1 Marx, Karl, Capital, vol. 1 (New York: International Publishers 1967), 193Google Scholar. Emphasis in the original.

2 Morishima, Michio, Marx’s Economics (Cambridge: Cambridge University Press 1973)Google Scholar, ch. 5. Cf. also Roemer, John, Analytical Foundations of Marxian Economic Theory (Cambridge: Cambridge University Press 1981), ch. 2.4.CrossRefGoogle Scholar

3 A number of writers have proposed such proofs, among them Robert Paul Wolff in his ‘A Critique and Reinterpretation of Marx’s Labor Theory of Value,’ Philosophy and Public Affairs 2 (1981) 89-120 and again in his Understanding Marx (Princeton: Princeton University Press 1984), 205-6; also Roemer, John, A General Theory of Exploitation and Class (Cambridge: Harvard University Press 1982)CrossRefGoogle Scholar, Appendix to chapter 7.

4 Cf. Hodgeson, Geoff, ‘A Theory of Exploitation Without the Labor Theory of Value,’ Science and Society 44 (Fall 1980) 257-73Google Scholar. Also see Cohen, G. A., ‘More on Exploitation and the Labor Theory of Value,’ Inquiry 26 (1983) 309-31Google Scholar.

5 Roemer, John, ‘New Directons in Marxian Theory of Exploitation and Class,’ in Roemer, John, ed., Analytical Marxism (Cambridge: Cambridge University Press 1986), 100-1Google Scholar

6 Ibid., 100

7 Marx, Capital I, 186-98. The quotations that follow are taken from these pages.

8 To call the price-value proportionality assertion the labor theory of value’ is in fact misleading, since Marx does not employ it as a theory but as a simplifying assumption. More will be said about this below. In the interim it will be useful to keep in view both the common designation and its problematic nature, so I will set off labor theory of value’ with quotes when the term signifies the assumption that prices and labor values are proportional.

9 As is well known, there exists a large controversy as to whether or not Marx’s argument is intended to be a moral argument. This controversy is not relèvant to the concern of this paper, since, whatever Marx’s overt intentions or theoretical commitments, the argument under consideration can be read as a moral argument and often is. It is with that reading that I am concerned.

10 The basic idea is this. Surplus value is generated by workers. If wages and the length of the working day are equal across industries, the more workers employed by an enterprise, the more surplus value created. Thus a labor-intensive enterprise produces more surplus value per unit capital than does a capital-intensive enterprise. Hence, if prices are proportional to labor values, the labor-intensive enterprise will show a higher rate of profit that a capital-intensive enterprise, thus violating the equilibrium assumption that the rate of profit be the same in all enterprises. This contradiction can be avoided only if prices cease to be proportional to labor values. See Jon Elster, Making Sense of Marx (Cambridge: Cambridge University Press 1985), 133, for a succinct formal proof.

11 Cf. Wolff, Understanding Marx, 90 ff.

12 That the equal organic composition of capital assumption together with the homogeneous labor and equilibrium assumptions require that prices be proportional to labor values can be seen as follows. Suppose two commodities, say a bushel of corn and a ton of steel, sell at the same price. Since market forces equalize the rate of profit in all industries, the costs of production must have been the same for both corn and steel. Since both industries have the same organic composition of capital, each must have made the same outlay for wages and the same outlay for raw materials. (For simplicity, we will ignore equipment depreciation.) The same wage outlay, given the assumption of a single wage rate, implies that exactly the same amount of direct labor was expended on each commodity.

To see that the same is true for indirect labor, we look at the raw materials that went into producing the corn and steel, and regard them as commodities produced in the preceding period. By exactly the same reasoning as before, we conclude that the amount of direct labor expended in that period to produce the raw materials that went into a bushel of corn was the same as the direct labor expended in that period to produce the raw materials that went into a ton of steel. Since we can continue the reduction indefinitely, looking at the direct labor and raw materials that went into producing the raw materials that went into the raw materials, etc., always concluding that the same amount of direct labor went into the predecessors of steel as the predecessors of corn, it follows that the total amount of labor, direct and indirect, must have been the same for both corn and steel.

The same argument can be made, mutatis mutandis, to show that when an equal cotton-organic composition of capital prevails, equal prices entail equal embodiments of direct and indirect cotton.

13 One can also calculate equilibrium prices, and investigate the conditions under which prices will be proportional to labor values, but that is a separate matter.

14 Since I am using corn and steel, its natural to think of the production period as a year, and the units of labor as person-days. In Marx’s example, the production period is one day, and the units of labor person-hours. Thus in our analysis, requiring more days of labor during a production period corresponds formally to lengthening the working day in Marx’s model.

15 The distinction drawn here between technical and social conditions may be regarded as the analogue in Marx’s economic theory of the famous distinction in his historical materialism between forces and relations of production. In neither case is distinction meant to imply independence. I noted that both worker consumption and the length of the working day are constrained by technical conditions. Similarly, as Marx himself has pointed out, a society’s choice of technology is determined in part by social conditions. (For example, choices of technology might be markedly different in societies of comparable development depending on how much voice the direct producers have in determining the choices and on how easy it is for decision makers to shift negative externality costs onto others.) Despite the interconnection of the technical and the social, the distinction is important, quite as important for Marx’s theory of exploitation as the forces/relations distinction is for his theory of history.

16 If such a reduction were to occur over time, industries would not all decline proportionally, since capitalist consumption need not have the same structure as worker consumption. The adjustment process would entail some shifting of the workforce, but in the end each worker would work only b₁x + b₂y days per year.

17 It is easy to prove that in the two-sector model corn exploitation varies directly with k. If we differentiate (**) with respect to k and solve, we get dw/dk = 1₂z/[1₂b₂-k (1-a₂₂)] and dz/dk = z (1-a₂₂) / [1₂b₂-k (1-a₂₂)]. Consider the denominator 1₂b₂–k (1 – a₂₂). The quantity b₂ represents the quantity of steel one worker will consume during a production period, while k (1-a₂₂)/1₂ represents the net output of one worker in the steel industry during that period. Clearly, if there is to be any surplus in the economy, the latter quantity must be larger than the former, which implies that dw/dk and dz/dk are both negative. But if w and z both vary inversely with k, so does the corn-value of corn, a₁₁ + a₁₂w + 1₁z. Hence, if the corn-value of corn decreases when k increases, the degree of corn exploitation increases, and vice-versa.

18 There are two other developments that would allow for our capitalist to make a profit, though each has been excluded by hypothesis. If workers’ real wages could be reduced without reducing the length of the working day, the equilibrium profit rate would become positive. It would also become positive if a new technology were introduced in a basic-goods industry that reduced the labor-value of a unit output. In each of these cases the correlation with exploitation is evident. In either case, the worker would be compelled to work longer than is necessary to replace the goods her wages will buy. In both cases the cotton-value of cotton would drop to less than one.

19 Even when x is labor-power, ‘exploitation’ does not follow simply from the fact that more labor extracted from that commodity than is embodied in it. As Marx makes clear, non-democratic compulsion is implicated in this state of affairs: in the historical process that transformed labor-power into a commodity in the first place; in the maintenance of property relations that restrict workers access to means of production; in the mechanisms of supervision that insure a ‘fair’ day’s work for a wage.

20 Marx, Capital I, 194

21 Of course, at the purely formal level, that of the mathematical symbolism, one cannot distinguish the a-’s, say, from the b¡’s. But the moment an economic interpretation is proposed the technical/social distinction becomes intelligible.

22 Elster, Making Sense of Marx, 141

23 My thanks to Robert Paul Wolff, Richard Schmitt, Julius Sensat, Drew Christie and Paul Wendt for their comments on earlier versions of this paper.