Consider a profit-maximizing monopolist who faces an inverse demand curve P = 300 1 /2Q and must set a single, constant price for each unit of its output. Marginal revenue is given by M R = 300 Q, and the marginal cost of production is M C = Q.

a) Find the firm's optimal choice of output and price, and the socially efficient output and price.

b) Sketch out the demand, marginal revenue, and marginal cost curves. Mark the points you found in a) on your diagram. In terms of consumer surplus, how much worse off are consumers at the monopolist's optimal choice than they would have been at the socially efficient level of output?