Second-Order Inequality: Clarifying and Modeling the Gini Coefficient with Measures of Internal Asymmetry

10 Pages Posted: 2 Jan 2019

See all articles by James Ming Chen

James Ming Chen

Michigan State University - College of Law

Date Written: December 17, 2018

Abstract

This paper presents a physical model of the Gini coefficient and its corresponding Lorenz curve. If the Lorenz curve is scaled to 1, then 1 represents gross domestic income, gross domestic product, or societal wealth. The value 1 also represents total population. On these assumptions, the value of x ∈ [0, 1] where the first derivative of the Gini coefficient equals one represents the population quantile that enjoys per capita income or wealth. This paper also describes methods for evaluating the internal asymmetry of any distribution corresponding to a particular Gini coefficient. It concludes with worked examples from Oxfam’s survey of global inequality and from French data on wealth inequality.

Keywords: Gini Coefficient, Inequality, Lorenz Asymmetry Coefficient, Polar Coordinates, Pareto Distribution, Lambert W Function, Physical Economics, Oxfam, France

JEL Classification: D63

Suggested Citation

Chen, James Ming, Second-Order Inequality: Clarifying and Modeling the Gini Coefficient with Measures of Internal Asymmetry (December 17, 2018). Available at SSRN: https://ssrn.com/abstract=3302339 or http://dx.doi.org/10.2139/ssrn.3302339

James Ming Chen (Contact Author)

Michigan State University - College of Law ( email )

318 Law College Building
East Lansing, MI 48824-1300
United States

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