Production Flexibility and the Behaviour of the Competitive Firm under Price Uncertainty

Abstract

There have been numerous studies in the literature of the competitive firm under price uncertainty. Recently, Sandmo [18] and Batra and Ullah [2] have analysed the behaviour of an expected utility maximizing firm which chooses its output level subject to uncertainty about the price that will prevail for its product. Both studies represent increased price uncertainty by a multiplicative shift of the random variable coupled with a translation so as to preserve the mean, and they consider the effect on output of increased product price uncertainty. While Sandmo is unable to sign the effect, Batra and Ullah show that output declines if absolute risk aversion is declining. In both [18] and [2] it is assumed that all decisions must be made ex ante. Turnovsky [19] has extended the model to allow the firm to modify its initial decisions, at additional cost, after it learns the true selling price of its product. He compares initial production when price expectations are certain and when they are uncertain with the same expected value. Hartman ([10] and [12]) has investigated the firm's reactions to increased price uncertainty when the technology permits some ex-post flexibility in adjusting to the prices that are eventually realized. In the former paper Hartman uses a multiperiod model to analyse the effects of future product and factor price uncertainty on the rate of investment in a single capital stock, given that the firm encounters convex adjustment costs in changing the level of its stock. Qualitative results are derived from the hypothesis of constant returns to scale in production. This hypothesis is dropped in the two-period model in [12] which considers a single output, two factor technology.' Capital is a quasi fixed factor and must be chosen ex ante, while the other input, labour, may be chosen after prices become known with certainty. In both studies increased variability is represented by a mean preserving spread (see Rothschild and Stiglitz [16]), and it is generally assumed that the firm maximizes the expected value of profits. In [12], Hartman also compares the capital input given certain price expectations with that in a situation involving a small amount of uncertainty, assuming that the firm is averse to profit uncertainty. In this paper we modify and generalize the above analyses in three principal ways. First, we adopt the Rothschild-Stiglitz definition of increased uncertainty and show that the findings of both Sandmo and Batra and Ullaht must subsequently be altered. Unlike the other studies, we also investigate the effects of mean utility preserving spreads (see Diamond and Stiglitz [5]). These spreads generate some intuitively appealing comparative statics results. With the exception of a paper by Dhrymes [4] which employs the restrictive meanvariance framework, in other studies, including all of the above, the firm's ex-ante decision variable is a scalar, e.g. the level of production or the input of a quasi-fixed factor. Most of our qualitative results are similarly restricted to aggregative models. However, for the