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Lorenz Curve

By Jim Frost

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A Lorenz curve is a graphical tool that depicts the income or wealthy inequality within a population. Developed by economist Max Lorenz, it visually shows how unequally income or wealth is distributed among a group.

On a Lorenz curve graph where the:

  • Horizontal axis represents the cumulative percentage of the population, ordered from lowest to highest income or wealth.
  • Vertical axis represents the cumulative percentage of total income or wealth held by that population.
  • Line of equality, which is a 45 degree straight diagonal line from the bottom-left to the top-right corner that represents a perfectly equal distribution.

The Lorenz curve itself typically bows below the line of equality, indicating some degree of inequality. A distribution that bows significantly below the line of equality indicates a large disparity, showing that a small portion of the population holds a disproportionately large share of the total income.

Each point on the Lorenz curve communicates a real-world comparison, such as “the bottom X% of households receive X% of total income.” These points make the curve an intuitive way to visualize how income or wealth is distributed across a population. We’ll explore that in the example below.

Lorenz curves are closely related to the Gini coefficient, a numerical measure of inequality calculated based on the area between the Lorenz curve and the line of equality. The more the line bows below the line of equality, the greater the inequality and the higher the Gini coefficient.

Lorenz Curve Example

The graph below shows a Lorenz curve for U.S. income distribution in 2022, based on data from the U.S. Census Bureau. The red dashed line represents perfect income equality, where each percentage of households earns an equal share of total income. The blue curve represents the actual distribution, which bows below the line of equality, illustrating the degree of inequality. The further the Lorenz curve lies below the diagonal, the greater the concentration of income among higher-earning households.

Lorenz curve displaying the distribution of U.S. incomes for 2022.

For example, on the 2022 graph, the point corresponding to the bottom 20% of U.S. households shows that they receive only about 3.1% of the total income—highlighting the degree of income inequality. Indeed, the bottom 80% of households receive only 40% of the total income. Conversely, the top 20% receive 60% of the total income.

Related

Related Articles:
  • A Statistical Thanksgiving: Global Income Distributions
  • Glossary: Gini Coefficient
  • A Statistical Thanksgiving: Global Income Distributions
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