262 0 A monopoly faces an inverse demand curve py 100 2y an

26.2 (0) A monopoly faces an inverse demand curve, p(y) = 100 2y, and has constant marginal costs of 20.

(a) What is its profitmaximizing level of output? __________

(b) What is its profitmaximizing price? __________

(c) What is the socially optimal price of this firm? __________

(d) What is the socially optimal output of this firm? __________

(e) What is the deadweight loss due to the monopolistic behavior of this firm? __________

(f) Suppose this monopolist could operate as a perfectly discriminating monopolist and sell each unit of output at the highest price it would fetch. The deadweight loss in this case would be __________

Solution

p = 100 - 2y

MC = 20

Total revenue, TR = p z y = 100y - 2y²

Marginal revenue, MR = dTR / dy = 100 - 4y

(a) A monopolist maximizes profit when he equates MR with MC:

100 - 4y = 20

4y = 80

y = 20

(b)

p = 100 - 2y = 100 - 40 = 60

(c)

Socially optimal price is obtained by equating price with marginal cost.

So, socially optimum price = MC = 20

(d)

When p = 20,

20 = 100 - 2y

2y = 100 - 20 = 80

y = 40

(e)

Deadweight loss = (1/2) x difference in price x difference in output

= (1/2) x (60 - 20) x (40 - 20) = (1/2) x 40 x 20 = 400

(f)

In such case, highest price is obtained by setting y = 0 in demand function:

p = 100 - 2y = 100 - 0 = 100

Deadweight loss = (1/2) x (100 - 20) x (40 - 0) = (1/2) x 80 x 40 = 1,600