Lorenz curves and Gini coefficients are standard tools for describing how unevenly income or wealth is distributed. They summarise inequality graphically and numerically, supporting clear comparisons across places, policies, and time.

What these measures capture

Economists often want more than an average (like mean income). Inequality measures describe how total income or wealth is spread across a population, from poorest to richest.

Both tools rely on the same idea: compare the actual distribution to perfect equality, where each percentile of households receives the same percentile of total income/wealth.

The Lorenz curve

A Lorenz curve is a cumulative-share graph constructed after sorting people (or households) from lowest to highest income/wealth.

Key features to know for AP Micro:

• Axes

  • Horizontal: cumulative share of population (0% to 100%), ranked poorest to richest

  • Vertical: cumulative share of income/wealth (0% to 100%)

• Line of equality (45° line): the benchmark where the bottom $x$ gets exactly $x$ of income/wealth.

• Bowing below the equality line indicates inequality:

  • If the bottom 40% holds 10% of income, the curve is far below the equality line at 40%.

• More bowed = more unequal: a Lorenz curve farther from the equality line represents greater concentration among higher-income groups.

When comparing two Lorenz curves:

• If one curve lies everywhere closer to the equality line, it indicates less inequality at all population shares.

• If curves cross, inequality rankings are ambiguous without an index (often the Gini coefficient) because one distribution may be “more equal” in one part and “less equal” in another.

The Gini coefficient

The Gini coefficient converts the Lorenz-curve information into a single number.

A key advantage is easy comparison across countries, policies, or time periods, even when the full Lorenz curves are not shown.

The standard area-based expression is:

The shaded regions show how the Gini coefficient is constructed from areas in a Lorenz-curve diagram. Area $A$ is the gap between the line of equality and the Lorenz curve, while area $B$ is the area under the Lorenz curve; the Gini coefficient is $A/(A+B)$. Source

Interpretation:

• $Gini=0$: perfect equality (Lorenz curve equals the 45° line; $A=0$).

• Higher Gini: more inequality (larger $A$ relative to $A+B$).

• $Gini$ near 1: extreme inequality (income/wealth highly concentrated at the top).

How to use them for comparisons

Lorenz curves and Gini coefficients are most useful for consistent comparisons:

• Across countries: two nations can have similar average income but very different inequality.

• Across time: a rising Gini suggests inequality has increased (the Lorenz curve generally bows further from equality).

• Across policies: if a policy is associated with a lower Gini (or a Lorenz curve closer to equality), the distribution is more equal under that policy environment.

Be careful about what is being measured:

• Inequality can refer to income or wealth; wealth distributions are typically more unequal.

• Changes in the Lorenz curve/Gini reflect distribution, not total income size.

Common interpretation pitfalls (AP-relevant)

• A lower Gini does not automatically mean “better” outcomes; it only indicates more equality.

• The Lorenz curve and Gini do not identify why inequality differs; they only describe how much and in what pattern.

• Always specify the base: households vs individuals, and income vs wealth, because comparisons require consistent definitions.