Income inequality made visible: how far the income distribution sags from perfect equality, and the single number that summarises it.
Warming up the engine…
The Lorenz curve plots the cumulative share of income earned by the poorest p% of the population; the further it sags below the 45-degree line of equality, the more unequal the distribution. The Gini coefficient is the sagging area as a fraction of the whole triangle: 0 is perfect equality, 1 is one person earning everything.
Gini = A / (A + B), the area between equality line and Lorenz curve over the total area beneath the equality line
Line up every household from poorest to richest and keep a running total of income. With perfect equality the running total climbs along the diagonal; in reality the bottom half holds far less than half, so the curve sags. Taxes and transfers visibly pull the after-tax curve back toward the diagonal, which is why exam questions love before-and-after Lorenz pairs.
Draw BOTH curves when comparing distributions, and remember a lower Gini means MORE equal. Two Lorenz curves that cross cannot be ranked by Gini alone, a favourite trick question.
Now prove you have it
Move the curve to where you think it lands, and get told exactly which part you got right.
Real-world scenarios on this model
Equilibrium at p 0.6, L(p) 0.4.
Equilibrium: p* = 0.6, L(p)* = 0.4
Current equations