Pareto Distribution of Consumption Values as an Origin of Utility Functions over Wealth with Constant Elasticity

Abstract

This paper proposes a new theoretical foundation for utility functions over wealth with a constant elasticity. The key idea is that, when decision makers face an underlying distribution of consumption values for which they allocate their wealth to attain, then their utility over that wealth is shaped by that distribution. When the distribution has a Pareto tail, the implied utility function exhibits a constant elasticity when the wealth level is low. As its exponent approaches 1 (i.e. Zipf's Law), the utility function becomes approximately logarithmic. These results apply to many situations regardless of their contextual details thanks to statistical theories such as the generalized Central Limit Theorem. Besides this benchmark, most other standard distributions imply a decreasing elasticity, while some exceptions suggest an increasing elasticity. When applied to the labor supply elasticity, this approach predicts values of the compensated and uncompensated elasticity that are in accord with the evidence.