Question

1. Monopoly. The Metro Electric Company produces and distributes electricity to residential customers in the metropolitan area. This monopoly firm is regulated, as are other investor owned electric companies. The company faces the following demand function:

P = 0.04 - 0.01Q

Its marginal cost function is:

MC = 0.005 + 0.0075Q,

where Q is in millions of kilowatt hours and P is in dollars per kilowatt hour. Find the deadweight loss that would result if this company were allowed to operate as a profit maximizing firm, assuming that P=MC under regulation.

Answer 1

Monopolist produces where MR = MC.

TR = P*Q = (0.04 - 0.01Q)Q = 0.04Q - 0.01Q2
MR = d(TR)/dQ = 0.04 - 2(0.01Q) = 0.04 - 0.02Q
So, MR = MC gives,
0.04 - 0.02Q = 0.005 + 0.0075Q
So, 0.0075Q + 0.02Q = 0.04 - 0.005
So, 0.0275Q = 0.035
So, Q = 0.035/0.0275
So, Qm = 1.27

Pm = 0.04 - 0.01Q = 0.04 - 0.01(1.27) = 0.04 - 0.0127 = 0.0273

MC = 0.005 + 0.0075Q = 0.005 + 0.0075(1.27) = 0.005 + 0.0095 = 0.0145

At P = MC, 0.04 - 0.01Q = 0.005 + 0.0075Q
So, 0.0075Q + 0.01Q = 0.04 - 0.005
So, 0.0175Q = 0.035
So, Q = 0.035/0.0175
So, Qc = 2

Deadweight loss, DWL = area of triangle = (1/2)*base *height = (1/2)*(Qc-Qm)*(Pm-MC)
So, DWL = (1/2)*(2-1.27)*(0.0273 - 0.0145) = (1/2)*(0.73)*(0.0128) = 0.0047