Abstract
Traditionally, risk aversion (both absolute and relative) has been expressed as a function of wealth alone. The characteristics of risk aversion as wealth changes have been extensively studied. However, prices, as well as wealth, enter the indirect utility function, from which the typical risk aversion measures are calculated. Given that, changes in prices will affect risk aversion, although exactly how has not been considered in the literature. This paper provides such an analysis. In particular, we firstly remind the reader that both absolute and relative risk aversion are homogeneous functions, and as such independently of their particular slopes in wealth, there is a natural effect that holds relative risk aversion constant and decreases absolute risk aversion when prices and wealth are increased by a common factor. We also show that the size of relative risk aversion as compared to the number 1, which is of much importance to the comparative statics of the economics of risk and uncertainty, depends on how changes in prices affect marginal utility. Under plausible (and standard) theoretical assumptions we find that relative risk aversion is likely to be increasing, and that increases in prices will have a tempering effect on risk aversion.
Highlights
Risk aversion is one of the most useful concepts in the microeconomics of risk and uncertainty
We firstly remind the reader that both absolute and relative risk aversion are homogeneous functions, and as such independently of their particular slopes in wealth, there is a natural effect that holds relative risk aversion constant and decreases absolute risk aversion when prices and wealth are increased by a common factor
We show that the size of relative risk aversion as compared to the number 1, which is of much importance to the comparative statics of the economics of risk and uncertainty, depends on how changes in prices affect marginal utility
Summary
Risk aversion is one of the most useful concepts in the microeconomics of risk and uncertainty. Relative risk aversion is an extremely useful concept in microeconomics, both because it is the elasticity of marginal utility, and because it is reasonably easy to get empirical estimations of it. Without formal proof) that for reasonable values of wealth, relative risk aversion should be greater than 1 and increasing, something that is very often found to be so in empirical studies.. A good deal of comparative statics results (see, for example, the literature on the simultaneous choice of insurance and risk; [2,3,4]) only go through for the case of relative risk aversion less than 1. In this paper the relationship between relative risk aversion and the number 1 is reconsidered taking into account explicitly the effect of prices as well as wealth
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