to Marx in Capital Volume III, the principle that 'capitals of equal magnitude yield equal profits in equal periods' applies 'only to capitals of the same organic composition' with 'the same rate of surplus-value'. Moreover, as we have just seen, in Marx's (1974 ) view 'these statements hold good', on the assumption 'which has been the basis of all our analyses so far', that 'commodities are sold at their values' (p. 153). These remarks support the claim that in Capital Volume I Marx assumes both that commodities sell at their values and that organic compositions of capital are equal. It seems clear enough, however, that, as a matter of logic, they also commit Marx to the view that, in such a scenario, there is, quantitatively speaking, no distinction to be made between the labour-time which is actually required for the production of a commodity and that which is socially necessary for its production. Hence also there is no difference between a commodity's individual value and its social value.
It should be emphasised that this third assumption is implicit rather than explicit. It is, however, an assumption to which Marx is logically committed, given the fact that he has already made the first two assumptions identified earlier. So, either Marx does make this third assumption (implicitly) or, given that he has already made the first two assumptions, he must contradict himself. In my opinion, with respect to this particular issue, Marx does not contradict himself. He consistently makes all three of the assumptions identified above throughout Capital Volumes I and II and only considers the implications of relaxing one or more of them in Volume III.
It is arguable that, when discussing the transformation problem in Capital Volume III, as soon as Marx relinquishes the first two of these assumptions and considers both the possibility that the organic composition of capital of different production units might not be equal and the possibility that commodities might not, in consequence, sell at their (individual) values, he really ought to abandon this third assumption also. He ought to factor into his analysis the fact that the actual labour-time required for the production of a commodity, and the socially necessary labour-time required for its production might be numerically different. In fact, however, Marx continues to assume that no such difference exists. It is this, above all, which lends support to the claim that Marx does contradict himself at this point in his argument.
The traditional understanding of Marx on the transformation problem
What we now call 'the transformation problem' is discussed by Marx in Chapter IX of Part II of Capital Volume III (Marx 1974 : 154-172). Central to the discussion is the concept of prices of production (Produktionspreise). According to the traditional understanding of this issue, Marx's prices of production are monetary prices. The transformation problem is about the transformation of values into prices (Baumol 1974: 51; Carchedi 1984: 431, 1993: 197-203; Fine & Harris 1979: 34; Fine & Saad-Filho 2004: 130; Glick & Ehrbar 1987: 295; Laibman 1973: 407-408; Langston 1984; Meek 1977; Parys 1982; Sweezy 1942; Von Bortkiewicz 1952; Winternitz 1948; Yaffe 1976). When discussing this problem, Marx considers how to explain the deviation which sometimes exists between the prices of commodities and their values, while retaining and not contradicting the...