Preferences and Production under Uncertainty

The Arrow-Savage-Debreu formalism (state space, consequence space, acts) for modelling a stochastic decision is introduced. Preferences over stochastic outcomes framed as maps (acts) from the state space to the consequence space are studied and related to nonstochastic preference structures. Distance function representations of preferences are developed and their superdifferential correspondences are shown to define subjective probability measures. Structural restrictions including uncertainty aversion, constant absolute uncertainty aversion, and constant relative uncertainty aversion are examined and related to parallel restrictions for nonstochastic preference or production structures. A model of a stochastic technology that has the nonstochastic production model as a special case is introduced, and distance function representations of it are discussed. Structural assumptions on the stochastic technology are discussed.