Post on 10-Apr-2018
transcript
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Cournot Oligopoly and Welfare
by
Kevin Hinde
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Aims
In this session we will explore the
interdependence between firms using the
Cournot oligopoly models. We will see that interdependence in the
market (i.e. actual competition even among
a few firms) reduces the welfare losses of
market power but does not eradicate them.
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Learning Outcomes
By the end of this session you will be able
to
construct a reaction curve diagram and seehow this translates into the traditional
monopoly diagram.
work through a numerical examplecomparing and contrasting Cournot
oligopoly with other market structures. More mathematical students will be able to consider the finer aspects
of the model.
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Welfare and (Tight) Oligopoly To understand the welfare implications of
oligopoly we need to examine
interdependence between firms in themarket.
Welfare depends upon the number of firms
in the industry and the conduct they adopt.
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Augustin Cournot (1838)
Cournots model involves competition in
quantities (sales volume, in modern
language) and price is less explicit. The biggest assumption made by Cournot
was that a firm will embrace another's
output decisions in selecting its profit
maximising output but take that decision as
fixed, i.e.. unalterable by the competitor.
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If Firm 1 believes that Firm 2 will supply the entire
industry output it will supply zero.
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If Firm 1 believes that Firm 2 will supply the entire
industry output it will supply zero.
QQ2
Q1
AC=MC
Residual
Demand forFirm1
Market
Demand
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If Firm 1 believes that Firm 2 will supply zero output
it becomes a monopoly supplier.
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If Firm 1 believes that Firm 2 will supply zero output
it becomes a monopoly supplier.
MC=AC
QQ2
MR D
P
30
Mark t Demand
Q1
Residual
Demand
for irm 1
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0
Q1
Q2
Firm 1s
reaction
Curve
Perfect
Competition;P=MC
Monopoly ;
P>MC
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If Firm 2 makes the same conjectures then we get the
following:
0
Q1
Q2
Firm 2s Reaction
Curve; Q2=f (Q1)
Firm 1s
Reaction Curve;
Q1=f (Q2)
Cournot Equilibrium
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Convergence to Equilibrium
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Convergence to Equilibrium
0
Q1
Q2
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A numerical example
Assume market demand to be
P = 30 - Q
where Q= Q1 + Q2ie industry output constitutes firm 1 and firm 2s
output respectively
Further, assume Q1 = Q2
and average (AC) and marginal cost (MC)
AC = MC = 12
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To find the profit maximising output of Firm 1
given Firm 2s output we need to find Firm 1s
marginal revenue (MR) and set it equal to MC.
So,
Firm 1s Total Revenue is
R1 = (30 - Q) Q1
R1 = [30 - (Q1 + Q2)] Q1= 30Q1 - Q12 - Q1Q2
Firm 1s MR is thus
MR1 =30 - 2Q1 - Q2
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If MC=12 then
Q1 = 9 - 1 Q2
2This is Firm 1s Reaction Curve.
If we had begun by examining Firm 2sprofit
maximising output we would find its reaction
curve, i.e.
Q2 = 9 - 1 Q1
2
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We can solve these 2 equations and find
equilibrium quantity and price.
Solving for Q1 we find
Q1 = 9 - 1 (9 - 1 Q1)
2 2
Q1 = 6
Similarly,
Q2 = 6
and P = 18
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18
09
9
18
Q1
Q2
Q2= 9 - 1 Q1
2
Q1= 9 - 1 Q2
2
Cournot
E uilibrium
6
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Perfect Competition
Under perfect competition firms set prices equal to
MC. So,
P= 12
and equilibrium quantity
Q= 18
Assuming both supply equal amounts, Firm 1
supplies 9 and so does Firm 2.
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18
09
9
18
Q1
Q2
4.5
4.5
6
Q2= 9 - 1 Q1
2
Q1= 9 - 1 Q2
2
Competitive
E uilibrium
6
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Monopoly
They would then maximise industryprofits and
share the spoils.
TR =PQ =(30 - Q)Q = 30Q - Q2
MR =30 - 2Q
As MC equals 12 industry profits are maximisedwhere
30 -2Q = 12
Q = 9
So Q1 = Q2 = 4.5
Equilibrium price
P= 21
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18
09
9
18
Q1
Q2
4.5
4.5
6
Q2= 9 - 1 Q1
2
Q1= 9 - 1 Q2
2
Monopol
E uilibrium
6
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1
0 9
9
1
Q1
Q2
4.
4.
Q2=9 - 1 Q1
2
Q1= 9 - 1 Q2
2
Cournot
uili rium
6
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Cournot Equilibrium compared using a traditional
Monopoly diagram
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Cournot Equilibrium compared using a traditional
Monopoly diagram
21
12 MC=AC
Q0 9
MR D
P
18 30
Monopol
Perfect
Competition
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Cournot Equilibrium compared using a traditional
Monopoly diagram
21
12 MC=AC
Q0 9MR D
P
1 30
1
Cournot
Perfect
Competition
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A further point that must be considered is that if
the number of firms increases then the Cournot
equilibrium approaches the competitive
equilibrium.
In our example the Cournot equilibrium output
was 2/3s that of the perfectly competitive output.
It can be shown that if there were 3 firms actingunder Cournot assumption then they would
produce 3/4s of the perfectly competitive output
level.
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Firm numbers matter
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Firm numbers matter
21
12 MC=AC
Q0 9MR D
P
1 30
1
2Firm
Cournot
Firm
Cournot
12 1
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And Finally...
A summary
Have you covered the learning outcomes?
Any questions?