A monopolist faces the following demand curve: Q  144/P2, where Q is the quantity demanded and P is price. Its average variable cost is AVC  Q1/2, and its fixed cost is 5.
a. What are its profit-maximizing price and quantity? What is the resulting profit?
b. Suppose the government regulates the price to be no greater than $4 per unit. How much will the monopolist produce? What will its profit be?
c. Suppose the government wants to set a ceiling price that induces the monopolist to produce the largest possible output. What price will accomplish this goal?