Positive Mathematical Programming with Generalized Risk

Abstract

Price risk in a mathematical programming framework has been confined for a long time to a constant risk aversion specification originally introduced by Freund in 1956. This paper extends the treatment of risk 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 PMP specification that allows the estimation of the preference parameters and calibrates the model to the base data within an admissible small deviation. The PMP approach under generalized risk allows also the estimation of output supply elasticities. The approach is applied to a sample of large farms.