Lorenz Curve vs Gini Coefficient
Lorenz Curve and Gini Coefficient are two Market Failure & Government concepts in AP Economics that students often mix up. The Lorenz curve is a graphical representation of income or wealth distribution within a population, comparing actual distribution to perfect equality. The Gini coefficient is a numerical measure of income or wealth inequality ranging from 0 (perfect equality) to 1 (perfect inequality). Here is how they compare side by side.
It plots cumulative percentages of income against cumulative percentages of households, with perfect equality shown as a 45-degree line. The further the curve is from this line, the greater the inequality. It is used to visualize the extent of income disparity in a society.
It is calculated as the ratio of the area between the Lorenz curve and the line of perfect equality to the total area under the line of perfect equality. A higher Gini coefficient indicates greater inequality. It is commonly used to compare income distribution across countries or over time.
Lorenz Curve vs Gini Coefficient: The Picture and the Number It Produces
| Lorenz Curve | Gini Coefficient | |
|---|---|---|
| What you can read off it | The income share held by any bottom slice, such as the poorest fifth | The overall degree of inequality only, never where in the distribution it sits |
| How you build it from data | Cumulate the quintile shares and plot the five points | Divide the area between curve and diagonal by the whole area under the diagonal |
| What worsening inequality looks like | The curve bows further away from the diagonal | The value climbs toward one |
| Comparing two countries | Ranks cleanly only when one curve lies entirely inside the other | Always returns a ranking, even when that ranking is not trustworthy |
| Where it lets you down | Cannot rank two curves that cross | Two very different distributions can share the same value |
| Question type that signals it | A diagram with shaded regions labeled A and B | A table of quintile shares, or a ratio you are asked to compute |
The Gini is a summary of the curve, so it can only lose information
Every Gini starts life as a Lorenz curve, because the coefficient is the area between the curve and the line of equality divided by the whole triangle beneath that line. Compression is the point of it and also the cost of it. One number ranks any two countries instantly, which a pair of curves cannot always do. But the number cannot tell you whether inequality lives at the bottom, where the poorest fifth holds almost nothing, or at the top, where a thin slice holds most of the income. Two societies with identical coefficients can call for opposite policies, one for a floor under the poorest households and one for a ceiling on concentrated wealth. Read the curve when the question is where inequality sits. Read the coefficient when the question is how much there is. Mixing the two is what produces answers that sound informed and say nothing.
Two distributions, one Gini: a worked case where the number hides the difference
Take quintile income shares of 4, 8, 14, 24, and 50 percent. Cumulating gives 4, 12, 26, 50, and 100, and the trapezoid method puts the area under the curve at 0.284, so the gap above it is 0.216 and the Gini is 0.432. Now take shares of 6, 9, 12, 17, and 56 percent, which cumulate to 6, 15, 27, 44, and 100. That second distribution is kinder to the poorest fifth, six percent rather than four, and harsher at the very top, fifty-six percent rather than fifty. Its area works out to the same 0.284, so its Gini is also 0.432. The two Lorenz curves cross inside the fourth quintile, since the second curve sits above the first at the sixtieth percentile, 27 against 26, and below it at the eightieth, 44 against 50. Once curves cross, no single number can rank them without a judgment about which end of the distribution matters more. That is the strongest reason to sketch the curve even when the answer line asks only for the coefficient.
Neither measure says anything about how rich the country is
A Lorenz curve and a Gini coefficient both describe shares, so both are silent about levels. Two economies whose poorest fifth receives eight percent of income can differ enormously in what that eight percent buys, and a country can raise every household's income by a fifth without moving either measure at all, because every cumulative share stays exactly where it was. An answer that treats a rising Gini as proof of falling living standards is therefore wrong on its own terms, since the number rose when shares shifted, not when output fell. The same caution applies to which income you measure. A Gini computed on market income, before taxes and transfers, normally sits above one computed on disposable income for the same country in the same period, so comparing one against the other tells you about the tax and transfer system rather than about inequality. State the income concept before you compare anything.
Frequently asked questions
How do you calculate the Gini coefficient from a Lorenz curve?
The Gini coefficient equals area A divided by the sum of areas A and B, where A is the gap between the line of equality and the Lorenz curve, and B is the region under the curve. Since the entire triangle under the diagonal is half of a unit square, or 0.5, the shortcut is that the Gini equals A divided by 0.5, which is simply twice A. Given quintile shares and no diagram, cumulate the shares, use trapezoids to find B, then take A as 0.5 minus B.
Can two countries have the same Gini but different Lorenz curves?
Two countries can share a Gini of 0.432 while their Lorenz curves look quite different. Quintile shares of 4, 8, 14, 24, and 50 percent produce that value, and so do shares of 6, 9, 12, 17, and 56 percent, even though the second is gentler at the bottom and more concentrated at the top. Their curves cross inside the fourth quintile, which is exactly the situation where one summary number stops ranking reliably. When a prompt hands you full distributions and asks which country is more unequal, check for crossing before committing to an answer.
Does a Gini of 0.43 mean 43 percent of income goes to the rich?
A Gini of 0.43 names no group's income share at all. The coefficient measures how far the actual distribution sits from perfect equality, on a scale where zero means every household receives an identical amount and one means a single household receives everything. Reading the value as a share is the most common error on this topic and it is easy for a grader to spot. If you want an income share, return to the Lorenz curve and read the cumulative percentage at the quintile you care about, which is a different quantity.
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