OligopolyOligopoly

StructureStructure

AssumeAssume DuopolyDuopoly

Firms know information about market demandFirms know information about market demand

Perfect InformationPerfect Information

StrategyStrategy

Simultaneous MovementSimultaneous Movement

CooperativeCooperative

QuantityQuantity Cournot ModelCournot Model

PricePrice Bertrand ModelBertrand Model

Non - CooperativeNon - Cooperative

CartelCartel

StrategyStrategy

Sequential MovementSequential Movement

QuantityQuantity Stackelberg ModelStackelberg Model

PricePrice Price Leadership ModelPrice Leadership Model

Cournot ModelCournot Model

AssumeAssume Homogeneous goodsHomogeneous goods

Given other Firm quantity is constant, and choose my quantityGiven other Firm quantity is constant, and choose my quantity

Simultaneous DecisionSimultaneous Decision

Each firm want to maximize profitEach firm want to maximize profit

Quantity TakerQuantity Taker

DMD50

MR50

80

20

B = 50

Firm AFirm A

3020

Quantity 20 is best respond when B produce 50 Units

MCA

Q

P

DM

D20MR20

B = 20

Firm AFirm A

35

Quantity 35 is best respond when B produce 20 Units

MCA

Q

P

A output

Cournot Equilibrium

Cournot Reaction CurveCournot Reaction CurveB output

Firm B reaction curve

Firm A reaction curve

Firm A’ s output is a best respond to firm B’ s output.Firm A’ s output is a best respond to firm B’ s output.

Firm B’ s output is a best respond to firm A’ s output.Firm B’ s output is a best respond to firm A’ s output.

P

QDMD30

MC

30

B = 30

Firm A

MR30

P

QDMD30

MC

30

A = 30

Firm B

MR30

Linear Demand and Zero Marginal CostLinear Demand and Zero Marginal Cost

1 2P(q ,q )=a-bq1 2P(q ,q )=a-bq 1 2q + q = q

1 2q + q = q

1 2 1 2P( q , q )=a - b( q + q )1 2 1 2P( q , q )=a - b( q + q )

Firm 1Firm 1

1 1 2 1 1 1π = (a - bq -bq )q - C (q )1 1 2 1 1 1π = (a - bq -bq )q - C (q )

Firm 2Firm 2

2 1 2 2 2 2π = (a - bq -bq )q - C (q )2 1 2 2 2 2π = (a - bq -bq )q - C (q )

11 2 1 1

1

π = a - 2bq -bq - MC (q ) = 0

q

11 2 1 1

1

π = a - 2bq -bq - MC (q ) = 0

q

22 1 2 2

2

π = a - 2bq -bq - MC (q ) = 0

q

22 1 2 2

2

π = a - 2bq -bq - MC (q ) = 0

q

21

a-bqq =

2b2

1

a-bqq =

2b

12

a-bqq =

2b1

2

a-bqq =

2b

1 2

a a 2aq = , q = , q =

3b 3b 3b1 2

a a 2aq = , q = , q =

3b 3b 3b

Demand : P = 100 – Q ; Q = Q1 + Q2

Marginal Cost : MC1 = MC2 = 10

Demand : P = 100 – Q ; Q = Q1 + Q2

Marginal Cost : MC1 = MC2 = 10

Firm 1Firm 1

TR = PQ1 = ( 100 – Q1 – Q2 )Q1

TR = PQ1 = ( 100 – Q1 – Q2 )Q1

= 100Q1 – Q1

2 – Q2Q1

= 100Q1 – Q12

– Q2Q1

MR = 100 – 2Q1 – Q2

MR = 100 – 2Q1 – Q2

Firm 1Firm 1

MR = 100 – 2Q1 – Q2 = MC

MR = 100 – 2Q1 – Q2 = MC

MR = 100 – 2Q1 – Q2 = 10

MR = 100 – 2Q1 – Q2 = 10

21

90-qQ =

22

1

90-qQ =

2Reaction Curve of Firm 1Reaction Curve of Firm 1

Q2 MR = 100 – 2Q1-Q2 Q1

0 100 – 2Q1 45

50 50 – 2Q1 20

75 25 – 2Q1 7.5

90 10 – 2Q1 0

Q1

P

D1( 0 )MR1( 0 )

D1( 50 )

MC

4520

Demand : P = 30 – Q ; Q = Q1 + Q2

Marginal Cost : MC1 = MC2 = 0

Demand : P = 30 – Q ; Q = Q1 + Q2

Marginal Cost : MC1 = MC2 = 0

Oligopoly ( 2 Firms )Oligopoly ( 2 Firms )

Competitive MarketCompetitive Market

Cartel ( 2 Firms )Cartel ( 2 Firms )

Q1

Q2

Firm 2 ’ s Reaction Curve

Firm 1 ’ s Reaction Curve

Many Firms in Cournot EquilibriumMany Firms in Cournot Equilibrium

Assume : there are n FirmsAssume : there are n Firms

1 2 nq +q ...+q = q1 2 nq +q ...+q = q

)MC(qqΔq

ΔPP(q) ii )MC(qq

Δq

ΔPP(q) ii

)MC(qP(q)

q

Δq

ΔP1P(q) i

i

)MC(q

P(q)

q

Δq

ΔP1P(q) i

i

)MC(qq

q

P(q)

q

Δq

ΔP1P(q) i

i

)MC(q

q

q

P(q)

q

Δq

ΔP1P(q) i

i

q

qS i

i q

qS i

i Given

)MC(q(q)

S1P(q) i

i

)MC(q(q)

S1P(q) i

i

ExerciseExercise

(a) Suppose that inverse demand is given by P = a – bQ, and that firms have identical marginal cost given by C. Assume that a > C so that part of the demand curve lies above the marginal cost curve ( otherwise the industry would not produce any input ). What is the monopoly equilibrium in this market?

(a) Suppose that inverse demand is given by P = a – bQ, and that firms have identical marginal cost given by C. Assume that a > C so that part of the demand curve lies above the marginal cost curve ( otherwise the industry would not produce any input ). What is the monopoly equilibrium in this market?

(b) What is the perfect competitive market outcome?(b) What is the perfect competitive market outcome?

(c) What is the Cournot equilibrium in market with two firms?(c) What is the Cournot equilibrium in market with two firms?

(d) Suppose the market consists of N identical firms. What is the Cournot equilibrium quantity per firm, market quantity, and price?

(d) Suppose the market consists of N identical firms. What is the Cournot equilibrium quantity per firm, market quantity, and price?

Stackelberg ModelStackelberg Model

Homogeneous ProductHomogeneous Product

Firm 1 moves firstFirm 1 moves first

Firm 2 knows firm 1’ s output, and decide his outputFirm 2 knows firm 1’ s output, and decide his output

Firm 1 sets output by reaction function of firm 2Firm 1 sets output by reaction function of firm 2

Follower’s ProblemFollower’s Problem Assume MCF = 0Assume MCF = 0

)(qC)qqP(qMax FFFFLqF

)(qC)qqP(qMax FFFFLqF

FL2FFF qbqbqaqπ

FL2FFF qbqbqaqπ

Contract IsoprofitContract Isoprofit

QL

QF

QL*

F2 (QL*)

Reaction Curve for firm F

Isoprofit line for firm 2

Leader’s ProblemLeader’s Problem Assume MCL = 0Assume MCL = 0

)(qC)qqP(qMax L1LFLqL

)(qC)qqP(qMax L1LFLqL

2b

bqa)(qfq L

LFF

2b

bqa)(qfq L

LFF

S.t.S.t.

FL2LLL qbqbqaqπ

FL2LLL qbqbqaqπ

)2b

bq-a(bqbqaqπ L

L2LLL )

2b

bq-a(bqbqaqπ L

L2LLL

2LLL q

2

bq

2

aπ 2

LLL q2

bq

2

aπ

0MCq2

b

2

aMR LLL 0MCq

2

b

2

aMR LLL

2b

aqL

2b

aqL

4b

aqF

4b

aqF

QL

QF

QL*

F2 (QL*)

Firm 1

Demand : P = 30 – Q ; Q = Q1 + Q2

Marginal Cost : MC1 = MC2 = 0

Demand : P = 30 – Q ; Q = Q1 + Q2

Marginal Cost : MC1 = MC2 = 0

Firm 1 Move FirstFirm 1 Move First

ExerciseExercise

ExerciseExercise

Demand : P = 100 – Q ; Q = Q1 + Q2

Marginal Cost : ACi = MC1 = MC2 = 10

Demand : P = 100 – Q ; Q = Q1 + Q2

Marginal Cost : ACi = MC1 = MC2 = 10

Bertrand Model ( Price Competition )Bertrand Model ( Price Competition )

Price of other firm is constant and Simultaneous Movement Price of other firm is constant and Simultaneous Movement

Case 1 : Homogeneous Product

Demand : P = 30 – Q ; Q = Q1 + Q2

Marginal Cost : MC1 = MC2 = 3

Demand : P = 30 – Q ; Q = Q1 + Q2

Marginal Cost : MC1 = MC2 = 3

MC = MRMC = MR

Demand : P = 100 – Q ; Q = Q1 + Q2

Marginal Cost : MC1 = MC2 = 10

Demand : P = 100 – Q ; Q = Q1 + Q2

Marginal Cost : MC1 = MC2 = 10

Case 2 : Differentiated Product

Firm 1 ‘s Demand : Q1 = 12 – 2P1 + P2

Firm 2 ‘s Demand : Q2 = 12 – 2P2 + P1

Fixed Cost = 20 and MC1 = MC2 = 0

Firm 1 ‘s Demand : Q1 = 12 – 2P1 + P2

Firm 2 ‘s Demand : Q2 = 12 – 2P2 + P1

Fixed Cost = 20 and MC1 = MC2 = 0

P2 Demand P1

0 6 – 0.5Q1 3

8 10 – 0.5Q1 5

16 14 – 0.5Q1 7

Firm 1’s Reaction Curve

P1

P2 Firm 2’s Reaction Curve

o

Price Leadership ModelPrice Leadership Model

Homogeneous ProductHomogeneous Product

Leader ( MC lower ) will set price firstLeader ( MC lower ) will set price first

Follower ( MC higher ) will set price follow LeaderFollower ( MC higher ) will set price follow Leader

Q

P MCFDM

DL

MRL

MCL

QL

DCB

QTQF

PL

P1A

0

CartelCartel Maximization profit of CartelMaximization profit of Cartel

Same MC Structure ( for Simple )Same MC Structure ( for Simple )

P P

QQ

Total MC

DMR

MCi

ACi

QM

EPe

PM S

QF* Q2

)(qC)(qC]q)[qqP(q)q,π(q 2211212121 )(qC)(qC]q)[qqP(q)q,π(q 2211212121

Assume Cost = oAssume Cost = o

)q)}(qqb(q{aπ 2121 )q)}(qqb(q{aπ 2121

22121 )qb(q)qa(qπ 2

2121 )qb(q)qa(qπ

)q2b(qaMR 21Cartel )q2b(qaMR 21Cartel

2b

aqq 21

2b

aqq 21

Q1

Q2

a/2b

a/2b

Firm 2

Punishment StrategyPunishment Strategy

“If you stay at the production level that maximize joint industry project, fine. But if I discover you cheating by producing more than this amount, I will punish you by producing the Cournot level for output forever.”

“If you stay at the production level that maximize joint industry project, fine. But if I discover you cheating by producing more than this amount, I will punish you by producing the Cournot level for output forever.”

CournotM ππ CournotM ππ MDefect ππ

MDefect ππ

r

ππ M

M r

ππ M

M Cartel Behavior

Defect Behavior

r

ππ Cournot

D r

ππ Cournot

D

r

ππ

r

ππ Cournot

DM

M r

ππ

r

ππ Cournot

DM

M

Keep Cartel BehaviorKeep Cartel Behavior

MD

CournotM*

π-π

π-πr

MD

CournotM*

π-π

π-πr