Question

The city of Springfield has granted the Springfield Nuclear Power Plant the right to be the sole provider of power to the city! As a monopolist, the Power Plant faces a demand for power given by p(Q) = 40 – 2Q and has a cost function, CQ) = 2Q(8 points total) (a) In order to maximize profit, how much power should the Springfield Nuclear Power Plant sell? What will be the resulting price? How much will the Power Plant earn in profits? (2 points) (b) Calculate the Lerner index at the profit-maximizing quantity for the Power Plant and provide an interpretation of this value. (2 points) (C) Calculate the consumer surplus, producer surplus, and deadweight loss in this market. (2 points) (d) Suppose that Mayor Quimby and other city officials in Springfield desperately want to improve social welfare and have been able to obtain perfect information about demand and the Power Plant's marginal cost. What price ceiling should city officials set in order to optimally regulate the Power Plant? How would consumer surplus, producer surplus, and deadweight loss change under optimal price regulation? (2 points)

Answer 1

IS 202 Demand function p= 40-20 TR= P.B = 400-207, Mradores = 40 - 4-0 TC= 202, MC. d (TC) - 40 des (Q.) At the equilibrium MR = MC or 40- 40 - 49 8Q 340 or 5 ( equilibrium 8) Put in demand function Pa 40-2x5 on p = 30 (equilibrium D Profit =(TR-TC) 40g -202-202 = (4085) - 2x48 - 2464p 136 b.) Lerier's inden - D-me - Thus the firm exercses monopely power as Layo 30 - 435 30 - "=0,39 some pros of ton - CS-A AEG x 1025:23 Disa DBDEGT AEDE (30-20) x (5-0) + Ex(20-4) (5-0) = 50 + 40 go DWL = O BCD = 3x430-20) x (6.67-59 = 8:35 IMR 5 6.67 when AR=MC or Pame on 70-20 249 ar 69:40 Q = 6:57 set (D) with optimal faire regulation the government a frice ceiling that equates competitive deadweight loss Bedie Cha MC). The espulátion eliminates IA I not to scale ! 40 zos 268 4 ht CS = DAUBE ti (40-36 67)2-6467 =44742 PS=0DBC=13668-4776.64 =75.63 6.67 This es investes, PS decereases and due 60 = 40, 6-6.67 P= 40 = 4x6.67 = 26.68 gels eliminated) when P2 MC or 40-20 = 48