In 1956, Freund introduced the analysis of price risk in a mathematical programming framework. This paper generalizes the treatment of price risk preferences in a mathematical programming framework along the lines suggested by Meyer (1987) who demonstrated the equivalence of expected utility and a wide class of probability distributions that differ only by location and scale. This paper shows how to formulate a Positive Mathematical Programming (PMP) specification that allows the estimation of the risk preference parameters and calibrates the model to the base data within admissible small deviations. The PMP approach under generalized risk allows also the estimation of output supply elasticities and the response analysis of decoupled farm subsidies that, recently, has interested policy makers. The approach is applied to a sample of large farms. Not all farms produce all commodities.