Analysis of Production Functions by “G-Neutral” Types of Technical Change

Abstract

This is a continuation of the previous chapter. The main purpose of this chapter is to develop a general theory of neutral technical changes from the point of view of Lie theory, without assuming that production functions are homogeneous of degree one with respect to the productive factors. The concepts and methods used in this work are completely the same as in Chapter 3. In II, we shall define the concepts of G-neutrality of technical change, equations of G-neutrality, and G-neutral production functions, for a Lie transformation group G of the 3-space. The Lie theory of transformation groups is applicable to find the form of equations of G-neutrality and G-neutral production functions. From a natural reason we might assume that these groups are Lie subgroups of the general projective group GP(3, R) of the 3-space. In IV, some details on a G₃-neutrality which contains as special cases Hicks, Harrod, and Solow neutralities are described. In V, as further illustrative examples, Sato-Beckmann types of neutralities [1968]are investigated.