Constrained Choices under Risk

Abstract

There has recently been a revival of interest in the implications of rationing for economic theory. Extending the work of Samuelson [21], Tobin and Houthakker [24], and Pollak [16], recent papers by Bruno [3], Howard [8], Latham [13] and Neary and Roberts [15] have explored the theory of producer and consumer behavior under quantity rationing. These developments have provided useful hypotheses in the investigation of economic behavior. For example, they have stimulated a reexamination of macroeconomic disequilibrium. However, previous work seems to have focused on economic models in the absence of uncertainty. Yet, given that production decisions are often made before output prices are known, and in the absence of complete contingent markets, Sandmo [22], Batra and Ullah [2] and others have developed the theory of the competitive firm under price uncertainty. Under the expected utility maximization hypothesis, such a theory provides useful information about the influence of changing economic conditions or of risk behavior on production decisions. But because of the presence of short run adjustment costs leading to short run input fixity, or because of regulatory or institutional constraints, quantity rationing often influences production decisions. In order to evaluate how rationing influences such decisions, there is a need to develop a conceptual model of constrained choices of the firm under risk. The objective of this paper is to explore the implications of quantity rationing in the context of production theory under price uncertainty. By introducing risk and risk behavior, it extends the classical analysis of quantity constrained production decisions [3; 21]. The implications of quantity constraints for risk responsive choice functions are derived using the concepts of compensated choice functions and virtual prices. It is shown that expected price effects can be decomposed into substitution effects and wealth effects. The substitution effects measure the effects of a change in expected price on the compensated choice functions, the compensation being made through a change in initial wealth holding expected utility constant. The wealth effects characterize risk preferences since a non-zero wealth effect reflects a departure from an Arrow-Pratt constant absolute risk aversion utility function. The influence of rationing on the properties of ordinary as well as compensated choice functions is analyzed in details. By deriving the implications of quantity constraints for firm behavior under uncertainty, the paper presents a number of useful results concerning the influence of risk or technology on economic behavior under rationing. For example, a