Invariant Relationships for Homothetic Production Functions

Abstract

An operational approach to production functions must recognize the limitations imposed on our knowledge by the observability and measurability of variables and of the relationships defining production functions. One important limitation on our knowledge arises through the presence of technical change, another through the difficulty of measuring the marginal product of capital or even the capital stock itself. Depending on what we assume to be observable we find ourselves restricted to a smaller or broader class of admissible production functions. Further restrictions are imposed by the limitations of statistical technique. Thus in practice most estimated relationships are assumed linear either in the variables or in some suitable transformation, usually a logarithmic one.

I am indebted to Professors Ryuzo Sato and Wolfgang Eichhorn for their stimulating comments.