Market Demand Functions in the CAPM

Abstract

In this book we study the CAPM as a general equilibrium model in which the natural questions of existence and uniqueness of an equilibrium play an important role. Similar to Nielsen [1990b] and Allingham [1991] in the previous chapter we have given general proofs of existence within this framework where consumption sets are not bounded below and satiation is possible. As shown by an example with two equilibria constructed by Nielsen [1988], there is, however, no reason to expect uniqueness in general. We will continue along this line of research and will analyze the structure of market demand in the CAPM. We will show that given any choice of a finite number of normalized price systems and the respective demands satisfying Walras’ Law and the Tobin Separation Property, there exist two variance-averse agents whose market demand coincides with the preassigned values. This result parallels the result proved in Chapter 3 which itself was a generalization of results known in the general equilibrium literature as the Sonnenschein-Mantel-Debreu result on the structure of market excess demand functions. The result proved in this chapter for the CAPM considers the market excess demand function on a finite set of prices which is then similar to the result of Andreu [1982].