Tariffs and Quotas

The small-country tariff diagram

Start with the simplest, most informative model: a small open economy facing a fixed world price P_w. Domestic demand D(P) slopes down, domestic supply S(P) slopes up. Under free trade the home country can import as much as it wants at P_w, so the equilibrium domestic price equals the world price and imports plug the gap M = D(P_w) − S(P_w).

Now levy a per-unit tariff t on imports. Imports must pay the tariff at the border, so they only enter the home market at a delivered price of P_w + t. Domestic producers can charge up to that delivered price too — undercutting by even a penny would not gain market share, since imports would still flow at a finite quantity. The new domestic price is therefore

P_d  =  P_w + t      (small country, no terms-of-trade effect)

At this higher price, four things happen simultaneously:

• Domestic supply expands from S(P_w) to S(P_w+t).
• Domestic demand contracts from D(P_w) to D(P_w+t).
• Imports shrink to M' = D(P_w+t) − S(P_w+t).
• Government collects revenue R = t × M'.

Reading off the textbook diagram with letters a, b, c, d for the four areas between the old and new price lines:

Block	Geometry	Welfare meaning	Direction
a	Trapezoid above S, left of new Qs	Producer surplus gained	+ to producers
b	Triangle on the supply side, between Qs0 and Qs1	Production-distortion deadweight loss	− (burned)
c	Rectangle of width t × M'	Government tariff revenue	+ to treasury
d	Triangle on the demand side, between Qd1 and Qd0	Consumption-distortion deadweight loss	− (burned)

The consumer-surplus loss equals a + b + c + d. The producer-surplus gain equals a. The government revenue equals c. Net welfare change for the small country is therefore

ΔW  =  −(a + b + c + d) + a + c  =  −(b + d)

The two triangles b and d are pure waste. Their sum, by elementary geometry, is approximately

DWL  ≈  (1/2) × t × ΔM
     =  (1/2) × t × (M − M')

This is the small-country result. For a country with no influence on world prices, any tariff is strictly welfare-reducing. The optimal small-country tariff is zero — free trade.

Why a large country can have a positive optimal tariff

The small-country result rests on a single assumption: imports do not affect the world price. Drop that assumption and the picture changes qualitatively. A "large" country is one whose imports are a non-trivial share of world supply — the United States in soybeans, the EU in beef, China in iron ore. When a large country cuts its imports, world demand for the good falls; if foreign export supply is upward-sloping (less than perfectly elastic), the world price falls. The foreign price drop is a transfer from foreign producers to the home treasury — a terms-of-trade gain.

Reading off the revised diagram with P_w^old and P_w^new, the home treasury collects revenue equal to t times M' as before, but t is now divided between the foreign-price drop (P_w^old − P_w^new) and the home-price rise (P_d − P_w^old). The home-price rise creates two domestic deadweight-loss triangles as before; the foreign-price drop is a clean transfer to home. Optimality balances these.

The classical first-order condition, derived for an isoelastic foreign export supply curve with elasticity ε_x*, gives the optimum tariff rate

t*/(1 + t*)  =  1 / ε_x*

Two limits sharpen the intuition. If ε_x* → ∞ (perfectly elastic foreign supply, i.e., the small-country case), t* → 0. If ε_x* is finite, the optimal tariff is strictly positive. Empirical estimates of ε_x* for the US in aggregate cluster in the 1.5–4 range, implying optimal tariff rates of roughly 25%–67% — but that bound ignores retaliation. Once you allow other countries to optimise too, the Nash equilibrium is mutual protection that destroys most of the unilateral gain (Johnson 1953). The lesson: the unilateral optimum exists in theory, but it is a beggar-thy-neighbour optimum that, in equilibrium with retaliation, collapses.

Quotas — same picture, different rectangle

Replace the tariff with an import quota that limits imports to exactly M' (the same volume the tariff would have produced). The domestic supply available to consumers is S(P) + M' for any P. Setting this equal to demand pins down the new domestic price at exactly P_w + t. Geometrically the picture is identical: a + b + c + d are exactly the same. The consumer-surplus loss is the same; the producer-surplus gain is the same; both deadweight-loss triangles b and d are burned for the same reason.

The crucial difference is rectangle c. Under a tariff it is government revenue. Under a quota it is the rent earned by whoever is permitted to import at world price P_w and sell at domestic price P_w+t. Who that is depends on how licences are allocated:

• Competitive auction. The government auctions licences. If the auction is competitive, bidders compete the rent down to zero — i.e., the government captures c just as it would with a tariff. This is the welfare-equivalent quota.
• Allocation to importers. Licences are given (free or below market price) to existing importers. The rent accrues to those firms as a windfall, which they may dissipate in lobbying — a "tariff for friends".
• Allocation to foreign exporters (VER). The exporting country administers the cap; rents accrue abroad. The home country bears a + b + d as before but does not collect c — strictly worse than a tariff.
• Smuggling and corruption. If licences are leakily enforced, c becomes informal rents to whoever can move goods around customs.

Where tariff-quota equivalence breaks

Under perfect competition, certainty, and identical import volume, a tariff and a quota are welfare-equivalent (assuming licences are auctioned to the government). Real economies satisfy none of those conditions, and the divergence between the two instruments shows up in three places.

1. Domestic monopoly. A tariff still exposes the domestic producer to price discipline at the margin — any price above P_w+t loses sales to imports. A quota does not: once the quantitative cap binds, the marginal import is zero regardless of domestic price. A monopolist protected by a quota can therefore raise the home price above P_w+t and capture additional rents at the expense of consumers. Bhagwati's "non-equivalence" result (1965).
2. Demand uncertainty. If demand shifts unpredictably, a tariff lets the import volume absorb the shock (price stays at P_w+t, imports go up or down); a quota fixes the volume and forces all the adjustment onto the price. Variance in the domestic price under quotas is higher, which is a welfare cost under risk aversion or convex production-side costs (Weitzman 1974, in price-vs-quantity form).
3. Innovation and quality. Quotas constrain quantity, not value. Exporters subject to a binding quota upgrade product mix toward higher-margin units — exactly what Japanese automakers did under the 1981 VER, shifting from cheap economy cars into Acura, Lexus and Infiniti luxury lines. The home-market effect is partly to undo the import-volume restriction in value terms.

The optimal-trade-policy hierarchy

Country type	Best policy	Justification
Small open economy, no externalities	Free trade	Any tariff or quota burns DWL with no offsetting gain
Large open economy, no retaliation	Positive optimal tariff	Terms-of-trade gain compensates for DWL up to t* = 1/εx*
Large country, with retaliation	Free trade via multilateral commitment (GATT/WTO)	Nash equilibrium of tariffs is worse than mutual disarmament
Infant industry with learning spillovers	Production subsidy (not tariff)	Targets the distortion directly; no consumption-side DWL
National-security concern	Targeted production subsidy or strategic stockpile	Tariff is a blunt instrument
Pure revenue-raising for poor administration	Tariff as a second-best	Easy to collect at the border; broad-base VAT preferable when feasible

The general principle of trade theory is that, for almost any distortion you can name, a domestic instrument targeted at that distortion dominates a tariff. The exceptions are the terms-of-trade case (which requires a large country and no retaliation) and the revenue-administration case (which prefers a VAT once enforcement capacity exists). Most actual trade policy is neither — it is political-economy redistribution to politically organised producer groups.

Empirical episodes that pin the welfare numbers down

Smoot-Hawley (1930)

The Smoot-Hawley Tariff Act, signed by Herbert Hoover in June 1930 over the protest of 1,028 economists, raised duties on more than 20,000 imported goods. Average ad valorem rates on dutiable imports climbed from about 40% in 1929 to a peak of 59% in 1932. Retaliation by Canada, France, the UK and others followed within months. World trade volumes collapsed by 25%–30% in real terms over 1930–33; US exports fell more than 60% in dollar terms. While the Depression had other causes — the collapse of the US money supply documented by Friedman & Schwartz, the gold-standard transmission of contractionary shocks documented by Eichengreen — most modern accounts treat Smoot-Hawley as a non-negligible amplifier through trade collapse, financial-uncertainty channels, and policy disorganisation. The episode became the founding political argument for the multilateral tariff-cutting project that gave us the GATT in 1947 and the WTO in 1995.

Japan-US auto VER (1981–1994)

Under threat of an import quota, Japan agreed in 1981 to cap car exports to the US at 1.68 million units (rising over the 1980s). The Japanese government allocated the export licences to its automakers, who therefore captured the rent rectangle themselves — estimated at 4–8 billion US dollars per year at peak. Three lessons emerged that are now textbook:

• Quality upgrading: Japanese makers shifted toward larger, higher-margin models; Honda introduced the Acura division (1986), Toyota launched Lexus (1989), Nissan launched Infiniti (1989). The dollar value of US imports rose despite the unit cap.
• FDI as an escape valve: Honda began US production in Marysville, Ohio in 1982; Toyota and Nissan followed. By the late 1980s, transplant production exceeded restricted imports.
• VER is the worst instrument: The rent rectangle accrued to Japanese firms, not the US treasury — about $5 billion per year of pure foreign transfer. A tariff producing the same import volume would have captured that for US revenue.

Trump's 2018–2019 China tariffs

Between January 2018 and December 2019, the Trump administration imposed tariffs on roughly $370 billion of imports from China across four waves (Section 201 solar/washers; Section 232 steel/aluminum; Section 301 list 1, 2, 3, 4A — averaging 10–25% on the affected goods). Because the tariffs were narrowly targeted by HS code and the data were granular, this became the most-studied tariff episode in modern empirical economics. The three most influential studies — Amiti, Redding & Weinstein (2019, 2020); Fajgelbaum, Goldberg, Kennedy & Khandelwal (2020); Cavallo, Gopinath, Neiman & Tang (2021) — converge on a few hard findings:

• Near-complete pass-through to US import prices. Import prices of affected categories rose almost one-for-one with the tariff. Foreign exporters did not absorb material shares; US buyers paid.
• Annual aggregate consumer cost ≈ $1,500 per US household. The Amiti-Redding-Weinstein 2019 NBER paper produced this widely-cited number; later updates revised it modestly but did not overturn it.
• No measurable boost to protected-sector employment. Manufacturing employment in tariff-protected industries was statistically indistinguishable from the counterfactual.
• Retaliation hit US agriculture hard. Soybean and pork exports to China collapsed; the Trump administration deployed roughly $28 billion in offsetting farm subsidies (the Market Facilitation Program).
• Trade was diverted, not destroyed. Imports from Vietnam, Mexico and other unaffected sources rose; total US imports were only modestly reduced. The economic costs were front-loaded into rerouting supply chains.

Why trade policy looks the way it does

If the economics is so unambiguous about free trade for small countries, why do tariffs persist? The political-economy answer was formalised by Grossman & Helpman (1994) in "Protection for Sale": industries with high concentration, low import-demand elasticity, and active political-action committees buy protection from a government weighing votes against campaign contributions. Three empirical regularities follow.

• Concentrated benefits, dispersed costs. A 5% tariff on steel raises steel-industry profits by hundreds of millions, paid in tiny increments by car buyers, can manufacturers, and construction firms — who individually find it not worth lobbying against. Olson's logic of collective action.
• Tariffs as redistribution to the median Republican district. Empirical work by Goldberg & Pavcnik finds tariff variation across industries correlates strongly with measures of industry political organisation rather than externality or terms-of-trade rationales.
• "Temporary" tariffs become permanent. The US sugar quota, dating from the 1930s, is still in force. The US chicken tax (1964) on European pickups survives. Quotas and tariffs build constituencies that defend them.

Common pitfalls

• Conflating statutory and economic incidence. The importer pays the customs cheque, but for a small country the burden falls on domestic consumers via the higher domestic price. Saying "China pays the tariff" is empirically wrong absent a terms-of-trade channel; for granular goods the data show near-complete pass-through to US buyers.
• Treating tariffs and quotas as equivalent. They are equivalent only under perfect competition, certainty, and competitive-auctioned licences. Real-world quotas (especially VERs) are unambiguously worse for the home country.
• Forgetting retaliation in the optimal-tariff calculation. A unilateral optimum exists; a Nash equilibrium of mutual optima does not preserve it. The case for free-trade multilateralism (WTO) rests precisely on this prisoner's-dilemma escape.
• Using a tariff to address a non-trade distortion. Infant-industry learning, externalities, national-security concerns — every textbook case argues that a domestic instrument (subsidy, regulation, stockpile) dominates a tariff. Tariffs are first-best for exactly one distortion: market power in trade.
• Ignoring exchange-rate offset (Lerner symmetry). A tariff on imports raises the home currency, hitting exports. Net trade-balance effects are smaller than the partial-equilibrium diagram suggests.