Question

A natural monopolist faces the following demand curve: P = 602 - 3Q, its total cost is given by: TC = 5700 + 2Q (marginal cost is the slope of total cost).

(a) If the government regulates the monopolist to charge a socially optimal price, what price will it charge and how many units will it sell? How much are the profit, consumer surplus and producer surplus? (1+2+2+2+1 = 8 points)

(b) If it is not a regulated monopolist, what is its profit maximizing price and quantity (assuming single price monopolist)? How much are the profit, consumer surplus, producer surplus and dead weight loss? (2+2+2+2+2+2 = 12 points)

(c) If the regulated monopolist is allowed to charge a fair return price (which is $32), how much are the consumer surplus, producer surplus and dead weight loss? (2+2+2 = 6 points)

Answer 1

A natural monopolist faces the following demand curve: P = 602 - 3Q, its total cost is given by: TC = 5700 + 2Q and marginal cost = $2

(a) This price will follow a rule P = MC

602 - 3Q = 2

Q = 600/3 = 200 units and price = $2. Profit = TR - TC = 2*200 - 5700 - 2*200 = -5700. CS = 0.5*(602 - 2)*200 = $60000 and PS = $0.

(b) In this case MR = MC rule is followed

602 - 6Q = 2

Q = 100 and P = $302. CS = 0.5*(602 - 302)*100 = 15000. PS = (302 - 2)*100 = $30000. DWL = 0.5*(200 - 100)*(302 - 2) = 15000. Profit = TR - TC = 30200 - 5700 - 2*100 = 24300

(c) If the regulated monopolist is allowed to charge a fair return price (which is $32), how much are the consumer surplus, producer surplus and dead weight loss? (2+2+2 = 6 points)

When P = 32, Q = 190. CS = 0.5*(602 - 32)*190 = 54150. PS = 0.5*(32 - 2)*190 = 2850 and DWL = 0.5*(200 - 190)*(32 - 2) = 150.