Oligopoly Models

1
Oligopoly Models

• Chapter 9 (skip discussion on Sweezy Oligopoly)

2
Oligopoly

• Definition-
• A market structure in which there are only a few
  firms each of which is large relative to the
  total industry (results in strategic interaction)

3
Warning

• Due to the complexity involved in analyzing
  oligopolies and the differences across
  industries/markets, there is no single model that
  is relevant to all oligopolies.

4
Types of Oligopoly

• Cournot Oligopoly
• Stackelberg Oligopoly
• Bertrand Oligopoly

5
Cournot Oligopoly

• Few firms in market serving many customers.
• Firms produce either differentiated or
  homogeneous products.
• Each firm believes rivals will hold their output
  constant if it changes its output.
• Barriers to entry exist.

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Numerical Example of Cournot Oligopoly

• Two Firms Firm 1 and Firm 2
• Firms produce a homogenous product
• Market Demand is P100-Q
• QQ1Q2 where Q1 is Firm 1s output and Q2 is
  Firm 2s output
• Each firm has constant marginal cost of 20 and
  zero fixed costs.

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What if the firms perfectly collude? What total
output should they produce?
Q40. Cant have more profits than what a
monopolist would.

MR
8
Suppose firms collude where both firms produce an
output of 20 (i.e., Q1Q220)
Firm 1s Profits 6020-2020800

Firm 2s Profits 6020-2020800
AVCATC
9
Why might you expect that the firms will not be
able to collude in this manner?
If Firm 1 thinks Firm 2 will produce 20, then
Firm 1 can increase his profits to 900 if produce
30.

Firm 1s Profits 5030-2030900
Firm 2s Profits 5020-2020600
AVCATC
10
What output would Firm 1 produce if Firm 1
expected Firm 2 to produce an output of 0?
Q140

Firm 1s Profits 6040-20401600
D1
AVCATC
MR1
11
What output would Firm 1 produce if Firm 1
expected Firm 2 to produce an output of 20?
Q130

D1
AVCATC
0
30
40
60
50
10
20
Firm 1s Output
70
80
Q2
MR1
12
What output would Firm 1 produce if Firm 1
expected Firm 2 to produce an output of 40?
Q120

D1
AVCATC
30
20
0
40
60
50
10
Firm 1s Output
MR1
Q2
13
What output would Firm 1 produce if Firm 1
expected Firm 2 to produce an output of 80?
Q10

AVCATC
D1
0
10
20
Firm 1s Output
MR1
Q2
14
Graphing the Reaction Function (or Best Response
Function) of Firm 1

Note The x-axis depicts the quantity produced by
Firm 1 and the y-axis depicts the quantity
produced by Firm 2.
r1(Q2)
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Reaction Functions of Firm 1 and Firm 2

r1(Q2)
r2(Q1)
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Cournot Equilibrium

• A situation in which neither firm has an
  incentive to change its output given the other
  firms output.

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Cournot Equilibrium Q126.67 and Q226.67

r1(Q2)
26.67
r2(Q1)
26.67
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Profits from Cournot Equilibrium Q126.67 and
Q226.67 so QQ1Q253.3

Firm 1 Profits46.6626.67-2026.67 713
Firm 2 Profits46.6626.67-2026.67 713
46.66
AVCATC
53.33
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Cournot Equilibrium compared to Perfect Collusion

• Cournot Equilibrium
• Q126.67 , Firm 1 Profits 713
• Q226.67 , Firm 2 Profits 713
• Perfect Collusion
• Q120 , Firm 1 Profits 800
• Q220 , Firm 2 Profits 800

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Why cant achieve Perfect Collusion with Q120
and Q220?
Both Firms have incentive to cheat!!

Note that we are assuming the firms interact just
once.
r1(Q2)
26.67
r2(Q1)
26.67
Perfectly Collude at Q1Q220 results in profits
of 800 for each firm.
Cournot Q1Q226.67 and Profits of both firms
are 713.
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Industry Characteristics that Facilitate Collusion

• Repeated Interaction
• Suppose Firm 1 thinks Firm 2 wont deviate from
  Q220 if Firm 1 doesnt deviate from collusive
  agreement of Q120 and Q220. In addition, Firm 1
  thinks Firm 2 will produce at an output of 80 in
  all future periods if Firm 1 deviates from
  collusive agreement of Q120 and Q220.
• Firm 1s profits from not cheating
• Firm 1s profits from cheating (by producing
  Q130 Today)

Today In 1 Year In 2 Years In 3 Years In 4 Years
800 800 800 800 800

Today In 1 Year In 2 Years In 3 Years In 4 Years
900 0 0 0 0
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Industry Characteristics that Facilitate Collusion

1. Stable Industry
2. Few Number of Firms
3. If a firm cheats on a collusive agreement, the
   probability the firm is caught is high.
4. Ability to Credibly Punish in a Severe Manner.
5. Industry demand is growing.
6. Expectation of firms behavior is clear.

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My All Time Favorite example of how expectations
are formed

• Coca-Cola, PepsiCo Set To Call Off Bitter
  Soft-Drink Price War
• Staff Reporter of The Wall Street Journal
• ATLANTA -- A brief but bitter pricing war within
  the soft-drink industry might be drawing to a
  close -- all because no one wants to be blamed
  for having fired the first shot.
• Coca-Cola Enterprises Inc., Coca-Cola Co.'s
  biggest bottler, said in a recent memorandum to
  executives that it will "attempt to increase
  prices" after July 4 amid concern that heavy
  price discounting in most of the industry is
  squeezing profit margins.
• The memo is a response to statements made to
  analysts last week by top PepsiCo Inc.
  executives. Pepsi, of Purchase, N.Y., said
  "irrational" pricing in much of the soft-drink
  industry might temporarily squeeze domestic
  profits, and it laid the blame for the price cuts
  at Coke's door.

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My All Time Favorite example of how expectations
are formed

• In the June 5 memo, Summerfield K. Johnston Jr.
  and Henry A. Schimberg, the chief executive and
  the president of Coca-Cola Enterprises,
  respectively, said the bottler's plan is to
  "succeed based on superior marketing programs and
  execution rather than the short-term approach of
  buying share through price discounting."
• "This is a first step to disengagement," said
  Andrew Conway, an analyst in New York for Morgan
  Stanley Co. "Coke and Pepsi are out to improve
  profitability for the category, not destroy it,
  so this would bode for a stabilization."
• For all the signals of a truce, though, Coca-Cola
  Enterprises' memo could just as easily be seen as
  throwing down the gauntlet. Messrs. Johnston and
  Schimberg said in the memo that should "the
  competition" view the attempt to raise prices "as
  an opportunity to gain share through predatory
  pricing, we will, as we have in the past, respond
  immediately."

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Stackelberg Oligopoly

• Few firms in market serving many customers.
• Firms produce either differentiated or
  homogeneous products.
• A single firm (the leader) chooses an output
  before all other firms choose their outputs.
• All other firms (the followers) take as given the
  output of the leader and choose outputs that
  maximize profits given the leaders output.
• Barriers to entry exist.

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Same numerical example as Cournot but assume that
Firm 1 is the Leader. What do you expect to
happen?
Firm 1 knows the response it will get from Firm 2
(i.e. what Firm 2 will produce depending on how
much Firm 1 produces). Therefore, Firm 1 will
select output to maximize profits given the
response function of Firm 2.

r1(Q2)
In this example, Firm 1 will produce Q140 so
Firm 2 produces Q220. Firm 1s profits are
4040-2040800 and Firm 2s profits are
4020-2020400.
r2(Q1)
FIRST MOVER ADVANTAGE!!
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Bertrand Oligopoly

• Few firms in market serving many customers.
• Firms produce a homogeneous product at a constant
  marginal cost (need not actually be the case).
• Firms engage in price competition and react
  optimally to prices charged by competitors.
• Consumers have perfect information and there are
  no transaction costs.
• Barriers to entry exist.

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What if Firm 1 and Firm 2 choose price and react
optimally to price charged by other firm?Will
firms be able to collude on a price of 60?
Firms could not collude on a price of 60 because
each firm would have incentive to undercut other
firm. In the end, you would expect both firms to
set a price of 20 (equal to MC) and have zero
profits.

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Some Conclusions

• Level of Competition Depends on Many Different
  Characteristics of the Industry not just Number
  of Firms.
• Level of Competition Depends on whether the Firms
  Select Quantity or Price and whether or not these
  Decisions are made Sequentially.
• Increased Competition is usually good for
  Consumers (lower prices) and bad for Firms (lower
  profits)