Tariffs and quotas: every case, from autarky to a large country

Trade-policy questions look varied, but past papers sort into eight kinds. Each is answered from the same diagram, which this page builds up case by case.

This page covers the case for and against an instrument in a single market. For the theory of why countries trade at all, see the international trade module, and for protection arguments such as infant industries and dumping, the page on those is planned for the next batch.

Everything below uses one market for shirts. Home buyers demand Q_d = 100 − 2P and home firms supply Q_s = −20 + 2P. With no trade at all, a condition called autarky, demand meets supply at ₹30 and 40 shirts. Consumer surplus is the area under the demand curve and above the price, here 400. Producer surplus is the area above the supply curve and below the price, here 400.

Now open the market. A small country is one whose purchases do not move the world price, so it can buy any amount at the world price. At ₹20, which is below ₹30, buyers want 60 shirts and home firms make 20, so the country imports 40. Consumers gain 500, producers lose 300, and the country as a whole gains −200: that is the net gain from trade. Every policy below is measured against this free-trade point.

Move the world price. Below ₹30 the country imports; above ₹30 it exports. The trade module’s lesson on the gains from opening a market goes further into why.

A tariff is a tax on imports. It comes in three forms, and UGC NET 2024 matches them: an ad valorem tariff is a percentage of the value, a specific tariff is a fixed sum per unit, and a compound tariff combines the two. A tariff of ₹5 on a ₹20 shirt is the same as an ad valorem tariff of 25%.

The result you need to know, and the derivation that follows it, is that a small country always loses.

Reading the effects, in the form papers ask them

Compared with free trade, a tariff on a good in a small country raises the domestic price (₹20 to ₹25), raises domestic output (20 to 30), cuts consumption (60 to 50) and imports (40 to 20), and creates tariff revenue where there was none. JNU 2020 asks which of the four rise: output, price and revenue (not demand). CUET 2024 asks which statement is false: that producer surplus decreases. UGC NET 2026 gives prices up and consumption down.

A tariff also redistributes within the country. It raises the price of the import-competing good, so, as the Stolper-Samuelson theorem says, the factor used intensively in that good gains and the other loses. JNU 2016 asks it with a capital-abundant country that taxes the labour-intensive import: labour gains and capital loses (see the trade module’s lesson on the theorems).

Make the tariff higher and higher. When it reaches ₹10, domestic buyers are willing to pay no more than the autarky price of ₹30 even with no imports, so imports stop. A tariff at or above this level is prohibitive (Hyderabad 2013: it means no imports), and it has the same effect as an outright ban or an infinite tariff. The domestic price is the autarky price, revenue is zero, and the country loses the whole gain from trade: 200 here.

JNU 2021 puts a number on it. India’s demand for petrol is 1000 − 5P and supply 500 + 10P. If India bans imports completely, the price is whatever clears the home market: 1000 − 5P = 500 + 10P, so P = 500 ÷ 15 = 33.33. A ban is just a return to autarky.

An import quota is a limit on the quantity imported. It works on the quantity, not on the price, and the price adjusts: it rises until buyers want exactly as much as home firms and the permitted imports can supply. To find the new price, set demand minus home supply equal to the quota and solve.

With a quota of 20 (half of free-trade imports), that gives 120 − 4P = 20, so P = ₹25. The result is exactly the tariff of ₹5: the same price, the same output, the same imports. What changes is area c, and it changes names: it is no longer tariff revenue but a licence rent. Importers who may bring in a shirt for ₹20 can sell it for ₹25, so the right to import is worth ₹5. Whoever holds the licences gets the rent, and there are three ways to hand them out:

• The government sells them by auction. It collects the rent, which is then just like tariff revenue, and the country loses only triangles b and d.
• The government gives them to importers by historical share or on request. Importers pocket the rent, and people spend real resources competing to get licences. UGC NET 2024: when imports are restricted with a quota instead of a tariff, the cost is sometimes magnified by rent seeking.
• The exporting country limits its own sales, a voluntary export restraint (VER). Foreign exporters earn the rent, so the importing country loses b + c + d. The cost here is 150 against 50 for the auctioned quota. Japan’s restraint on car exports to the United States in the 1980s is the standard example.

For a competitive industry, in a world that stands still, a quota and its equivalent tariff do the same thing. That is the tariff-quota equivalence. The papers ask where it breaks, and the answers are three:

• Revenue against rent. A tariff produces government revenue. A quota produces a rent that goes to the licence holders unless the licences are sold. This is the answer to Hyderabad 2020 (the main difference is that a tariff generates revenue, while a quota, unless it is sold, does not), and JNU 2020 notes the similarities: both raise the price and the producer surplus.
• When demand changes. A tariff pins the price at the world price plus the tariff and lets imports adjust. A quota pins imports and lets the price adjust.
• When the domestic industry is a monopoly. A tariff leaves it exposed to import competition at the capped price. A quota leaves it facing only the demand left over after the imports, which gives it market power.

The tariff-rate quota

A tariff-rate quota (TRQ) combines the two. Imports up to the quota pay a low, perhaps zero, tariff; imports above it pay a high one. Take a tariff of 0% in quota, 10% above it, and a quota of 15 on the shirts market. At ₹30 no one would import above the quota, so the quota binds and the domestic price is ₹26.25, imports are 15, and the licence rent on the cheap imports is ₹93.75. With a quota of 10 and an out-of-quota tariff of ₹5, imports rise above the quota to 20: the domestic price is ₹25, the government collects ₹50 on the out-of-quota units, and the holders of in-quota licences earn ₹50. TRQs are commonly used for farm goods.

So far the country could not move the world price. A large country can: if it buys much of the world’s supply, cutting its purchases pushes the price down. Foreign exporters now face a supply curve that slopes up, and the diagram stacks it on the home supply curve. A tariff shifts that stack up by the amount of the tariff, so the equilibrium price rises by less than the tariff, and the price foreign exporters actually get falls.

Take a tariff of ₹5 in this market. The world price falls from ₹20 to ₹16.67, the home price rises only to ₹21.67, and foreigners bear 67% of the tariff. The new area e is the terms-of-trade gain: what the country saves by paying less per unit on the 33 it still imports. The country now gains when e is larger than the two triangles: 111 against 6, a net gain of 106, where the same tariff cost a small country 50.

Push the tariff up in the lab: the gain peaks and then falls, because each extra rupee of tariff adds a little less terms-of-trade gain (imports are shrinking) and more deadweight loss (the triangles grow with the square of the tariff). The best tariff is the optimum tariff, and what it depends on, what retaliation does to it, and the strange case where the tariff lowers the domestic price are on the optimum tariff page. Four questions on this page’s theme: CUET 2022 (welfare improves when the terms-of-trade gain exceeds the two losses), JNU 2018 (a country can raise welfare with a tariff if it is large and there is no retaliation), and JNU 2011 and 2014 (free trade is best for a small country; restricted trade can beat it for a large one).

A government that wants to help a home industry can pay it instead of taxing its competitors. A production subsidy of ₹5 raises the price producers get to ₹25 while consumers still pay the world price of ₹20. Output rises to 30, the same as under the tariff, but nothing distorts consumption. The cost is the area a + b, and the loss to the country is only triangle b: 25, half of the tariff’s 50. That is the standard reason economists prefer subsidies to tariffs for protecting a home industry, though a subsidy needs a budget, and a tariff raises revenue.

An export subsidy works on the other side of the market. For a country that exports at ₹40, a subsidy of ₹5 per shirt lifts the price at home to ₹45, so home buyers lose 75, producers gain 325, the government pays 300, and the country as a whole loses 50: the same two triangles again. If the country is large, the extra exports also push the world price down, a further loss.

Instruments you may be asked to classify

• Tariffs (ad valorem, specific, compound) are taxes on imports. A tax on imports is a trade barrier (Hyderabad 2015).
• Quotas and VERs restrict quantities. Instruments of trade policy include tariffs, quotas and anti-dumping duties, but not sales taxes (CUET 2024).
• Subsidies include grants and tax holidays (CUET 2024).
• Non-tariff barriers include domestic-content rules, government procurement policies, and health, safety and environmental standards. Anti-dumping or countervailing duties are tariffs, not non-tariff barriers (Hyderabad 2021).

A tariff of 10% on cars protects a car assembler by less than that if the assembler pays 10% more for imported engines, and by more than that if engines come in free. The nominal tariff says nothing about the second case, so economists measure the effective rate of protection: the percentage by which tariffs raise the industry’s value added. The formula, and why it is that formula, is a short derivation; the lab inside it lets you change the three numbers.

The same market, every policy, with the changes measured against free trade at ₹20. Every figure is computed from the demand and supply curves above.

Read down the last column. A subsidy loses the least of the ways of protecting a home industry in a small country. A tariff and a quota with the rent kept at home cost the same. A voluntary export restraint costs more because the rent leaves. A ban costs the most. Only a large country, in the last row, can come out ahead.

Graded by each paper’s own difficulty. Two questions are left out because of their keys: JNU 2021 on lentils, whose key treats a quota as a target to import when it is a ceiling that cannot lower the price below the world price, and Hyderabad 2015, whose key (a tariff lowers social welfare) holds for a small country but not a large one, and the stem does not say which. The reasons are listed at the top of the source file.