Inequality — AP Microeconomics Study Guide

For: AP Microeconomics candidates sitting AP Microeconomics.

Covers: Lorenz curve construction, Gini coefficient calculation and interpretation, poverty measurement, progressive/regressive/proportional taxation, equity-efficiency tradeoff, and redistributive policy evaluation.

You should already know: Basic utility theory, the role of government in correcting market failure, and labor market supply and demand.

A note on the practice questions: All worked questions in the "Practice Questions" section below are original problems written by us in the AP Microeconomics style for educational use. They are not reproductions of past College Board / Cambridge / IB papers and may differ in wording, numerical values, or context. Use them to practise the technique; cross-check with official mark schemes for grading conventions.

1. What Is Inequality?

Inequality in AP Microeconomics refers to the unequal distribution of economic resources (most commonly income, the annual flow of earnings from work and capital, or wealth, the stock of accumulated assets like property or stocks) across households in a market economy. This topic is explicitly listed in the AP Microeconomics Course and Exam Description (CED) as part of Unit 6: Market Failure and the Role of Government, which accounts for 12-18% of the total exam score. Inequality questions regularly appear in both multiple-choice (MCQ) and free-response (FRQ) sections, typically as a 1-2 part question in a longer FRQ on government policy or as a standalone MCQ testing measurement or interpretation. AP Microeconomics focuses primarily on income inequality, how it is measured, the tradeoffs involved in government policies to reduce it, and how inequality can be a result of unregulated market outcomes. Unlike casual usage, the AP exam distinguishes between income inequality (flow of annual resources) and wealth inequality (stock of accumulated assets), so you will need to be clear on this distinction for full credit.

2. Lorenz Curve

The Lorenz curve is the standard graphical tool used to visualize income inequality. It plots the cumulative percentage of households (ordered from lowest to highest income on the x-axis, 0% to 100%) against the cumulative percentage of total national income held by that share of households (on the y-axis, 0% to 100%). The 45-degree line drawn from (0,0) to (100,100) is called the line of perfect equality: if income were perfectly equally distributed, 10% of households would hold 10% of total income, 50% of households would hold 50% of total income, and so on, so the Lorenz curve would lie directly on this line. The further the actual Lorenz curve is below the 45-degree line, the more unequal the distribution of income. If one household held 100% of all income, the Lorenz curve would run along the x-axis from (0,0) to (100,0), then jump straight up to (100,100), representing maximum possible inequality.

Worked Example

Five households have annual incomes of $15,000, $25,000, $40,000, $60,000, and $160,000. Identify the coordinates of all key points needed to plot the Lorenz curve.

1. First, confirm the households are already ordered from lowest to highest income. Calculate total income across all households: $15+25+40+60+160=300$ thousand dollars.
2. Calculate cumulative percentage of households: Each household represents 20% of the total, so cumulative shares are 20% after 1 household, 40% after 2, 60% after 3, 80% after 4, and 100% after 5.
3. Calculate cumulative income for each step: After 1 household: $15k = 15/300 = 5% of total income. After 2 households: $(15+25)/300=40/300\approx 13.3$. After 3 households: $(15+25+40)/300=80/300\approx 26.7$. After 4 households: $(15+25+40+60)/300=140/300\approx 46.7$. After 5 households: 100% of total income.
4. The key points to plot are: $(0,0)$, $(20,5)$, $(40,13.3)$, $(60,26.7)$, $(80,46.7)$, $(100,100)$. Connecting these points gives the Lorenz curve, which lies below the 45-degree line of perfect equality.

Exam tip: Never order households from highest to lowest income before plotting. AP exam graders will immediately deduct points for a reversed Lorenz curve that lies above the 45-degree line, as this reflects a fundamental misunderstanding of the graph.

3. Gini Coefficient

The Gini coefficient is a numerical summary statistic that quantifies the level of inequality shown by a Lorenz curve. It is defined as the ratio of the area between the line of perfect equality and the Lorenz curve (called area A) to the total area under the line of perfect equality (A + B, where B is the area under the Lorenz curve). The formula is: $$G=\frac{A}{A+B}$$ Since the graph is a 1x1 unit square, the area of the triangle under the 45-degree line (A+B) is always $\frac{1}{2}\times 1\times 1=0.5$, so we can simplify the formula to $G=2A$, which makes calculation faster. The Gini coefficient ranges from 0 to 1: a Gini of 0 means perfect equality (the Lorenz curve is on the 45-degree line, so A=0), while a Gini of 1 means perfect inequality (one household holds all income, so B=0 and G=1). Higher Gini coefficients always mean more income inequality. For AP exams, you will usually be asked to calculate Gini for discrete income distributions (like quintiles or quartiles) using the trapezoid rule to find area B, then solve for G.

Worked Example

Using the 5-household income distribution from the earlier Lorenz example, calculate the Gini coefficient.

1. Convert all percentages to decimals to calculate area: each x interval between points is 0.2 (20% of households).
2. Calculate the area B (under the Lorenz curve) as the sum of trapezoid areas between each consecutive pair of points:
   • Trapezoid 1 (0 to 0.2 x): $\frac{0+0.05}{2}\times 0.2=0.005$
   • Trapezoid 2 (0.2 to 0.4 x): $\frac{0.05+0.133}{2}\times 0.2\approx 0.0183$
   • Trapezoid 3 (0.4 to 0.6 x): $\frac{0.133+0.267}{2}\times 0.2=0.04$
   • Trapezoid 4 (0.6 to 0.8 x): $\frac{0.267+0.467}{2}\times 0.2\approx 0.0734$
   • Trapezoid 5 (0.8 to 1.0 x): $\frac{0.467+1}{2}\times 0.2\approx 0.1467$
3. Sum all trapezoid areas: $B\approx 0.005+0.0183+0.04+0.0734+0.1467\approx 0.2834$
4. Calculate A = $0.5-B\approx 0.5-0.2834=0.2166$. Then $G=2A\approx 0.433$, so the Gini coefficient is approximately 0.43.

Exam tip: If asked to shade area A on an FRQ, always shade the gap between the 45-degree line and the Lorenz curve. A common mistake is shading the area under the Lorenz (area B), which will lose you the point.

4. Redistributive Policy and the Equity-Efficiency Tradeoff

Governments use fiscal policy to reduce income inequality, and AP Microeconomics requires you to evaluate these policies and their tradeoffs. First, tax systems are classified by their average tax rate (ATR = total tax paid / total income):

• Progressive: ATR increases as income increases (higher income households pay a larger share of their income in tax)
• Proportional: ATR is constant across all income levels (flat tax)
• Regressive: ATR decreases as income increases (higher income households pay a smaller share of their income in tax) Only progressive taxation reduces income inequality, when combined with transfer payments to low-income households (like welfare, unemployment insurance, or refundable tax credits). The core concept here is the equity-efficiency tradeoff: while redistribution increases equity (a more equal distribution of income), it can reduce efficiency by distorting incentives. For example, high marginal tax rates on high earners can reduce the incentive to work or invest, leading to lower total output and a deadweight loss. Some policies, however, can increase both equity and efficiency (like public education, which corrects credit market failures that prevent low-income households from investing in human capital).

Worked Example

A country has a progressive income tax with brackets: 10% on income up to $30,000, 20% on income between $30,000 and $100,000, and 40% on income above $100,000. Calculate the average tax rate for a low-income household earning $40,000 and a high-income household earning $200,000, then explain how this system reduces inequality.

1. Calculate total tax for the low-income household: Tax on first $30,000 = $0.10\ast 30,000=\$3,000$. Tax on remaining $10,000 = $0.20\ast 10,000=\$2,000$. Total tax = $5,000.
2. ATR for low-income household: $5,000/40,000=0.125=12.5\%$.
3. Calculate total tax for the high-income household: Tax on first $30,000 = $3,000, tax on next $70,000 = $0.20\ast 70,000=\$14,000,taxonremaining\$100,000=$0.40 * 100,000 = $40,000. Total tax = 3,000 + 14,000 + 40,000 = $57,000.
4. ATR for high-income household: $57,000/200,000=0.285=28.5\%$.
5. Explanation: The high-income household pays a higher average tax rate. Tax revenue is used to fund transfers to low-income households, so after-tax and transfer income is much more equal than pre-tax income, reducing overall inequality.

Exam tip: When asked to explain the equity-efficiency tradeoff, always explicitly mention both sides: higher equity from redistribution, but potential efficiency losses from distorted incentives. You will not get full credit for only discussing one side.

5. Common Pitfalls (and how to avoid them)

• Wrong move: Calling a proportional tax progressive because high-income households pay more total tax than low-income households. Why: Students confuse total tax paid with average tax rate, which is the correct metric for classifying tax systems. Correct move: Always use the average tax rate (share of income paid in tax) to classify a tax system as progressive, proportional, or regressive.
• Wrong move: Interpreting a higher Gini coefficient as meaning more equal income distribution. Why: Students mix up what the Gini measures, confusing the area A definition. Correct move: Memorize that Gini = 0 is perfect equality, Gini = 1 is perfect inequality, so Gini increases as inequality increases.
• Wrong move: Confusing income inequality with wealth inequality on the exam. Why: The terms are used interchangeably in casual discussion, but they have distinct definitions tested on the AP exam. Correct move: Remember income is a flow of annual earnings, while wealth is a stock of accumulated assets; always use the term the question asks for.
• Wrong move: Claiming all redistribution policies always reduce economic efficiency. Why: Students overgeneralize the equity-efficiency tradeoff, ignoring market failures that redistribution can correct. Correct move: Acknowledge that while high marginal taxes can reduce efficiency, policies like public education or EITC can increase efficiency by correcting credit or labor market failures.
• Wrong move: Forgetting to order households from lowest to highest income when calculating cumulative shares for the Lorenz curve. Why: Students skip the sorting step when working with unsorted data, leading to an incorrect curve. Correct move: Always sort household incomes in ascending order before calculating any cumulative percentages.

6. Practice Questions (AP Microeconomics Style)

Question 1 (Multiple Choice)

The Gini coefficient for Country A is 0.38, and the Gini coefficient for Country B is 0.48. Which of the following statements is correct? A) Country A has a more equal distribution of income than Country B. B) Country B has a more equal distribution of income than Country A. C) The Lorenz curve for Country A lies further from the line of perfect equality than the Lorenz curve for Country B. D) Total income in Country A is lower than total income in Country B.

Worked Solution: The Gini coefficient ranges from 0 (perfect equality) to 1 (perfect inequality), so a lower Gini coefficient means less inequality and a more equal distribution of income. A Gini of 0.38 (Country A) is lower than 0.48 (Country B), so Country A has a more equal distribution. A lower Gini also means the Lorenz curve lies closer to the line of perfect equality, and the Gini does not measure total income, only distribution. The only correct statement is option A.

Question 2 (Free Response)

The pre-tax income distribution for Country Z is divided into 5 quintiles (each quintile is 20% of households, ordered from lowest to highest income):

• Quintile 1: 4% of total pre-tax income
• Quintile 2: 10% of total pre-tax income
• Quintile 3: 16% of total pre-tax income
• Quintile 4: 25% of total pre-tax income
• Quintile 5: 45% of total pre-tax income

(a) Identify all key points (with coordinates) for the pre-tax Lorenz curve. (b) Calculate the pre-tax Gini coefficient using the trapezoid method. (c) After progressive taxation and transfers, the Gini coefficient falls to 0.29. Explain what this change means, and identify one potential efficiency cost of this policy.

Worked Solution: (a) Cumulative shares of households: 20%, 40%, 60%, 80%, 100%. Cumulative shares of income: 4%, 14%, 30%, 55%, 100%. Key points are $(0,0)$, $(20,4)$, $(40,14)$, $(60,30)$, $(80,55)$, $(100,100)$. (b) Convert to decimals, each x interval = 0.2. Calculate area B: $$B=\frac{0+0.04}{2}(0.2)+\frac{0.04+0.14}{2}(0.2)+\frac{0.14+0.3}{2}(0.2)+\frac{0.3+0.55}{2}(0.2)+\frac{0.55+1}{2}(0.2)=0.326$$ $A=0.5-0.326=0.174$, so $G=2A=0.348\approx 0.35$. The pre-tax Gini coefficient is 0.35. (c) The fall in Gini from 0.35 to 0.29 means the progressive policy reduced income inequality, making the distribution of after-tax income more equal. One potential efficiency cost is that higher marginal tax rates on high-income households reduce the incentive to work or invest, leading to lower total national output and a deadweight loss.

Question 3 (Application / Real-World Style)

A U.S. state is evaluating two policies to reduce income inequality. Policy 1 is a 15% increase in the state minimum wage, which is projected to reduce the state Gini coefficient from 0.45 to 0.42, and will cause a 2% reduction in low-wage employment. Policy 2 is an expansion of the state’s earned income tax credit (EITC) for low-income working households, which is projected to reduce the Gini coefficient from 0.45 to 0.41, with no net loss of employment. Which policy achieves greater inequality reduction with a lower efficiency cost, and why?

Worked Solution: First, calculate the change in Gini for each policy: Policy 1 reduces Gini by 0.45 - 0.42 = 0.03, while Policy 2 reduces Gini by 0.45 - 0.41 = 0.04. This means Policy 2 achieves greater inequality reduction than Policy 1. Policy 1 (a higher minimum wage) raises labor costs for firms, leading to lower employment and deadweight loss in the low-wage labor market, which is a large efficiency cost. Policy 2 (EITC expansion) subsidizes work for low-income households, increasing their after-tax wage without raising costs for firms, so it does not reduce employment (and may even increase labor force participation), leading to a lower efficiency cost. In context: Policy 2 is the better option here, delivering more inequality reduction at a smaller efficiency cost to the state economy.

7. Quick Reference Cheatsheet

8. What's Next

This chapter on inequality is the capstone topic in Unit 6: Market Failure and the Role of Government, which makes up 12-18% of the AP Microeconomics exam score. Mastery of inequality measurement and the equity-efficiency tradeoff is required to answer full-length FRQs that ask students to evaluate government intervention beyond just correcting efficiency market failures. This topic builds on your earlier knowledge of factor markets, where you learned how income is distributed across different factors of production. Without understanding how to measure and evaluate inequality, you will not be able to fully answer policy evaluation questions that require balancing equity and efficiency goals. Next you will review all Unit 6 concepts, and if you continue to AP Macroeconomics, you will extend this analysis to the effects of inequality on long-run economic growth.

• Factor Distribution of Income
• Externalities
• Public Goods
• Government Failure