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OLIGOPOLY

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Oligopoly

-

Collusion Stackelberg games

Bertrand equilibrium

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A monopoly is an industry consisting a single firm.

A duopoly is an industry consisting of two firms. An oligopoly is an industry consisting of a few firms.

articu ar y, eac irms own price or output ecisionsaffect its competitors profits.

We will examine in further duopoly case.

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Assume that firms compete by choosing their output

level.

If firm 1 produces y1 units and firm 2 produces y2 unitsthen total quantity supplied is y1 + y2. The market price

will be p(y1+ y2).

The firms total cost functions are c1(y1) and c2(y2).

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Supposefirm1takesfirm2soutputlevelchoicey2 as

iven. Then firm 1 sees its rofit function as

The roblem is now iven what out ut level1 1 2 1 2 1 1 1( ; ) ( ) ( ).y y p y y y c y= +

maximizes firm 1s profit?

Suppose inverse demand curve of the market is:

Firms, I and 2, total cost curves are as following

p y yT T( ) = 60

c y y1 1 12

( ) = c y y y2 2 2 2215( ) .= +

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2Given y2, firm 1s profit:

y2 .1 2 1 2 1 1

= Firm 1s best response to y2 :

60

y R y y1 1 2 2

151

4= = ( ) .

y115

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2=Like as previous, given y1, firm 2s profit:

2 .2 1 1 2 2 2 2=

Firm 2s best response to y1:

y R y2 2 11

4

= = ( ) .

45

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An equilibrium is when each firmsy2

the other firms output level, forthen neither wants to deviate from

60

its output level.

* *( )y R y=* *( )y R y=

(y1*,y2*) is Cournot-Nash8

Cournot equilibrium( ) ( )y y1 2 13 8* *, , .=equ r um.

y14813

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y2Firm 1s response function y R y1 1 2= ( ).

= 2 2 1= .

y1* = R1(y2*) y2* = R2(y1*)

y2*

y1y1*

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There are profit incentives for both firms to cooperate

.

This is collusion.

.

Suppose the two firms want to maximize their total profit

.

cooperatively output levels y1 and y2 that maximize

y y p y y y y c y c y( , ) ( )( ) ( ) ( ).1 2 1 2 1 2 1 1 2 2= + +

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A profit-seeking cartel in which firms

oop v y ou pu v

fundamentally unstable since if one of the firms

see s o ncrease pro y ecreas ng pr ce.

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We studied cases that assumed firms choose their output

What if firm 1 chooses its output level first and then, firm2 responds to this choice?

Lets assume firm 1 is a leader and firm 2 is a follower.

The competition is a sequential game in which the outputlevels are the strategic variables.

Such games are Stackelberg games.

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The response that follower firm 2 can make to the choice

=

Firm 1 knows this reaction and so perfectly anticipatesfirm 2s reaction to any y1 chosen by firm 1.

Leaders profit function:

+ 1 1 1 2 1 1 1 1y p y y y c y .= +

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Market inverse demand: p = 60 - yT.

rms tota cost unct ons are respect ve y c1 y1 = y1 c2(y2) = 15y2 + y22.

.

= =1

2 2 1

45( )

4

yy R y

= 2s

profit function: =

211 1 1

45(60 )

yy y y

In equilibrium:=1 13.9

sy = =2 2 1( ) 7.8s sy R y

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Games in which firms use only price strategies and

.

Each firms marginal production cost is constant at c.

.

Suppose one firm sets its price higher than another firms

price.

Then the higher-priced firm would have no customers.

Hence, at an equilibrium, all firms must set the same price.

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Asymmetric Information

0 signaling0moral hazard

0 incentives contracting