The Cournot Model
45
Lectures in Microeconomics-Charles W. Upton The Cournot Model A ’s Output B’s Output A ’s Reaction Function B’s Reaction Function 45 45 90 90
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Transcript of The Cournot Model
Lectures in Microeconomics-Charles W. Upton
The Cournot ModelA’s Output
B’s Output
A’s Reaction Function
B’s Reaction Function
45
45
90
90
The Cournot Model
Assumptions
• Two firms A, and B produce widgets
The Cournot Model
Assumptions
• Two firms A, and B produce widgets
• The industry demand function is D
D
P
Q
The Cournot Model
Assumptions
• Two firms A, and B produce widgets
• The industry demand function is D
• Firm A produces qA; firm B produces qB
D
P
Q
The Cournot Model
Assumptions
• Two firms A, and B produce widgets
• The industry demand function is D
• Firm A produces qA; firm B produces qB
• Firm A takes its demand function as D -qB
D
P
Q
qb
Da
The Cournot Model
Assumptions
• Two firms A, and B produce widgets
• The industry demand function is D
• Firm A produces qA; firm B produces qB
• Firm A takes its demand function as D -qB
D
P
Q
qb
Da
An important assumption, the heart of the Cournot model.
The Cournot Model
Solving A’s problem
DDa
The Cournot Model
Solving A’s problem
DDa
MCMR
The Cournot Model
Solving A’s problem
DDa
MCMR
qa*
p*
The Cournot Model
Symmetry
• Just as Firm A is choosing qA to maximize profits, so too is Firm B choosing qB to maximize profits.
The Cournot Model
Symmetry
• Just as Firm A is choosing qA to maximize profits, so too is Firm B choosing qB to maximize profits.
• If B changes its output, A will react by changing its output.
The Cournot Model
A Reaction Function
• We do the mathematical approach first and then the graphical approach.
The Cournot Model
A Reaction Function
• The industry demand function
Q = 100 – 2p.
The Cournot Model
A Reaction Function
• The industry demand function Q = 100 – 2p.
• The inverse demand function isP = 50 – (1/2)Q
The Cournot Model
A Reaction Function
• The industry demand function Q = 100 – 2p.
• The inverse demand function isP = 50 – (1/2)Q
• A’s demand function is thenP = 50 –(1/2)(qA+qB)
The Cournot Model
A Reaction Function
A’s demand function is thenP = 50 –(1/2)(qA +qB)
• The firm’s profits are = PqA – 5qA
The Cournot Model
A Reaction Function
A’s demand function is thenP = 50 –(1/2)(qA +qB)
• The firm’s profits are = [50 –(1/2)(qA +qB)]qA – 5qA
The Cournot Model
A Reaction Function
= [50 –(1/2)(qA + qB)]qA – 5qA
The Cournot Model
A Reaction Function
= [50 –(1/2)(qA + qB)]qA – 5qA
= 50 qA–(1/2) qA 2– (1/2)qBqA – 5qA
The Cournot Model
A Reaction Function
= [50 –(1/2)(qA + qB)]qA – 5qA
= 50 qA–(1/2) qA 2– (1/2)qBqA – 5qA
= 45qA –(1/2)qA2 – (1/2)qBqA
The Cournot Model
A Reaction Function
baaa qqqq21
2145 2
The Cournot Model
A Reaction Function
baa
baaa
qqdqd
qqqq
2145
21
2145 2
The Cournot Model
A Reaction Function
ba
baa
qqdqd
2145
02145
The Cournot Model
Symmetry
•There is a similar reaction function for B
qB = 45 – (1/2)qA
qA = 45 – (1/2)qB
The Cournot Model
Solving for A’s Output
qA = 45 – (1/2)qB
qB = 45 – (1/2)qA
qA = 45 – (1/2)[45 – (1/2)qA]
The Cournot Model
Solving for A’s Output
qA = 45 – (1/2)[45 – (1/2)qA]qA = 22.5 + (1/4)qA
The Cournot Model
Solving for A’s Output
qA = 45 – (1/2)[45 – (1/2)qA]qA = 22.5 + (1/4)qA
(3/4)qA = 22.5
The Cournot Model
Solving for A’s Output
qA = 45 – (1/2)[45 – (1/2)qA]qA = 22.5 + (1/4)qA
(3/4)qA = 22.5qA = (4/3)22.5
The Cournot Model
Solving for A’s Output
qA = 45 – (1/2)[45 – (1/2)qA]qA = 22.5 + (1/4)qA
(3/4)qA = 22.5qA = (4/3)22.5
qA = 30qB = 30
The Cournot Model
A Graphical Approach
qA = 45 – (1/2)qB
• We want to use the reaction function to come to a graphical solution,
The Cournot Model
A Graphical Approach
qA = 45 – (1/2)qB
• When B produces nothing A should react by producing the monopoly output (45).
The Cournot Model
A Graphical Approach
qA = 45 – (1/2)qB
• When B produces nothing A should react by producing the monopoly output (45).
• When B produces the output of the competitive industry (90), A should react by producing nothing.
The Cournot Model
A Graphical Approach
qA = 45 – (1/2)qB
• When B produces nothing A should react by producing the monopoly output (45).
• When B produces the output of the competitive industry (90), A should react by producing nothing.
• Similar rules apply for B’s reactions.
The Cournot Model
Graphing the Reaction FunctionA’s Output
B’s Output
The Cournot Model
Graphing the Reaction FunctionA’s Output
B’s Output
If B produces the competitive
output, A produces nothing.
If B produces
nothing, A acts like a monopoly45
90
900
The Cournot Model
Graphing the Reaction FunctionA’s Output
B’s Output
A’s Reaction Function
45
90
The Cournot Model
Graphing the Reaction FunctionA’s Output
B’s Output
A’s Reaction Function
If A produces the competitive output, B produces nothing.
If A produces nothing, B acts like
a monopoly.45
45
90
90
The Cournot Model
Graphing the Reaction FunctionA’s Output
B’s Output
A’s Reaction Function
B’s Reaction Function
45
45
90
90
The Cournot Model
Graphing the Reaction FunctionA’s Output
B’s Output
If A and B are off their reaction functions, they react and change output. Here B expands, A contracts.
90
45
9045
The Cournot Model
Graphing the Reaction FunctionA’s Output
B’s Output
The Cournot Model
Graphing the Reaction FunctionA’s Output
B’s Output
If A is here, B wants to
be here
The Cournot Model
Graphing the Reaction FunctionA’s Output
B’s Output
If B is here, A wants to
be here
The Cournot Model
EquilibriumA’s Output
B’s Output
A’s Reaction Function
B’s Reaction Function
The Cournot Model
The Basic Steps
• Plot the reaction functions– If B produces nothing, A behaves like a
monopoly– If B produces competitive output, A produces
nothing• Solve for their intersection
The Cournot Model
End
©2003 Charles W. Upton
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