Quantitative Methods for Business Decisions

1
Quantitative Methods for Business Decisions

• Oligopoly

2
Oligopoly

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

3
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

4
Oligopoly

• Management Challenges
• Strategic actions
• Rival behavior
• Question
• What are the possible rival responses to a 10
  price cut by Mobitel?

5
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.

6
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.

7
Oligopoly

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

8
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
9
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
10
Oligopoly

• The Reaction Curve
• A firms profit-maximizing output is a decreasing
  schedule of the expected output of Firm 2.

11
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
12
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
13
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
14
Oligopoly

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

15
Oligopoly

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

16
Oligopoly

• An Example of the Cournot Equilibrium

17
Oligopoly

• An Example of the Cournot Equilibrium

18
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
19
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
20
Oligopoly

• Profit Maximization with Collusion

21
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?

22
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.

23
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.

24
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?

25
Price Competition

• The Bertrand model demonstrates the importance of
  the strategic variable (price versus output).

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

26
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.

27
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.

28
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

29
Price Competition with differentiation

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

30
Price Competition with differentiation

• Determining Prices and Output
• If P2 is fixed

31
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
32
Nash Equilibrium in Prices

• Question
• 1) What impact would collusion have on price and
  profit?

33
Nash Equilibrium in Prices
P1
Firm 1s Reaction Curve
Collusive Equilibrium
6
4
Firm 2s Reaction Curve
Nash Equilibrium
P2
4
6
34
Competition Versus Collusion The Prisoners
Dilemma

• Assume

35
Competition Versus Collusion The Prisoners
Dilemma

• Possible Pricing Outcomes

36
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
37
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?

38
Competition Versus Collusion The Prisoners
Dilemma

• An example in game theory, called the Prisoners
  Dilemma, illustrates the problem oligopolistic
  firms face.

39
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.

40
Payoff Matrix forPrisoners Dilemma
Prisoner B
Confess
Dont confess
Confess
-5, -5
-1, -10
Prisoner A
Dont confess
-2, -2
-10, -1
41
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

42
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

43
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?

44
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

45
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?

46
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
47
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.

48
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.