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Gini Coefficient: A measure of inequality

W. Christian

By looking at the distribution of wealth among the agents we were able to conclude that various forms of taxation and distribution can lead to greater or lesser wealth equality. However, it is useful to introduce an explicit measure of wealth inequality so that we can reach more quantitative conclusions.

A common measure of wealth inequality is the *Gini coefficient* (or Gini index), G G . A small value of G G indicates a more equal wealth distribution with G = 0 G=0 corresponding to complete equality. In contrast, G = 1 G=1 corresponds to one person having all the wealth. The Gini coefficient for wealth varies from about 0.55 for Japan to 0.85 for Namibia, and is about 0.80 for the United States. Denmark, which has a strong welfare program, has a Gini coefficient of 0.81. The Gini coefficient for disposable income is typically lower, between 0.3 and 0.5, and is about 0.45 in the United States and 0.30 in Denmark.

The meaning of the Gini coefficient can be best understood by looking at Figures 1(a) and 1(b), which show plots of the percentage of the total wealth of a population owned by a given percentage of the population, starting from the poorest person. This percentage is an example of a *cumulative distribution* and is equal to the percentage of the population having wealth less than or equal to a given amount. As this amount is increased, the cumulative wealth distribution must also increase. Figure 1(a) corresponds to perfect wealth equality and G = 0 G=0 . For perfect wealth equality the cumulative wealth distribution grows linearly with the number of people. If wealth is distributed unequally, as in Figure 1(b), we obtain a curve for the cumulative wealth instead of a straight line. If the beginning of the curve is flat, that means many people have very little wealth. The end of the curve on the right must reach 100% of the total wealth in the economy. A very sharp rise near the right of the curve indicates that a few people have most of the wealth.

Excerpt From: Tobochnik, Christian, and Gould. “Modeling Wealth Inequality.” iBooks.