Introduction

This chapter is devoted to a systematic and intense investigation of the technical theory of production in the special case of linearly homogeneous production functions. This might seem unnecessary inasmuch as this class of functions is a highly simplified form of the general class considered in chapter 4. Yet such a discussion is worthwhile. First, the assumption of linear homogeneity is so specialized and simplifying that it leads to some significant extensions of the general theory of production. Even more important, perhaps, this assumption seems to be an accurate empirical approximation of production conditions in a wide range of circumstances. Thus these extensions appear to have important empirical applications. Second, the case of linear homogeneity is so important in the analyses of distribution and aggregate production that it merits special attention. Finally, and somewhat surprisingly, there seems to be a widespread misunderstanding of certain aspects of the technical theory of production under conditions of linear homogeneity.

The last point is illustrated by the recent argument concerning ‘diminishing returns and linear homogeneity’. The argument was begun, innocently enough, by Nutter. He cited the following textbook statements, one of which is attributable to negligence, the other to error. The first is from Liebhafsky: