Firm Z faces the price equation P = 50 + A.5 - Q, and the cost function C = 20Q + A, where A denotes advertising spending.
a. Other things (price) held constant, does an increase in advertising spending lead to greater sales? Does advertising spending represent a fixed cost or a variable cost?
b. Find the firm’s profit-maximizing quantity as a function of A. (Treating A as fixed, we have MR = 50 + A.5 - 2Q.) Do the same for the firm’s price. Explain these results.
c. Using the results in part (b), write the firm’s profit expression in terms of A alone. Find the firm’s optimal level of advertising. Find its optimal quantity and price.