Hamish is a monopolist who faces inverse market demand function P (Q, ) = 10 3Q, where is the advertising level of Hamish's product. Hamish has cost function C (Q) = 30Q.

(a) For now, suppose Hamish's advertising level is fixed at = 6.

(i) Determine Hamish's optimal output level and profits.

(ii) Determine aggregate surplus. [3 points]

(iii) Determine Hamish's output level such that aggregate surplus is maximized. What are Hamish's profits in this case?

Suppose advertising is costly. Specifically, assume that Hamish must pay I() = (50/21)2. Thus, Hamish's total profits are (Q, ) = P (Q, ) Q C (Q) I().

(b) How much advertising will Hamish's use and how many units will he produce?