Income inequality describes how unevenly income is distributed across people or households in an economy. This cheat sheet helps students compare inequality using income shares, Lorenz curves, and the Gini coefficient. These tools are important because inequality affects living standards, opportunity, social mobility, and public policy debates.
Students need a clear reference to connect graphs, formulas, and real-world interpretations.
The core idea is to compare an actual income distribution with perfect equality, where every group receives the same share of total income. A Lorenz curve shows cumulative population share on the x-axis and cumulative income share on the y-axis. The Gini coefficient measures the area between the line of equality and the Lorenz curve as a number from 0 to 1.
Higher Gini values mean greater inequality, while taxes, transfers, education, and labor market policies can change the distribution of income.
Key Facts
- Perfect income equality means each percentage of the population receives the same percentage of total income, such as 20% of people receiving 20% of income.
- A Lorenz curve plots cumulative share of population on the x-axis and cumulative share of income on the y-axis.
- The line of equality is the 45-degree line where cumulative population share equals cumulative income share.
- The Gini coefficient is calculated as Gini = A / (A + B), where A is the area between the equality line and the Lorenz curve and B is the area under the Lorenz curve.
- A Gini coefficient of 0 means perfect equality, and a Gini coefficient of 1 means one person or household receives all income.
- If the Lorenz curve bows farther away from the line of equality, the Gini coefficient increases.
- Income share for a group is calculated as income share = group income / total income x 100%.
- Redistribution through progressive taxes and transfer payments can reduce after-tax income inequality.
Vocabulary
- Income Inequality
- Income inequality is the uneven distribution of income among individuals, households, or groups in an economy.
- Lorenz Curve
- A Lorenz curve is a graph that shows the cumulative share of income received by the cumulative share of the population.
- Gini Coefficient
- The Gini coefficient is a numerical measure of income inequality ranging from 0 for perfect equality to 1 for maximum inequality.
- Line of Equality
- The line of equality is a 45-degree line showing a situation where each share of the population receives the same share of income.
- Quintile
- A quintile is one of five equal groups, each containing 20% of the population, often used to compare income shares.
- Redistribution
- Redistribution is the use of taxes, transfers, or public programs to change the distribution of income after market incomes are earned.
Common Mistakes to Avoid
- Confusing income with wealth is wrong because income is money earned over a period, while wealth is the total value of assets owned at a point in time.
- Reading the Lorenz curve as individual income is wrong because each point shows cumulative population share and cumulative income share, not one person's earnings.
- Thinking a higher Gini coefficient means more equality is wrong because Gini values rise as the Lorenz curve moves farther from the line of equality.
- Ignoring taxes and transfers is wrong because market income inequality and after-tax income inequality can be very different.
- Comparing Gini coefficients without context is misleading because countries may differ in data quality, household size, cost of living, and public services.
Practice Questions
- 1 In a country, the bottom 20% of households receive 6% of total income. What income share does this quintile receive, and how does it compare with perfect equality?
- 2 A Lorenz curve has area A = 0.18 between the equality line and the curve, and area B = 0.32 under the curve. Calculate the Gini coefficient using Gini = A / (A + B).
- 3 The richest 20% of households receive 50% of total income, while the poorest 20% receive 4%. By how many percentage points does the richest quintile's share exceed the poorest quintile's share?
- 4 Explain why two countries with the same Gini coefficient might still have different levels of poverty or different standards of living.