CHAPTER 9 - THE GROUP STRUCTURE AND THE THEORY OF OBSERVABLE MARKET BEHAVIOR

Abstract

This chapter discusses the group structure and the theory of observable market behavior. The chapter focuses on the analysis and abstraction of the formal group structure exhibited in many observable market behaviors dealt with in economic theory. Many of the well-known results in economic theory are restated in the group theoretical and differential geometric framework in a more consistent manner. This enables one to study some of the basic problems still unresolved in economics in a more fruitful and unified manner. Thus, for instance, the well-known theory of revealed preference in the consumer's demand analysis is regarded as the involution conditions of the group action of a Lie group on a differentiable manifold. Economic optimization, such as cost minimization and utility maximization is regarded as defining contact transformations. If rational economic behavior is market observable as a system of mixed variables of prices and quantities, the underlying production technology or the preference ordering can be recoverable by the use of the fundamental properties of contact transformations. The Frobenius existence theorem is fundamental to the group theoretic/differential geometric approach to the theory of observable behavior.