Uncertainty and Factor Proportions

Abstract

Stewart (1978) examined the theory of the firm's factor proportion decision under input price uncertainty and concludes the uncertainty will induce the risk averse manager to hire more of the certain priced factor of production than his risk neutral counterpart. He then adds output price uncertainty to the model and concludes that it doesn't affect the direction of factor substitution for the risk averse firm. The purpose of this paper is to show that the direction of factor substitution can be reversed when output price uncertainty is added to the model. Stewart set up a model of the competitive firm producing a single output (q) using an input (X2), chosen prior to the production period, purchased at a known price (r2). In addition, the firm combines X2 with another input (XI), purchased in competitive markets at a price (rl) which is not known when the level of X2 is chosen. It is also assumed that r1 is subject to random fluctuations during the production period and has a subjective probability density 4>(rl), known to the firm's manager at the time X2 is chosen. Output and the price of X2 are known with certainty, so that the manager chooses X2 to maximize E u('7r) where u is a von Neumann-Morgenstem utility function with profit as it's argument and E is the expectations operator. In addition, the production constraint is solved for XI and substituted into the objective function so that T= pq rlg(X2,q) r2X2, and a necessary condition for utility maximization is