The Generalized Envelope Theorem and Price Uncertainty

Silberberg recently extended Samuelson's development of the envelope theorem deriving comparative static and reciprocity conditions for the competitive firm in the case of certainty. In the context of these results, the competitive firm is examined under price uncertainty. It is assumed tha decisions are made prior to the realization of stochastic prices.Nonlinear risk preferences indicate more ambiguous results than those obtained under risk neutrality. In particular, reciprocity conditions do not indicate output supply and input demand symmetries. In general the reciprocity conditions are empirically cumbersome. Sufficient conditions have been derived that allow qualitative results similar to the certainty case to be obtained. These conditions led to a class of utility functions where the major certainty propositions regarding symmetry and reciprocity hold.