On the Restrictive nature of Constant Elasticity Demand Functions

Abstract

While the properties of constant elasticity of substitution technologies have been studied extensively (see McFadden (1963), Hanoch (1978) and the references cited therein) the same attention does not seem to have been accorded constant own-price elasticity demand functions. These demand functions have been widely used in empirical work, and in the study of the welfare implications of price stabilisation (see Tumovsky (1976), and Newbery and Stiglitz (1981), for example). Economic literature has considered the implications of systems of constant own-price demand (and income elasticities), but the restrictions imposed by the assumption that a subset of demand functions of a system has constant own-price elasticities have not been presented. The importance of such restrictions lies in the question: do such systems allow relaxation of the restrictive nature of full constant elasticity systems? This paper points out that if a system of firm or consumer demand functions has one demand function with a constant own-price elasticity then, in order to be integrable, significant restrictions must be placed upon the system and that elasticity. Here the term integrable is used to denote the case where unconditional, and conditional firm (consumer) demand functions imply and are implied by profit (indirect utility) functions, without significant restrictions on the nature and domains of these functions.