Question

1. Consider a monopolist facing the demand curve p = 90 - 2q with cost function clg)0.252 (a) Find the profit maximizing quantity qm and price pm What are the monopo- list's profits? (b) What is the value of the Lerner index at qm? (c) Find the efficient quantity and draw a graph depicting the deadweight loss under monopoly (d) What is the consumers' surplus under monopoly

Answer 1

P = 90- 2Q TR= P.Q = [90-2010 -900- 20² MR = dTR da - 90(1) - HQ = 90-uo TC = 0.25 Q2 세양 condition = o.sa Monopoly profit-maxintizing MR=MC 590 -4 Q = 0.5Q 90 = 4Qtoosa. 90 = yosa - - 90 4.5 Qm=20 units substituting a into price p=90-2 (20) -90-yo equation

Penso Profit = TR - TC =P.2 - 0.25 (2032 Esoxao -0.25 & you = 1ooo - 100 = 900 MC=O:S (20) = lo Laner Index at am -MC = Socio so - yo so condition Efficient production P = MC TTTTTTTTTTTTTTINI

90-2Q = o.sQ 90 = O'SQ +2.00 Go - 2sQ a = 90 units into price @=36 substituting ac equcation R = 90-2(36) -go-72 -18

: Price pis DWL MR O S 10 15 20 25 30 35 40 us so - Quantity consumer Surplus undor Monopoly = Area of A = XBXH sos X (20-0 ) (90-50) = 0 SX 2o xuo =400