Question

Hints: In problem 11.7 the marginal cost is 20. For both problems it will be useful to know that for a linear demand curve, written with price as a function of quantity (P=0-bQ) marginal revenue is MR=a-2bQ. For problem 12.20, for some steps you will have to re-arrange the demand so to give price as a function of quantity rather than quantity as a function of price. Part a of 12.20 is the same as what we did in the demand topic when we found market demand from two different individual demands. For part d it is asking for an answer in words that describes a strategy La Duranzo might use (there is more than one possible answer). Problem 3: A market with a monopoly producer has inverse demand P = 120 - 2Q (which gives marginal revenue MR = 120 - 4Q). The monopolist has marginal costs are MCQ) = 4Q and no fixed costs. a) What is the monopolist's producer surplus when it charges the profit maximizing uniform price. b) What is the deadweight loss due to monopoly in this market? c) What would the monopolist's producer surplus be if it could engage in first degree price discrimination (i.e. if it knew all consumers' exact willingness to pay for the good).

Answer 1

MR = 120-40 mc = "Q demand op 12642a a) The profit maximing hing is where is where alla MR=me 120-40 = 40 H120=isco 115 120 = 0 ] So; p= 120-2 43 12on2 (is) Dia r io 903" 90 y ho auantity O Producer surplus Aro De Fu - Ar ofs of 4 I coor CF)C PC) { [04[47) ET 90+30) (15)-1(15)[10) 1 .260,615) - 15 (30) 30, 615.) = 450. b) Deadweight loss o Equilibinum in market umbetikon : pama 12-20 = 40 [20=0] so; dead weight loss = Area of D (EF = + ((F)(HE)

Decal weight loss = {(30) (5) = $75 3 c) I of it can engage in first degree price discrimention hen it will supply till : Pame => 120-26=46 [20=6] 1202 A y s cuantity prochecer surfiles = L 147(38.73 £1120)(26) = 41200