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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
6
Price
# S. Firms
Qs
Qd
Qd - Qs
Cost
Profit
7
8
48
240
192
1030
506
9
10
11
Small Firms
12
q
MC
AC
P - MC
Firm Profit
13
14
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
Find the Herfindahl index for the industry composed of a) three firms-one with the 70 percent of the market, and the other two with 20 and 10 percent of the market, respectively; b)one firm with a 50 percent share of the market and 10 other equalized..
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