Import Tariffs as Price Wedges

Introduction

A country that imports a good can buy it at the world price when trade is unrestricted. A specific tariff—a fixed charge on each imported unit—raises the cost of bringing that good into the domestic market. In a competitive small-country model, the tariff is represented as a vertical gap between the world price and the domestic price, provided imports continue.

The key qualification is “provided imports continue.” If the tariff-inclusive price would exceed the price at which domestic supply can meet domestic demand, imports cease. The tariff wedge is therefore useful both as a diagrammatic representation and as a way to check whether the assumed importing equilibrium is possible.

Definition: Let $P_w$ be the world price of a good and $t$ a specific import tariff, measured in currency per unit. The tariff-inclusive import price is $P_w+t$. In a small, competitive importing economy with positive imports, the domestic price $P_d$ equals $P_w+t$. The import gap at a price $P$ is $Q_d(P)-Q_s(P)$, where $Q_d(P)$ is domestic quantity demanded and $Q_s(P)$ is domestic quantity supplied.

Reading the Tariff Wedge on a Diagram

Put quantity on the horizontal axis and price per unit on the vertical axis. Draw the domestic demand curve sloping downward and the domestic supply curve sloping upward. Under free trade, the horizontal world-price line is at $P_w$. At that price, domestic demand exceeds domestic supply, and the difference is imported.

With a specific tariff and continued imports, draw a second horizontal line at $P_w+t$. The vertical distance between the two price lines is exactly $t$. At the higher domestic price, buyers pay $P_w+t$ for the good, while foreign sellers receive $P_w$ per unit in this model; the tariff accounts for the difference. The distance is a per-unit price wedge, not a quantity.

The domestic quantities associated with the tariff-inclusive price are read from the intersections of that price line with the demand and supply curves. Their horizontal difference is the import gap. This diagrammatic description does not itself measure welfare or calculate tariff revenue; those are separate questions.

Assumptions for the price-wedge result: The country is small enough that its purchases do not change the world price; the good is homogeneous and traded competitively; the tariff is a fixed amount per imported unit; and there are no additional transport costs, binding trade restrictions, or other price distortions. The domestic market clears, and the tariff-inclusive price is relevant to domestic sales. If the tariff eliminates imports, the relation $P_d=P_w+t$ need not describe the domestic equilibrium price.

Why the Domestic Price Rises by the Tariff

Suppose imports remain available and domestic sellers can sell the same good at the domestic market price. If the domestic price were below $P_w+t$, importing would cost $P_w+t$, so competitive suppliers would not be willing to bring the good in at a loss. If the domestic price were above $P_w+t$, an importer could buy at the tariff-inclusive cost and sell at the higher domestic price, creating an incentive to expand imports. With competition and positive imports, these arbitrage pressures bring the domestic price to $P_w+t$.

This reasoning depends on the assumption that importing is feasible. To find when it is feasible in the standard supply-and-demand diagram, first find the autarky price $P_A$: the price at which domestic supply equals domestic demand without trade. At a domestic price above $P_A$, domestic supply exceeds domestic demand. Therefore, a tariff-inclusive price at or above $P_A$ cannot support positive imports in market equilibrium.

Q_s(P_A)=Q_d(P_A) \qquad\Longrightarrow\qquad t^*=P_A-P_w

Here $t^*$ is the threshold tariff for the importing case $P_w<P_A$. If $0\leq t<t^*$, then $P_w+t<P_A$, so domestic demand exceeds domestic supply and imports are positive. At $t=t^*$, the domestic price reaches $P_A$, and the import gap is zero. If $t>t^*$, the tariff-inclusive import price is above the autarky price; in the basic model, no imports occur and the domestic market clears at $P_A$. Thus $t^*$ is a threshold or supremum for tariffs allowing positive imports, not a largest tariff that still leaves positive imports.

Worked Applications

Worked Example: Marking the Wedge and Import Gap

A small country faces the world price $P_w=\$24$ per unit. Domestic supply and demand are $Q_s(P)=18+2P$ and $Q_d(P)=138-2P$, with price in dollars and quantities in units. A specific tariff of $t=\$4$ per unit is imposed. Find the free-trade import gap, the tariff-inclusive domestic price, and the import gap with the tariff. State what the diagram should show.

Method: evaluate domestic supply and demand at the relevant horizontal price lines. Under free trade, the price is $P_w=\$24$. Domestic supply is $Q_s(24)=18+2(24)=18+48=66$ units. Domestic demand is $Q_d(24)=138-2(24)=138-48=90$ units. The free-trade import gap is $90-66=24$ units.

With the tariff, the tariff-inclusive price is $P_w+t=\$24+\$4=\$28$ per unit. At that price, domestic supply is $Q_s(28)=18+2(28)=18+56=74$ units, and domestic demand is $Q_d(28)=138-2(28)=138-56=82$ units. The import gap is $82-74=8$ units.

Diagram and check. Draw horizontal lines at $\$24$ and $\$28$, separated vertically by $\$4$. At $\$28$, demand exceeds supply by 8 units, so the assumed importing equilibrium is consistent. The common mistake is to treat the $\$4$ vertical wedge as a four-unit import gap; the calculation shows that the price difference and the quantity difference have different units.

Worked Example: Finding the Zero-Import Threshold

In another small country, $Q_s(P)=5+P$, $Q_d(P)=95-P$, and $P_w=\$35$. Find the threshold tariff. Then determine whether a tariff of $\$10$ or $\$12$ per unit leaves positive imports and identify the domestic price in each case.

Method: find the autarky price first, then compare the tariff-inclusive price with it. Set domestic supply equal to domestic demand: $5+P=95-P$. Adding $P$ to both sides and subtracting 5 gives $2P=90$, so $P_A=\$45$. The threshold tariff is $t^*=P_A-P_w=\$45-\$35=\$10$ per unit.

For $t=\$10$, the tariff-inclusive price is $35+10=\$45$, exactly the autarky price. At that price, supply is $5+45=50$ units and demand is $95-45=50$ units. Imports are $50-50=0$. This tariff is the threshold, not a tariff that still permits positive imports.

For $t=\$12$, the tariff-inclusive import price would be $35+12=\$47$, which is above the autarky price of $\$45$. Imports are not viable in the model. Domestic supply and demand instead balance at $P_A=\$45$, with 50 units of each. The common mistake is to report $\$47$ as the domestic equilibrium price even after imports have stopped; $\$47$ is the cost of an imported unit, not the market-clearing domestic price in this no-import case.

Worked Example: Checking Whether a Diagram Represents an Importing Equilibrium

A diagram is described by $Q_s(P)=4P-20$, $Q_d(P)=180-2P$, and a world price of $\$25$. A tariff of $\$2$ per unit is proposed. Calculate the two price lines, the quantities at the tariff-inclusive price, and the import gap. Then verify whether the diagram should show positive imports.

Method: calculate the autarky threshold as a feasibility check, then evaluate quantities at the tariff-inclusive price. The autarky price solves $4P-20=180-2P$. Thus $6P=200$, so $P_A=\$33.333\ldots$. The threshold tariff is $P_A-P_w=33.333\ldots-25=\$8.333\ldots$ per unit. Since $\$2<\$8.333\ldots$, the proposed tariff is below the threshold.

The world-price line is $P_w=\$25$. The tariff-inclusive line is $P_w+t=25+2=\$27$; the vertical distance between the lines is $\$2$. At $P=\$27$, supply is $Q_s(27)=4(27)-20=108-20=88$ units. Demand is $Q_d(27)=180-2(27)=180-54=126$ units. The import gap is $126-88=38$ units.

Check. Demand exceeds supply by 38 units, so the tariff-inclusive price is consistent with positive imports. The common mistake is to check only that a tariff-inclusive price can be calculated. The separate feasibility check against the autarky price confirms that this price line belongs in an importing-equilibrium diagram.

Common Diagram Traps

Confusing the wedge with the import quantity. The wedge is a vertical price difference of $t$ dollars per unit. The import gap is a horizontal quantity difference, $Q_d(P_d)-Q_s(P_d)$.
Using the wrong price to read quantities. With an active tariff and positive imports, use $P_w+t$ to read domestic supply and demand, not $P_w$.
Calling the threshold a largest positive-import tariff. At $t=t^*$, the import gap is zero. Positive imports require the strict condition $t<t^*$; $t^*$ is the supremum of the tariffs that permit positive imports.
Assuming full pass-through after imports stop. When $t>t^*$, the domestic market clears at the autarky price in this basic model, not at a price above autarky just because $P_w+t$ is higher.
Ignoring the small-country assumption. The result $P_d=P_w+t$ assumes the country cannot change the world price. It is not the general result for a country large enough to affect the price received by foreign sellers.

Key takeaway: For a small importing economy with positive imports, a specific tariff creates a vertical price wedge $P_d-P_w=t$, and the import gap is measured horizontally at $P_d$. First check the threshold $t^*=P_A-P_w$: positive imports require $t<t^*$, equality gives zero imports, and a larger tariff is prohibitive in the basic model.

Check Your Understanding

For each problem, keep the vertical price wedge separate from the horizontal import gap, and check whether positive imports are possible.

A small country has $Q_s(P)=20+2P$, $Q_d(P)=140-2P$, and $P_w=\$20$. Find the autarky price and threshold tariff. State the exact condition on $t$ for positive imports. (Answer: $P_A=\$30$, $t^*=\$10$ per unit; positive imports exactly when $0\leq t<\$10$.)
For the country in Question 1, let $t=\$7$. Find the tariff-inclusive domestic price, domestic supply, domestic demand, and import gap. State the vertical wedge. (Answer: $P_d=\$27$, $Q_s=74$, $Q_d=86$, imports $=12$ units, wedge $=\$7$ per unit.)
A country has $Q_s(P)=12+2P$, $Q_d(P)=108-2P$, and $P_w=\$18$. Find the tariff at which imports just reach zero and the supply and demand at that price. (Answer: $P_A=\$24$, threshold tariff $=\$6$ per unit; at the threshold $Q_s=Q_d=60$, so imports are zero.)
A diagram uses $Q_s(P)=10+P$, $Q_d(P)=130-P$, $P_w=\$40$, and $t=\$3$. Calculate the tariff-inclusive price and import gap, and verify that the tariff is below the threshold. (Answer: $P_A=\$60$, threshold $=\$20$, $P_d=\$43$; $Q_s=53$, $Q_d=87$, imports $=34$ units, and the wedge is $\$3$ per unit.)

What You'll Learn