A country that imports at the world price (Trade at the World Price) can restrict trade with a tax on imports, a tariff, or a limit on their quantity, a quota. Both work like the excise tax of Per-Unit Taxes, applied only to imports.
Key idea
A tariff of $t$ per unit raises the domestic price to $P_w + t$. Domestic producers sell more, consumers buy less, imports fall. The government collects $t \times$ (new imports). Total surplus falls by two deadweight-loss triangles: one from inefficient domestic production, one from consumption given up. A quota that allows the same imports raises the price the same way, but the rectangle goes to whoever holds the import licenses (the quota rent), not the government.
Why it works
With the tariff, a foreign seller needs $P_w + t$ to cover the tax, so that becomes the domestic price. At the higher price, domestic firms expand, even though some of their extra units cost more to make than the world price: that's the production triangle. Buyers cut back on units they valued above the world price: the consumption triangle. A quota creates scarcity of imports directly; the price rises until the quantity demanded minus domestic supply equals the quota.
Worked example: A \$1 tariff
$Q_d = 20 - 2P$, $Q_s = -4 + 2P$, world price \$3. A \$1 tariff is imposed. Find imports before and after, the tariff revenue and the deadweight loss.
- Before: at \$3, $Q_d = 14$, $Q_s = 2$, imports 12.
- After: the price is \$4. $Q_d = 12$, $Q_s = 4$, imports 8.
- Revenue: $\$1 \times 8 = \$8$.
- DWL: $$\tfrac{1}{2}(1)(4 - 2) + \tfrac{1}{2}(1)(14 - 12) = \$1 + \$1 = \$2$$
Answer: Imports 12 → 8; revenue \$8; DWL \$2.
Worked example: The matching quota
Instead of the tariff, the country allows only 8 units of imports. What is the domestic price, and who gets the \$8 rectangle?
- Imports equal $Q_d - Q_s = (20 - 2P) - (-4 + 2P) = 24 - 4P$.
- Set $24 - 4P = 8$: $P = \$4$, the same as with the tariff.
- The gap between \$4 and the \$3 world price on 8 imported units, \$8, goes to license holders.
Answer: \$4; the \$8 goes to whoever holds the import licenses.
Common mistake
Thinking foreign producers pay the tariff. The importer sends the tax to the government, and in this model the domestic price rises by the full tariff, so domestic buyers bear it. Also, missing that a quota raises the price just like a tariff but hands the rectangle to license holders instead of the government. Check: who pays the higher domestic price? Buyers at home.
Economists broadly agree that tariffs raise domestic prices and create deadweight losses. Arguments for some protection (national security, young industries, a response to other countries' barriers) are debated, and the answers depend on the case.