Lorenz Curves and the Gini Coefficient

The Lorenz curve is a measure of the distribution of wealth (or income or other factors) in a society. The x value of the curve corresponds to a percentile of the population ordered according to the characteristic in question. The y value of the curve represents that portion of the total value of the characteristic in question held by people no wealthier than the x-valued percentile of the population. Thus, the value (0.7, 0.3) means that the bottom 70% of the population owns 30% of the total wealth in society. The Gini coefficient is the (shaded) area between the Lorenz curve that would exist in a perfectly egalitarian society (the dashed line) and the Lorenz curve that does exist, divided by the area under the Lorenz curve that would exist in a perfectly egalitarian society. The coefficients are thus normalized to run from zero in a perfectly egalitarian society, to one in a society in which the wealthiest person held all the wealth. By way of reference, the United States has a Gini coefficient of 0.4; Sweden has a Gini coefficient of 0.25; Bolivia has a Gini coefficient of 0.61. This Demonstration allows you to select a random distribution from which to draw the wealths of the members of a size-selectable population. It computes the corresponding Lorenz curve and Gini coefficient and insets the corresponding cumulative distribution of wealth.

THINGS TO TRY

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DETAILS

This Demonstration uses a numeric method (sampling) to compute the Gini coefficient for a given distribution. Analytic computation of this coefficient from a given distribution of wealth is often difficult.

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Contributed by: Seth J. Chandler

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