Measuring Inequality

1. The horizontal axis shows the cumulative percentage of the population, ranked from poorest to richest.
2. The vertical axis shows the cumulative percentage of total income received by that group.
3. The straight 45° line shows perfect equality, where any given share of the population earns exactly that share of income.
4. The actual distribution is drawn as a curve that sags below this line of equality.
5. The further the curve bows away from the 45° line, the more unequal the distribution.

Reading The Curve

1. Rank the population from poorest to richest and add up income shares as you go.
2. Each point on the curve answers the question: what share of income does the poorest x% receive?
3. The gap between the curve and the diagonal at any point shows how far that group falls short of an equal share.

From Curve To Gini

Gini coefficient formula

$$Gini\; coefficient=\frac{A}{A+B}$$

1. The Gini is read straight from the Lorenz-curve diagram by comparing two areas.
2. Area A is the gap between the line of equality and the Lorenz curve.
3. Area B lies beneath the Lorenz curve, so A + B is the whole triangle below the line of equality.
4. If the curve lies on the diagonal there is no gap, so area A = 0 and the Gini = 0.
5. If one person holds all the income the curve hugs the axes, area B disappears and the Gini approaches 1.

Comparing Distributions

1. Two Lorenz curves on one diagram let you rank countries or years by inequality.
2. The curve nearer the diagonal represents the more equal distribution and the lower Gini.
3. A country whose curve shifts towards the diagonal over time has become more equal.
4. Wealth is usually more unequally distributed than income, so its Lorenz curve bows out further.
5. A lower Gini looks more equitable, but reducing it can blunt work and investment incentives, so it trades some efficiency for equity — and whether that is worthwhile depends on how the fall is achieved.