In a perfectly competitive market, the cost structure of the typical firm is given by C = 25 + Q2- 4Q, and industry demand is given by Q = 400 - 20P. Currently, 24 firms serve the market.
a. Create a spreadsheet (similar to the given example) to model the short-run and long-run dynamics of this market. (Hint: Enter numerical values for the Price, # Firms, and QF cells; all other cells should be linked by formulas to these three cells.)
b. What equilibrium price will prevail in the short run? (Hint: Use the spreadsheet's optimizer and specify cell F8, the difference between demand and supply, as the target cell. However, instead of maximizing this cell, instruct the optimizer to set it equal to zero. In addition, include the constraint that P - MC in cell F14 must equal zero.)
|
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
|
1
|
|
|
|
|
|
|
|
|
|
2
|
|
|
Equilibrium in a Perfectly
|
|
|
|
|
3
|
|
|
Competitive Market
|
|
|
|
|
4
|
|
|
|
|
|
|
|
|
|
5
|
|
|
The Industry
|
|
|
|
|
6
|
|
Price
|
# Firms
|
Supply
|
Demand
|
D - S
|
Tot. Profit
|
|
|
7
|
|
|
|
|
|
|
|
|
|
8
|
|
10
|
24
|
192
|
200
|
8
|
552
|
|
|
9
|
|
|
|
|
|
|
|
|
|
10
|
|
|
|
|
|
|
|
|
|
11
|
|
|
The Typical Firm
|
|
|
|
|
12
|
|
QF
|
MC
|
Cost
|
AC
|
P - MC
|
Firm Profit
|
|
|
13
|
|
|
|
|
|
|
|
|
|
14
|
|
8
|
12
|
57
|
7.13
|
-2
|
23
|
|
|
15
|
|
|
|
|
|
|
|
|
|
16
|
|
|
|
|
|
|
|
|
|
17
|
|
SR: (1) D - S = 0 and (2) P = MC; Adjust: P & QF
|
|
|
18
|
|
LR: (1) and (2) and (3) P = AC; Adjust: P & QF & # Firms
|
|
|
19
|
|
|
|
|
|
|
c. What equilibrium price will prevail in the long run? (Hint: Include cell C8, the number of firms, as an adjustable cell, in addition to cells B8 and B14, and add the constraint that total profit in cell G8 must equal zero.)