Stochastic Returns and the Theory of the Firm
The theory of the firm under uncertainty has been discussed by P. A. Diamond and H. Leland in an elaboration of the expected utility maximization hypothesis. Leland's approach emphasizes the connection between the theory of the firm and inventory theory, with the price of the output being a stochastic variable. Diamond deals with technological uncertainty in a general equilibrium context; his theory explains, in part, the supply of financial assets by firms. Both approaches clearly have their origins in earlier literature on the theory of the firm under uncertainty, though Leland's seems to be much more closely related to the earlier quantitative literature. In inventory theory (see K. J. Arrow, S. Karlin, and H. Scarf), the firm minimizes the expected cost of holding inventories of the product it sells subject to stochastic demand, while in Leland's paper the firm produces output under what may be known and fixed production costs but sells output at a stochastic price. Diamond's paper can, with reinterpretation, be treated as the production function analogue of the theory of the demand for money under uncertainty, the stochastic input playing the role of the bond or asset with uncertain rate of return. Diamond's approach sharpens Jack Hirshleifer's hypothesis that the theory of investment under uncertainty involves an application of the expected utility maximization by presenting a specific source of uncertainty, the stochastic input in the neoclassical production function. In Diamond's paper, output by thejth firm is, in general,
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