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”. As an application of the expected utility theory developed here, we analyze the contract that a monopolist would offer in an insurance market that allowed for partial coverage of loss. We also define a utility function for monetary returns 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 returns, where states of nature correspond to mutually disjoint intervals in which monetary gains and losses may occur.