Question: Suppose a monopoly market has a demand function in which quantity demanded depends not only on market price (P) but also on the amount of advertising the firm does (A, measured in dollars). The specific form of this function is
Q = (20 - P)(1 + 0.1A - 0.01A2).
The monopolistic firm's cost function is given by
C = 10Q + 15 + A.
a. Suppose there is no advertising (A = 0). What output will the profit-maximizing firm choose? What market price will this yield? What will be the monopoly's profits?
b. Now let the firm also choose its optimal level of advertising expenditure. In this situation, what output level will be chosen? What price will this yield? What will the level of advertising be? What are the firm's profits in this case? Hint: This can be worked out most easily by assuming the monopoly chooses the profit-maximizing price rather than quantity.