Question

The annual demand for natural gas in Zuma is given by the formula

Q=60-2P

Where P is the price and Q is the quantity demanded. Marginal cost is constant at $20 per unit and there is no overhead.

a. If a monopolist controls natural gas production, 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 interest of efficiency, assuming all other industries in Zuma are perfectly competitive?

c. Disregarding questions of the 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.

Answer 1

Demand is given by Q = 60 - 2P.

Marginal cost is constant at $20 per unit and there is no overhead fixed cost.

a. If a monopolist controls natural gas production, its annual profit function is given as

π = (P - AC)*Q

π = (P - 20)(60 - 2P) or π = 100P - 2P^2 + 1200. Find π'(P) = 0 to get 100 - 4P or P = $25.

Annual profits are π = (25 - 20)*(60 - 50) = $50.

b. Suppose the government of Zuma nationalized the gas company. Now all other industries in Zuma are perfectly competitive and if Zuma also becomes competitive it would produce where P = MC. Hence its price is $20 which is equal to marginal cost and annual profits are $0.

c. Zuma is better off as a monopoly. Under monopoly, its producer surplus is (25 - 20)*10 = $50. Under efficient outcome, producer surplus is $0. Hence, it is better off as a monopoly

d. Now there are overhead costs of $75 per year. Monopolist will still produce 10 units at a price of $25 per unit, but now there is a loss of $25 per year. Hence it may leave the market if losses persist. If government takes over, there is a loss of $75 per year which is even greater. Hence it is not recommended.