Question

The inverse demand function a monopoly faces is P = 100 − Q. The firm’s cost curve isTC(Q) = 10 + 5Q.Suppose instead that the industry is perfectly competitive. The industry demand curve and firm cost function is same as given before.

(j) (4 points) What is the level of output produced? Compare it to the output of single price monopoly.

(k) (4 points) What is the equilibrium price for this industry? Compare it to the price charged of single price monopoly.

(l) (4 points) What is the consumer surplus for this industry? Compare it to the consumer surplus under single price monopoly.

(m) (4 points) What is the producer surplus for this industry? Compare it to the producer surplus under single price monopoly.

(n) (4 points) What is the deadweight loss created if the industry changes from perfectly competitive to a single-price, unregulated monopoly?

Answer 1

MC = dTC/dQ = 5

Total revenue (TR) = P x Q = 100Q - Q²

Marginal revenue (MR) = dTR/dQ = 100 - 2Q

A single price monopolist maximizes profit by equating MR and MC.

100 - 2Q = 5

2Q = 95

Q = 47.5

P = 100 - 47.5 = 52.5

(j)

A perfect competitor will equate P and MC.

100 - Q = 5

Q = 95

Therefore, quantity is higher by (95 - 47.5) = 47.5.

(k)

P = MC = 5

Therefore, price is higher by (52.5 - 5) = 47.5.

(l)

From demand function, when Q = 0, P = 100 (Vertical intercept of demand curve).

Consumer surplus (CS) = Area between demand curve and market price

CS in monopoly = (1/2) x (100 - 52.5) x 47.5 = (1/2) x 47.5 x 47.5 = 1,128.125

CS in perfect competition = (1/2) x (100 - 5) x 95 = (1/2) x 95 x 95 = 4,512.5

Therefore, CS is higher by (4,512.5 - 1,128.125) = 3,384.375

(m)

When Q = 47.5, MR = MC = 5.

Producer surplus (PS) = Area between MC curve and price

PS under monopoly = (52.5 - 5) x 47.5 = 47.5 x 47.5 = 2,256.25

PS under perfect competition = (1/2) x (5 - 5) x 95 = 0

Therefore, PS is lower by (2,256.25 - 0) = 2,256.25.

(n)

Deadweight loss = (1/2) x Change in price x Change in quantity = (1/2) x (52.5 - 5) x (95 - 47.5) = (1/2) x 47.5 x 47.5

= 1,128.125