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AP® Microeconomics · Unit 2 · Topic 2.9

International Trade and Public Policy: Study Guide (Microeconomics 2.9)

Learn how opening a market to trade changes price, quantity and surplus for importers and exporters, and how tariffs and quotas affect price, imports, revenue and total surplus.

From a closed market to an open one

So far in this unit, every market has been closed: only domestic buyers and domestic sellers. A country that does not trade with others is in autarky. Its price and quantity are set where domestic demand meets domestic supply.

When a country opens a market to trade, its buyers can also buy from foreign sellers, and its sellers can also sell to foreign buyers. In this topic we use a small economy: one whose buying and selling are too small to change the world price (Pw). It can buy or sell as much as it wants at Pw, so the world price acts like a horizontal line on the domestic graph.

At the world price, two things can happen:

  • Pw is below the autarky price. Domestic buyers want more than domestic sellers will supply at Pw. The gap is filled by imports: imports = Qd − Qs at Pw.
  • Pw is above the autarky price. Domestic sellers supply more than domestic buyers want at Pw. The extra is sold abroad as exports: exports = Qs − Qd at Pw.

Either way, the domestic price moves to the world price, and the gap between domestic demand and domestic supply is filled by trade. This guide builds on the surplus and deadweight-loss ideas from Topic 2.8.

Throughout, we use Tarvos, a fictional small country. Its domestic rice market is:

  • demand: Qd = 120 − 10P
  • supply: Qs = 10P

where P is the price in dollars per kg and Q is in thousand tonnes per year. Because 1 thousand tonnes is 1 million kg, an area of “$1 per kg × 1 thousand tonnes” is $1 million. Every surplus below is in millions of dollars.

The importing case on a graph

Under autarky, 120 − 10P = 10P, so P = $6 and Q = 60 thousand tonnes. The world price of rice is $3 per kg.

Tarvos rice market before and after opening to trade Price in dollars per kg on the vertical axis, 0 to 12, and rice in thousand tonnes per year on the horizontal axis, 0 to 120. Domestic demand D falls from 12 dollars at zero quantity to zero price at 120. Domestic supply S rises from the origin to 12 dollars at 120. They cross at the autarky point, 6 dollars and 60 thousand tonnes. A dashed horizontal line at the world price of 3 dollars meets supply at 30 thousand tonnes and demand at 90 thousand tonnes; the gap of 60 thousand tonnes is labelled imports. Area A is the triangle under demand and above 6 dollars. Area B is the rectangle from 0 to 30 thousand tonnes between 3 and 6 dollars. Area C is the triangle between 3 and 6 dollars from 30 to 60 thousand tonnes, left of the supply curve. Area E, hatched, is the triangle with corners at supply and demand on the world price line and the autarky point. Area F is the triangle under 3 dollars above the supply curve. 0 30 60 90 120 0 3 6 9 12 Rice (thousand tonnes per year) Price ($ per kg) D S autarky Pw = $3 (world price) A B C E F imports = 60
Figure 1. Tarvos opens its rice market to trade (fictional data). The price falls from the autarky price of $6 to the world price of $3. Domestic output falls to 30, consumption rises to 90, and the gap of 60 is imported. Letters mark areas; E (hatched) is the net gain from trade.

Read the surplus areas from Figure 1:

Autarky (P = $6) Free trade (P = $3)
Consumer surplus A A + B + C + E
Producer surplus B + C + F F
Total surplus A + B + C + F A + B + C + E + F

Three things to notice:

  1. B + C used to be producer surplus. After trade it belongs to consumers. It is a transfer, not a gain for the country.
  2. E is new surplus that did not exist before. It is the gain from trade: total surplus rises by E.
  3. Producers lose (they sell less at a lower price) and consumers gain (they buy more at a lower price). The gain to consumers is larger than the loss to producers.

The exporting case

If the world price is above the autarky price, everything flips. Domestic buyers face a higher price and buy less; domestic sellers get a higher price and sell more, shipping the extra abroad. Producers gain, consumers lose, and total surplus still rises. Worked example 3 shows this with numbers and Figure 3.

Pw below autarky price Pw above autarky price
Domestic price falls to Pw rises to Pw
Domestic quantity supplied falls rises
Domestic quantity demanded rises falls
Trade imports = Qd − Qs exports = Qs − Qd
Consumer surplus rises falls
Producer surplus falls rises
Total surplus rises rises

Tariffs and quotas: why and how

Governments sometimes restrict imports, often to protect domestic producers and their workers, or to raise revenue. The two tools in this topic are:

  • A tariff: a tax on each unit of an imported good. With a per-unit tariff t, imports cost Pw + t, so the domestic price rises to Pw + t.
  • An import quota: a legal limit on the quantity of a good that may be imported in a period.

Both raise the domestic price above the world price, so both help domestic producers and hurt domestic consumers. Both reduce total surplus compared with free trade.

Worked example 1: surplus before and after trade

Question. Use the Tarvos rice market and Figure 1, with Pw = $3. (a) Find domestic quantity demanded, quantity supplied and imports at the world price. (b) Calculate consumer, producer and total surplus under autarky and under free trade. (c) How much do consumers gain, how much do producers lose, and what is the net gain?

(a) At P = 3: Qd = 120 − 30 = 90; Qs = 10 × 3 = 30; imports = 90 − 30 = 60 thousand tonnes.

(b) Demand meets the price axis at $12 (where Qd = 0). Supply starts at the origin.

Autarky (P = 6, Q = 60):

  1. CS = ½ × 60 × (12 − 6) = 180.
  2. PS = ½ × 60 × (6 − 0) = 180.
  3. Total surplus = 360 ($ million).

Free trade (P = 3, Qd = 90, Qs = 30):

  1. CS = ½ × 90 × (12 − 3) = 405.
  2. PS = ½ × 30 × (3 − 0) = 45.
  3. Total surplus = 450 ($ million).

(c) Consumers gain 405 − 180 = 225. Producers lose 180 − 45 = 135. Net gain = 225 − 135 = 90 ($ million).

Check with the areas. B = 30 × 3 = 90 and C = ½ × 30 × 3 = 45, so B + C = 135: the producers’ loss. E is a triangle with base 90 − 30 = 60 (the imports) and height 6 − 3 = 3, so E = ½ × 60 × 3 = 90: the net gain. Consumers gain B + C + E = 225. Everything agrees.

Worked example 2: a tariff on rice

Question. Tarvos rice farmers ask for protection. The government puts a tariff of $1 per kg on imported rice. The world price stays at $3. (a) Find the new domestic price, quantity supplied, quantity demanded and imports. (b) Calculate government revenue. (c) Find the changes in consumer and producer surplus, and the deadweight loss. (d) What tariff would stop all imports?

Effect of a 1 dollar per kg tariff on the Tarvos rice market Same curves as Figure 1, with the price axis enlarged to show 0 to 8 dollars. The dashed world price line is at 3 dollars. A dotted line at 4 dollars shows the world price plus the tariff. At 4 dollars domestic supply is 40 thousand tonnes and domestic demand is 80 thousand tonnes, so imports are 40 thousand tonnes, down from 60. Area H lies between 3 and 4 dollars left of the supply curve. Area J, hatched, is the small triangle between 30 and 40 thousand tonnes, above 3 dollars and right of supply. Area K, a white rectangle, runs from 40 to 80 thousand tonnes between 3 and 4 dollars. Area L, hatched, is the small triangle between 80 and 90 thousand tonnes, above 3 dollars and below demand. 0 30 40 60 80 90 120 0 2 3 4 6 8 Rice (thousand tonnes per year) Price ($ per kg) D S Pw + tariff = $4 Pw = $3 H J K L imports = 40
Figure 2. A tariff of $1 per kg raises the Tarvos rice price from $3 to $4 (fictional data). H is the gain in producer surplus, K (white rectangle) is tariff revenue, and J and L (hatched) are the deadweight loss. Consumers lose H + J + K + L.

(a) Domestic price = Pw + t = 3 + 1 = $4. Qs = 10 × 4 = 40. Qd = 120 − 40 = 80. Imports = 80 − 40 = 40 thousand tonnes, down from 60.

(b) The tariff is paid on each imported unit: revenue = t × imports = 1 × 40 = $40 million (area K).

(c)

  1. New CS = ½ × 80 × (12 − 4) = 320. Change = 320 − 405 = −85.
  2. New PS = ½ × 40 × 4 = 80. Change = 80 − 45 = +35 (area H).
  3. Deadweight loss: J = ½ × (40 − 30) × 1 = 5 and L = ½ × (90 − 80) × 1 = 5, so DWL = 10.
  4. Check: total surplus = CS + PS + revenue = 320 + 80 + 40 = 440, compared with 450 under free trade. It fell by 10, the deadweight loss.

Why two triangles? J is lost because Tarvos now grows 10 thousand tonnes at a cost above the world price, when it could have imported them for $3. L is lost because buyers who valued rice above $3 (but below $4) no longer buy those 10 thousand tonnes.

(d) Imports stop when the domestic price reaches the autarky price, $6. So any tariff of $3 or more per kg is prohibitive: imports fall to zero, revenue is zero, and the market returns to autarky.

Interpretation. The tariff moves the market partway back towards autarky. Producers gain and the government collects revenue, but consumers lose more than both together.

Worked example 3: opening to trade as an exporter

Question. Tarvos also grows tea. Domestic demand is Qd = 50 − 5P and domestic supply is Qs = 5P − 10 (P in dollars per kg, Q in thousand tonnes per year). The world price of tea is $8 per kg. (a) Find the autarky price and quantity. (b) Find exports under free trade. (c) Calculate the change in consumer, producer and total surplus.

Tarvos tea market before and after opening to trade Price in dollars per kg on the vertical axis, 0 to 10, and tea in thousand tonnes per year on the horizontal axis, 0 to 50. Domestic demand D falls from 10 dollars at zero quantity to zero price at 50. Domestic supply S rises from 2 dollars at zero quantity to 10 dollars at 40. They cross at the autarky point, 6 dollars and 20 thousand tonnes. A dashed horizontal line at the world price of 8 dollars meets demand at 10 thousand tonnes and supply at 30 thousand tonnes; the gap of 20 thousand tonnes is labelled exports. Area R is the rectangle from 0 to 10 thousand tonnes between 6 and 8 dollars. Area T is the triangle between 6 and 8 dollars from 10 to 20 thousand tonnes, under demand. Area W, hatched, is the triangle with corners at demand and supply on the world price line and the autarky point. 0 10 20 30 40 50 0 2 4 6 8 10 Tea (thousand tonnes per year) Price ($ per kg) autarky D S Pw = $8 (world price) R T W exports = 20
Figure 3. Tarvos opens its tea market to trade (fictional data). The price rises from $6 to the world price of $8. Consumers lose R + T to producers, and W (hatched) is the net gain from trade.

(a) 50 − 5P = 5P − 10, so 10P = 60, P = $6 and Q = 50 − 30 = 20 thousand tonnes.

(b) At P = 8: Qd = 50 − 40 = 10; Qs = 40 − 10 = 30. Exports = 30 − 10 = 20 thousand tonnes.

(c) Demand meets the price axis at $10; supply meets it at $2.

  1. CS: autarky ½ × 20 × (10 − 6) = 40; trade ½ × 10 × (10 − 8) = 10. Change = −30.
  2. PS: autarky ½ × 20 × (6 − 2) = 40; trade ½ × 30 × (8 − 2) = 90. Change = +50.
  3. Total surplus: 80 → 100, a rise of 20 ($ million).

Check. W is a triangle with base 20 (the exports) and height 8 − 6 = 2: ½ × 20 × 2 = 20. R = 10 × 2 = 20 and T = ½ × 10 × 2 = 10, so consumers lose R + T = 30, which producers gain along with W.

Quotas: effects without a graph

You will not be asked to draw a quota, but you must explain its effects. Suppose Tarvos allows at most 40 thousand tonnes of rice imports a year, instead of a tariff.

At the world price of $3, buyers want 60 thousand tonnes more than farmers supply, but only 40 may come in. There is a shortage, so the domestic price rises. It keeps rising until the gap between Qd and Qs equals the quota:

Price ($ per kg) Qd Qs Qd − Qs
3.00 90 30 60
3.50 85 35 50
4.00 80 40 40
4.50 75 45 30

So the price settles at $4, the same as the $1 tariff. The effects:

  • Domestic production rises from 30 to 40 thousand tonnes. Domestic farmers fill part of the gap the quota leaves.
  • Price rises and consumption falls (90 to 80), so consumer surplus falls.
  • Total surplus falls: the same deadweight loss appears, because too much is grown at home and too little is consumed.
  • No tariff revenue. The government collects nothing. The gap between the domestic price and the world price on each imported unit goes to whoever holds the right to import (background: this is often called quota rent).

A quota set at or above free-trade imports (60 here) has no effect: it does not bind.

Common misconceptions

  • “Imports equal the quantity demanded at the world price.” Imports are the gap: Qd − Qs. Tarvos buys 90 but grows 30 itself, so it imports 60.
  • “Free trade makes everyone in the country better off.” Total surplus rises, but one group loses: producers when the country imports, consumers when it exports.
  • “Producers’ lost surplus is a loss to the country.” Most of it (B + C) is a transfer to domestic consumers. The country’s net change is the gain triangle.
  • “A tariff shifts the domestic supply curve.” The domestic supply curve does not move. The price at which imports are available rises from Pw to Pw + t, and producers move along their supply curve.
  • “Tariff revenue is part of the deadweight loss.” Revenue is a transfer from consumers to the government. It stays in the country’s total surplus. Only J and L are lost.
  • “A small country’s tariff lowers the world price, so foreign sellers pay it.” In this model the world price does not change; the domestic price rises by the full tariff.
  • “A quota raises revenue like a tariff.” The government earns nothing from a quota (unless it sells import licences, which is beyond this topic).
  • “Exporting raises the price, so total surplus falls.” Consumers lose, but producers gain more; total surplus rises.

Where this leads

This topic ends Unit 2. Next, Unit 3 looks inside the firm, starting with the production function: how output changes as a firm adds workers. Test yourself with the practice questions, then use the revision notes and the checklist to consolidate. For per-unit taxes and deadweight loss in a closed market, look back at Topic 2.8.

Quick questions

If trade raises total surplus, why do some groups oppose it?

Because the gain is not shared evenly. When a country imports, domestic producers lose surplus; when it exports, domestic consumers lose surplus. The winners gain more than the losers lose, but the losers are real.

Do I need to draw a quota on a graph?

No. Graphing a quota is outside the course. You do need to explain how a quota changes the quantity produced at home, the price, consumer surplus and total surplus.

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