Marginal Productivity Theory

The Proposition

A profit-maximising firm uses any factor up to the point where the value of that factor's marginal product equals its price. Applied to labour: the wage equals the value of the output added by the last worker hired. The conclusion rests on the assumption that marginal productivity diminishes as more of a factor is added.

So far this is a technical proposition about factor demand. In that form it describes one side of wage determination and does not by itself explain why wages stand where they do. Wicksteed, Barone and Walras, who formulated it in the 1890s, largely kept it there and worked it into general equilibrium theory.

Clark's Extension: From Technique to Justification

The trouble comes with the extension. John Bates Clark used it not as a theory of the firm but as a principle for the social distribution of the national product. The political message of The Distribution of Wealth (1899) reduces to one sentence:

'What a social class gets is, under natural law, what it contributes to the general output of industry.'

Two things happen in that sentence at once. A description becomes a norm: if each receives what each makes, the existing distribution is just. And capital becomes a contributing agent alongside labour: if capital draws its own marginal product, then a share appropriated without payment (surplus value) does not exist by definition. Exploitation is not refuted; it is spelled out of the vocabulary.

The Cambridge Capital Controversy

Clark's extension carried a technical price. To explain distribution across society this way you need 'capital' as a single magnitude aggregating heterogeneous machines, buildings and stocks. Clark handled capital as homogeneous jelly.

In 1953 Joan Robinson put her finger on it: valuing capital requires knowing the rate of profit, which is the very quantity the production function is supposed to determine. That is a circle. Work in Sraffa's line then produced reswitching and capital reversing: the capital intensity of the techniques chosen does not move monotonically with the rate of profit, and a higher profit rate can go with a more capital-intensive technique. The picture in which factor prices register scarcity and productivity breaks down there.

In 1966 Paul Samuelson conceded it in 'A Summing Up' in the Quarterly Journal of Economics: 'the simple tale told by Jevons, Böhm-Bawerk, Wicksell and other neoclassical writers… cannot be universally valid.'

It is worth being exact about what was conceded. What broke is the aggregate version that needs a single quantity of capital. Marginal analysis at the level of the firm was not abolished by the controversy, and the reach of the result is still argued over. But what Clark set out to do, explain and justify the distribution between social classes by each one's contribution to production, requires precisely the version that broke.

Two Different Questions

The Marxist objection is not arithmetical but a separation of questions. What contributes to production and who appropriates what are two different questions. Between the fact that a machine is necessary to production and the claim that the machine's owner should receive its product stands the social institution of ownership. Marginal productivity theory steps over that institution by calling it a law of nature.

Capital answers the wage question from the other side: the general movement of wages is regulated not by the productivity of the last worker but by the expansion and contraction of the industrial reserve army, by the movement of accumulation.

Where the Theory Stands Now

Marginal productivity is the working grammar of labour economics today. The argument that raising the minimum wage destroys jobs whose marginal product falls below it, the argument that automation lowers the marginal product of labour, the argument that wage gaps register productivity gaps: all are written in it.

Using that grammar and claiming that it justifies the distribution are different acts. Delete 'under natural law' from Clark's sentence and what remains is a description of how much of a factor a firm uses under stated conditions; leave it in and what remains is the claim that the present distribution is right. Reading those two apart is what this entry is for.