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Income
Inequality

Explore how economists measure and analyze the distribution of income using Lorenz curves, Gini coefficients, and quintile analysis.

AP Microeconomics

What Is Income Inequality?

Income inequality refers to the uneven distribution of income across the members of an economy. It measures how far the actual distribution departs from a perfectly equal one, where every household earns the same share of total income.

Why Inequality Matters in Microeconomics

Efficiency
Some inequality provides incentives for investment, education, and innovation: the efficiency argument.
Equity
Excessive inequality may reduce social welfare and violate normative standards of fairness.
Policy
Taxes, transfers, and minimum wages alter the distribution: understanding measurement is key.

Key Measurement Tools

1
Quintile distribution: Divide all households into five equal groups and compare each group's share of total income.
2
Lorenz curve: A graphical device plotting the cumulative percentage of income against the cumulative percentage of households.
3
Gini coefficient: A single number between \(0\) and \(1\) that summarizes the degree of inequality from the Lorenz curve.

The Lorenz Curve

A B Cumulative % of Households Cumulative % of Income 0 20 40 60 80 100 0 20 40 60 80 100 Perfect Equality Lorenz Curve

The Gini Coefficient

The Gini coefficient is derived directly from the Lorenz curve. It equals the ratio of the area between the line of equality and the Lorenz curve to the total area under the line of equality:

\(\text{Gini} = 0\)
Perfect equality: every household earns the same income share.
\(\text{Gini} = 1\)
Perfect inequality: one household earns all income, everyone else earns nothing.

Quintile Income Distribution

3% 9% 15% 23% 50% Lowest Second Third Fourth Highest Income Quintile % of Total Income 0 10 20 30 40 50

Lorenz Curve vs Gini Coefficient

Lorenz Curve Gini Coefficient
Type Graph Single number
Shows Shape of distribution Summary magnitude
Range Visual comparison \(0\) to \(1\)
Best for Comparing two distributions visually Ranking countries or time periods
Limitation Curves can cross: ambiguous ranking Hides where in the distribution inequality lies

Sources of Income Inequality

Human Capital
Differences in education, training, and skills lead to wage gaps.
Market Power
Monopoly, monopsony, and rent-seeking concentrate income at the top.
Discrimination
Wage discrimination by race, gender, or other factors distorts earnings.

How to Analyze Inequality

1
Gather quintile data: Obtain the income share earned by each 20% group of households.
2
Compute cumulative shares: Add each quintile's share cumulatively (e.g., bottom 20%, bottom 40%, ...).
3
Plot the Lorenz curve: Plot cumulative % of households (x-axis) vs cumulative % of income (y-axis).
4
Calculate the Gini: \(\text{Gini} = \frac{A}{A+B}\). A larger area A means more inequality.
5
Interpret: Compare across time or across countries. Closer to \(0\) = more equal.

Worked Example: Building a Lorenz Curve

Suppose a five-household economy has incomes: \(\$10{,}000\), \(\$20{,}000\), \(\$30{,}000\), \(\$40{,}000\), \(\$100{,}000\). Total income is \(\$200{,}000\).

Quintile Income Share Cumulative Share
Bottom 20%5%5%
Second 20%10%15%
Third 20%15%30%
Fourth 20%20%50%
Top 20%50%100%

Worked Example: Estimating the Gini

Using the trapezoidal method to estimate the area under the Lorenz curve from the previous slide:

Comparing Two Economies

0 20 40 60 80 100 0 20 40 60 80 100 Equality
Country A (\(\text{Gini} \approx 0.25\))
Country B (\(\text{Gini} \approx 0.50\))
 Cumulative % of Households

Policy Responses to Inequality

Progressive Taxes
Higher-income earners pay a larger percentage, reducing post-tax inequality.
Transfer Payments
Social Security, welfare, and food stamps redistribute income to lower quintiles.
Minimum Wage
Sets a price floor on labor, raising earnings for the lowest-paid workers.

Common Mistakes

✕ Confusing Income and Wealth
Income is a flow (earnings per year); wealth is a stock (accumulated assets). The Lorenz curve on the AP exam measures income distribution.
✕ Gini Direction
Students often think a higher Gini means more equality. Remember: higher Gini = more inequality (closer to \(1\)).
✕ Crossing Lorenz Curves
If two Lorenz curves cross, you cannot determine which country is more unequal just by looking at the curves: compare their Gini coefficients instead.

Question 1 of 5

The Lorenz curve plots cumulative percentage of income on the vertical axis against cumulative percentage of households on the horizontal axis. If a country has perfect equality, its Lorenz curve would be:

Question 2 of 5

A country's Gini coefficient changes from \(0.35\) to \(0.45\). Which statement is correct?

Question 3 of 5

In a five-quintile distribution, the bottom 40% of households earn 12% of total income. Under perfect equality, what share would the bottom 40% earn?

Question 4 of 5

Which government policy is most likely to reduce income inequality?

Question 5 of 5

Two countries have Lorenz curves that cross each other. Which of the following is true?