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What is the Lorenz Curve?

By Leo Zimmermann
Updated May 17, 2024
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The Lorenz curve is a simple graphical representation of inequality. It represents the way a variable is distributed proportionally to a set of units. The Lorenz curve is often used by economists to describe social inequality, but it has also been appropriated by other fields. It was invented in 1905 by Max Lorenz.

Plotting a Lorenz curve requires a two-dimensional graph. Both axes represent percentages, and are thus numbered from zero to 100 or zero to one. The x-axis usually represents a population of individuals. The y-axis describes some resource or feature which the individuals on the x-axis have in different degrees. The individuals on the x-axis are ranked according to the variable on the y-axis.

The result is a curve lying somewhere between a straight diagonal line and a ninety-degree angle. The straight diagonal line represents the most possible equality. It has a slope of one; it always has the same value for x and y. The implication of this line is that members of the population do not differ according to the variable on the y-axis. The opposite condition, complete inequality, has a slope of zero until it reaches the end of the x-axis, at which point it becomes abruptly vertical. This condition suggests that only one member of the population has any of the resource or property on the y-axis. All curves in between represent intermediate inequality.

The most common use of the Lorenz curve is in economics. The x-axis represents households and the y-axis corresponds to their income. Lines on this graph correspond to ideas like "the poorest 40% of households earn 15% of the total income." The further away the curve is from a straight diagonal line, the worse the inequality. Because it is two dimensional, the graph represents more than just the amount of inequality. It can show where in a population the lines of inequality are drawn. It can also represent inequality as gradual or severe.

Economists use a number called the Gini coefficient to summarize the inequality represented by the Lorenz curve. The Gini coefficient is calculated by dividing the area between the actual curve and the line of perfect equality by the total area of the triangle beneath the line. The Gini coefficient can fall anywhere between zero and one, moving from complete equality to complete inequality. Performing this calculation for economies in the real world yields a range of results, with Northern Europe at the bottom and Africa and South America at the top.

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Discussion Comments
By allenJo — On Sep 28, 2011

@nony - To answer your question, I don’t think that societies can do what you’ve asked. This inequality, in my opinion, does not arise out of a concerted effort to skew income and wealth.

It’s not a conspiracy; it’s the result of decisions people make. Also, it should be pointed out that people who take a bigger piece of the pie have done so because they’ve made bigger sacrifices, and they also wind up paying the largest share of the taxes.

I’ve been in economic classes in college, but I have yet to see a so-called Lorenz curve for who pays the most in taxes. I guarantee you, it will be the people up in the top brackets.

By nony — On Sep 27, 2011

I’ve seen people graph Lorenz curve charts as a measure of social inequality. The numbers are always interesting to look at, as is the skewing of the line graph one way or another.

Either way you look at it, the rich get richer and the poor get poorer in my opinion, whether you are graphing income inequality or inequality of wealth or whatever. Perhaps I am a bit cynical, but that has been my view.

What I don’t understand however is how societies can rectify the inequality so that the line can be more “equal” and instead of being a measure of social inequality, it can be a measure of social equality or prosperity.

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