oligopoly

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

QQ

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