Question

Consider a small country where the demand and supply curves of a particular commodity are respectively, Q_d = 10 – P and Q_s = P/3, where Q_d is the quantity demanded, Q_s the quantity supplied and P the price. Assume that the international price of this commodity is 6.

a)  Compute Q_d, Q_s, imports (M), the consumer surplus (CS) and the producer surplus (PS).   

b) Next, assume that the country imposes a tariff t = 1. Compute Q_d, Q_s, M, the change in the welfare measures of all parties involved, i.e., consumers, producers, and the government, and the overall social welfare. Explain your results.

Answer 1

Qd = 10 - P

Qs = (P / 3)

a) At equilibrium, demand = supply

10 - P = (P / 3)

P = 7.5

At this price, Q = 2.5

If world price is 6, quantity demanded at this price is 4 while quantity supplied is 2. It means there is imports of 2.

• Consumer surplus is area of portion A + B + C + E + F + G + H + I + J whose sum is (1/2) * (10 - 6) * (4 - 0) = 8
• Producer surplus is area of portion D whose sum is (1/2) * (6 - 0) * (2 - 0) = 6

b) There is tariff of $2 which raise the price to $7. Quantity demanded at this price is 3 and quantity supplied is 2.33 which means there is imports of 0.67 units.

• Consumer surplus is area of portion A + B + E + F whose sum is (1/2) * (10 - 7) * (3 - 0) = 4.5
• Producer surplus is area of portion D + C whose sum is (1/2) * (7 - 0) * (2.33 - 0) = 8.155
• Government revenue is area of portion H + I whose sum is (3 - 2.33) * (7 - 6) = 0.67
• Deadweight loss is area of portion G + J whose sum is (1/2) * (7 - 6) * (2.33 - 2) + (1/2) * (7 - 6) * (4 - 3) = 0.165 + 0.5 = 0.665