State-Dependent Linear Utility Functions for Monetary Returns

Abstract

We present a theory of expected utility with state-dependent linear utility function for monetary returns that includes results on first order stochastic dominance, mean-preserving spread, increasing-concave linear utility profiles, and risk aversion. Applying the expected utility theory developed here, we analyze the contract a monopolist would offer in an insurance market, allowing partial loss coverage. We also define a utility function for monetary wealth that, in a certain sense, reconciles state-dependent constant average utility of money with loss aversion and the Friedman-Savage hypothesis. As an immediate consequence of such a utility function, we obtain a profile of state-dependent linear utility functions for monetary wealth, where states of nature correspond to intervals in which monetary wealth may occur. The intervals are mutually disjointed, and an interval corresponding to greater monetary wealth has a lower positive average utility of monetary wealth.