On the integrability of demand functions

Abstract

This paper deals with the properties of demand functions derived from utility maximization. Such properties may be either “finite” (involving finite sets of points) or “infinitesimal” (involving the derivatives of the demand functions). The “revealed preference” approach, pioneered by P. A. Samuelson and developed by H. S. Houthakker, is of the “finite” type. In what follows, we shall confine ourselves to the “infinitesimal” type of analysis, dealing with “substitution terms.” This analysis has been carried out in terms of the “direct” demand functions (quantities taken as functions of prices and incomes) by Slutsky, Hicks, Allen, Samuelson, and the “indirect” demand function (relative prices as functions of the quantities taken) by the “rediscovered” Antonelli, and also by Samuelson. The present paper deals only with the “direct” demand functions.