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
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