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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?