Question

7. A monopolist in the market for widgets is facing a demand curve P= 60 - Q. The marginal cost of producing Q units is equal to $Q. (a) Calculate the monopolist's profit maximizing price and quantity. Calculate producer, consumer, and total surplus, and deadweight loss. (b) The government wants to impose a price ceiling that will maximize the total surplus in the market. What price ceiling should the government set? What would be the new values of consumer and producer surplus, and deadweight loss?

Answer 1

(a) P = GO-Q MR = 60- 20 Mc = Q MR = MC 60-20=0 = 60= 8+20 30 = 60 a=20 P = 60-20 p=40 mc=0 ?м Чо 20 F- MR 30 60 u am CS = 1 160-40) (20) = 200 PS : 140-20) (20) + (20-02 (20-0) = 20X20 + 20X10 = 400 + 200 = 600 IS = cst Ps = 200+ 600 800 For computing dead weight loss we have to find competitive output and price which is given by P=mc

60 - 0 = 0 бо = 2 0 2 6 = 30 Р= 60 - 30 = 30 PIC бо м ( = 9 Рw Чон - - ft 30 - - ---- Ти d 20 -- -- — 20 9 м 20 Вс

DWL = 1 (40-20) (30- 20) = {X20X10 = 100 To ta surpeur which is sum total of cs and Ps, is maximised when there is no dead weight loss. This is possible when socially optimum output or competitive output es procluced which is given by p= mc 60 - Q = Q → 60 = 20 Q=30 p=60-30 =30 Therefore goul han to set price P=30 or price ceiling P = 30 to maximere total surpeus in the market. At this price P = 30 моторея Log Scu 30 маь оf output (s = Į 160-30) (30) = 450 PS = 1 130-0) 1302= 450 Is - cst PS = 450+ 450 =goo DWL = 0