The Lorenz Curve and Various Economic Indices

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The Lorenz curve is a plot of the cumulative share of the income earned by the cumulative share of the population, with population ordered from lowest to highest incomes. The Gini coefficient is the area between the line of perfect equality and the Lorenz curve divided by the total area under the line of perfect equality, with 0 representing perfect equality and 1 representing perfect inequality. The Hoover index is the portion of income that would need to be redistributed to achieve perfect equality. The Theil index is an entropy index that can be viewed as a measure of redundancy; it is the weighted average of inequality within subgroups and, unlike the Gini coefficient, can be decomposed to view the individual Theil index of subgroups.


Use the sliders in this Demonstration to set the total population and total income of three subgroups in a society, where a subgroup is defined as a section of a society composed of individuals with similar incomes; these values can be regarded as weights rather than actual numerical values.


Contributed by: Shreyas S. Gandlur and Craig Soares (June 2015)
Open content licensed under CC BY-NC-SA



Special thanks to the NetMath Program at the University of Illinois at Urbana-Champaign and the Math Department at Schaumburg High School.


[1] P. D. Allison, "Measures of Inequality," American Sociological Review, 43(6), 1978 pp. 865–880.

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