Economics » Poverty and Economic Inequality » Income Inequality: Measurement and Causes

# Lorenz Curve

## Lorenz Curve

The data on income inequality can be presented in various ways. For example, you could draw a bar graph that showed the share of income going to each fifth of the income distribution. This figure presents an alternative way of showing inequality data in what is called a Lorenz curve. The Lorenz curve shows the cumulative share of population on the horizontal axis and the cumulative percentage of total income received on the vertical axis.

The Lorenz Curve

A Lorenz curve graphs the cumulative shares of income received by everyone up to a certain quintile. The income distribution in 1980 was closer to the perfect equality line than the income distribution in 2011—that is, the U.S. income distribution became more unequal over time.

Every Lorenz curve diagram begins with a line sloping up at a 45-degree angle, shown as a dashed line in this figure. The points along this line show what perfect equality of the income distribution looks like. It would mean, for example, that the bottom 20% of the income distribution receives 20% of the total income, the bottom 40% gets 40% of total income, and so on. The other lines reflect actual U.S. data on inequality for 1980 and 2011.

The trick in graphing a Lorenz curve is that you must change the shares of income for each specific quintile, which are shown in the first column of numbers in this table, into cumulative income, shown in the second column of numbers. For example, the bottom 40% of the cumulative income distribution will be the sum of the first and second quintiles; the bottom 60% of the cumulative income distribution will be the sum of the first, second, and third quintiles, and so on. The final entry in the cumulative income column needs to be 100%, because by definition, 100% of the population receives 100% of the income.

### Calculating the Lorenz Curve

Income CategoryShare of Income in 1980 (%)Cumulative Share of Income in 1980 (%)Share of Income in 2013 (%)Cumulative Share of Income in 2013 (%)
First quintile4.24.23.23.2
Second quintile10.214.48.411.6
Third quintile16.831.214.426.0
Fourth quintile24.755.923.049.0
Fifth quintile44.1100.051.0100.0

In a Lorenz curve diagram, a more unequal distribution of income will loop farther down and away from the 45-degree line, while a more equal distribution of income will move the line closer to the 45-degree line. The greater inequality of the U.S. income distribution between 1980 and 2013 is illustrated in this figure because the Lorenz curve for 2013 is farther from the 45-degree line than the Lorenz curve for 1980. The Lorenz curve is a useful way of presenting the quintile data that provides an image of all the quintile data at once. The next Clear It Up feature shows how income inequality differs in various countries compared to the United States.

### How does economic inequality vary around the world?

The U.S. economy has a relatively high degree of income inequality by global standards. As this table shows, based on a variety of national surveys done for a selection of years in the last five years of the 2000s (with the exception of Germany, and adjusted to make the measures more comparable), the U.S. economy has greater inequality than Germany (along with most Western European countries). The region of the world with the highest level of income inequality is Latin America, illustrated in the numbers for Brazil and Mexico. The level of inequality in the United States is lower than in some of the low-income countries of the world, like China and Nigeria, or some middle-income countries like the Russian Federation. However, not all poor countries have highly unequal income distributions; India provides a counterexample.

Income Distribution in Select Countries (Source: U.S. data from U.S. Census Bureau Table 2. Other data from The World Bank Poverty and Inequality Data Base, http://databank.worldbank.org/data/views/reports/tableview.aspx)

CountrySurvey YearFirst QuintileSecond QuintileThird QuintileFourth QuintileFifth Quintile
United States20133.2%8.4%14.4%23.0%51.0%
Germany20008.5%13.7%17.8%23.1%36.9%
Brazil20092.9%7.1%12.4%19.0%58.6%
Mexico20104.9%8.8%13.3%20.2%52.8%
China20094.7%9.7%15.3%23.2%47.1%
India20108.5%12.1%15.7%20.8%42.8%
Russia20096.1%10.4%14.8%21.3%47.1%
Nigeria20104.4%8.3%13.0%20.3%54.0%

Check out the video of wealth inequality across the world: