The Lorenz Curve

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Income inequality is a pressing issue both in the United States and around the world. In general, it is assumed that high-income inequality has negative consequences, so it's fairly important to develop a simple way to describe income inequality graphically.

The Lorenz Curve is one way to graph inequality in income distribution.

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The Lorenz Curve

The Lorenz curve is a simple way to describe income distribution using a two-dimensional graph. To do this, imagine lining people (or households, depending on context) in an economy up in order of income from smallest to largest. The horizontal axis of the Lorenz curve is then the cumulative percentage of these lined up people that are being considered.

For example, the number 20 on the horizontal axis represents the bottom 20 percent of income earners, the number 50 represents the bottom half of income earners, and so on.

The vertical axis of the Lorenz curve is the percent of total income in the economy.

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Given Ends of the Lorenz Curve

We can start plotting the curve itself by noting that the points (0,0) and (100,100) have to be the ends of the curve. This is simply because the bottom 0 percent of the population (which has no people) has, by definition, zero percent of the economy's income, and 100 percent of the population has 100 percent of the income.

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Plotting the Lorenz Curve

The rest of the curve is then constructed by looking at all of the percentages of the population between 0 and 100 percent and plotting the corresponding percentages of income.

In this example, the point (25,5) represents the hypothetical fact that the bottom 25 percent of people have 5 percent of the income. The point (50,20) shows that the bottom 50 percent of people have 20 percent of the income, and the point (75,40) shows that the bottom 75 percent of people have 40 percent of the income.

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Characteristics of the Lorenz Curve

Because of the way that the Lorenz curve is constructed, it will always be bowed downwards as in the example above. This is simply because it is mathematically impossible for the bottom 20 percent of earners to make more than 20 percent of the income, for the bottom 50 percent of earners to make more than 50 percent of the income, and so on.

The dotted line on the diagram is the 45-degree line that represents perfect income equality in an economy. Perfect income equality is if everyone makes the same amount of money. That means the bottom 5 percent has 5 percent of the income, the bottom 10 percent has 10 percent of the income, and so on.

Therefore, we can conclude that Lorenz curves that are bowed further away from this diagonal correspond to economies with more income inequality.

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Your Citation
Beggs, Jodi. "The Lorenz Curve." ThoughtCo, Oct. 27, 2017, thoughtco.com/the-lorenz-curve-1147712. Beggs, Jodi. (2017, October 27). The Lorenz Curve. Retrieved from https://www.thoughtco.com/the-lorenz-curve-1147712 Beggs, Jodi. "The Lorenz Curve." ThoughtCo. https://www.thoughtco.com/the-lorenz-curve-1147712 (accessed May 23, 2018).