The annual demand for cars in a certain country is given by D = 20,000 – P where P is the price of a car in dollars. The annual supply of cars by domestic producers is given by S = 5,000 + 0.5P. Suppose this economy opens to trade while the world price of a car is $6,000. As a result of automobile industry union’s lobby, the government decided to impose a quota allowing 3,000 cars to be imported annually. How much import tariff per car would lead to the same equilibrium price and quantity as the import quota?Single choice
A
a. $1000.
B
b. $2,000.
C
c. $3,000.
D
d. $4,000

Question

The annual demand for cars in a certain country is given by D = 20,000 – P where P is the price of a car in dollars. The annual supply of cars by domestic producers is given by S = 5,000 + 0.5P. Suppose this economy opens to trade while the world price of a car is $6,000. As a result of automobile industry union’s lobby, the government decided to impose a quota allowing 3,000 cars to be imported annually. How much import tariff per car would lead to the same equilibrium price and quantity as the import quota?Single choice

A

a. $1000.

B

b. $2,000.

C

c. $3,000.

D

d. $4,000

BlackTom AI · Accepted Answer

We start by outlining the basic relationships: demand is D = 20,000 − P and domestic supply is S = 5,000 + 0.5P, where P is the price per car in dollars.

First, analyze the import quota scenario. With a quota of 3,000 imports, the total imports equal Qd − Qs, so set (20,000 − P) − (5,000 + 0.5P) = 3,000. Working this out gives 15000 − 1.5P = 3,000, which yields P = 8,000. The corresponding quantity demanded is Qd = 20,000 − 8,000 = 12,000, and domestic supply is Qs = 5,000 + 0.5×8,000 = 9,000, so imports = 12,000 − 9,000 = 3,000 as required.

Next, consider the tariff scenario. With a tariff t per car, the domestic price becomes P_t = 6,000 + t (world price plus tariff). The quantity demanded is D = 20,000 − P_t and the quantity supplied is S = 5,000 + 0.5P_t. Imports are then  (20,000 − P_t) − (5,000 + 0.5P_t) = 15,000 − 1.5P_t.

To replicate the quota outcome, we want imports to equal 3,000. Set 15,000 − 1.5P_t = 3,000. Solving gives −1.5P_t = −12,000, so P_t = 8,000. This means the domestic price with the tariff must be 8,000, which corresponds to a tariff t = P_t − world price = 8,000 − 6,000 = 2,000.

Now evaluate the answer choices:
- Option a: $1,000. If the tariff were $1,000, the domestic price would be 7,000, yielding imports of 15,000 − 1.5×7,000 = 15,000 − 10,500 = 4,500, which is greater than the quota of 3,000 and does not replicate the quota outcome. This shows the mis-match between price and import volume.
- Option b: $2,000. This option sets P_t = 8,000, resulting in imports of 15,000 − 1.5×8,000 = 3,000, exactly the quota level, and a market price of 8,000 that parallels the quota equilibrium. This matches the required condition.
- Option c: $3,000. A tariff that high would push the price to 9,000, giving imports of 15,000 − 1.5×9,000 = 15,000 − 13,500 = 1,500, which is well below the quota, so it does not reproduce the same outcome.
- Option d: $4,000. With a 4,000 tariff, the price becomes 10,000, and imports drop to 15,000 − 1.5×10,000 = 0, which is far from the 3,000 imports under the quota and thus not equivalent.

Putting it together, only a tariff of $2,000 yields the same price (8,000) and the same import quantity (3,000) as the quota, by aligning the market-clearing conditions under tariff and quota alike.

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