Invariance Principle and “G-Neutral” Types of Technical Change

In Sato [1980, 1981] it is shown that the method of Lie group theory is a powerful technique to characterize the production function and technical change. The main purpose of this paper is to develop a general theory of neutral technical change from the point of view of Lie theory, without assuming that the production function is homogeneous of degree one with respect to the productive factors. The concepts and methods used in this work are completely the same as in Sato [1981]. 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 used 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 III, as illustrative examples, Sato-Beckmann types of neutralities [1968] are investigated for different types of technical change.