Question

international economics Exercises

I.   Tariff and Quota in the presence of a monopoly
A commodity market is characterized by the following equations:
Demand: P = 90 – 2 (QD)

1. Assume that the firm in this market is a monopoly and that the total cost of producing the good is TC = 20 + 10 (quantity) + 2 (quantity)(quantity).

a. Determine the no trade equilibrium output and price and illustrate it graphically.

b. What is the value of the DWL?

c. What is the free trade equilibrium if this firm faces a world price of $55?

d. Illustrate it graphically. Is there a DWL? Why? Why not?

2. Now assume that the government imposes a tariff of $3 for each unit imported , what is the equilibrium trade?

a. Determine the value of the following economic effects:

b. Loss of consumer surplus

c. Increase in Producer surplus

d. Increase in revenue

e. Net effect on home welfare

3. Instead of a tariff, the government set a quota of 3/4 of the import at the world price.
Illustrate graphically the economic effects of the quota

a. Determine the output and price that the firm will produce and charge.

b. Determine the value of the economic rent

Answer 1

Demand: P = 90 - 2Q

TC = 20+ 10Q + 2Q²

MC = dTC/dQ = 10 + 4Q

(1)

(a) In pre-trade equilibrium, Marginal revenue (MR) equals MC.

Total revenue (TR) = P x Q = 90Q - 2Q²

MR = dTR/dQ = 90 - 4Q

90 - 4Q = 10 + 4Q

8Q = 80

Q = 10

P = 90 - (2 x 10) = 90 - 20 = 70

In following graph, pre-trade equilibrium is at point A where MR intersects MC with price P0 (= 70) and output Q0 (= 10).

(b) In efficient outcome, P = MC.

90 - 2Q = 10 + 4Q

6Q = 80

Q = 13.33

P = 90 - (2 x 13.33) = 90 - 26.66 = 63.34

DWL due to monopoly = (1/2) x Change in P x Change in Q = (1/2) x (70 - 63.34) x (13.33 - 10) = (1/2) x 6.66 x 3.33 = 11.09

(c) When P = $55, from demand function,

55 = 90 - 2Q

2Q = 35

Q = 17.5

(d) In above graph, Pw is the world price (= 55) and Q1 (= 17.5) is the free-trade equilibrium output.

Since Pw is not equal to (less than) the efficient price Pc (= 63.34), there is still a deadweight loss. In above graph, pre-trade DWL equals area ABC and free-trade DWL equals area CEF.

NOTE: As per Answering Policy, 1st 4 parts of the first sub-part have been answered.