Question

Suppose that a domestic monopolist in a small country faces demand of P = 200 – Q and has a constant MC of $40 per unit.
a. (2’)Calculate the value of consumer and producer surplus in autarky.
b. (2’)Now suppose that trade occurs with a world price of $50. Calculate the value of consumer and producer surplus.
c. (1’)By how much did the monopolist's profits fall as a result of the opening of trade?

Answer 1

A) Monopolist produces where MR = MC.Here MR = 200 - 2Q and MC = 40. This implies autarky prduction is

MR = MC

200 - 2Q = 40

Q = 160/2 = 80 and P = 200 - 80 = $120.

CS = 0.5*(Max price - current price)*current qty = 0.5*(200 - 120)*80 = $3200 and PS = (P - MC)*Q = (120 - 40)*80 = $6400.

B) At the new of 50, quantity demanded = 200 - 50 = 150 units and at this price, monopoly produces 150. Hence monopoly supplies 150 and CS = 0.5*(200 - 50)*150 = $11250 and PS = (50 - 40)*150 = 1500

c) With trade monopoly's profit fall from 6400 to 1500, by $4900