Our Example
Extending the Cournot Model
A’s 90
Output
Q = 100 – 2p
MC=5
B+C
Reaction
Function
45
B+C
Output
45
Lectures in Microeconomics-Charles W. Upton
The Reaction Function
Extending the Cournot Model
Graphing the Reaction Function
A’s 90
Output
B’s
Reaction
Function
qA = 45 – (1/2)qB
qB = 45 – (1/2)qA
Extending the Cournot Model
New Assumptions
A’s
Reaction
Function
45
45
90
B’s
Output
Extending the Cournot Model
The Reaction Function
• Three firms, A, B, C
Q = 100 – 2p
MC=5
qA = 45 – (1/2)(qB+qC)
qB = 45 – (1/2)(qA +qC)
Extending the Cournot Model
Extending the Cournot Model
1
The Reaction Function
The Reaction Function
qA = 45 – (1/2)(qB+qC)
qA = 45 – (1/2)(qB+qC)
qA = 45 – (1/2)(qA+qA)
Extending the Cournot Model
Extending the Cournot Model
The Reaction Function
The Reaction Function
qA = 45 – (1/2)(qB+qC)
qA = 45 – (1/2)(qA+qA)
qA = 22.5
qA = 45 – (1/2)(qB+qC)
qA = 45 – (1/2)(qA+qA)
qA = 22.5
qA+ qB+ qC = 67.5
Extending the Cournot Model
The Reaction Function
1
Q1 = Qc
3– (1/2)(q +q2 )
=
45
q
67A.5 = 90 QB = 2CQ
qA = 454– (1/2)(qA2 +q3A) c
qA = 22.5
3
Qc
qA+ qB+ qC = Q
67.5
3 =
4
Extending the Cournot Model
Extending the Cournot Model
Graphing the Reaction Function
A’s 90
Output
B’s
Reaction
Function
A’s
Reaction
Function
45
45
90
B’s
Output
Extending the Cournot Model
2
With Three Firms
A’s 90
Output
The Pattern
B+C
Reaction
Function
• With n firms, output is a fraction
A’s
Reaction
Function
45
B+C
B’s
Output
45
90
Output
Extending the Cournot Model
The Wudget Problem
• To Review
Q = 630,000 – 300 p
Extending the Cournot Model
The Wudget Problem
• If
ToMC
Review
= $400 in
= 630,000 – 300 p
year one,Q the
monopoly MC = $500
• maximizes
A monopolyprofits
maximizes profits by selling
240,000
units atand
a price of $1300
with
P= $1250
n
n +1
of the amount demanded in perfect
competition
Extending the Cournot Model
The Wudget Problem
• To Review
Q = 630,000 – 300 p
MC = $500
• A monopoly maximizes profits by selling
240,000 units at a price of $1300.
• Let’s call this year zero.
Extending the Cournot Model
The Wudget Problem
• Now suppose that in year two a second firm
starts making the wudget. MC = $400.
Q= 255,000
Extending the Cournot Model
Extending the Cournot Model
3
The Wudget Problem
The Wudget Problem
• Now suppose that in the second year a
second firm starts making the wudget. MC
= $400.
QC = 640,000 – 300 (400) =
630,000-120,000 = 510,000
• Now suppose that in the second year a
second firm starts making the wudget. MC
= $400.
QC = 630,000 – 300 (400) =
630,000-120,000 = 510,000
Q = (2/3)510,000 = 340,000
P = $967
Extending the Cournot Model
Year Three Sales
• A third firm starts making the Wudget.
MC =$400.
Extending the Cournot Model
Extending the Cournot Model
Year Three Sales and Price
QC = 510,000
Extending the Cournot Model
Year Three Sales and Price
Year Three Sales and Price
QC = 510,000
Q=(3/4)510,000=382,500
q = 127,500
QC = 510,000
Q=(3/4)510,000=382,500
q = 127,500
P = (630,000-382,500)/300 = $825
Extending the Cournot Model
Extending the Cournot Model
4
Years Four and Five
• A new firm enters each year
Years Four and Five
• A new firm enters each year.
• Without going through the algebra…
Extending the Cournot Model
Extending the Cournot Model
Years Four and Five
• A new firm enters each year.
• Without going through the algebra…
• Year Four:
Q = 408,000, q = 102,000, P = $740
Years Four and Five
• A new firm enters each year.
• Without going through the algebra…
• Year Four:
Q = 408,000, q = 102,000, P = $740
• Year Five:
Q = 425,000, q = 85,000, P = $683
Extending the Cournot Model
Extending the Cournot Model
Year by Year Summary
Year
0
1
2
3
4
5
Price
Quantity
$1300
$1250
$967
$825
$740
$683
Extending the Cournot Model
240,000
255,000
340,000
382,500
408,000
425,000
Year by Year Summary
Year
0
1
2
3
4
5
Price
Quantity
$1300
$1250
$967
$825
$740
$683
240,000
255,000
340,000
382,500
408,000
425,000
Extending the Cournot Model
5
The Appeal of the Cournot
Model
Conclusion
• As the number of firms grows,
P→ MC
• The Cournot model gives us a series of
predictions about how that will occur.
• With two firms, why not simply try the
cooperative solution.
• With five firms…
Extending the Cournot Model
Extending the Cournot Model
How Many Economists
does it take…?
• In fact we know the world is not as simple
as the Cournot model
• So, how many firms does it take to get to
the competitive price?
How Many Economists
does it take…?
• Leonard Wiess Studied the process
Extending the Cournot Model
Extending the Cournot Model
How Many Economists
does it take…?
Pm
How Many Economists
does it take…?
Pm
Number of Bidders
Number of Bidders
Extending the Cournot Model
Extending the Cournot Model
6
How Many Economists
does it take…?
How Many Economists
does it take…?
Pm
Pm
Pc
Pc
4-8
Number of Bidders
Number of Bidders
Extending the Cournot Model
Extending the Cournot Model
How Many Economists
does it take…?
Pm
Pc
With that
many firms,
you
essentially
have perfect
competition
4-8
End
©2003 Charles
W. Upton
Number of Bidders
Extending the Cournot Model
Extending the Cournot Model
7