12 - Estimations of Self-Dual Demand Functions: An International Comparison

Abstract

This chapter discusses systems of theoretically plausible demand functions that can be integrated into consumers' utility functions. In the traditional demand analysis for an individual consumer, a system of direct demand functions is derived from the assumption of rational behavior, given his preference ordering and the budget constraint. The type of observable market behavior manifested in the direct demand functions crucially depends on the type of preference ordering expressed in the form of his or her direct utility function. But as the preference ordering is subjective, it cannot be observed directly. The chapter discusses the reverse, the process of analysis by first studying observable market behavior and then inferring the underlying properties of the preference ordering. This process finds one set of linear demand functions and ten sets of log-linear demand functions that satisfy the conditions of theoretical plausibility and self-duality. For each set of demand functions, the corresponding explicit form of the underlying utility function is derived. The objectives of the empirical study are to examine the plausibility of these self-dual demand functions, and the other objective is to make an international comparison between American and Japanese consumption behavior. It fits self-dual demand functions to United States and Japanese data and find that these functions, except the linear case, explain the United States and Japanese demand far better than expected. It also find that a system of nonhomothetic CES type demand functions that is most plausible and practical among all sets of self-dual demand functions. This system of self-dual demand functions is very simple in that demands are functions only of their own real prices.