# International Trade and Public Policy

> AP Microeconomics · Unit 2: Supply and Demand
> Source: https://www.owlsprep.com/study/ap-microeconomics-u2-international-trade-and-public-policy/

This sub-topic applies supply and demand welfare analysis to cross-border trade and government trade restrictions for small open economies. You will learn to calculate net gains from trade and analyze deadweight loss from tariffs and quotas.

**Prerequisites:** Calculating consumer and producer surplus from supply and demand curves; Solving for closed domestic market equilibrium; [Comparative advantage and opportunity cost](https://www.owlsprep.com/study/ap-microeconomics-comparative-advantage/)

## Learning objectives

- Define core trade concepts including world price, autarky, tariffs, and quotas
- Calculate welfare changes from opening to trade for small open economies
- Analyze the welfare effects of tariffs and import quotas
- Identify deadweight loss from trade restrictions
- Distinguish between equivalent tariff and quota outcomes

## Core Framework: Small Open Economy Assumption

International Trade and Public Policy applies core supply-and-demand welfare analysis to study the effects of cross-border trade and government trade restrictions on domestic consumers, producers, and overall social welfare. This topic accounts for roughly 2-3% of the total AP Microeconomics exam score, appearing in both multiple-choice and free-response sections.

**Small Open Economy** — A domestic economy too small to influence the global price of a good, so world price is treated as a fixed, exogenous value.

*Notation:* P_w

*Example:* A small Caribbean nation's wheat market does not affect global wheat prices, so it is modeled as a small open economy.

For all AP Microeconomics trade problems, world supply is drawn as a perfectly elastic horizontal line at the fixed world price $P_w$. AP Micro focuses exclusively on partial equilibrium analysis of a single market, aligned with the Unit 2 focus on supply and demand fundamentals.

## Gains From Trade in an Open Economy

In autarky (a closed economy with no trade), the domestic market settles at its own equilibrium price $P^*$ and quantity $Q^*$. When the economy opens to trade, domestic price converges to the fixed world price $P_w$.

- If $P_w < P^*$: Domestic price falls to $P_w$, domestic quantity supplied is less than domestic quantity demanded, and the gap is filled by imports.
- If $P_w > P^*$: Domestic price rises to $P_w$, domestic quantity supplied is more than domestic quantity demanded, and the gap is exported.

Welfare is measured as total surplus (TS), equal to the sum of consumer surplus (CS) and producer surplus (PS):

$$TS = CS + PS$$

Opening to trade always increases total surplus, meaning there are net gains from trade. While one group loses surplus, the other group's gains exceed the losses, so overall social welfare increases.

**Worked example:** The domestic market for cotton t-shirts in Country A has demand $P = 30 - 0.5Q$ and supply $P = 2 + 0.5Q$. The world price of t-shirts is \$8. Calculate the change in total surplus from opening to trade and confirm net gains.

1. Find autarky equilibrium by setting demand equal to supply:

   $$30 - 0.5Q = 2 + 0.5Q \implies Q^* = 28, P^* = 2 + 0.5(28) = \$16$$
2. Compare prices: $P_w = 8 < 16$, so Country A will import t-shirts.
3. Find domestic quantity supplied and demanded at $P_w = 8$:

   $$8 = 2 + 0.5Q_s \implies Q_s = 12; 8 = 30 - 0.5Q_d \implies Q_d = 44$$
4. Calculate total surplus before and after trade:

   $$\text{Autarky: } CS = 0.5(30 - 16)(28) = 196, PS = 0.5(16 - 2)(28) = 196, TS = 392
\\
\text{Free trade: } CS = 0.5(30 - 8)(44) = 484, PS = 0.5(8 - 2)(12) = 36, TS = 520$$
5. Change in $TS = 520 - 392 = +128$, so there is a net gain of \$128 from opening trade.

> **Exam tip:** Always label CS, PS, and any surplus changes clearly on your graph for FRQs; AP readers award points for correctly shaded regions even if your numerical calculation is slightly off.

## Welfare Effects of Import Tariffs

**Import Tariff** — A per-unit tax on imported goods that raises the domestic price of imported goods for a small open economy, without changing the fixed world price.

*Notation:* P_t = P_w + t

*Example:* A \$3 per-unit tariff on imported t-shirts raises domestic price from \$8 to \$11, while world price remains \$8.

Higher domestic prices from a tariff have four key welfare effects: (1) domestic producers increase output, so producer surplus rises, (2) consumers reduce consumption, so consumer surplus falls, (3) the government collects tariff revenue equal to $t \times \text{imports after the tariff}$, (4) there is net deadweight loss (DWL) from two efficiency losses: inefficient domestic production and lost consumer surplus from reduced consumption.

$$DWL = \frac{1}{2}t \Delta Q_s + \frac{1}{2}t \Delta Q_d$$

Where $\Delta Q_s$ is the increase in domestic output, and $\Delta Q_d$ is the decrease in domestic consumption after the tariff.

**Worked example:** Using the t-shirt market from the previous example ($P=30-0.5Q$ demand, $P=2+0.5Q$ supply, $P_w=8$), a \$3 per unit import tariff is imposed. Calculate the deadweight loss from the tariff and identify who gains and loses.

1. New domestic price after tariff:

   $$P_t = 8 + 3 = \$11$$
2. Calculate new $Q_s$ and $Q_d$ at $P_t=11$:

   $$11=2+0.5Q_s \implies Q_{s,t}=18; 11=30-0.5Q_d \implies Q_{d,t}=38. Imports after tariff: 38-18=20, down from 32 under free trade.$$
3. Calculate changes in quantity:

   $$\Delta Q_s = 18 - 12 = 6, \Delta Q_d = 44 - 38 = 6$$
4. Calculate DWL:

   $$DWL = 0.5(3)(6) + 0.5(3)(6) = 9 + 9 = 18$$
5. Welfare outcomes: Domestic producers gain \$45 of surplus, the government gains \$60 of tariff revenue, consumers lose \$123 of surplus, and net deadweight loss to the economy is \$18.

> **Exam tip:** Never forget that a tariff for a small open economy does NOT change the world price, only the domestic price; large country tariff effects are not tested on AP Micro.

## Welfare Effects of Import Quotas

**Binding Import Quota** — A legal limit on the quantity of imported goods that is set below the level of imports that would occur under free trade, so it affects market outcomes. Non-binding quotas (set above free trade imports) have no effect.

*Example:* If a country imports 32 million t-shirts under free trade, a quota of 20 million is binding, while a quota of 40 million is non-binding.

Binding quotas work almost exactly like tariffs: by restricting supply, they raise the domestic price above the world price. The only key difference is who receives the *quota rent* (the gap between domestic price and world price multiplied by the quota quantity, equivalent to tariff revenue):

- If the government auctions quota licenses to domestic importers: the government keeps the quota rent, and the outcome is identical to an equivalent tariff.
- If the government gives quota licenses to foreign producers for free: the quota rent leaves the domestic economy, so total domestic loss equals DWL plus the entire quota rent.

**Worked example:** Using the same t-shirt market (demand $P=30-0.5Q$, supply $P=2+0.5Q$, $P_w=8$), a binding quota of 20 imports is imposed. Compare the outcome to the \$3 tariff that also resulted in 20 imports.

1. Free trade imports are 32, so 20 is a binding quota. We know $Q_d - Q_s = 20$ under the quota.
2. Rewrite demand and supply as functions of price:

   $$Q_d = 60 - 2P, Q_s = 2P - 4. Imports = (60 - 2P_q) - (2P_q - 4) = 64 - 4P_q = 20$$
3. Solve for domestic price:

   $$4P_q = 44 \implies P_q = \$11, the same price as under the \$3 tariff.$$
4. Calculate DWL: the two efficiency triangles are identical to the tariff, so DWL = \$18, same as the tariff.
5. Comparison: The only difference is the quota rent of $3 \times 20 = \$60$. If the government auctions quota licenses, it keeps the \$60 rent and the outcome is identical to the tariff. If the government gives licenses to foreign producers, the \$60 rent leaves the domestic economy, so total domestic loss is $18 + 60 = \$78$, far higher than the tariff.

> **Exam tip:** Always check if a quota is binding first: if the quota limit is higher than free trade imports, it has no effect on price, quantity, or welfare.

## AP-Style Concept Check

**Check your understanding**

Test your understanding of core concepts with this AP-style multiple-choice question:

1. The autarky equilibrium price of wheat in Country B is \$6 per bushel, and the world price is \$4 per bushel. Country B is a small open economy. When opening to free trade, which of the following is true?

   - Country B will export wheat, consumer surplus increases, producer surplus decreases, total surplus increases
   - Country B will import wheat, consumer surplus increases, producer surplus decreases, total surplus increases
   - Country B will import wheat, consumer surplus decreases, producer surplus increases, total surplus decreases
   - Country B will export wheat, consumer surplus decreases, producer surplus increases, total surplus decreases

   *Answer:* Country B will import wheat, consumer surplus increases, producer surplus decreases, total surplus increases

   *Why:* Correct! World price is lower than autarky price, so the country imports, consumers gain, producers lose, and total surplus increases due to net gains from trade.

## Common pitfalls

- **Wrong:** Calculating deadweight loss from a tariff by forgetting to add government revenue back into total surplus when comparing to free trade.
  - Why it fails: Students remember CS falls and PS rises, but overlook that tariff revenue is a benefit to the domestic government that counts toward total surplus.
  - Correct: When calculating total surplus after a tariff, always compute $TS = CS + PS + \text{tariff revenue}$ before comparing to free trade TS.
- **Wrong:** Claiming total surplus decreases when a country opens to export a good because consumer surplus falls.
  - Why it fails: Students only track one group's outcome and ignore the larger gain to producers.
  - Correct: Always calculate total surplus as the sum of CS + PS; net gains from open trade are always positive for a small open economy.
- **Wrong:** Calculating tariff revenue as $t \times$ total domestic consumption after the tariff, instead of $t \times$ imports after the tariff.
  - Why it fails: Students confuse tariffs with a general per-unit tax on all units, but tariffs only apply to imported goods.
  - Correct: Tariff revenue = per-unit tariff $\times$ (domestic quantity demanded - domestic quantity supplied after tariff).
- **Wrong:** Treating quota rent as part of deadweight loss when the government auctions quota licenses.
  - Why it fails: Students assume all price gaps are deadweight loss, regardless of who gets the revenue.
  - Correct: Only the two triangular efficiency areas count as DWL for quotas; quota rent is a transfer, not an efficiency loss, unless it accrues to foreigners.
- **Wrong:** Stating that a tariff increases both consumer and producer surplus.
  - Why it fails: Students mix up the effect of higher prices on the two groups.
  - Correct: Higher domestic prices from tariffs/quotas always increase producer surplus and decrease consumer surplus.
- **Wrong:** Drawing a downward-sloping world supply curve for a small open economy problem.
  - Why it fails: Students confuse domestic supply with world supply.
  - Correct: For all AP Micro trade problems, draw world supply as a horizontal line at the fixed world price.

## Cheatsheet

| Category | Formula / Rule | Notes |
| --- | --- | --- |
| Autarky Equilibrium | $Q_d = Q_s$ | Solve for domestic equilibrium price $P^*$ with no trade |
| Trade Status | If $P_w < P^*$: Import; If $P_w > P^*$: Export | Applies only to small open economy (fixed world price) |
| Imports / Exports | Imports = $Q_d - Q_s$; Exports = $Q_s - Q_d$ | Values calculated at current market price; only positive values are meaningful |
| Total Welfare (Free Trade) | $TS = CS + PS$ | Always sum all domestic components to calculate net welfare |
| Total Welfare (Tariff) | $TS = CS + PS + \text{Tariff Revenue}$ | Always sum all domestic components to calculate net welfare |
| Tariff Domestic Price | $P_t = P_w + t$ | World price unchanged for small open economy |
| Tariff Revenue | Revenue = $t \times (Q_d^t - Q_s^t)$ | Only applied to imported quantity, not total domestic consumption |
| Tariff Deadweight Loss | $DWL = \frac{1}{2}t \Delta Q_s + \frac{1}{2}t \Delta Q_d$ | $\Delta Q_s$ = change in domestic supply, $\Delta Q_d$ = change in domestic demand |
| Binding Quota Condition | Quota limit < Free trade imports | If quota limit > free trade imports, no effect on market outcomes |
| Equivalent Quota Price | Solve for $P_q$: $Q_d(P_q) - Q_s(P_q) = \text{Quota limit}$ | Outcome identical to equivalent tariff if government keeps quota rent |

## What's next

This topic is the first full application of supply and demand welfare analysis to real-world public policy, a framework that powers the rest of the AP Microeconomics course. The skills you practice here — tracking how policy changes surplus for different groups, calculating net efficiency loss, and comparing policy outcomes — are tested repeatedly across both MCQ and FRQ sections of the exam. Mastery of these tools is critical for analyzing all other public policy topics in the course. Immediately next in Unit 2, you will apply the exact same consumer surplus, producer surplus, and deadweight loss framework to analyze domestic policies like price ceilings, price floors, and per-unit taxes. Without mastering how to track welfare changes here, you will struggle to correctly apply these tools to other policy problems later.

- [Production, Cost, and Perfect Competition](https://www.owlsprep.com/study/ap-microeconomics-u3-overview/)
- [The Production Function](https://www.owlsprep.com/study/ap-microeconomics-u3-the-production-function/)
- [AP Microeconomics Short-Run Costs](https://www.owlsprep.com/study/ap-microeconomics-u3-short-run-costs/)

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