Suppose a firm wants to determine it optimal advertising and research budgets. It determines that its demand curve is Q = 5 - .25 P, its MC =$10 and uses these to calculate its optimal price (P*). The company then determines that its demand curve with advertising is Q = 5 -.25 P + .5 A2 where A is measured in millions of dollars spent on advertising and advertising adds $1.00 to its marginal cost. Analysis shows its demand curve with research is Q = 5 - .25P +3 R2 where R is millions of dollars for research and research adds $0.40 to its marginal cost.

(a) What is the optimal advertising budget? What is the optimal research budget?

(b) A new Pepperdine graduate joins the discussion and asks if the advertising and research budgets are really optimal and suggests using the rule MPA/MCA = MPR/MCR where MPA is (dQ/dA) and MCA is the marginal cost of advertising , MPR is (dQ/dR), and MCR is the marginal cost of research. If the total budget for advertising and research is $1.554 million calculate the optimal budgets for advertising and research? Explain why there is a difference between budgets for part a) And part b).

(c) Explain how you calculated the optimal amounts of advertising and research. Prove that the amounts are optimal?