Portfolio Choice and Saving in an Optimal Consumption-Leisure Plan

Abstract

Economists have for some time been interested in analysis of a consumer's choice of savings rate and portfolio composition in the presence of uncertain returns. Theorems have been proved for a large number of cases involving utility functions with various special functional forms.3 There are no papers in the literature which prove theorems which hold for the class of all continuous, increasing, strictly quasi-concave utility of consumption and leisure functions.4 This is in marked contrast to the situation in the theory of consumer demand under certainty where the general case,5 as well as various special cases,6 has received considerable attention. The paucity of theorems which hold for the general case is somewhat surprising since strict quasi-concavity of utility functions has a particularly appealing interpretation in models which admit uncertain outcomes. This interpretation is that of the weakest form of risk-aversion [5, p. 101]. The present paper is concerned with the implications of the strict quasi-concavity hypothesis for the consumer's choice of savings rate and portfolio composition.7 The only results in the uncertainty literature which do not require hypotheses about the form of a consumer's utility function 8 which are stronger than strict quasi-concavity are general equilibrium theorems, such as those of Arrow and Debreu.9 The authors who use the Arrow-Debreu contingent commodity approach in the analysis of a consumer's