Lorenz Curve

What Is a Lorenz Curve?

A Lorenz curve is a graph that shows how evenly income, wealth, consumption, or another resource is distributed across a population. It ranks the population from lowest to highest and then plots the cumulative share of the resource received by the cumulative share of the population.

The curve is most often used to explain income or wealth inequality. If every household had the same income, the Lorenz curve would follow a straight 45-degree line of perfect equality. The more the actual curve bows below that line, the more unequal the distribution.

How to Read the Curve

Suppose the bottom 40% of households receive 15% of total income. A Lorenz curve would plot that point and connect it with other cumulative points across the distribution. If the bottom 80% receive 55% of income, the curve remains below the equality line because income is concentrated among the top 20%.

The graph does not say whether a country is rich or poor. It shows distribution. A high-income country and a low-income country can have similarly shaped Lorenz curves but very different living standards. The curve also depends on what is measured: before-tax income, after-tax income, consumption, or wealth can each tell a different story.

Connection to the Gini Coefficient

The Lorenz curve is the visual foundation for the Gini coefficient. The Gini compares the area between the line of perfect equality and the Lorenz curve with the total area under the equality line.

In this expression, G is the Gini coefficient, A is the area between the equality line and the Lorenz curve, and B is the area under the Lorenz curve. A curve close to the equality line leaves a small area A and produces a lower Gini. A curve that bows sharply downward creates a larger area A and produces a higher Gini.

What It Reveals

The Lorenz curve is useful because it shows where inequality sits across the distribution. A single Gini number compresses inequality into one statistic. The curve lets a reader see whether the bottom half receives a very small share, whether the top tail is especially dominant, or whether differences are more evenly spread across the population.

This makes it useful for policy and economic interpretation. A tax-and-transfer system might move the after-tax Lorenz curve closer to equality than the pre-tax curve. A wealth distribution will usually bow more sharply than an income distribution because assets are often more concentrated than wages.

Where It Can Mislead

A Lorenz curve still leaves out important facts. It does not show mobility, household size, regional cost of living, public benefits, debt burdens, or absolute income levels. It also does not explain why inequality exists. Two economies can have similar curves for very different reasons: education gaps, asset ownership, tax policy, demographics, sector mix, or labor-market structure.

The curve is strongest when paired with context. Readers should ask what population is included, what resource is measured, whether the data are before or after taxes and transfers, and whether the same method is used across comparisons.

The Bottom Line

A Lorenz curve is a visual tool for understanding distribution. It shows how far a real-world income or wealth distribution bends away from perfect equality, and it provides the graphical basis for the Gini coefficient.