research department has estimated that the demand for this product is Q(P,A) = 11,600 - 1000P + 20A^1/2, where Q is annual output, P is the price, and A the annual expenditure for advertising. The total cost of producing the new good is C(Q) = .001Q^2 + 4Q. This implies that the marginal cost of production is MC(Q) = .002Q + 4. The unit cost of advertising is constant and equal to one or T=1.
a. Find the inverse demand function P(Q,A), and show that the marginal revenue from an additional dollar of advertising is MR a = QA^-1/2 / 100
b. calculate the optimal output level Q* price P* and advertising level A* for the firm
c. What is firm profit if it follows this optimal strategy?
d. What is consumer surplus if the firm adopts this strategy