Price Variability, Utility and Savings

Abstract

The observation that an increase in the variation of the price of a commodity about its mean raises the expected consumer surplus generated by that commodity originates with Waugh (1944). Waugh and subsequent investigators (e.g. Massell (1969), Turnovsky (1976) and Bradford and Kelejian (1977)) use this result to derive propositions on the welfare and distributional effects of price stabilization schemes.' This approach ignores the uncertainty in real income generated by price variability. It also fails to consider the role of hedging against price variation through appropriate portfolio diversification. In this paper demand theory is used to show that relative price variability has an ambiguous effect on expected utility when only a single asset is available as a store of value. A positive effect is more likely when the demand elasticity is large relative to the degree of relative risk aversion and when the marginal propensity to consume the commodity in question is large. When there exists a futures market for each commodity, the consumer can hedge against price variation to insure a positive effect. Increased variance in a log-normally distributed price unambiguously raises expected utility when the consumer hedges optimally. A second purpose of this paper is to explore the implications of price variability for optimal savings as well as for expected utility. While the effects of uncertainty in the value of future endowments and assets on optimal savings have been explored extensively scant attention has been paid to the effects of relative price uncertainty.2 The present paper attempts to fill this gap for the case in which utility is intertemporally additively separable. Section 2 presents a general framework for analysing expected utility maximization in a two-period, multi-commodity, multi-asset environment in wh;- prices and income in the second period are stochastic. Section 3 analyses the effect on expected utility of increased variability in the relative price of a single commodity in a two-commodity context. Here and in Section 5 the geometric mean preserving spread of Flemming, Turnovsky and Kemp (1977) provides a definition of increased variability. Section 4 derives optimal portfolio behaviour for the special case in which the relative price is log-normally distributed. The effect of price variability on optimal savings in a two-period context is considered in Section 5. Some concluding observations and an extension to a general equilibrium problem appear in Section 6.