Lorenz Curve
The Lorenz curve is a graphical representation of the distribution of income or wealth within a population. It plots the cumulative share of income received against the cumulative share of the population, from poorest to richest. The curve was developed by the American economist Max O. Lorenz in 1905.[1]
Construction
The Lorenz curve plots the cumulative percentage of total income (on the vertical axis) against the cumulative percentage of the population (on the horizontal axis), with individuals ordered from poorest to richest. A straight diagonal line—the line of perfect equality—represents a situation in which income is distributed equally. The Lorenz curve lies below this line whenever income is unequally distributed, and the further it lies below, the greater the inequality.[1]
Relationship to the Gini coefficient
The Gini coefficient is derived directly from the Lorenz curve. It is defined as the ratio of the area between the line of perfect equality and the Lorenz curve (area A) to the total area under the line of perfect equality (area A + B):
- Gini coefficient = A ÷ (A + B)
The Gini coefficient therefore provides a single-number summary of the inequality depicted by the Lorenz curve.[1]
Interpretation
| Curve position | Meaning |
|---|---|
| On the diagonal | Perfect equality. |
| Below the diagonal | Inequality, with greater distance indicating greater inequality. |
| On the horizontal axis | Perfect inequality, with all income received by one person. |
Uses
The Lorenz curve is widely used to illustrate income and wealth inequality and to compare distributions across countries or over time. It is complemented by other measures such as the Gini coefficient and poverty indices.[1]