Mean utility preserving increases in risk for state dependent utility functions

This paperThis paper is revised version of Essay 2 of my Ph.D. dissertation written at The John Hopkins University. I am grateful to my thesis advisers, Edi Kami and Itzhak Zilcha, to Mark Machina, who discussed the paper at the Winter 1984 meeting of the Econometric Society in Dallas, and to Fanny Demers for valuable comments. I also thank the Social Sciences and Humanities Research Council of Canada and the Ministry of Education of the government of Quebec for financial support. defines the concept of a mean utility preserving spread across states (MUPSAS) for state dependent utility functions and analyzes the behavioural impact of shifts in the probability distribution of wealth across states such that overall mean utility is preserved. The main result provides an alternative way of ranking state dependent utility functions according to their degree of risk aversion (thus extending Kami's theorem of comparative risk aversion) and establishes a link between increases in risk and risk aversion for state dependent preferences. In a portfolio problem where preferences and the rate of return of the risky venture are state dependent, we find sufficient conditions to determine the impact of a MUPSAS on the optimal share of the portfolio invested in the risky asset