Source: Perloff. Some parts: © 2004 Pearson Addison-Wesley. All rights reserved

Oligopoly

Perloff Chapter 13

Source: Perloff. Some parts: © 2004 Pearson Addison-Wesley. All rights reserved

Market Structure

Source: Perloff. Some parts: © 2004 Pearson Addison-Wesley. All rights reserved

Nash EquilbriumWhere each firm chooses the best action assuming that other firms do the same.

Source: Perloff. Some parts: © 2004 Pearson Addison-Wesley. All rights reserved

Collusion

• Both firms could collude to earn higher profits.

• In collusion each firm has an incentive to cheat.

• Multiperiod game– Signalling– Punishment

Source: Perloff. Some parts: © 2004 Pearson Addison-Wesley. All rights reserved

Punishment

• American produces 48 as long as United does.• If United produces 64, American will do the same in all subsequent

periods.• Increase profits for one period outweighed by reduced profits in all

subsequent periods.• But the argument breaks down if there is a know stopping point.

Source: Perloff. Some parts: © 2004 Pearson Addison-Wesley. All rights reserved

Why do Cartels Form• Each firm in competition only considers the effects of its own actions on price.• In a Cartel the collective actions of all firms are considered.

(a) Firm

qc q*qm

Quantity, q, Unitsper year

S

MR

Market demand

AC

MC

pm

MCm

pc

pm

em

ec

MCm

pc

(b) Market

Qm Qc

Quantity, Q, Unitsper year

Pric

e, p

, $ p

er u

nit

Pric

e, p

, $ p

er u

nit

Source: Perloff. Some parts: © 2004 Pearson Addison-Wesley. All rights reserved

Why do cartels fail(a) Firm

qc q*qm

Quantity, q, Unitsper year

S

MR

Market demand

AC

MC

pm

MCm

pc

pm

em

ec

MCm

pc

(b) Market

Qm Qc

Quantity, Q, Unitsper year

Pric

e, p

, $ p

er u

nit

Pric

e, p

, $ p

er u

nit

Source: Perloff. Some parts: © 2004 Pearson Addison-Wesley. All rights reserved

Models of Non-cooperative Oligopoly

• Firms cannot set both price and quantity.

• Cournot model.– Firms simultaneously set quantity.

• Stackelberg model.– Firms set quantities sequantially.

• Bertrand model.– Firms set prices.

Source: Perloff. Some parts: © 2004 Pearson Addison-Wesley. All rights reserved

Assumptions

• Two firms (duopoly).

• Identical products.

• Market only lasts one period.

Source: Perloff. Some parts: © 2004 Pearson Addison-Wesley. All rights reserved

Deriving the Cournot Reaction Curve

Shows one firms profit maximising output given the output of the other firm

MC

MR D

339

147

243

0 339169.596

p, $

per

pas

seng

er

qA, Thousand American Airlinespassengers per quarter

MRr Dr D

MCqU = 64

339

147

275

211

0 339275137.564 128

p, $

per

pas

seng

er

qA, Thousand American Airlinespassengers per quarter

Source: Perloff. Some parts: © 2004 Pearson Addison-Wesley. All rights reserved

American and United’s best response (reaction) curves

United’s best-response curve

Cournot equilibrium

American’s best-response curve

qA, Thousand Americanpassengers per quarter

192

64

48

96

0 1929664

q u

, T

hous

and

Uni

ted

pass

enge

rs p

er q

uar

ter

Nash Equilibrium: Neither firm can increase profits by choosing another output level.

Source: Perloff. Some parts: © 2004 Pearson Addison-Wesley. All rights reserved

Stackelberg model

• One firm is the leader:– They are able to choose their output before the

other firm (the follower)

• Leader realises that once it sets it ouput, the follower will use its reaction curve to determine its output.

Source: Perloff. Some parts: © 2004 Pearson Addison-Wesley. All rights reserved

Stackelberg decision tree

American

64

96

48(4.6, 4.6)

(3.8, 5.1)

(2.3, 4.6)

48

Leader’s decision Follower’s decision Profits (πA, πU)

64

96

48(5.1, 3.8)

(4.1, 4.1)

(2.0, 3.1)

64

64

96

48(4.6, 2.3)

(3.1, 2.0)

(0, 0)

96

United

United

United

Source: Perloff. Some parts: © 2004 Pearson Addison-Wesley. All rights reserved

Stackelberg Graphical Model

qA, Thousand American passengers per quarter

qU = 48

96

0 qA = 96

MR r

D r

D

MC

(a) Residual Demand American Faces

qA , Thousand American passengers per quarter

qU = 48

339

195

243

147

0 339192

192

qA = 96 Q = 144

United’s best-response curve

(b) United’s Best-Response Curve

p,

$ p

er

pas

sen

ger

q u

, T

hou

sand

Un

ited

pa

sse

ng

ers

pe

r q

ua

rter

Source: Perloff. Some parts: © 2004 Pearson Addison-Wesley. All rights reserved

The effects of a subsidy on Cournot equilibrium

MC1

MC2

MRr D r D

qA = 64

339

147

275

99

0 339275137.564 88

192

88

64

48

96

120

0 192 24048 64 96

e2

e1

United’s new best-responsecurve (MC = $99)

United’s original best-responsecurve (MC = $147)

American’s best-response curve (MC = $147)

q

u, T

ho

usa

nd

Un

ited

pa

sse

ng

ers

pe

r q

ua

rte

r

qA, Thousand Americanpassengers per quarter

p,

$ p

er

pa

sse

ng

er

qU, Thousand Unitedpassengers per quarter

Source: Perloff. Some parts: © 2004 Pearson Addison-Wesley. All rights reserved

Bertrand Equilibrium with undifferentiated products

• Price setting• MC=AC=$5 for both• Suppose firm 1 sets

p=$10• Firm 2 will set p=$9.99• If firm 1 sets p=$5• Firm 2 sets p=0

Firm 2’sbest-response curve

Firm 1’s best-response curve

45° line

e

p1 , Price of Firm 1, $ per unit

10

5

0 5 109.99

p 2,

Pric

e o

f F

irm 2

, $

pe

r u

nit

Source: Perloff. Some parts: © 2004 Pearson Addison-Wesley. All rights reserved

Bertrand equilibrium with differentiated products

Pepsi’s best-responsecurve (MCp = $5) Coke’s best-response

curve (MCc = $14.50)

Coke’s best-responsecurve (MCc = $5)

p , Price of Pepsi, $ per unit

25

18

13

0 2513 14

e1

e2

p c,

Pric

e o

f C

oke,

$ p

er u

nit