1 30 points Suppose a monopolist faces the following demand

1. (30 points) 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) (5 points) What is the monopolist’s profit maximizing level of output?
b) (5 points) What price will the profit maximizing monopolist charge?
c) (5 points) How much profit will the monopolist make if she
maximizes her profit?
d) (5 points) What would be the value of consumer surplus if the
market were perfectly competitive?
e) (5 points) What is the value of the deadweight loss when the market
is a monopoly?
f) (5 points) What is the value of the Lerner Index for this monopoly?

Solution

(a) Profit is maximized when Marginal revenue (MR) equals MC.

P = 750 - Q

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

MR = dTR/dQ = 750 - 2Q

Equating MR and MC,

750 - 2Q = 30

2Q = 720

Q = 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) If market were perfectly competitive, profit is maximized by equating price with MC.

When P = MC = $30, Q = 750 - P = 750 - 30 = 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 = (1/2) x Difference in price x Difference in quantity = (12) 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