Practice Worksheet

Chapter 9 — Application: International Trade

Part 1

Short Answer — Trade Direction & Gains

Given In the domestic market for steel, demand is P = 50 − 2Q_d and supply is P = 10 + 2Q_s. The country is considering opening to trade.

Question a

What is the no-trade equilibrium price and quantity?

Equilibrium Price ($)

Equilibrium Quantity

Hint Set demand equal to supply: 50 − 2Q = 10 + 2Q. Solve for Q, then substitute back.

Explanation 50 − 2Q = 10 + 2Q gives 40 = 4Q, so Q* = 10. Substituting: P* = 50 − 2(10) = $30. This is the benchmark — trade is beneficial whenever the world price differs from $30.

New scenario The world price of steel is $20 per ton. The country opens to free trade.

Question b

At the world price of $20, what are the domestic quantity demanded, quantity supplied, and volume of trade? Does the country export or import?

Quantity Demanded

Quantity Supplied

Import Volume

Hint At P = $20: plug into demand to get Q_d, plug into supply to get Q_s. Since world price ($20) < domestic equilibrium ($30), the country imports. Imports = Q_d − Q_s.

Explanation At P = $20: Q_d = (50 − 20) / 2 = 15 and Q_s = (20 − 10) / 2 = 5. Since P_W = $20 < P* = $30, the country imports. Import volume = 15 − 5 = 10 tons.

Question c

Calculate consumer surplus, producer surplus, and total surplus after trade opens at P_W = $20. Compare each to the no-trade values.

Consumer Surplus ($)

Producer Surplus ($)

Total Surplus ($)

Hint CS = ½ × Q_d × (P_{demand intercept} − P_W). PS = ½ × Q_s × (P_W − P_{supply intercept}). The demand intercept is $50 (where P=50 at Q=0). The supply intercept is $10.

Explanation CS = ½ × (50 − 20) × 15 = ½ × 30 × 15 = $225 (up from $100 at no-trade).

PS = ½ × (20 − 10) × 5 = ½ × 10 × 5 = $25 (down from $100 at no-trade).

TS = $225 + $25 = $250 (up from $200 at no-trade — trade gains $50). Consumers gain $125, producers lose $75, net gain = $50.

Part 2

Short Answer — Tariff Effects

New scenario Same steel market. World price = $20. The government imposes a $6 tariff on steel imports. Use the demand P = 50 − 2Q and supply P = 10 + 2Q.

Question d

After the tariff, what is the domestic price? What are the new domestic Q_s and Q_d, and the new import volume?

Domestic Price ($)

Q Supplied

Q Demanded

Imports

Hint The tariff raises the domestic price by the tariff amount. New price = P_W + tariff = $20 + $6 = ? Then plug that price into demand and supply equations.

Explanation Domestic price = $20 + $6 = $26.

Q_s = (26 − 10) / 2 = 8 tons
Q_d = (50 − 26) / 2 = 12 tons
Imports = 12 − 8 = 4 tons (down from 10 tons under free trade).

Question e

Calculate the new consumer surplus, producer surplus, government revenue, total surplus, and deadweight loss under the $6 tariff.

Consumer Surplus ($)

Producer Surplus ($)

Gov Revenue ($)

Total Surplus ($)

Deadweight Loss ($)

Hint CS = ½ × Q_d × (50 − 26). PS = ½ × Q_s × (26 − 10). Gov revenue = tariff × import quantity. DWL = free-trade TS − tariff TS.

Explanation CS = ½ × (50 − 26) × 12 = ½ × 24 × 12 = $144
PS = ½ × (26 − 10) × 8 = ½ × 16 × 8 = $64
Gov revenue = $6 × 4 = $24
TS = $144 + $64 + $24 = $232
DWL = $250 (free trade) − $232 = $18 (Two triangles: B = ½×$6×3 = $9 and D = ½×$6×3 = $9, total $18)

Part 3

Multiple Choice

Figure 9-1 — Tariff in an Importing Country

Question 1

Refer to Figure 9-1. Under free trade (before the tariff), consumer surplus is

E only E + A + B + C + D E + B + D A + F

Hint Under free trade, the price is P_W = $20 and Q_d = 15. Consumer surplus is everything above $20 and below the demand curve. Which areas fall in that region?

Explanation Under free trade at P_W = $20, the domestic price is $20 and consumers buy 15 units. CS is the entire triangle above $20 and below the demand curve — that includes areas E + A + B + C + D. After the tariff, consumers lose A + B + C + D, retaining only E.

Question 2

Refer to Figure 9-1. When the tariff is imposed, the change in producer surplus is

+A (producers gain area A) −A (producers lose area A) +A + F (producers gain all PS) +B + D (producers gain DWL)

Hint Before the tariff, PS = F. After the tariff, PS = A + F. The change is the difference.

Explanation Before the tariff, PS = F (triangle below $20, above supply curve up to Q_s=5). After the tariff, PS = A + F (now domestic producers sell 8 units at $26). The change in PS = +A. Area A is the gain to producers — they sell more units at a higher price.

Question 3

Refer to Figure 9-1. The deadweight loss from the tariff equals

C only (the government revenue rectangle) B + D (two triangles) A + B + C + D B + C + D

Hint DWL is surplus that is lost to nobody. CS falls by A+B+C+D. Of that: A goes to producers, C goes to government. What's left?

Explanation CS falls by A+B+C+D. Area A is recaptured by producers (+PS). Area C is recaptured by government (+revenue). Areas B and D are lost to everyone — nobody captures them. Those two triangles are the deadweight loss: trades that would have occurred at free trade but don't happen under the tariff.

Question 4

Compared to a tariff that reduces imports to the same level, an import quota

always produces a smaller deadweight loss produces the same effects if import licenses are auctioned at market price always raises more government revenue always leads to higher domestic prices than a tariff

Hint What happens to the area C (equivalent of tariff revenue) under a quota? Who gets it?

Explanation A tariff and a quota that restrict imports to the same quantity have identical effects on price, quantity demanded, quantity supplied, and the DWL triangles B and D. The key difference is area C: under a tariff it's government revenue; under a quota it's quota rent captured by license holders. If the government auctions import licenses at their market value, it captures C as revenue — making the quota equivalent to the tariff. The answer is b.

Question 5

If the domestic equilibrium price of wheat in Country A is $8 per bushel and the world price is $5 per bushel, then when Country A opens to free trade it will

export wheat and domestic producers will benefit import wheat and domestic consumers will benefit export wheat and domestic consumers will benefit import wheat and domestic producers will benefit

Hint Compare the world price ($5) to the domestic equilibrium price ($8). Which is lower? What does that tell you about trade direction?

Explanation World price ($5) < domestic equilibrium price ($8). This means domestic consumers can now buy wheat at a lower world price, so they will demand more — and the country will import wheat. Domestic consumers benefit from the lower price (CS rises). Domestic producers are hurt (they must now sell at $5 instead of $8, so PS falls). Answer: b.

Question 6

A country exports soybeans. Which of the following correctly describes the effect of free trade on this market?

CS rises and PS falls; total surplus increases CS falls and PS rises; total surplus increases CS falls and PS falls; total surplus decreases CS rises and PS rises; total surplus increases

Hint If the country exports, the world price must be above the domestic equilibrium price. What happens to CS and PS when price rises above equilibrium?

Explanation Exporting means the world price is above the domestic equilibrium. Domestic consumers now face a higher price (CS falls — they pay more). Domestic producers receive a higher price (PS rises — they gain). But the gain to producers exceeds the loss to consumers, so total surplus increases. Answer: b.

Question 7

The "infant industry" argument for trade protection suggests that

old, declining industries should receive permanent tariff protection new industries may need temporary protection until they can compete globally free trade always benefits infant industries by increasing competition countries should only import goods they cannot produce domestically

Hint The argument applies to new industries that might eventually become competitive — but need time to mature. Think about "infant" vs. "adult."

Explanation The infant industry argument says that new industries may not yet be efficient enough to compete with established foreign competitors, but could become competitive over time if given temporary protection. The concern economists raise: "temporary" often becomes permanent, and it's hard to identify which infants will grow up. Answer: b.

Question 8

When a foreign government subsidizes one of its industries, this is harmful to the domestic economy of the importing country because

domestic consumers pay higher prices for the imported good domestic producers of the good are harmed by lower prices it creates more deadweight loss in the domestic market than free trade would the foreign subsidy creates a trade surplus in the domestic country

Hint A foreign subsidy lowers the world price of that good. How does a lower world price affect domestic consumers vs. domestic producers?

Explanation A foreign subsidy lowers the world price, making imports cheaper. Domestic consumers pay lower prices (CS rises — they benefit). But domestic producers of that good face lower prices and produce less (PS falls). Overall, the economy gains from cheaper imports — the foreign subsidy is actually a gift to domestic consumers. The harm falls specifically on domestic producers. Answer: b.

Part 4

True or False

Question 9

When a country opens to free trade, total surplus always increases regardless of whether the country exports or imports.

Hint In our Isoland example, TS was $200 at no-trade and $250 under both the export and import scenarios.

Explanation True. Whether the world price is above or below the domestic equilibrium, opening to trade moves the country to a more efficient allocation. Exports occur when the world price is above domestic — producers gain more than consumers lose. Imports occur when the world price is below domestic — consumers gain more than producers lose. Either way, total surplus (CS + PS) increases.

Question 10

A tariff on imports always increases total surplus in the importing country.

Hint The tariff creates DWL triangles B and D. Does collecting government revenue C fully offset those losses?

Explanation False. A tariff always creates deadweight loss (triangles B and D). Consumers lose A+B+C+D, producers gain A, and the government gains C. The net change = −(B+D) < 0. So total surplus falls relative to free trade. The tariff moves the economy away from the efficient allocation and creates lost gains from trade.

Question 11

If the world price equals the domestic equilibrium price, opening to trade has no effect on consumer surplus, producer surplus, or the volume of imports and exports.

Hint If P_W = P*, what is the incentive to trade?

Explanation True. If the world price equals the domestic equilibrium price, there is no incentive to trade — domestic buyers and sellers already clear the market at that price. Q_d = Q_s at P* = P_W, so there are no imports or exports. CS and PS remain at their no-trade levels.

Question 12

An import quota that restricts imports to zero has the same effect as prohibiting trade entirely.

Hint Think about what happens to price and quantity when the import quota is set to zero.

Explanation True. If a quota restricts imports to zero, the domestic market must clear using only domestic supply and demand. This is identical to the no-trade situation — domestic price returns to P*, Q_d = Q_s, and there is no international trade. A zero quota is equivalent to autarky (no trade).

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