Question

- 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

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