Fixed Coefficients of Production Revisited

Abstract

rT | HE EXISTENCE of fixed coefficients of production raises certain problems in marginal productivity theory, notably the demand for factors of production. In such instances it may be neither meaningful nor possible to discuss the returns to factors of production in terms of their respective marginal productivities.1 The present note discusses the reconcilement between marginal productivity theory and fixed coefficients of production proposed by Georgescu-Roegen [3] in 1935 and extends the analysis to include cases of imperfect competition. The similarity between this model and the treatment of costs in marketing theory is also discussed. It is convenient at first to review the definition of limitational and substitutable factors given by Georgescu-Roegen [3]. Given a production function q=F(a, b), we can consider two points Mi(ai, b) and Mj(aj, b) such that ai>aj. If Fi(ai, b)>Fj(aj, b), then the factor b is called substitutable. If, however, there are certain points for which Fi(ai, b)=Fj(aj, b), then the factor b is called limitational. In this case the production process is described by the system: q=f(a) =g(b). The above analysis can be extended to the case where a and b represent groups of factors rather than single factors of production. In the case where the groups must be used in a certain fixed proportion and assuming two substitutable factors in each group, we have the following system of production: