Neutrality of Inventions and the Structure of Production Functions

Abstract

In the previous two chapters we introduced the concept of G-neutrality of technical change for a Lie transformation group G. In this chapter, first in Section II, we shall present a general formulation of G-neutrality of technical change for the production function with arbitrary number of factor inputs. In Section III, we determine the group G of neutrality of technical change as an invariance group, i.e., a symmetry group with respect to the well-known general properties of production functions. For a given Lie group G of transformations, we can find the form of production function for G-neutral technical change by solving a system of partial differential equations of the first order. Finally, in IV, we present some important examples of neutral invention and technical change.