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Measuring Inequality: Lorenz Curves & the Gini Coefficient

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The Lorenz curve

A Lorenz curve plots the cumulative share of income on the vertical axis against the cumulative share of population, ranked poorest to richest, on the horizontal. Perfect equality would be the 45-degree line — the poorest 20% would have 20% of income. Real curves bow below it, and the further they bow, the greater the inequality. A curve running along the bottom and then straight up would be perfect inequality, with one person holding everything.

The Gini coefficient
Gini = area between the 45° line and the Lorenz curve ÷ total area under the 45° line
0 is perfect equality, 1 is perfect inequality. It is a ratio of areas, so it is dimensionless and comparable across countries and years.

What the number does and does not tell you

The Gini summarizes a whole distribution in one number, which makes it comparable — and means it discards information. Two very different distributions can share a Gini: one where the gap is between the middle and the top, another where it is between the bottom and the middle. So a Gini comparison establishes that distributions differ in overall spread, and nothing about where in the distribution the difference lies. Reporting a Gini alongside decile shares is what avoids the trap.

Income versus wealth

Income is a flow — earnings over a period. Wealth is a stock — assets held at a moment. Wealth is distributed far more unequally than income in essentially every country, because it accumulates, is inherited, and generates further income. A study reporting one and a claim about the other are not interchangeable, and the exam is careful about which it asks for.

Sources and the efficiency trade-off

Inequality arises from differences in human capital, inherited wealth, discrimination, market power, and luck. Redistributive policy — progressive taxation, transfers, public education — reduces measured inequality, and the standard objection is that it can reduce incentives to work, save and take risks. That is a real trade-off between equity and efficiency, and the honest position is that its size is empirically contested rather than settled by theory.

Worked example

In country A the poorest 40% receive 20% of income; in country B the poorest 40% receive 12%. Compare the Lorenz curves and Gini coefficients, and state one thing this comparison does not establish.

  1. 1.Both Lorenz curves bow below the 45-degree line, since neither is equal.
  2. 2.At the 40% point, A is at 20% and B is at 12%, so B's curve lies further below.
  3. 3.A larger gap from the diagonal means a larger area between them, so B has the higher Gini.
  4. 4.What it does not establish: where the rest of the difference lies — B's inequality could be concentrated at the very top or spread through the middle.
Answer: Country B has the more unequal distribution and the higher Gini coefficient. But the single comparison at the 40th percentile, and the Gini itself, say nothing about whether B's inequality comes from an extremely rich top or a broadly compressed bottom — which matters for policy and requires the full distribution to answer.
Watch out

A Gini of 0.4 is not "40% inequality" and has no percentage interpretation. It is a ratio of areas on the Lorenz diagram, meaningful only in comparison with another Gini.

Checkpoint

A Lorenz curve that lies closer to the 45-degree line indicates:

Checkpoint

A Gini coefficient of 0 would mean:

Checkpoint

Wealth is typically distributed more unequally than income because wealth:

On the exam

When a question gives cumulative shares, sketch the Lorenz curve before comparing. The comparison is visual — which curve is further from the diagonal — and attempting it from the numbers alone invites errors.

Answer the 3 checkpoints as you read.

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