Multi-Output Firm Under Price Uncertainty

A closed-form dual representation of the multi-output production problem is developed under CARA and the large exponential family of multivariate price distributions. System-wide response analysis allows an understanding of second moment and risk tolerance effects, and provides insights on distorting subsidies admissible under World Trade Organization agreements. We demonstrate second-order flexibility in the sense that any empirical first and second moments can be imposed. Production complementarity results are identified for a special linearized version of the model. Incentives under the class of elliptically contoured distributions are studied, as are speculation decisions in the presence of futures markets.