ECON6023 · International Trade
Trade Policy I: Import Tariffs and Quotas
Week 10 analyses import tariffs and quotas under competitive markets, computing consumer surplus, producer surplus, government revenue and deadweight loss for a small country (a pure welfare loss) and a large country (a possible terms-of-trade gain), plus tariff-quota equivalence and the quota-under-monopoly case. This is the applied exam Q3, and in-class Quiz 2 falls in this week.
What this chapter covers
- 01Welfare tools: consumer surplus (below demand, above price), producer surplus (above supply, below price)
- 02Import demand M(P) = home demand − home supply; zero at the autarky price
- 03Small-country tariff: domestic price = P_W + t; areas a (PS gain), b (production loss), c (revenue), d (consumption loss)
- 04Small-country net welfare = −(b + d); the prohibitive-tariff check against the autarky price
- 05Large-country tariff: foreign price falls; net welfare = e − (b + d); a terms-of-trade gain e is possible
- 06Optimal tariff t* = 1/E*ₓ (elasticity of foreign export supply); prohibitive tariff reverts to autarky
- 07Import quotas: equivalent to a tariff except for the quota rents (area c); licences, rent-seeking, auction, VER
- 08Tariff vs quota with a home monopoly: a quota restores market power and raises price above the equivalent tariff
Small-country import tariff: CS, PS, revenue and deadweight loss
- +1Prohibitive check. Autarky price solves Q_D = Q_S: 100 − 2P = 3P − 20 ⟹ 120 = 5P ⟹ P_A = 24. The tariff-inclusive price 14 is below 24, so imports remain positive — the tariff is not prohibitive.
- +1Quantities. At P_W = 10: D = 80, S = 10, imports M = 70. At the domestic price 14: D = 100 − 28 = 72, S = 42 − 20 = 22, imports M₂ = 50.
- +1Producer surplus and revenue. ΔPS (area a) is the trapezoid between the supply curve over the price rise 10 → 14: ½(10 + 22)(4) = +64. Government revenue = t × M₂ = 4 × 50 = +200.
- +1Consumer surplus. ΔCS is minus the trapezoid between the demand curve over 10 → 14: −½(80 + 72)(4) = −304, i.e. ΔCS = −(a + b + c + d) = −304.
- +1Deadweight loss and net welfare. DWL = b + d, with b = ½(22 − 10)(4) = 24 (production loss) and d = ½(80 − 72)(4) = 16 (consumption loss), so DWL = 40. Net welfare = ΔCS + ΔPS + revenue = −304 + 64 + 200 = −40 = −(b + d). The small country loses.
Key terms
- Consumer surplus
- The area below the demand curve and above the price paid. A tariff raises the domestic price, so consumer surplus falls by the trapezoid −(a + b + c + d).
- Producer surplus
- The area above the supply curve and below the price received. A tariff raises the price to home producers, so producer surplus rises by area a.
- Deadweight loss
- The net efficiency loss from a tariff, b + d: the production loss b (home units made at a marginal cost above the world price) plus the consumption loss d (surplus on units no longer bought).
- Prohibitive tariff
- A tariff large enough that the tariff-inclusive price reaches or exceeds the autarky price, eliminating all imports and reverting the economy to autarky. Government revenue is then zero.
- Quota rents
- Area c, the value of the right to import under a quota. Who captures it (home licence-holders, an auction, or foreign exporters under a VER) determines whether the net loss is −(b + d) or −(b + c + d).
- Quota under monopoly
- With a home monopoly, a quota shifts the firm's residual demand to D − M̄, letting it set MR = MC and price above the equivalent tariff — the quota restores market power and causes a larger welfare loss, a key reason the WTO prefers tariffs.
Trade Policy I: Import Tariffs and Quotas FAQ
Why does a small country always lose from a tariff?
Because it cannot affect the world price, so there is no terms-of-trade gain to offset the distortions. The tariff transfers area a from consumers to producers and area c to the government, but the production loss b and the consumption loss d are pure deadweight — units made domestically at too high a cost and units no longer consumed. Net welfare is −(b + d), always negative. Only a large country can gain, via a terms-of-trade effect.
When are a tariff and a quota equivalent, and when not?
In a competitive market a quota of M̄ raises the price by the same amount as the equivalent tariff, so the price and quantity effects match — the only difference is area c: a tariff gives it to the government as revenue, while a quota gives it to whoever holds the licences (which may be foreign exporters under a VER). Equivalence breaks down under a home monopoly, where a quota restores market power and pushes the price above the tariff outcome.
Can AI help me with tariff and quota welfare problems?
Yes. Sia can draw the supply-demand diagram, label areas a-e, run the prohibitive-tariff check, and compute CS, PS, revenue and deadweight loss step by step for both small and large countries, then set fresh practice. It explains the method and checks your working; it does not do graded assessment, and USyd academic-integrity rules apply. Confirm Quiz 2 timing on Canvas.
What is the optimal tariff for a large country?
t* = 1/E*ₓ, where E*ₓ is the elasticity of foreign export supply. Welfare rises with the tariff up to t* (the terms-of-trade gain e outweighs the deadweight loss b + d) and falls beyond it; a prohibitive tariff would throw away all the gains from trade. As the country becomes small (E*ₓ → ∞), t* → 0, recovering the small-country result that any tariff is welfare-reducing.
Exam move
Drill the small-country tariff until the four areas are automatic, and make the prohibitive-tariff check your first move on every policy question. Then layer on the large-country case (foreign price falls, net welfare = e − (b + d)) and the optimal tariff t* = 1/E*ₓ. Practise tariff-quota equivalence and, crucially, the quota-under-monopoly result where a quota revives market power — a distinction the exam likes. Always label diagrams with lettered areas and give signed dollar values, because that is where the applied-question marks sit. Confirm Quiz 2 and exam timing on Canvas.
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