Functional forms for technical change functions

In this paper we examine the four properties of technical change functions introduced by Sato 1980, 1981], paying particular attention to the composition property. We show by way of examples that two of the properties are independent, but that a third is a necessary consequence of two others. A theorem providing a necessary condition for the composition property is stated and proved. Finally, we identify the general continuous functional form of technical change functions for which the efficiency of factor i is independent of the quantities of all factors j i. Noting an unappealing characteristic of a member of this class of transformations, we propose an additional property for technical change functions and note that it is independent of the others.The refereeing process of this paper was handled through S.T. Hackman.