Question

A monopolist faces an inverse demand of P(Q) = 250−2Q and constant marginal costs.

a) Calculate the optimal price, quantity and total revenues, for MC = 10 and MC = 30.

b) Repeat question a) under perfect competition with constant marginal costs for MC = 10 and MC = 30.

c) Discuss how the marginal cost increase from 10 to 30 affects revenue in the monopoly case vs perfect competition. Relate your answer to the price elasticity of demand

d) Take the monopoly equilibrium at MC=10. Now the government imposes a maximum price of $50. Discuss the effects of this measure.

e) Instead of the maximum price, the government gives the monopoly a subsidy of $10, so the marginal cost of the monopoly effectively drops to zero. Discuss the welfare effects and compare with perfect competition.

Answer 1

(a) Monopolist maximizes profit when MR = MC.

TR = PQ = 250Q - 2Q²

MR = dTR/dQ = 250 - 4Q

(i) When MC = 10,

250 - 4Q = 10

4Q = 240

Q = 60

P = 250 - (2 x 60) = 250 - 120 = 130

TR = 130 x 60 = 7800

(ii) When MC = 30,

250 - 4Q = 30

4Q = 220

Q = 55

P = 250 - (2 x 55) = 250 - 110 = 140

TR = 140 x 55 = 7700

(b) In perfect competition, P = MC.

(i) When P = 10,

250 - 2Q = 10

2Q = 240

Q = 120

P = 10

TR = 10 x 120 = 1200

(ii) When P = 30,

250 - 2Q = 30

2Q = 220

Q = 110

P = 30

TR = 30 x 110 = 3300

(c) Increase in MC decreases revenue for monopolist but increases revenue for perfect competitor. This is because monopolist faces an imperfectly elastic demand while perfect competitor faces perfectly elastic demand.

(d) When MC = 10, P = 130 and Q = 60.

When price = 50, from demand function,

250 - 2Q = 50

2Q = 200

Q = 100

TR = 50 x 100 = 5000

Therefore quantity demanded will increase and total revenue will decrease.

NOTE: As per Answering Policy, 1st 4 parts are answered.