Intermediate Microeconomics I: Production
1 Monopoly profit maximization
Pfeitzer is a monopolist for a new drug that makes people feel thinner. The total cost function is C(Q) = 100 + 12Q + 2Q2 . The inverse demand function is p(Q) = 84 - 2Q.
(a) By how much do revenues increase if Pfeitzer sells one more (small) unit of output? By how much does its cost go up if it produces one more (small) unit of output?
(b) What is the optimal price and quantity the monopolist should charge / sell? (4 points) (c) What is the profit the monopolist makes? Should the firm shut down in the short or long run?
2 Market Power
Consider the same firm as in the problem above, the Pfeitzer Corporation.
(a) If the company increases its price by a small fraction, by what proportion does demand go down?
(b) What percentage of the price is due to costs and what is due to markup?
3 Welfare Consequences
Consider the same firm as in the last problem.
(a) What are the efficiency losses of the monopoly pricing compared to competitive prices?
(b) Pfeitzer argues that other firms should not be allowed to enter the market, since it is a natural monopoly. A potential competitor argues that it is not a natural monopoly. Show why both are right at the same time.