Symmetry Restrictions in the Analysis of the Competitive Firm Under Price Uncertainty
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.
Dalal, Ardeshir J. "Symmetry restrictions in the analysis of the competitive firm under price uncertainty." International Economic Review (1990): 207-211.