This paper supposes an individual cares about his/her own wealth not only directly but also via the relative standing that this wealth induces. The implications for risk-taking are investigated in particular. Such a model provides a natural explanation of the "concave-convex-concave" utility described by M. Friedman and L. Savage (1948). However, there are a number of key differences between the present model and any model based on own wealth alone. For example, an equilibrium wealth distribution here may have a middle class. Further, the status interaction involves an externality and an equilibrium wealth distribution may be Pareto inefficient. Copyright 1992 by The Econometric Society.

This paper studies endogenous risk-taking by embedding a concern for status (relative consumption) into an otherwise conventional model of economic growth. We prove that if the intertemporal production function is strictly concave, an equilibrium must converge to a unique steady state in which there is recurrent endogenous risk-taking. (The role played by concavity is clarified by considering a special case in which the production function is instead convex, in which there is no persistent risk-taking.) The steady state is fully characterized. It displays features that are consistent with the stylized facts that individuals both insure downside risk and gamble over upside risk, and it generates similar patterns of risk-taking and avoidance across environments with quite different overall wealth levels. Endogenous risk-taking here is generally Pareto-inefficient. A concern for status thus implies that persistent and inefficient risk-taking hinders the attainment of full equality.

Christopher Harris, Philip Reny, Arthur Robson, The Existence of Subgame-Perfect Equilibrium in Continuous Games with Almost Perfect Information: A Case for Public Randomization, Econometrica, Vol. 63, No. 3 (May, 1995), pp. 507-544