Symmetry Restrictions in the Analysis of the Competitive Firm Under Price Uncertainty
证明，在价格不确定性下，若生产函数受到适当限制，竞争性企业在确定性下成立的某些对称性（互易性）结果仍然成立，且不依赖于效用函数的具体形式。
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.