Heterogeneous Labour and the Fundamental Marxian Theorem

Abstract

As was pointed out by Morishima at the end of his famous book on Marx's Economics, the heterogeneity of labour is a serious dilemma for Marx's theory of exploitation, especially for the so called Fundamental Marxian Theorem. The problem, which should be separated from the peculiarities of joint production, consists in finding an appropriate reduction of the various types of labour to one common unit. Recently Bowles and Gintis have undertaken an interesting reformulation of the Marxian theory of value with respect to heterogeneous labour by avoiding any reduction at all (Bowles and Gintis 1977, 1978. Cf. also Steedman 1977, Holliinder 1978). But for the purpose of the Fundamental Marxian Theorem this only shifts the problem from the heterogeneity of labour to the heterogeneity of the respective rates of exploitation. The aim of the present paper is to extend the Fundamental Marxian Theorem (without joint production) from homogeneous to heterogeneous labour (Section 3). This extension is based on a new concept called the standard reduction of labour, because of its dual relationship to Sraffa's standard commodity (Section 2). For some arguments a certain type of matrices, called Sraffa matrices, is needed, which generalize the quasiirreducible matrices as introduced by Bowles and Gintis (Appendix). Standard reduction implies always a uniform rate of exploitation, whereas the same is true for the reduction by wage rates only in special cases (for example: uniform consumption; labour inputs only; prices proportional to labour values. For the first two cases cf. Morishima 1978). Hence, in general standard reduction and reduction by wage rates are different.