CHAPTER 6 - SELF-DUAL PREFERENCES AND TECHNOLOGIES

Abstract

The invariance property of Lie group transformations serves as an extremely powerful tool for the study of production functions and, thus, of utility functions and preference orderings also. The chapter presents the aspect of the invariance property exhibited in utility and production analysis, the self-duality property of preferences and technologies. Papers by H. S. Houthakker, Paul A. Samuelson, Sir John Hicks, R. A. Pollak, Ryuzo Sato, Samuelson and S. Swamy, and Professor Wahidul Haque deal with the question of the existence of a nontrivial preference ordering that exhibits the same mathematical properties in terms of both direct and indirect utility functions. Samuelson raised the question of whether there exists a nontrivial self-dual preference ordering that may require more stringent conditions than homogeneity and separability. A self-dual preference is defined to be a preference ordering such that the direct utility function is exactly identical with the corresponding indirect utility function. The chapter also presents a more complete solution to the problem of self-duality by a group theoretic approach.