Q1 Locksmith Co. is a monopoly in the door lock industry. Its cost is C(Q) = 100 - 5Q + Q², and it faces the demand curve p = 55 - 2Q.

(a) What is the profit-maximizing price and quantity for Locksmith Co.? What is its profit? How much consumer surplus does Locksmith Co. generate?

(b) If Locksmith Co. acts like a perfectly competitive firm, what profit and consumer surplus would be generated? What is the size of deadweight loss from the monopoly?

(c) Concerned about the high price under monopoly, the government sets a price ceiling at $27. How affect price, quantity, consumer surplus and profit? What is the resulting deadweight loss with the price ceiling? Will the price ceiling improve social welfare compared to the monopoly without a price ceiling in question (a)?