Total Price Uncertainty and the Theory of the Competitive Firm

Abstract

In the past ten years our understanding of the behaviour of the firm under uncertainty has developed rapidly.1 This has been due to research in two broad areas: the sources of uncertainty in the firm's operations, and the pricing of that uncertainty by the firm's stockholders. In the first area, Baron (1968), Sandmo (1971), Leland (1972), and Batra and Ullah (1974) have all examined the impact of price uncertainty; Blair (1974), Holthausen (1976) and Hartman (1976), the impact of factor cost uncertainty; and Hartman (1972), Turnovsky (1973) and Epstein (1978) the extent to which technological flexibility affects the impact of price and cost uncertainty. These original contributions have invariably assumed that the objective of the firm is to maximize a shareholder's expected utility function. This approach implicitly assumes that the price of risk is affected by the firm's decision and thus that the firm is a monopolist in the financial market that allocates risk. Concurrent with this literature has been the development of theories of market valuation under uncertainty. Arrow (1971), Debreu (1959) and Hirshleifer (1970) have developed the time-state preference model (TSP), and Sharpe (1964) and Lintner (1965) the capital asset pricing model (CAP), to provide a specification of the firm's market value under uncertainty. Hence, if the equilibrium assumptions of either model hold, the managers of the firm can maximize shareholder utility by maximizing an objective market value of the firm. Then, as Hite (1978) and Nielsen (1975) have shown, the theory of the firm under uncertainty is formally identical to the theory of the firm under certainty. The only difference is that the value is replaced by the certainty equivalent value, determined from the equilibrium valuation equation. Unfortunately, it is not realistic to assume that markets are either complete or perfect. The most obvious incompleteness is the lack of full commodity markets. Some commodity markets do exist; however, the firm cannot remove technology or wage risk. The result is that stock markets exist to allocate residual income risk, whereas in a complete market all of the components of that risk would have their own commodity market, thus making the stock 2 market redundant. Hence, this paper will consider the joint interaction of total price uncertainty, that is, product price and factor cost uncertainty, in a model where there is only a stock market to allocate residual income risk. Moreover, we will allow the completeness of this residual income market to vary to examine its impact on the firm's operating decisions. This paper can therefore be considered a synthesis and generalization of previous work in this area.