Labor markets set wages (Shifts in Labor Demand and Supply), and wages are most of most people's income. How evenly is income shared? Economists summarize it with shares of a whole, the idea from Percent Means per 100.
Key idea
Line up households from lowest income to highest and split them into five equal groups (quintiles). The Lorenz curve plots the cumulative share of households against the cumulative share of income. Perfect equality is the diagonal line. The Gini coefficient is $A/(A + B)$, where $A$ is the area between the diagonal and the Lorenz curve and $B$ is the area under the curve: 0 means perfect equality; values near 1 mean extreme inequality.
Why it works
With perfect equality, the bottom 20% of households would have 20% of income, the bottom 40% would have 40%, and so on: the diagonal. Any real distribution gives the bottom groups less than their share, so the curve sags below the diagonal. The more it sags, the bigger area $A$ and the larger the Gini. Because $A + B$ is the whole triangle under the diagonal (area $\tfrac{1}{2}$), $\text{Gini} = A / \tfrac{1}{2} = 1 - 2B$.
Worked example: Cumulative shares
Income shares by quintile, poorest first: 4%, 9%, 15%, 23%, 49%. What share of income goes to the bottom 60%?
- Add the first three: $4\% + 9\% + 15\% = 28\%$.
- So the bottom 60% of households get 28% of income; the top 20% alone get 49%.
Answer: 28%.
Worked example: A Gini from five points
Using the same shares, estimate the Gini coefficient with trapezoids.
- Cumulative shares: 0, 0.04, 0.13, 0.28, 0.51, 1.00.
- Area $B$, five trapezoids of width 0.2: $$0.2 \times \tfrac{1}{2}\left[(0 + 0.04) + (0.04 + 0.13) + (0.13 + 0.28) + (0.28 + 0.51) + (0.51 + 1)\right] = 0.2 \times 1.46 = 0.292$$
- $\text{Gini} = 1 - 2(0.292) = 0.416$.
Answer: About 0.42.
Common mistake
Reading a Lorenz curve farther from the diagonal as more equal, or a higher Gini as more equal. The diagonal is equality, so distance from it measures inequality, and the Gini grows with that distance. Check: a Gini of 0 is the diagonal itself.
For current U.S. figures, use the Census Bureau's income tables; numbers vary by year and by how income is measured (before or after taxes and transfers). What causes inequality and how much to reduce it are debated, and the answers mix evidence with values.