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Quantitative Methods for Business Decisions

- Oligopoly

Oligopoly

- Characteristics
- Small number of firms
- Product differentiation may or may not exist
- Barriers to entry
- Oligopoly markets commonly exist

Oligopoly

- Examples
- Automobiles - Steel
- Aluminum - Petrochemicals
- Electrical equipment - Computers

- The barriers to entry are
- Natural Strategic action
- Scale economies - Flooding the market
- Patents - Controlling an

essential input - Technology
- Name recognition

Oligopoly

- Management Challenges
- Strategic actions
- Rival behavior
- Question
- What are the possible rival responses to a 10

price cut by Mobitel?

Oligopoly

- Equilibrium in an Oligopolistic Market
- In perfect competition and monopoly the producers

did not have to consider a rivals response when

choosing output and price. - In oligopoly the producers must consider the

response of competitors when choosing output and

price.

Oligopoly

- Equilibrium in an Oligopolistic Market
- Defining Equilibrium
- Firms doing the best they can and have no

incentive to change their output or price - All firms assume competitors are taking rival

decisions into account.

- Nash Equilibrium
- Each firm is doing the best it can given what its

competitors are doing.

Oligopoly

- The Cournot Model
- Duopoly
- Two firms competing with each other
- Homogenous good
- The output of the other firm is fixed

Firm 1s Output Decision

P1

D1(0)

If Firm 1 thinks Firm 2 will produce nothing,

its demand curve, D1(0), is the market demand

curve.

The corresponding MR curve, intersects the

marginal cost curve at an output of 50 units.

MR1(0)

MC1

50

Q1

Firm 1s Output Decision

P1

D1(0)

If firm 1 thinks Firm 2 will produce 50 units,

its demand curve is shifted to the left by this

amount. The profit maximizing output is now 25

units.

If firm 1 thinks Firm 2 will produce 75 units,

its demand curve is shifted to the left by this

amount. The profit maximizing output is now 12.5

units.

MR1(0)

D1(75)

MR1(75)

MC1

What is the output of Firm 1 if Firm 2 produces

100 units?

D1(50)

MR1(50)

50

25

12.5

Q1

Oligopoly

- The Reaction Curve
- A firms profit-maximizing output is a decreasing

schedule of the expected output of Firm 2.

Reaction Curves and Cournot Equilibrium

Q1

100

Firm 1s reaction curve shows how much it will

produce as a function of how much it thinks Firm

2 will produce. The xs correspond to the

previous model.

75

x

50

x

25

Firm 1s Reaction Curve Q1(Q2)

x

x

25

50

75

100

Q2

Reaction Curves and Cournot Equilibrium

Q1

100

Firm 2s reaction curve shows how much it will

produce as a function of how much it thinks Firm

1 will produce.

75

Firm 2s Reaction Curve Q2(Q2)

x

50

x

25

Firm 1s Reaction Curve Q1(Q2)

x

x

25

50

75

100

Q2

Reaction Curves and Cournot Equilibrium

Q1

100

In Cournot equilibrium, each firm correctly

assumes how much its competitors will produce and

thereby maximize its own profits.

75

Firm 2s Reaction Curve Q2(Q2)

x

50

Cournot Equilibrium

x

25

Firm 1s Reaction Curve Q1(Q2)

x

x

25

50

75

100

Q2

Oligopoly

- An Example of the Cournot Equilibrium
- Duopoly
- Market demand is P 30 - Q where Q Q1 Q2
- MC1 MC2 0

Oligopoly

- An Example of the Cournot Equilibrium
- Firms 1 Reaction Curve

Oligopoly

- An Example of the Cournot Equilibrium

Oligopoly

- An Example of the Cournot Equilibrium

Duopoly Example

Q1

30

Firm 1s Reaction Curve

The demand curve is P 30 - Q and both firms

have 0 marginal cost.

Cournot Equilibrium

15

10

Firm 1s Reaction Curve

15

30

10

Q2

Duopoly Example

Q1

30

Firm 1s Reaction Curve

Cournot Equilibrium

15

Collusive Equilibrium

10

Firm 1s Reaction Curve

7.5

Q2

15

30

10

7.5

Oligopoly

- Profit Maximization with Collusion

Oligopoly

- Contract Curve
- Q1 Q2 15
- Shows all pairs of output Q1 and Q2 that maximize

total profits - Q1 Q2 7.5
- Less output and higher profits than the Cournot

equilibrium

- Question
- How does each output level compare to perfect

competition?

Price Competition

- Competition in an oligopolistic industry may

occur with price instead of output. - The Bertrand Model is used to illustrate price

competition in an oligopolistic industry with

homogenous goods.

Price Competition

- Assumptions
- Homogenous good
- Market demand is P 30 - Q where

Q Q1 Q2 - MC 3 for both firms, so MC1 MC2 3
- Question
- What would be the output, price and profit with a

Cournot equilibrium? (Q1 Q2 9, P 12) - Assume the firms compete with price, not quantity.

Price Competition

- Questions
- 1) How will consumers respond to a price

differential? (Hint Consider homogeneity) - 2) What is the Nash equilibrium?
- 3) Why not charge a higher price to raise

profits? - 4) How does the Bertrand outcome compare to the

Cournot outcome?

Price Competition

- The Bertrand model demonstrates the importance of

the strategic variable (price versus output).

- Question
- What are some criticisms of the Bertrand model?

Price Competition

- Answer
- When firms produce a homogenous good, it is more

natural to compete by setting quantities rather

than prices. - Even if the firms do set prices and choose the

same price, what share of total sales will go to

each one? - It may not be equally divided.

Price Competition with differentiation

- Price Competition with Differentiated Products
- Market shares are now determined not just by

prices, but by differences in the design,

performance, and durability of each firms

product.

Price Competition with differentiation

- Assumptions
- Duopoly
- FC 20
- VC 0
- Firm 1s demand is Q1 12 - 2P1 P2
- Firm 2s demand is Q2 12 - 2P2 P1
- P1 and P2 are prices firms 1 and 2 charge

respectively - Q1 and Q2 are the resulting quantities they sell

Price Competition with differentiation

- Determining Prices and Output
- Set prices at the same time

Price Competition with differentiation

- Determining Prices and Output
- If P2 is fixed

Nash Equilibrium in Prices

P1

Firm 2s Reaction Curve

Here two firms sell a differentiated produce, and

each firms demand depends on it its own price

and its competitors price.

The Nash Equilibrium is at the intersection of

the two reaction curves when each firs is doing

the best it can given its competitors price, and

it has no incentive to change price.

6

4

Firm 1s Reaction Curve

Nash Equilibrium

P2

4

6

Nash Equilibrium in Prices

- Question
- 1) What impact would collusion have on price and

profit?

Nash Equilibrium in Prices

P1

Firm 1s Reaction Curve

Collusive Equilibrium

6

4

Firm 2s Reaction Curve

Nash Equilibrium

P2

4

6

Competition Versus Collusion The Prisoners

Dilemma

- Assume

Competition Versus Collusion The Prisoners

Dilemma

- Possible Pricing Outcomes

Payoff Matrix for Pricing Game

Firm 2

Charge 4

Charge 6

Charge 4

12, 12

20, 4

Firm 1

Charge 6

16, 16

4, 20

Competition Versus Collusion The Prisoners

Dilemma

- These two firms are playing a noncooperative

game. - Each firm independently does the best it can

taking its competitor into account. - Question
- Why will both firms choose 4 when 6 will yield

higher profits?

Competition Versus Collusion The Prisoners

Dilemma

- An example in game theory, called the Prisoners

Dilemma, illustrates the problem oligopolistic

firms face.

Competition Versus Collusion The Prisoners

Dilemma

- Scenario
- Two prisoners have been accused of collaborating

in a crime. - They are in separate jail cells and cannot

communicate. - Each has been asked to confess to the crime.
- A payoff matrix results from their decision.

Payoff Matrix forPrisoners Dilemma

Prisoner B

Confess

Dont confess

Confess

-5, -5

-1, -10

Prisoner A

Dont confess

-2, -2

-10, -1

Payoff Matrix forPrisoners Dilemma

- Conclusions Oligipolistic Markets
- 1) Collusion will lead to greater profits
- 2) Explicit and implicit collusion is possible
- 3) Once collusion exists, the profit motive to

break and lower price is significant

Example A Pricing Problem for Procter Gamble

- Scenario
- 1) Procter Gamble, Kao Soap, Ltd., and

Unilever, Ltd were entering the market for Gypsy

Moth Tape. - 2) All three would be choosing their prices at

the same time. - 3) Procter Gamble had to consider

competitors prices when setting their price. - 4) FC 480,000/month and VC 1/unit for all

firms

Example A Pricing Problem for Procter Gamble

- Scenario
- 5) PGs demand curve was
- Q 2,275P-3.5(PU).25(PK).25
- where P, PU , PK are PGs, Unilevers, and Kaos

prices respectively - Problem
- What price should PG choose and what is the

expected profit?

PGs Profit (in thousands of per month)

Competitors (Equal) Prices ()

PGs Price () 1.10 1.20 1.30 1.40 1.50 1.60 1.7

0 1.80

- 1.10 -226 -215 -204 -194 -183 -174 -165 -155
- 1.20 -106 -89 -73 -58 -43 -28 -15 -2
- 1.30 -56 -37 -19 2 15 31 47 62
- 1.40 -44 -25 -6 12 29 46 62 78
- 1.50 -52 -32 -15 3 20 36 52 68
- 1.60 -70 -51 -34 -18 -1 14 30 44
- 1.70 -93 -76 -59 -44 -28 -13 1 15
- 1.80 -118 -102 -87 -72 -57 -44 -30 -17

Example A Pricing Problem for Procter Gamble

- Questions
- 1) What is the Nash equilibrium price?
- 2) What is the profit maximizing price with

collusion? - 3) Why wouldnt each firm set the collusion price

independently and earn the higher profits that

occur with explicit collusion?

Payoff Matrix forPricing Problem

Unilever and Kao

Charge 1.40

Charge 1.50

Charge 1.40

12, 12

29, 3

PG

Charge 1.50

3, 29

20, 20

Implications of the Prisoners Dilemma for

Oligipolistic Pricing

- Observations of Oligopoly Behavior
- 1) In some oligopoly markets, pricing behavior

in time can create a predictable pricing

environment and implied collusion may occur

(Tacit collusion). - 2) In other oligopoly markets, the firms are

very aggressive and collusion is not possible. - Firms are reluctant to change price because of

the likely response of their competitors. - In this case prices tend to be relatively rigid.

Summary

- In an oligopolistic market, only a few firms

account for most or all of production. - In the Cournot model of oligopoly, firms make

their output decisions at the same time, each

taking the others output as fixed. - The Nash equilibrium concept can also be applied

to markets in which firms produce substitute

goods and compete by setting price. - Firms would earn higher profits by collusively

agreeing to raise prices, but the antitrust laws

usually prohibit this.

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