Lesson 15: Government, Income Distribution & Exam Strategy

Warm-Up

Two countries have identical average incomes. In one, most households cluster near the average; in the other, a thin slice holds most of the income. Same average, radically different economies. Measuring that difference is Unit 6's last job — and then this lesson turns to the only topic left: how to convert fifteen lessons of microeconomics into the highest AP score you can produce in 2 hours and 10 minutes.

Core Concept

The Lorenz curve

The Lorenz curve plots the cumulative percentage of income (y-axis) received by the cumulative percentage of households (x-axis), poorest first.

[GRAPH: Lorenz curve. X-axis: "Cumulative % of households (poorest → richest)" 0–100. Y-axis: "Cumulative % of income" 0–100. A 45° diagonal labeled "line of perfect equality". A bowed-below curve labeled "Lorenz curve": e.g., poorest 20% receive 5% of income, poorest 60% receive 30%, poorest 80% receive 55%. Area between diagonal and curve labeled "A"; area under Lorenz curve labeled "B".]

• 45° line = perfect equality (poorest 20% earn exactly 20%, etc.).
• The farther the Lorenz curve bows below the diagonal, the more unequal the distribution.

The Gini coefficient

Gini = A / (A + B) — the bowed-out area as a share of the whole triangle.

• Gini = 0 → perfect equality (Lorenz curve is the diagonal)
• Gini = 1 → perfect inequality (one household earns everything)
• Real countries: roughly 0.25 (Nordic) to 0.6+ (highly unequal)

Sources of income differences: human capital and education, ability, discrimination, market power, inheritance/wealth, luck, and factor-market outcomes (Lesson 13 — wages = MRP means productivity differences become income differences).

Tax structures

Classify by what happens to the average tax rate (ATR = taxes paid ÷ income) as income rises:

• Progressive taxes and transfer programs pull the Lorenz curve toward the diagonal (Gini ↓).
• Marginal tax rate = tax on the next dollar; a progressive system has MTR > ATR. A tax can have a flat rate on spending yet be regressive in income terms — the sales-tax trap.

Antitrust & the government toolkit (course wrap)

The full government menu you've assembled across the course: - Price controls (L5): ceilings/floors — cause shortages/surpluses and DWL in competitive markets - Taxes/subsidies (L5, L14): shift curves; optimal Pigouvian size = the externality - Regulation of natural monopoly (L11): fair-return P = ATC vs. socially optimal P = MC - Antitrust law (Sherman/Clayton tradition): blocking collusion (L12's cartels are illegal in the U.S.), reviewing mergers, breaking up or restraining monopolies that aren't natural - Public provision (L14): public goods financed by taxes - Redistribution (this lesson): progressive taxation and transfers

PART II: THE COMPLETE EXAM PLAYBOOK

Format and timing

No penalty for wrong answers — answer all 60. A four-function calculator is allowed; every computation is hand-doable.

MC strategy

1. Two passes. Bank the easy ~40 first; mark and return to the rest. Never let one graph puzzle eat four questions' time.
2. Draw tiny graphs. For any shift question, a 3-second sketch in the margin beats mental rotation — the #1 self-inflicted error is flipping a shift direction.
3. Kill distractors by category. Most wrong answers are one of: movement-vs-shift confusion, price-from-MR instead of demand, absolute-vs-comparative advantage, raw-MU instead of MU-per-dollar, accounting-vs-economic profit.
4. Indeterminate is an answer. Double-shift questions usually include it, and it's usually right for one variable.

FRQ strategy

1. Use the 10-minute reading period on the long FRQ. Sketch its graph skeleton mentally; identify which model each part wants.
2. Label everything. Axes, curves, equilibrium points, dashed lines to axes. Points are awarded per label — an unlabeled correct curve scores zero.
3. Answer-then-explain. "Price rises (1 sentence: because demand increased while supply was constant)." State the direction FIRST, then justify. Graders hunt for the assertion + the because.
4. Show the chain: rule → numbers → conclusion. "Hire where MRP = MFC; MRP(4) = $70 = W; hire 4 workers."
5. Don't abandon parts. Later parts often don't depend on earlier ones. Attempt everything.

The master graph checklist (draw each from memory before exam day)

1. PPC — bowed, with efficient/inefficient/unattainable points (L1)
2. Supply & demand: 4 single shifts + 4 double shifts (L3)
3. Surplus areas: CS, PS at equilibrium (L5)
4. Price ceiling (shortage) and floor (surplus) with DWL (L5)
5. Per-unit tax: wedge, incidence rectangles, revenue, DWL (L5)
6. Cost family: MC through minimums of AVC & ATC; AFC falling (L7)
7. LRATC with scale regions and MES (L8)
8. Side-by-side perfect competition: profit, loss, shutdown, long-run (L9) ★
9. Monopoly: profit, DWL, efficient point (L10) ★
10. Perfect price discrimination (L11)
11. Natural monopoly: unregulated / fair-return / socially optimal (L11)
12. Monopolistic competition: short-run profit and long-run tangency (L12)
13. Payoff matrix protocol (not a graph — a ritual) (L12)
14. Side-by-side labor market; monopsony (L13)
15. Negative externality (MSC above MPC); positive externality (MSB above MPB) (L14)
16. Lorenz curve (L15)

★ = highest historical FRQ frequency. If you can draw all sixteen cold, you are structurally unable to fail the graphing points.

The five commandments (course-level errors that outrank all others)

1. Price comes from the demand curve (never MR/MC) — and wage from the supply curve under monopsony.
2. MR = MC / MRP = MFC picks quantity; comparing P to ATC picks profit. Two separate steps, always.
3. Movement along vs. shift — own price moves along; everything else shifts.
4. Compare per-dollar (MU/P, MP/$), never raw marginals across different prices.
5. Zero economic profit is normal — it's where free entry finishes its work.

Worked Examples

Example 1 (easy): Reading a Lorenz curve

In Country Q, the poorest 40% of households receive 12% of income; the poorest 80% receive 50%. In Country R, the corresponding figures are 25% and 65%. Which country has the higher Gini coefficient?

Solution: Q's Lorenz curve lies farther below the diagonal at every point (12 < 25, 50 < 65) → more inequality → Q has the higher Gini.

Interpretation: Farther bow = bigger area A = higher Gini. No integration required — comparison suffices.

Example 2 (medium): Classify the tax

A country taxes all grocery purchases at 8%. A household earning $20,000 spends $8,000 on groceries; a household earning $200,000 spends $20,000. Classify this tax with respect to income.

Solution: Tax paid: $640 vs. $1,600. ATR: 640/20,000 = 3.2% vs. 1,600/200,000 = 0.8%. ATR falls as income rises → regressive, despite the flat 8% rate on purchases.

Interpretation: Always compute tax ÷ income. Flat-on-spending ≠ proportional-on-income.

Example 3 (AP-style): Synthesis sprint

One-line answers, mixing the whole course: (i) A firm's MR = MC output has P < AVC — output? (ii) Payoff matrix shows no player can improve unilaterally at (Low, Low) — what is this cell? (iii) A subsidy for solar panels corrects what? (iv) In long-run monopolistic competition, why is P = ATC but > min ATC?

Solution: (i) Zero — shut down. (ii) Nash equilibrium. (iii) A positive externality (MSB > MPB → underproduction). (iv) Free entry forces tangency (zero profit) but tangency on a downward demand curve must occur left of ATC's minimum — excess capacity.

Interpretation: The exam mixes units within single questions; your recall must be structured by model, not by lesson number.

Common Mistakes

1. Putting income on the wrong Lorenz axis. Households (cumulative %) on X, income (cumulative %) on Y — the poorest-first ordering is what makes the curve bow below.
2. Calling a flat sales tax "proportional." Test against income, not against the tax base. Spending share falls as income rises → regressive.
3. Confusing marginal and average tax rates. A 37% top marginal bracket does not mean 37% of total income is taxed.
4. Exam-day: leaving graphs unlabeled. The rubric pays per label. Sixty seconds of labeling is the best-paid minute of your year.
5. Spending 25 minutes on a short FRQ. The long FRQ carries roughly double weight — protect its time first.

Practice Problems

9. (FRQ-style) Country Z's income distribution: poorest 20% → 4% of income; next 20% → 8%; middle 20% → 15%; fourth 20% → 23%; richest 20% → 50%. (a) Compute the cumulative income shares at 20/40/60/80/100% of households. (b) Draw a correctly labeled Lorenz curve for Country Z, including the line of perfect equality. (c) Country Z replaces a flat sales tax with a progressive income tax funding cash transfers to the bottom two quintiles. Show/describe the effect on your Lorenz curve and state what happens to the Gini coefficient. (d) Identify one possible efficiency cost of the new policy.