The Lorenz Curve and the Gini Coefficient

Average income tells you nothing about who gets what. A country where everyone earns 40,000 and a country where one person earns 4 million and everyone else earns nothing can have the same average. The Lorenz curve fixes that by plotting cumulative share of population, poorest first, against cumulative share of income. The 45 degree diagonal is perfect equality: the bottom 20 percent hold exactly 20 percent of income, the bottom 50 percent hold 50 percent, and so on. Real economies bow below that line, because the poorest X percent always hold less than X percent of income. The deeper the bow, the more income is concentrated at the top.

Put two countries' curves on the same graph and the one that sags further from the diagonal is more unequal. The bulge between the two curves is the visual difference in how income is split between rich and poor, even if both countries have identical average income. The Gini coefficient compresses that whole picture into one number: it is the area between the Lorenz curve and the diagonal, divided by the total area under the diagonal. A Gini of 0 means the curve sits right on the diagonal, perfect equality. A Gini of 1 means one person holds all the income. Higher Gini, more unequal.

This sits in the unit as the measurement tool behind redistribution policy. Governments justify taxes, transfers, and welfare programs by pointing to a high Gini or a sagging Lorenz curve, and judge those policies partly by whether the curve moves back toward the diagonal afterward.