Question

Suppose a monopolist faces the following demand curve: P = 750 – Q.If the long run marginal cost of production is constant and equal to $30.

a) What is the monopolist’s profit maximizing level of output?

b) What price will the profit maximizing monopolist charge?

c) How much profit will the monopolist make if she maximizes her profit?

d) What would be the value of consumer surplus if the market were perfectly

competitive?

e) What is the value of the deadweight loss when the market is a monopoly?

f) What is the value of the Lerner Index for this monopoly?

Answer 1

(a) Monopolist maximizes profit by equating Marginal revenue (MR) with MC.

P = 750 - Q

Total revenue (TR) = P x Q = 750Q - Q²

MR = dTR/dQ = 750 - 2Q

Equating with MC,

750 - 2Q = 30

2Q = 720

Q = 720/2 = 360

(b) When Q = 360,

P = 750 - 360 = $390

(c) Profit = Q x (P - MC) = 360 x $(390 - 30) = 360 x $360 = $129,600

(d) In perfect competition, P = MC = $30

750 - Q = 30

Q = 720

From demand function, when Q = 0, P = $750 (Reservation price)

Consumer surplus = Area between demand curve & market price = (1/2) x $(750 - 30) x 720 = 360 x $720

= $259,200

(e) Deadweight loss in monopoly = (1/2) x Difference in price x Difference in quantity

= (1/2) x $(390 - 30) x (720 - 360) = (1/2) x $360 x 360 = $64,800

(f) Lerner index = (P - MC) / P = $(390 - 30) / $390 = $360 / $390 = 0.92