Lorenz curve

By:

James Knight

James is a lead editor for Invezz, where he covers topics from across the financial world, from the stock… read more.

Updated: Aug 20, 2021

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A curve which shows the relation between the cumulative percentage of same group of units (e.g. firms or households) and the cumulative percentage of the total amount of same variable (e.g. employment or income) which they account for. The units are arranged in order of increasing size. For example, from information on the size distribution of firms we might construct the following table:

Cumulative percentage of firms Cumulative percentage of total employment which they account for 10 % 2 % 20 % 6 % 30 % 11 % 40 % 18 % 50 % 26 % 60 % 38 % 70 % 51 % 80 % 65 % 90 % 80 % 100 % 100 %

This shows that the smallest 10 per cent of firms had only 2 per cent of the total employment, while the !argest I 0 per cent of firms had 20 per cent of total employment. We would then draw the Lorenz curve as in the following diagram:

The purpose of the Lorenz curve is to show the degree of inequality in the distribution from which it is taken. If there was perfect equality, each successive equal step up in the cumulative percentage of firms in the above table would be accompanied by a similar increase in the cumulative percentage of employment. Hence the curve, when graphed, would be a straight line as shown in the diagram. The greater the curvature of the Lorenz curve, the greater is the degree of inequality, since the smaller the proportion of employment accounted for by the smallest firms, the greater is that of the largest firms. The Lorenz curve is also aften used to show the inequality in the income distribution.

Reference: The Penguin Dictionary og Economics, 3rd edt.