Oligopoly
Feb 22, 2016
Oligopoly
Structure
Assume Duopoly
Firms know information about market demand
Perfect Information
Strategy
Simultaneous Movement
Cooperative
Quantity Cournot Model
Price Bertrand Model
Non - Cooperative
Cartel
Strategy
Sequential Movement
Quantity Stackelberg Model
Price Price Leadership Model
Cournot Model
Assume Homogeneous goods
Given other Firm quantity is constant, and choose my quantity
Simultaneous Decision
Each firm want to maximize profit
Quantity Taker
DMD50MR50
80
20
B = 50
Firm A
3020
Quantity 20 is best respond when B produce 50 Units
MCA
Q
P
DM
D20MR20
B = 20
Firm A
35
Quantity 35 is best respond when B produce 20 Units
MCA
Q
P
A output
Cournot Equilibrium
Cournot 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 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 Cost
1 2P(q ,q )=a-bq 1 2q + q = q
1 2 1 2P( q , q )=a - b( q + q )
Firm 1
1 1 2 1 1 1π = (a - bq -bq )q - C (q )
Firm 2
2 1 2 2 2 2π = (a - bq -bq )q - C (q )
11 2 1 1
1
π = a - 2bq -bq - MC (q ) = 0q
22 1 2 2
2
π = a - 2bq -bq - MC (q ) = 0q
21
a-bqq =2b
12
a-bqq =2b
1 2a a 2aq = , q = , q =
3b 3b 3b
Demand : P = 100 – Q ; Q = Q1 + Q2
Marginal Cost : MC1 = MC2 = 10
Firm 1
TR = PQ1 = ( 100 – Q1 – Q2 )Q1
= 100Q1 – Q1
2 – Q2Q1
MR = 100 – 2Q1 – Q2
Firm 1
MR = 100 – 2Q1 – Q2 = MC
MR = 100 – 2Q1 – Q2 = 10
21
90-qQ =2
Reaction 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
Oligopoly ( 2 Firms )
Competitive Market
Cartel ( 2 Firms )
Q1
Q2
Firm 2 ’ s Reaction Curve
Firm 1 ’ s Reaction Curve
Many Firms in Cournot Equilibrium
Assume : there are n Firms
1 2 nq +q ...+q = q
)MC(qqΔqΔPP(q) ii
)MC(qP(q)q
ΔqΔP1P(q) i
i
)MC(qqq
P(q)q
ΔqΔP1P(q) i
i
qqS i
i Given
)MC(q(q)S1P(q) i
i
Exercise
(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?
(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?
Stackelberg Model
Homogeneous Product
Firm 1 moves first
Firm 2 knows firm 1’ s output, and decide his output
Firm 1 sets output by reaction function of firm 2
Follower’s Problem Assume MCF = 0
)(qC)qqP(qMax FFFFLqF
FL2FFF qbqbqaqπ
Contract Isoprofit
QL
QF
QL*
F2 (QL*)
Reaction Curve for firm F
Isoprofit line for firm 2
Leader’s Problem Assume MCL = 0
)(qC)qqP(qMax L1LFLqL
2bbqa)(qfq L
LFF
S.t.
FL2LLL qbqbqaqπ
)2bbq-a(bqbqaqπ L
L2LLL
2LLL q
2bq
2aπ
0MCq2b
2aMR LLL
2baqL
4baqF
QL
QF
QL*
F2 (QL*)
Firm 1
Demand : P = 30 – Q ; Q = Q1 + Q2
Marginal Cost : MC1 = MC2 = 0
Firm 1 Move First
Exercise
Exercise
Demand : P = 100 – Q ; Q = Q1 + Q2
Marginal Cost : ACi = MC1 = MC2 = 10
Bertrand Model ( Price Competition )
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
MC = MR
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
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 Model
Homogeneous Product
Leader ( MC lower ) will set price first
Follower ( MC higher ) will set price follow Leader
Q
P MCFDM
DL
MRL
MCL
QL
DCB
QTQF
PL
P1A
0
Cartel Maximization profit of Cartel
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
Assume Cost = o
)q)}(qqb(q{aπ 2121
22121 )qb(q)qa(qπ
)q2b(qaMR 21Cartel
2baqq 21
Q1
Q2
a/2b
a/2b
Firm 2
Punishment 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.”
CournotM ππ MDefect ππ
rππ M
M Cartel Behavior
Defect Behavior
rππ Cournot
D
rππ
rππ Cournot
DM
M
Keep Cartel Behavior
MD
CournotM*
π-ππ-πr