A monopoly faces market demand Q = 30P and has a cost function C(Q) = Q^2.

(a) Find the profit maximizing price and quantity and the resulting profit to the monopoly.

(b) What is the socially optimal price? Calculate the deadweight loss (DWL) due to the monopolist behavior of this firm. Calculate consumer surplus (CS) and producer surplus (PS) given the profit maximizing price.

(c) Assume that the government puts a price ceiling on the monopolist at P =22. How much output will the monopolist produce? What will be the profit of the monopolist? Calculate CS, PS, and DWL.

(d) Assume that the government put a price ceiling on the monopolist in order to maximize the total (i.e. consumer plus producer) surplus. What price ceiling should it choose? How much output will the monopolist produce at this price ceiling? What will the profit of the monopolist be? What is the DWL?