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 paticular. Such a model provides a natural explantion of the “concave-convex-concave” utility described by Friedman and Savage. However, there are a number of key differences between the present medel 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.
KEYWORDS: Friedman-Savage, attitude to risk, relative wealth, status,Pareto efficiency.
1.INTRODUCTION
THE NATION THAT AN INDIVIUAL might care not only about his/her own wealth but also about the implied relative standing in the distribution of wealth a long but checkered history. (A early exponent of such ideas was, of course, Veblen (1899).) It is indeed a nation which most economists reject, albeit usually without explicit omment. (A notable and articulate exception, however, is Frank (1985), for example. See also the references Frank cites on pp. 33-34.) It is, however, a nation with substantial intuitive appeal and it seems useful to ascertain its consequences before coming to a final judgement as to its merits.
The present paper is concerned with deriving the consequences of such valuation of status for risk taking. What seems to be the sharpest possible model is adopted here. This assumes that what is essentially ordinal rank in the wealth distribution enters von Neumann-Morgenstern utility as an argument in addition to wealth itself. Thus higher wealth increases utility not only directly but also indirectly via higher status. In the interests of both simplicity and drama, it is typically assumed here that all individuals have identical utility functions which are concave in wealth but convex in status.
Section 2 discusses how the model provides a natural explanation of the fundamental phenomenon addressed by Friedman and Savage (1948) that individuals may simultaneously purchase insurance and paticipate in lotteries. Although each individual here has a utility function which is concave in wealth itselt, utility can nevertheless be convex in wealth over some range when the indirect effect via status is included. This effect is enhanced by the convexity of utility in statis, but will follow in any case if increasing wealth entails movng up in status much more rapidly than losing wealth entails moving down. It is shown
Initial versions of this paper were writen while visiting the University of Michigan and the Center for Economic Research at Tilburg University. Usefui comments were made by participants in a number of seminars, especially those at Cambrige and the Chicago. I also thank Ted Bergstrom, Phill Reny, Andreu Mas-Colell, and the referees for very hrlpful discussions and suggestons.