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What price seems to be most profitable

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Reference no: EM13880731

A dominant firm in an industry has costs given by C = 70 + 5qL. The dom- inant firm sets the market price, and the eight "small" firms coexisting in the market take this price as given. Each small firm has costs given by C = 25 + q2 - 4q. Total industry demand is given by Qd = 400 - 20P.

a. Create a spreadsheet similar to the example to model price setting by the dominant firm. (If you completed Problem S1 of Chapter 7, you need only make slight modifications in that spreadsheet.)

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.)


 

A

B

C

D

E

F

G

H

I

J

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

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Reference no: EM13880731

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