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 + 2Q 2 . 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?
(c) What is the profit the monopolist makes? Should the firm shut down in the short or long run?