Oligopoly
Structure
Assume
Duopoly
Firms know information
about market demand
Perfect Information
Strategy
Simultaneous Movement
Non - Cooperative
Quantity
Cournot Model
Price
Bertrand Model
Cooperative
Cartel
Strategy
Sequential Movement
Price
Quantity
Price Leadership Model
Stackelberg 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
P
Firm A
Quantity 20 is best respond when B produce 50 Units
B = 50
20
MCA
MR50
20
DM
D50
30
80
Q
P
Firm A
Quantity 35 is best respond when B produce 20 Units
B = 20
MR20
D20
MCA
DM
Q
35
B output
Cournot Reaction Curve
Firm A reaction curve
Cournot Equilibrium
Firm B reaction curve
A 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.
P
P
Firm A
Firm B
B = 30
A = 30
MC
MR30
30
D30
DM
MC
MR30
Q
30
D30
DM
Q
Linear Demand and Zero Marginal Cost
P(q1 ,q 2 )=a-bq
q1 + q 2 = q
P( q1 , q 2 )=a - b( q1 + q 2 )
Firm 1
π1 = (a - bq1 -bq 2 )q1 - C 1 (q1 )
Firm 2
π 2 = (a - bq1 -bq 2 )q 2 - C 2 (q 2 )
π1
= a - 2bq1 -bq 2 - MC 1 (q1 ) = 0
q1
π 2
= a - 2bq 2 -bq1 - MC 2 (q 2 ) = 0
q 2
a-bq 2
q1 =
2b
a-bq1
q2 =
2b
a
a
2a
q1 =
, q2 =
, 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 – Q12 – Q2Q1
MR = 100 – 2Q1 – Q2
Firm 1
MR = 100 – 2Q1 – Q2 = MC
MR = 100 – 2Q1 – Q2 = 10
90-q 2
Q1 =
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
P
D1( 50 )
MR1( 0 )
D 1( 0 )
MC
Q1
20
45
Demand : P = 30 – Q ; Q = Q1 + Q2
Marginal Cost : MC1 = MC2 = 0
Oligopoly ( 2 Firms )
Competitive Market
Cartel ( 2 Firms )
Q2
Firm 1 ’ s Reaction Curve
Firm 2 ’ s Reaction Curve
Q1
Many Firms in Cournot Equilibrium
Assume : there are n Firms
q1 +q 2 ...+q n = q
ΔP
P(q) 
q i  MC(q i )
Δq
 ΔP q i 
P(q) 1 
 MC(q i )

 Δq P(q) 
 ΔP q q i 
P(q) 1 
 MC(q i )

 Δq P(q) q 
Given
qi
Si 
q

Si 
P(q) 1 
  MC(q i )
  (q) 
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
Max P(q L  q F )q F  CF (q F )
qF
π F  aq F  bq  bq L q F
2
F
Contract Isoprofit
QF
Isoprofit line for firm 2
F2 (QL*)
Reaction Curve for firm F
QL *
QL
Leader’s Problem
Assume MCL = 0
Max P(q L  q F )q L  C1 (q L )
qL
S.t.
a  bq L
q F  f F (q L ) 
2b
π L  aq L  bq  bq L q F
2
L
a - bq L
π L  aq L  bq  bq L (
)
2b
2
L
a
b 2
πL  qL  qL
2
2
a b
MR L   q L  MC L  0
2 2
a
qL 
2b
a
qF 
4b
QF
Firm 1
F2 (QL*)
QL *
Exercise
Demand : P = 30 – Q ; Q = Q1 + Q2
Marginal Cost : MC1 = MC2 = 0
Firm 1 Move First
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
MC = MR
Demand : P = 100 – Q ; Q = Q1 + Q2
Marginal Cost : MC1 = MC2 = 10
Demand : P = 30 – Q ; Q = Q1 + Q2
Marginal Cost : MC1 = MC2 = 3
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
P2
Firm 2’s Reaction Curve
Firm 1’s Reaction Curve
o
P1
Price Leadership Model
Homogeneous Product
Leader ( MC lower ) will set price first
Follower ( MC higher ) will set price follow Leader
P
MCF
DM
P1
A
DL
PL
B
C
D
MCL
0
Q
QF QL
MRL
QT
Maximization profit of Cartel
Cartel
Same MC Structure ( for Simple )
P
P
MCi
Total MC
ACi
PM
S
E
Pe
MR
QF*
Q2
Q
QM
D
Q
π(q1 , q 2 )  P(q1  q 2 )[q1  q 2 ]  C1 (q1 )  C2 (q 2 )
Assume Cost = o
π  {a  b(q1  q 2 )}(q1  q 2 )
π  a(q1  q 2 )  b(q1  q 2 )
MR Cartel  a  2b(q1  q 2 )
a
q1  q 2 
2b
2
Q2
Firm 2
a/2b
a/2b
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.”
π Defect  π M
Cartel Behavior
Defect Behavior
π M  π Cournot
πM
πM 
r
π Cournot
πD 
r
Keep Cartel Behavior
π Cournot
πM
πM 
 πD 
r
r
π M - π Cournot
r 
πD - πM
*