Question

A typical inhabitant of Satan City has a demand function for electricity q(p) = 800 − 20p,
where p is the price (in cents) per kw-hour and q is the kw-hour consumption per week. The electricity
is being provided by Toyo Electricity, at a total cost of c(q) = 100 + 10q cents per kw-hour.

a) Determine the price pm and the quantity qm that Toyo will decide under uniform (linear)
monopoly pricing. Compute the corresponding consumer surplus and prot per inhabitant.

b) Satan, the mayor of Satan city, is concerned that the price of electricity is too high. He decides to impose the competitive price on Toyo. What is that price? What is the corresponding quantity? Call them p∗ and q∗. What is the problem with imposing that here?

c) Hayami, the CEO of Toyo, is powerful, and lobbies the government to be allowed to
charge a two-part tari (weekly fee + per kw-hour price) instead of a linear price. What are the fee
and unit price Toyo should set? Call them p0 and F. If the government cared about the consumer surplus only, would it allow that type of tariff when comparing to (a)? Explain.

Answer 1

a) Given demand function is

q = 800-20p

=> 20p = 800 - q

=> p = (800 - q) / 20

Total Revenue (TR) = p*q = [(800 - q)/20] * q

Marginal Revenue (MR) = d(TR)/dq = (800 - 2q) /20

Total Cost (TC) = 100 + 10q

Marginal Cost (MC) = 10

Equibrium condition under monopoly is

MR = MC

Therefore,

(800 - 2q) /20 = 10

=> 800 - 2q = 200

=> 2q = 600

=> q = 300 units.

so, p = (800-300)/20 = $25

b) Now the condition is, P = MC

Therefore, (800 - q)/20 = 10

or, q* = 800 - 200 = 600 units

p* = $10