Profits and Safety in the Theory of the Firm under Price Uncertainty

Abstract

THIS PAPER studies quantity-setting behavior under price uncertainty when preferences are based upon expected profits and the probability of loss. These preferences have been suggested over the years by several authors [1], [5], [6], [9], [10], [13] as alternatives to the abstract notion of a utility function and are not generally compatible with the axioms of utility theory.1 Previous studies on the subject have been based on the restrictive assumption of normality or on Tchebychev's inequality.2 This paper derives exact distribution-free results by the straightforward use of the monotonicity property of distributions. Section 2 presents the equilibrium conditions of competitive and monopolistic firms under alternative profit-safety preferences. It shows that the conclusions of Day, Aigner and Smith [5] are valid for arbitrary distributions under a rather general form of price uncertainty, which includes both additive and multiplicative uncertainty as special cases. Section 3 derives the comparative statics properties of the solutions for changes in fixed costs, price and taxes and shows that the response of optimal output depends critically on the form of the preference function. Section 4 compares the results of this paper with those of traditional theory and expected utility maximization.

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