Symmetry Restrictions in the Analysis of the Competitive Firm Under Price Uncertainty

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. This paper shows that if the production function is appropriately restricted some symmetry (reciprocity) results which hold for a competitive firm under certainty continue to hold under price uncertainty, for any strictly concave utility function. In contrast, earlier analyses have established these symmetry relations by imposing restrictions on the utility function. The present analysis uses the envelope theorem, the indirect utility function, and the duality between production and cost.

Comparative statics effects independent of the utility function. When do we act the same way under risk?

“…The first model with this structure that we have found in this field is the seminal model proposed by Sandmo (1971). Since then, many authors have changed this model by considering, for instance, a source of uncertainty different from the price, such as the output (see Dalal & Alghalith, 2009) or the demand (see Leland, 1972 andCoes, 1977); or new decision-making variables, such as the firm's hedge level (see Holthausen, 1979) or new parameters, such as the price of inputs (see Dalal, 1990). Other authors have considered that the firm's goal is not to maximize its profit but to maximize the EU of income per worker (see Bughin, 1995;Feder, 1977;Hey, 1981;and Muzondo, 1979).…”

Production decisions under joint price and production uncertainty

“…This is because the expected utility maximization problem can be viewed as the second stage in a two stage process, where the first stage is the minimization of costs for any given level of y. As Chavas (1985) and Dalal (1990) where X i is the ith input demand and b X i is the corresponding conditional input demand. Clearly, for s ¼ p; r; h,…”

Domestic and Foreign Sales When Prices in Both Markets are Uncertain

“…Allowing q and q* to change, but 2 A shift parameter such as H has been shown to be a useful construct for both theoretical and empirical analyses of behaviour under uncertainty. See Dalal (1983Dalal ( , 1990Dalal ( , 1994 for examples of its use and interpretation.…”

“…An interpretation for the sign of Z 12 can be provided based on whether foreign and domestic sales are substitutes or complements. Following Dalal (1983Dalal ( , 1990, the substitution effect of a change in any parameter is defined as the effect of such a change on optimal sales when the shift parameter (H) is adjusted to hold maximum expected utility (V) constant. 8 Now suppose that Y p increases and dV ¼ 0.…”

“…where Á ( Z 11 Z 22 À Z 2 12 ) > 0 from the second-order conditions for the maximization problem in (1), S qp * (dq=dY p*) j dV ¼ 0 is the substitution effect of a change in Y p* on q, and the symmetry of the cross-price substitution terms may either be established directly (as in (18) and (19)) or by appealing to the results obtained by Dalal (1990). 9 8 That is, the substitution effect on, say, q of a change in some parameter is defined as:…”