AP® Microeconomics review sheet from Aim for Five (aimforfive.com/micro/units/6/6-5)
Unit 6 · Topic 6.5
6.5 Inequality
Economists measure how evenly income is shared with the Lorenz curve and the Gini coefficient. Inequality comes from differences in skills, inherited wealth, discrimination and other sources. Taxes and transfer payments can reduce it, and you need to classify a tax as progressive, regressive or proportional.
Key terms
- Lorenz curve
- Gini coefficient
- progressive tax
- regressive tax
- proportional tax
- transfer payments
The Lorenz curve
Line up all households from the lowest income to the highest. The horizontal axis shows the cumulative percentage of households, from 0% to 100%. The vertical axis shows the cumulative percentage of total income those households earn, also from 0% to 100%.
The 45-degree line from the bottom-left corner to the top-right corner is the line of perfect equality: the bottom 20% earn 20% of income, the bottom 50% earn 50%, and so on.
A real Lorenz curve sags below that line, because the poorest households earn less than their share. It always starts at (0%, 0%) and ends at (100%, 100%). The farther it bows away from the 45-degree line, the more unequal incomes are.
Reading a point: if a Lorenz curve passes through (40%, 15%), the poorest 40% of households earn 15% of total income.
The Gini coefficient
The Gini coefficient sums up a Lorenz curve in one number. It compares the area between the line of perfect equality and the Lorenz curve with the whole area under the line of perfect equality.
It runs from 0 to 1. Zero means perfect equality (the Lorenz curve is the 45-degree line). One means total inequality (one household gets all the income). A higher Gini means more inequality.
On the exam you compare Lorenz curves or Gini coefficients you're given. You won't be asked to draw a Lorenz curve or calculate a Gini coefficient.
Where inequality comes from
Income and wealth are different. Income is a flow: what you earn over a period, like a year. Wealth is a stock: the value of what you own minus what you owe at one moment. Wealth is usually shared much more unequally than income.
- Differences in human capital: education, training and skills that raise a worker's productivity and MRP (5.1).
- Inherited wealth and family background.
- Discrimination in hiring or pay based on race, gender or other characteristics.
- Differences in ability, effort, job choice and the risks people take.
- Market power in product or labor markets, and luck.
- The tax system and how much the government transfers to lower-income households.
Taxes and transfers
Classify a tax by the share of income it takes (the average tax rate), not by the number of dollars paid.
- Transfer payments are government payments that aren't for a good or service in return, like unemployment benefits, food assistance or Social Security. Many go mainly to lower-income households, so they reduce inequality.
- After progressive taxes and transfers, the Lorenz curve moves closer to the line of perfect equality and the Gini coefficient falls.
| Type | Share of income taken as income rises | Example | Effect on inequality |
|---|---|---|---|
| Progressive | Rises | The U.S. federal income tax | Reduces it |
| Proportional | Stays the same | A flat income tax | No change in shares |
| Regressive | Falls | Sales taxes, since lower-income households spend a larger share of their income | Increases it |
Worked examples
Try each one yourself first, then open the solution.
- Example 1
Comparing Lorenz curves
In Country A, the Lorenz curve shows that the poorest 50% of households earn 30% of income. In Country B, the poorest 50% earn 15%. (a) Which country has more income inequality, and which has the higher Gini coefficient? (b) Country A then expands its transfer payments to low-income households. What happens to its Lorenz curve and Gini coefficient?
Show the solutionHide the solution
- Step 1: (a) With perfect equality, the poorest 50% would earn 50%. Country B's curve (15%) sags farther below the 45-degree line than Country A's (30%), so Country B is more unequal and has the higher Gini coefficient.
- Step 2: (b) Bigger transfers raise the income share of the poorest households. Country A's Lorenz curve shifts toward the line of perfect equality, so its Gini coefficient falls.
Answer: (a) Country B is more unequal and has the higher Gini coefficient. (b) A's Lorenz curve moves toward the line of perfect equality, and its Gini coefficient falls.
- Example 2Calculator allowed
Classifying a tax (classic trap)
Under a new tax, a household earning $20,000 pays $2,000, and a household earning $100,000 pays $8,000. A student says the tax is progressive because the richer household pays more. Is that right?
Show the solutionHide the solution
- Step 1: Classify by the share of income, not the dollar amount.
- Step 2: Lower-income household: 2,000 ÷ 20,000 = 0.10, or 10%.
- Step 3: Higher-income household: 8,000 ÷ 100,000 = 0.08, or 8%.
- Step 4: The share falls as income rises, so the tax is regressive. Paying more dollars doesn't make a tax progressive.
Answer: No. The tax takes 10% of the lower income and 8% of the higher income, so it is regressive.
Common mistakes
- Calling a tax progressive because high earners pay more dollars. Compare the percentage of income paid.
- Thinking a Lorenz curve closer to the 45-degree line means more inequality. Closer means more equal, and a lower Gini coefficient.
- Saying a Gini coefficient of 1 means perfect equality. Zero is perfect equality; 1 is total inequality.
- Mixing up income (a flow over time) and wealth (a stock at one moment).
On the exam
- Expect to compare two Lorenz curves or Gini coefficients and say which shows more inequality, or to predict how a policy shifts the Lorenz curve.
- For tax questions, compute each household's tax as a percentage of income before you classify the tax.
Connected topics
Videos
Check yourself
4 questions on 6.5 Inequality. Pick an answer to see if you got it, and why.
| Cumulative share of households, poorest first | Country A | Country B | Country C |
|---|---|---|---|
| Poorest 20% | 6% | 3% | 10% |
| Poorest 40% | 18% | 10% | 26% |
| Poorest 60% | 36% | 22% | 46% |
| Poorest 80% | 60% | 42% | 70% |
| All households | 100% | 100% | 100% |
Hypothetical income data. Each column gives the cumulative share of total income earned by the poorest households, so each column is a set of points on that country's Lorenz curve.
In which country is income distributed most equally?
Which of the following ranks the countries from the highest Gini coefficient to the lowest?
In Country A, what share of total income goes to the richest 20% of households?
Country B starts paying larger transfer payments to low-income households and funds them with a progressive income tax. Its Lorenz curve will most likely
0 of 4 answered