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

30 Pages Posted: 6 Nov 2020 Last revised: 16 Nov 2020

See all articles by Chishio Furukawa

Chishio Furukawa

Department of Economics, Yokohama National University; affiliation not provided to SSRN

Date Written: September 17, 2020

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.

Keywords: Pareto Distributions, CRRA Utility Functions

JEL Classification: D11, D9

Suggested Citation

Furukawa, Chishio, Pareto Distribution of Consumption Values as an Origin of Utility Functions over Wealth with Constant Elasticity (September 17, 2020). Available at SSRN: https://ssrn.com/abstract=3694202 or http://dx.doi.org/10.2139/ssrn.3694202

Chishio Furukawa (Contact Author)

Department of Economics, Yokohama National University ( email )

Tokiwadai, Hodogaya-Ku, Yokohama
Yokohama, Kanagawa
Japan

affiliation not provided to SSRN

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