As Agreed 30

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Oligopoly: Cournot

BUS291 Microeconomics A

Session 9

Outline

• Oligopoly is possibly the most important

set of market models

• Some of the complexity of the real world

• This time our focus is Cournot

Oligopoly

• A few large firms dominate the market

• Rivalry

• Interdependence

• Strategic behaviour

• Indeterminacy

• Many models

Cournot Oligopoly

1 There are few firms in the market serving

many consumers

2 Firms can produce either a differentiated

or homogeneous product

3 Each firm believes rivals will hold their

exiting level of output constant

4 Barriers to entry exist

Cournot Reaction Functions

• For ease of analysis suppose we have a duopoly

• The Cournot reaction function shows the profit maximising level of output for a firm given each level of output for the other firm (output adjusting)

• Let Q1 be the output of firm one and Q2 the output of firm two

Q1 m

Q1 

Q2 

Q2 c

Reaction function of firm 1

0 Q1

Q1 c

ˆ Q 1

ˆ Q 2

Q2 m

Reaction function of firm 2

0 Q1

Cournot Equilibrium

• A situation in which neither firm has an

incentive to change its output given the

other firm’s output

• Each firm’s expectation about the other

firm’s level of output proves correct

• This is also a Nash equilibrium in that

each firm is maximising profits given the

strategy of its rival

Q1 m

Q2 m

B C

D E

0 Q1

Cournot equilibrium

A Costs Change and Cournot

Equilibrium • A change in costs for one of the firms will

see a change in the Cournot Equilibrium

• If one firm’s marginal cost were to fall, for every given level of output of the other firm, its profit maximising level of output would be greater

• The firm’s reaction function shifts out

ˆ Q 2

ˆ R 2

Firm 2’s marginal cost falls

f  Q1

e Q2

f  Q2

Q1 m

R2 

Q2 

0 Q1

Isoprofit Curves

• A better understanding of the firms’

strategic opportunities can be gleaned by

adding isoprofit curves to the Cournot

framework

• Isoprofit curves show the two firm output

combinations that yield a particular level of

profits for one firm

Isoprofit Curves: Properties

• Each firm has its own set of isoprofit

curves

• Isoprofit curves closer to the monopoly

level of output are associated with higher

levels of profits

• Isoprofit curves reach their peak where

they cross the firm’s reaction function

Q1 m

0 Q1

1 0

1 1

1 2

1 0

 1 1

 1 2

Isoprofit curves

D E

Q1 m

0 Q1

1 a

1 b

1 c

A B

C D Q2 

Q1 

Q1 b

Q1 a

Q1 d

1 a

 1 b

 1 c

Isoprofit curves

Q2 m

0 Q1

2 0

2 1 2

C D

2 0

 2 1

 2 2

Isoprofit curves

Cournot Equilibrium Revisited

• Equipped with isoprofit curves it is now possible to understand that the Cournot equilibrium is not the best possible outcome for the two firms

• There is a clear incentive for collusion to restrict industry output

• However, both firms have an incentive to cheat on any collusive arrangement!

Q2 m

Q1 m

Q1 N

Q2 N

1 n

2 n

0 Q1

A lens of opportunity:

Output combinations more

profitable for both firms

Collusion and Cheating

• Collusion is attractive because both firms

can earn higher profits if they can restrict

output and increase price

• Cheating is attractive because if one firm

keeps its output fixed at the collusion level

the other firm can increase its profits by

increasing its output

Q2 m

Q1 m

1 n

2 n

0 Q1

Both firms can increase profits

by colluding

1 n

Q2 m

Q1 m

0 Q1

Q2 c

Q1 c

1 d

1 c

2 c

2 d

Q1 d

1 d

 1 c

 1 n

2 d

 2 c

Conclusion

• Individual firm outcomes are dependent on

what rivals do

• There are incentives for collusion

• Successful collusion creates the

conditions for its destruction through

cheating

• Sometimes reaction behaviour is the best

firms can do

Oligopoly: Stackelberg,

Bertrand

and More

Outline

• Consider Stackelberg, which is really an extension of Cournot output adjusting behaviour

• Then put the question what if firms adjust price not output?

• Examine which is the better way to model oligopoly: price or output adjusting

• Start on the question of cooperation and punishment

Stackelberg Oligopoly

Introduced • In Cournot oligopoly the situation is

symmetric

• Firm 1 and 2 are mirrors of each other

• In the Stackelberg model we examine the

situation where one firm is in a superior

position

• Again we will stick with the duopoly case

Stackelberg Oligopoly Defined

1 There are a few firms (two) serving many customers

2 Firms can produce either a differentiated or homogeneous product

3 A single firm (the leader) chooses an output before other firms choose their outputs

Stackelberg Oligopoly Defined

4 All other firms, or the other firm, (the

follower) choose outputs that maximise

their profits given the leader’s output

5 Barriers to entry exist

Stackelberg Oligopoly in

Operation • The leader, firm 1, has a first-mover

advantage

• The leader knows or assumes that the

followers will just react and set its output

according to R2, the firm 2 reaction

function

• Firm 1 will seek to maximise its profits

subject to R2

1 n

Q2 m

2 n

2 s

1 s

 1 n

2 s

 2 n

Q2 s

Q1 s

1 s

Leader

Follower

0 Q1

Q2 R1

Q1 m

Stackelberg Oligopoly: Some

Observations • A great illustration of strategic behaviour

• Note however, that the leader’s increased profitability comes at the expense of the follower’s

• This can be unstable in a genuinely oligopolistic setting

• Consider what happens if both firms attempt to be leaders!

Q1 m

Q2 m

Leader

1 SL

0 Q1

A 2

Q1 SL

Q2 SL SW

Stackelberg Oligopoly: Further

Observations • Both firms attempting to lead (Stackelberg

warfare) damages both firm’s profitability

• Strategic behaviour, which might be

successful in the short-run, is potentially

dangerous

• The Cournot outcome perhaps looks the

most stable in long-run

Bertrand Oligopoly Introduced

• The dangers of Stackelberg warfare are

highlighted if firms adjust price rather than

output

• In the Bertrand model the outcome is the

same as for perfect competition

• Bertrand thought his model highlighted the

danger to firms of price competition with

collusion, in some form, the likely outcome

Bertrand Oligopoly Defined

1 There are a few firms in the market

serving many customers

2 The firms produce identical products at

constant marginal cost

3 Firms compete via price, and react

optimally to the price set by their rivals

Bertrand Oligopoly Defined

4 Consumers have perfect information and

there are no transaction costs

5 Barriers to entry exist

Bertrand Oligopoly in Operation

• Consider the two firm case

• Say firm 1 starts with the monopoly price!

• The optimal response of firm 2 is to set its price just below the price set by firm 1 and capture the whole market

• The optimal response of firm 1 is to set its price just below the price set by firm 2 and capture the whole market

Bertrand Oligopoly in Operation

• The optimal response of firm 2 to the lower

firm 1 price is to set its price just below this

price set by firm 1 and capture the whole

market

• And I think you get the idea

• The only stable outcome is when both

firms set their price equal to marginal cost

and earn zero profits

Bertrand Oligopoly: Some

Observations • Price competition is very dangerous for

firms, but great for consumers

• The clear incentive for firms is avoid price

competition

• The concentration of oligopolistic firms on

non-price competition is understandable

• Moreover, it is a form of tacit collusion

Which is the Best Way to Model

Oligopoly: Output or Price Adjusting?

• It depends!

• One key issue issue is whether a firm can

adjust output or price faster

• Seemingly odd result: firms with relatively rapid

price adjustment are often better modelled as

output adjusters and vice versa

• In the end this issue is not as critical as it might

seem, as assumptions are relaxed, predictions

tend to merge somewhat

Cooperation and Punishment

• The oligopoly models considered to date

are essentially one-shot games

– Firms simultaneously make a single choice

• Where firms make repeated choices,

punishment for cheating on a collusive

agreement becomes possible

• We defer this question to the ‘game

theory’ topic

Conclusion

• Strategic behaviour can be very profitable

• However, strategic behaviour and price

competition can be very dangerous

• The incentives for collusion are very real,

even tacit collusion

• The question of punishment is critical to

the persistence of collusive agreements