Second-Order Inequality: Clarifying and Modeling the Gini Coefficient with Measures of Internal Asymmetry
10 Pages Posted: 2 Jan 2019
Date Written: December 17, 2018
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: Suggested Citation