On Output Price Uncertainty and the Comparative Statics of Industry Equilibrium

Abstract

The analysis of firm response to output price variability has, until recently, been incomplete due to a failure to consider explicitly the effect of firm response on the attainment of competitive equilibrium at the industry level. A recent paper by Appelbaum and Katz [1] has addressed the issue of industry equilibrium under output price uncertainty. They show how the optimal number of firms might change through the process of exit and entry, and they characterize the collective influence of firms' decisions on expected market price. However, their analysis focuses on firms with a single-stage production process which allows no production flexibility (in the form of adjustment of output levels) after output price is revealed. An earlier paper by Hartman [3] has shown that, at the firm level, the optimal response to output price uncertainty will depend on whether production flexibility exists. Specifically, if firms employ a two-stage production process which is characterized by the presence of a quasi-fixed factor, then firm-level output may increase or decrease in response to changes in output price variability even if firms are risk neutral. The assumption that production flexibility exists changes those results initially developed by Sandmo [7], and applied more recently by Appelbaum and Katz [1], which are based on a single-stage production process. This paper provides an extension of the Appelbaum and Katz analysis to admit production flexibility. Equivalently, it extends the analysis of Hartman to consider explicitly the effect of firm response on the attainment of competitive equilibrium at the industry level. Appelbaum and Katz show that for an industry of identical risk-averse firms with a singlestage production technology, the effect of a mean-preserving increase in price uncertainty is to decrease industry output and to raise market price. A more recent comment by Ishii [5] shows that output per firm will also fall, yet none of these authors shows unambiguously whether the number of firms increases or decreases. Although not explicitly stated, the analysis in Appelbaum and Katz suggests there would be no firm or industry response to a mean-preserving change in price spread if firms were risk-neutral (expected-profit maximizers). The model employed in this paper is analogous to that of Appelbaum and Katz with two principal exceptions: (i) here an industry is composed of firms all of which are either risk neutral