Lorenz curve

The Lorenz curve was developed by [Max O. Lorenz]? as a graphical representation of income inequality. (While the Lorenz curve is normally used to measure income inequality, it can be used to measure inequality of assets as well.)

In economics, we frequently make statements like "the bottom twenty percent of all households have five percent of the total income". The Lorenz curve is based on such statements; every point on the curve represents one such statement.

The Lorenz curve is a graph that shows, for the bottom x% of households, the percentage y% of the total income which they have. The percentage of households is plotted on the x axis, the percentage of income on the y axis.

A perfectly equal society would be one in which one person every person has the same income. in this case, the bottom N percent of society would always have N percent of the income. Thus a perfectly equal society can be depicted by the straight line y=x; we call this line the line of perfect equality.

A perfectly inequal society, by contrast, would be one in which one person has all the income and everyone else has none. In that case, the curve would be at y=0 for all x<100, and y=100 when x=100. We call this curve the line of perfect inequality.

Note that it is impossible for the Lorenz curve to rise above the line of perfect equality, or sink below the line of perfect inequality.

The Lorenz curve is used to calculate the Gini coefficent.

The Lorenz curve looks like this: