A measure of income inequality.
We plot the proportion of income I(p) that the poorest proportion p of the population earns in an economy against p in a graph. (Eg I(0.8) = 0.2 means that the poorest 80% of the population earns only 20% of the total income. This is the case in the world economy today.)
If there is perfect income equality the graph of I(p) is the line segment between (0,0) and (1,1), the line of perfect equality. Otherwise the graph of I(p) is an increasing, convex curve that goes from (0,0) to (1,1) and lies below the line of perfect equality. The area between the line of perfect equality and the graph of I(p) is called the Gini coefficient. The less equal the income distribution, the larger the Gini coefficient.

The Gini coefficient is a measure of income equality developed by Corrado Gini 1912. After over a hundred years it is still the most commonly used metric in determining a county's income distribution, and is generally taken to be a sound indicator of a society's social inequality.

To find the Gini coefficient, you first have to find a population's Lorenz curve; this is a graph that shows a population's income as a distribution function. One axis of the graph represents a percentage of the population (from 0% up to 100%), and the other represents percent of income. In a perfectly equal system, increasing the percent of the population you were looking at would result in an exactly equal increase in the the amount of income earned; 10% of the population would earn 10% of the income, 50% of the population would earn 50% of the income -- resulting in a 'curve' that was actually a straight line angled at precisely 45 degrees. But the real world doesn't work like that, and in fact the Lorenz curve is a concave curve, with the 10% of the population that are the lowest earners making less than 10% of the wealth, and the 10% that are the highest earners making more than 10% of the wealth.

The Gini coefficient is calculated by comparing a perfectly equal Lorenz curve to the real-world curve (specifically, take the area between the observed curve and the perfectly equal curve and divide it by the total area under the perfectly equal curve). The result is often multiplied by 100 to make a percent.

A Gini coefficient of zero indicates perfectly equal incomes, where all people earn exactly the same; a Gini coefficient of one indicates the extreme case of unequal incomes in which one person has all the income and all others have none.

The World Bank estimates that the USA has a coefficient of 40.5 as of 2010 (up from 37.7 in 1986); the UK 32.6 (as of 2012); Norway 25.9 (2012); China 42.1 (2010); and Chile 50.5 (2013). The CIA world Factbook estimates that the worldwide Gini coefficient is 38.0.

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