The annual demand for natural gas in Zuma is given by the formula Q = 60-2P wher
ID: 1117076 • Letter: T
Question
The annual demand for natural gas in Zuma is given by the formula
Q = 60-2P
where P is the price and Q the quantity demanded. Marginal cost is constant at $20 per unit and there is
no overhead.
a. If natural gas production is controlled by a monopolist, what will be the monopolist's annual profits?
b. Suppose the government of Zuma nationalized the gas company. What would it produce and what
price would it charge in the interests of efficiency, assuming all other industries in Zuma are perfectly
competitive?
c. Disregarding questions of distribution, in which situation is Zuma better off- monopoly or
Government control? Calculate the approximate magnitude of the difference in welfare level between
the two situations.
d. Suppose that in fact there are additional overhead costs of $75 per year. What would the monopolist
do in this situation? Would you advise the Government to take over the industry now? Explain your
answer.
Explanation / Answer
Q = 60 - 2P
2P = 60 - Q
P = 30 - 0.5Q
MC = $20
(a) A monopolist will maximize profit by equating Marginal revenue (MR) with MC.
Total revenue (TR) = P x Q = 30Q - 0.5Q2
MR = dTR / dQ = 30 - Q
Equating with MC,
30 - Q = 20
Q = 10
P = 30 - (0.5 x 10) = 30 - 5 = $25
Profit = Q x (P - MC) = 10 x $(25 - 20) = 10 x $5 = $50
(b) A perfect competitor will maximize profit by equating Price with MC.
30 - 0.5Q = 20
0.5Q = 10
Q = 20
P = MC = $20
(c) Zuma is better off as a monopolist since it will earn an economic profit as a monopolist, but as a perfect competitor it will earn zero economic profit since price equals MC.
Difference in welfare = (1/2) x Difference in price x Difference in quantity = (1/2) x $(25 - 20) x (20 - 10)
= (1/2) x $5 x 10 = $25
(d) Overhead being a fixed cost will not change the MC, therefore profit-maximizing P & Q will remain unchanged for the monopolist.
With overhead cost, monopoly profit = Q x (P - MC) - Overhead cost = $25 - $75 = - $50
Since there is negative profit, government should either take over the industry or provide a subsidy to make the firm stay in business.
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