Tariff Pass-Through and Import-Supply Elasticity

Why Tariff Pass-Through Depends on Foreign Supply

An import tariff creates a gap between the price domestic buyers pay and the price foreign sellers receive. The tariff rate alone does not tell us how much the domestic price will rise. That depends on how readily foreign exporters can change the quantity they sell when the price they receive changes, as well as on how domestic import demand responds to its price.

The key contrast is between a small importing country, which faces a fixed foreign price, and an importing country that faces an upward-sloping foreign export-supply curve. In the first case, the tariff is fully passed through to domestic buyers. In the second, the foreign price can fall, so buyers may bear only part of the tariff wedge.

Definition: Let $P$ be the domestic price of an imported good and $P^*$ the price received by foreign sellers. A specific tariff $t$, measured in dollars per unit, creates the price wedge $P=P^*+t$. An ad valorem tariff at rate $\tau$, applied to the foreign price, creates the wedge $P=(1+\tau)P^*$. Pass-through describes how a change in the tariff changes these two prices.

Import Demand and Foreign Export Supply

Let $M(P)$ be the importing country’s quantity of imports demanded at domestic price $P$. It is typically downward sloping: a higher domestic price reduces the quantity buyers want relative to domestic production. Let $X(P^*)$ be foreign export supply at the price $P^*$ received by sellers. For the upward-sloping case, a higher received price increases the quantity foreign sellers are willing to export.

At equilibrium, the quantity imported equals the quantity exported, $M(P)=X(P^*)$, and the tariff determines the price wedge between them. The import-demand elasticity in absolute value is $\eta_M=-d\ln M/d\ln P$; the foreign export-supply elasticity is $\varepsilon_X=d\ln X/d\ln P^*$. Both are nonnegative under the usual downward-sloping import-demand and upward-sloping export-supply assumptions.

These relationships describe a competitive market for the imported good. They hold other determinants of demand and supply fixed and assume the tariff is fully collected, with no transport costs or other price wedges. The small-country case is the limiting case in which foreign export supply is perfectly elastic at the price taken as given by the importer.

Worked Example: Full Pass-Through for a Small Importer

A small country imports a food ingredient at a fixed foreign price of $40 per unit. Its domestic demand is $D(P)=200-2P$, and its domestic supply is $S(P)=20+P$, with quantities measured in units. The government imposes a specific tariff of $6 per unit. Find the domestic price, the price foreign sellers receive, and imports before and after the tariff.

Method and assumptions. Because the country is small, foreign export supply is perfectly elastic at $40: foreign sellers continue to receive $40 per unit. The tariff is a specific $6 charge, so the domestic price is the foreign price plus $6.

Before the tariff. The domestic price equals the fixed foreign price, $P=40$. Demand is $D(40)=200-2(40)=120$, and domestic supply is $S(40)=20+40=60$. Imports are $120-60=60$ units.

After the tariff. The price wedge gives $P=40+6=46$. Demand is $D(46)=200-2(46)=108$, and domestic supply is $S(46)=20+46=66$. Imports are $108-66=42$ units. Foreign sellers still receive $40.

Check and common mistake avoided. The price paid by domestic buyers rose by $6, exactly the tariff, while the foreign price did not change. The import quantity also equals the quantity supplied by foreigners at equilibrium; the fall from 60 to 42 units is consistent with lower domestic demand and higher domestic production. Adding the tariff to the foreign price and also subtracting it from that price would incorrectly count the wedge twice.

How Elasticities Divide a Tariff

When foreign export supply slopes upward, sellers can respond to the tariff by accepting a lower price. Domestic buyers then face an increase smaller than the full tariff, while foreign sellers receive less than before. The elasticities show how responsive the two sides of the market are.

For a small change in an ad valorem tariff, the percentage price changes satisfy a simple incidence rule. Differentiating the equilibrium condition $M(P)=X(P^*)$ gives the relationship between the two price changes. The tariff wedge then identifies their combined change.

-\eta_M\,d\ln P=\varepsilon_X\,d\ln P^*, \qquad d\ln P=d\ln P^*+d\ln(1+\tau).

Solving these two equations gives the local percentage pass-through shares. The domestic price share is $\varepsilon_X/(\eta_M+\varepsilon_X)$, and the foreign price reduction share is $\eta_M/(\eta_M+\varepsilon_X)$. These shares sum to one. A more elastic foreign export supply means sellers are less willing to absorb a price reduction, so more of the tariff reaches domestic buyers. A more elastic import demand means buyers reduce purchases more readily as the domestic price rises, which increases the adjustment in the foreign price.

\frac{d\ln P}{d\ln(1+\tau)} =\frac{\varepsilon_X}{\eta_M+\varepsilon_X}, \qquad \frac{d\ln P^*}{d\ln(1+\tau)} =-\frac{\eta_M}{\eta_M+\varepsilon_X}.

For a specific tariff, a related local formula follows by differentiating the market-clearing condition and the specific-tariff wedge. If the current equilibrium prices are $P$ and $P^*$, the exact local pass-through per additional dollar of specific tariff is $\varepsilon_X P/(\eta_M P^*+\varepsilon_X P)$. When there is no tariff, $P=P^*$, so this reduces to $\varepsilon_X/(\eta_M+\varepsilon_X)$. With a positive specific tariff, the price levels differ; using the unadjusted elasticity share as an exact specific-tariff formula can therefore give the wrong result.

\frac{dP}{dt} = \frac{\varepsilon_X P}{\eta_M P^*+\varepsilon_X P}.

The limiting case makes the small-country result clear. As foreign export-supply elasticity becomes arbitrarily large, the domestic price response approaches the full tariff change. If foreign export supply is upward sloping but not perfectly elastic, the response is generally partial. These are pass-through results; they do not by themselves measure the total welfare effect of a tariff.

Worked Example: Equal Price Changes with Linear Curves

An importing country has import demand $M(P)=180-2P$. Foreign export supply is $X(P^*)=-20+2P^*$. Quantities are in thousands of units and prices in dollars per unit. Find the free-trade equilibrium, then the equilibrium after a specific tariff of $8 per unit. Calculate the price changes and verify market clearing.

Method and assumptions. Use the two linear curves and the specific-tariff wedge $P=P^*+8$. The given curves are valid over the equilibrium quantities calculated below.

Free-trade equilibrium. Without a tariff, $P=P^*$, so $180-2P=-20+2P$. Rearranging gives $200=4P$, hence $P=P^*=50$. The traded quantity is $M(50)=180-100=80$, and foreign export supply is $X(50)=-20+100=80$. The free-trade equilibrium is therefore $50 and 80 thousand units.

Tariff equilibrium. Substitute $P=P^*+8$ into import demand and equate it to export supply: $180-2(P^*+8)=-20+2P^*$. Thus $164-2P^*=-20+2P^*$, so $184=4P^*$ and $P^*=46$. The domestic price is $P=46+8=54$.

Quantities and incidence check. Import demand is $M(54)=180-108=72$. Export supply is $X(46)=-20+92=72$, so the market clears. The domestic price rose by $4, while the foreign received price fell by $4. Together these changes equal the $8 tariff wedge.

At the free-trade price, both elasticities are $2(50)/80=1.25$, so the local ad valorem incidence rule assigns equal percentage price changes to the two sides. In this linear example, the specific tariff also produces equal dollar changes because the two curves have equal slopes. Common mistake avoided: applying an elasticity share as a dollar change without checking the model can be misleading; here the equal dollar changes follow from the linear curves and equal slopes, not just from the elasticity values.

Finite Ad Valorem Tariffs and Constant Elasticities

The elasticity share is a local result in a general market: it describes the response to a small tariff change at the current equilibrium. For a finite tariff change, elasticities and prices can change along the curves. One useful case permits an exact finite calculation: import demand and export supply have constant elasticities over the range being considered.

Suppose the initial free-trade price is $P_0$, and the initial import and export quantities are equal. With constant elasticities, quantities change in proportion to the relevant price ratios raised to their elasticity powers. Combining those quantity expressions with $P=(1+\tau)P^*$ gives the exact price ratios shown below.

\frac{P^*}{P_0}=(1+\tau)^{-\eta_M/(\eta_M+\varepsilon_X)}, \qquad \frac{P}{P_0}=(1+\tau)^{\varepsilon_X/(\eta_M+\varepsilon_X)}.

The result can be checked directly: the import-demand quantity ratio is $(P/P_0)^{-\eta_M}$, and the export-supply quantity ratio is $(P^*/P_0)^{\varepsilon_X}$. Substitution of the price ratios makes both quantity ratios equal, as equilibrium requires.

Worked Example: Exact Pass-Through Under Constant Elasticities

At free trade, an importer’s price is $100 and its import quantity is 100 units. Import demand has constant elasticity $\eta_M=2$, and foreign export supply has constant elasticity $\varepsilon_X=1$. An ad valorem tariff of 33.1% is imposed on the foreign price. Find the new domestic price, foreign price, and trade quantity.

Method and assumptions. Use the exact constant-elasticity formulas. The tariff factor is $1+\tau=1.331=1.1^3$, which makes the powers straightforward. Prices and quantities are positive, and the stated constant elasticities apply over this change.

Prices. The foreign price ratio is $1.331^{-2/3}=1.1^{-2}=1/1.21$. Thus $P^*=100/1.21=\$82.6446$ to four decimal places. The domestic price ratio is $1.331^{1/3}=1.1$, so $P=\$110$.

Quantity. Import demand changes by the ratio $(110/100)^{-2}=1/1.21=0.826446$. The new quantity is $100(0.826446)=82.6446$ units. Foreign export supply changes by $(82.6446/100)^1=0.826446$, giving the same quantity.

Wedge and incidence check. The tariff per unit is $0.331(82.6446)=\$27.3554$. The domestic price rose by $10; the foreign price fell by $100-82.6446=\$17.3554$. Their changes sum to $27.3554, the per-unit tariff at the new foreign price. Common mistake avoided: treating 33.1% as a $33.10 specific tariff would use the wrong price wedge. This is an ad valorem tariff, so the dollar wedge depends on the foreign price after adjustment.

Interpreting Pass-Through Carefully

A useful way to remember the incidence result is to ask which side is less able to adjust quantity. If foreign exporters can readily redirect sales elsewhere, their export supply to this market is more elastic; they are less likely to accept a substantial price reduction, and domestic buyers tend to bear more of the tariff. If foreign export supply is less elastic, foreign sellers have less scope to change the quantity they export, and the foreign received price can fall more.

In applying the result, distinguish percentage changes from dollar changes, and small changes from finite ones. The simple elasticity shares give local percentage pass-through for an ad valorem tariff. They also give the dollar shares for a small specific-tariff change when the two prices are equal. Away from that benchmark, use the price-level-adjusted specific-tariff formula for a local change, or solve the full equilibrium as in the worked examples.

Small country: foreign price is fixed, so a specific tariff is fully passed through to the domestic price.
Finite foreign export-supply elasticity: both the domestic and foreign prices can adjust, dividing the tariff’s price wedge.
More elastic foreign export supply: a larger share of an ad valorem tariff change reaches domestic buyers, all else equal.
Model check: after calculating prices, verify that import demand equals foreign export supply and that the price wedge matches the tariff definition.

Pass-through describes price adjustment in the importing market. It is distinct from the broader consequences of a tariff for other countries, strategic responses, or welfare. Keeping that distinction clear prevents a price-incidence calculation from being mistaken for a complete policy evaluation.

Key takeaway: In a small-country model, the foreign price is fixed and domestic buyers bear the full tariff. With upward-sloping foreign export supply, pass-through is generally partial: the import-demand and export-supply elasticities determine how the price wedge is divided.

Check Your Understanding

For each problem, use the stated tariff model and verify prices or quantities when enough information is provided.

A small importer faces a fixed foreign price of $72 and imposes a $9 specific tariff. What domestic price do buyers pay, and how much of the tariff is passed through? (Answer: Domestic price $81; full pass-through of $9.)
For a small change in an ad valorem tariff, import-demand elasticity is $\eta_M=1$ and foreign export-supply elasticity is $\varepsilon_X=3$. If the tariff factor $1+\tau$ rises by approximately 8% locally, what are the approximate percentage changes in the domestic and foreign prices? (Answer: Domestic price rises approximately 6%; foreign price falls approximately 2%.)
Import demand is $M(P)=240-3P$ and foreign export supply is $X(P^*)=-30+2P^*$. Find the free-trade price and quantity, then the prices and quantity with a $10 specific tariff. (Answer: Free trade $P=P^*=\$54$, quantity 78; with tariff $P=\$58$, $P^*=\$48$, quantity 66.)
Under constant elasticities, the initial free-trade price is $50, $\eta_M=1$, $\varepsilon_X=2$, and the ad valorem tariff factor is $1+\tau=1.728$. Find the new domestic and foreign prices. (Answer: Domestic price $72; foreign price approximately $41.67.)
At a current equilibrium, $P=\$120$, $P^*=\$100$, $\eta_M=1.5$, and $\varepsilon_X=2$. What is the local domestic-price pass-through per additional dollar of a specific tariff? (Answer: $240/(150+240)=0.6154$, or approximately 61.54%.)

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