Question

A natural monopolist faces the following demand curve: P = 409 - 2Q, its total cost is given by: TC = 12800 + 9Q (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?

(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?

(c) If the regulated monopolist is allowed to charge a fair return price (which is $89), how much are the consumer surplus, producer surplus and dead weight loss?

Answer 1

aws h o I socially 409 - 20, TC= 19800 +90 optimal price = MC = atclaa= $9, a) ET then from dd aowe P = 409-20 Q= 409-1) 12 = 400/2= 200 units And CS = All Va (409-9) x 200 P = 40000 Ang t= P.O-TC = 9x900 12800 - 9x200 = - 12800 Loss An - PS = -ve And Not a Regulated Monopolist then at Eqm MR = MC 409-40 = 9. 400 = 40, 0* Loo P=409_900= 209 Jane CS = [ 209 - 9) x 100 10000 $ ñ = PS= (209-9)x100. - 12800 I = 20000-12800 = $7200. And Deadwt loss = 21 200-100] [209-97 a 100x 100 = $ 10000 An -

elated Monopolist, P = 89, where dd awowe auts AC, - then = (409-89/2 = 160 • CS = 2x 160 al 409-9) = * X 160X (409-89) = (160x160)/2 = 80x160 = $12800. Ang • as P=AC 8o T = PS = zero. o deadwt loss & [ 200-160] [89-09) 0 = 05 (80) x 40 = 40x40