On the Samuelson-Etula Master Function and Marginal Productivity: some old and new critical remarks

The paper addresses the ambiguity that surrounds the conception of capital and its role in neoclassical price-and-distribution theory. The difficulties encountered in the various attempts to define the marginal product either of capital or of a capital good are recalled and the conclusion is drawn that neither concept appears theoretically sound. This is combined with critical discussion of the recent attempt by Samuelson and Etula to determine income distribution by means of their ‘Master Function’ and its ‘non-neoclassical’ marginal products. Rather than the existence of a continuum of alternative technical possibilities, Samuelson and Etula assume the simultaneous coexistence of a discrete number of methods of production for the same commodity. Even though each technique employs the inputs in fixed proportions, the coexistence of various techniques permits the full employment of an arbitrarily given vector of input endowments. As is shown here, however, the coexistence of methods required for the differentiability of the Samuelson-Etula Master Function can take place, if capital goods are used in production, neither in the case with stationary relative prices nor in the non-stationary Arrow-Debreu framework.