Question

The domestic demand for salmon in the U.S. has an inverse demand curve of p = 150 -3Q. The domestic supply of salmon has an inverse supply curve of p = .050Q. The price is $ per pound of salmon and Q is in millions of pounds of salmon. Assume that the market for salmon is perfectly competitive in a global marketplace.

a.           Provide a graph of the domestic supply and demand for salmon and then calculate and show the domestic supply and demand at a world price of $9 per pound.

b.           If the U.S. government puts a tariff of $3 per pound on salmon, calculate and show the effects of this tariff on the market for salmon, calculating a new quantity demanded and supplied.

c.           Calculate and explain the effects of the tariff on consumer surplus, producer surplus, government revenues and welfare (deadweight loss).

d.           Without reworking all of your answers, how would your answer to c. change if the U.S. government placed a quota on salmon instead of a tariff? Explain your answer.

Answer 1

Demand: p = 150 - 3Q

Supply: p = 0.5Q

a) At equilibrium, demand = supply

150 - 3Q = 0.5Q

Q = 42.86

At this output level, P = 21.43

At a world price of $9, quantity demanded is 47 units while quantity supplied is 4.5 units.

b) If there is a tariff of $3, price will rise to $12. New quantity demanded is 47 units and quantity supplied is 6 units which result in import of 47 - 6 = 41 units.

c)

Without tariff:

Consumer surplus in above diagram is area of portion A + B + C + D + E + G + H + I + J whose sum is (1/2) * (150 - 9) * (47 - 0) = 3,313.5

Producer surplus is area of portion F whose sum is (1/2) * (9 - 0) * (4.5 - 0) = 20.25

After tariff:

Consumer surplus in above diagram is area of portion A + B + C + D whose sum is (1/2) * (150 - 12) * (46 - 0) = 3,174

Producer surplus in above diagram is area of portion E + F whose sum is (1/2) * (12 - 0) * (6 - 0) = 36

Government revenue is area of portion H + I whose sum is 3 * (46 - 6) = 120

Deadweight loss is area of portion G + J whose sum is (1/2) * (12 - 9) * (6 - 4.5) + (1/2) * (12 - 9) * (47 - 46) = 3.75

	Without tariff	With tariff
Consumer surplus	3,313.5 (A + B + C + D + E + G + H + I + J)	3,174 (A + B + C + D)
Producer surplus	20.25 (F)	36 (E + F)
Government revenue	-	120 (H + I)
Deadweight loss	-	3.75 (G + J)

Without quota:

Consumer surplus in above diagram is area of portion A + B + C + D + E + F + G + H + I + J whose sum is (1/2) * (150 - 9) * (47 - 0) = 3,313.5

Producer surplus is area of portion K whose sum is (1/2) * (9 - 0) * (4.5 - 0) = 20.25

After Quota:

Consumer surplus in above diagram is area of portion A + B + C + D whose sum is (1/2) * (150 - 12) * (46 - 0) = 3,174

Producer surplus in above diagram is area of portion E + K whose sum is (1/2) * (12 - 0) * (6 - 0) = 36

Quota revenue is area of portion G + H + I whose sum is 3 * (46 - 6) = 120

Deadweight loss is area of portion F + J whose sum is (1/2) * (12 - 9) * (6 - 4.5) + (1/2) * (12 - 9) * (47 - 46) = 3.75

	Without Quota	With Quota
Consumer surplus	3,313.5 (A + B + C + D + E + F + G + H + I + J)	3,174 (A + B + C + D)
Producer surplus	20.25 (K)	36 (E + K)
Quota revenue	-	120 (G + H + I)
Deadweight loss	-	3.75 (F + J)