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, C(Q)=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

Demand! Cost: POQ) = 40 - 2Q. C(Q)= 202 Me= 4Q. 2 = [40-22]Q – 202. a) Profit 40-42-46-O 40=&Q=) (Q* -sl Price: p= 4o-215)= 30 1P*_30 Profit = (3015) - 2(25). 150 - so (T* b) MCQS - 20 Lerner Index = P-MC Р. LI= 30 - 20 30 c) Consumer Surplus (CS) = £ [40-30]*5. cs = 1x10x5 = 28 Produen surplus a (Pz Glit) PS= 100. DWL = 1/2 (30-20) x ( Q comp-Quran) DWL tx10x (205) IDWL = 2/3