9781118041581

Summary 389

S2. A firm faces a price equation P 12.5  .5A.5 .25Q and a cost equation

C 5Q A, where Q denotes its output and A denotes its level of adver-

tising expenditure.

a. Create a spreadsheet to describe the firm’s profit as it varies with

output and advertising. Set advertising spending at 50 and find the

firm’s optimal level of output.

b. Use your spreadsheet’s optimizer to find the firm’s optimal output

and level of advertising spending.

AB C D EFG H IJ

1

2 Dominant Firm

3 Price Leadership

4

5 Market Supply & Demand Dominant Firm

6 Price # S. Firms Qs Qd Qd  Qs Cost Profit

7

8 8 8 48 240 192 1030 506

9

10

11 Small Firms

12 q MC Cost AC P  MC Firm Profit

13

14 6 8 37 6.167 0 11.0

15

16

17 Small Firms’ supply is determined by P MC.

18 Large Firm maximizes profit given net demand.

19

b. Experiment with prices between P 7 and P 16. For each price,

determine the small firms’ supply by setting q such that P MC.

Taking into account the supply response of the eight other firms, what

price seems to be most profitable for the dominant firm?

c. Use your spreadsheet’s optimizer to find the dominant firm’s optimal

price. (Hint:Adjust cells B8 and B14 to maximize cell I8 subject to the

constraint G14 equal to zero.)

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