Question

. 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.

Answer 1

Total Revenue = PQ = 5P - 0.5P²

Marginal Revenue = 5 - P = MC =10

P = 15, with P being the optimal price level.

Now taking advertising into consideration, the total revenue equals = 5P - 0.25P² + 5A²P

Marginal Revenue at P = 15

5 - 0.5(15)+5A² = MC = 11

5A² = 13.5

A² = 13.5/5 = 2.7

A = 1.643

Thus the optimal advertising budget is 1.643 million

For research budget, the demand curve equation is

PQ = 5P - 0.25P²+3R²P

Marginal Revenue with P=15,

5-0.5(15)+3R² = 10.4

3R² =12.9

R²=4.3

R=2.07

Thus, 2.07 million is the optimal research budget