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Oligopoly Models

Chapter 9 (skip discussion on “Sweezy Oligopoly”)

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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)

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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.

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Types of Oligopoly

1. Cournot Oligopoly

2. Stackelberg Oligopoly

3. Bertrand Oligopoly

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Cournot Oligopoly

1. Few firms in market serving many customers.

2. Firms produce either differentiated or homogeneous products.

3. Each firm believes rivals will hold their output constant if it changes its output.

4. 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 P=100-Q Q=Q1+Q2 where Q1 is Firm 1’s

output and Q2 is Firm 2’s 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?

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MCQ

Q=40. Can’t have more profits than what a monopolist would.

MR

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Suppose firms collude where both firms produce an output of 20 (i.e., Q1=Q2=20)

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MCQ

=AVC=ATC

Firm 1’s Profits = 60*20-20*20=800

Firm 2’s Profits = 60*20-20*20=800

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Why might you expect that the firms will not be able to collude in this manner?

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MCQ

=AVC=ATC

Firm 1’s Profits = 50*30-20*30=900

Firm 2’s Profits = 50*20-20*20=600

If Firm 1 thinks Firm 2 will produce 20, then Firm 1 can increase his profits to 900 if produce 30.

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What output would Firm 1 produce if Firm 1 expected Firm 2 to produce an output of 0?

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MCQ

=AVC=ATC

Firm 1’s Profits = 60*40-20*40=1600

MR1

D1

Q1=40

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What output would Firm 1 produce if Firm 1 expected Firm 2 to produce an output of 20?

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D

MCQ

=AVC=ATC

MR1

D1

Q2

0 30 40 6050 70 8010 20 Firm 1’s Output

Q1=30

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What output would Firm 1 produce if Firm 1 expected Firm 2 to produce an output of 40?

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D

MCQ

=AVC=ATC

MR1

D1

Q2

0 30 40 605010 20 Firm 1’s Output

Q1=20

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What output would Firm 1 produce if Firm 1 expected Firm 2 to produce an output of 80?

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MCQ

=AVC=ATC

MR1

D1

Q2

0 10 20 Firm 1’s Output

Q1=0

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Graphing the Reaction Function (or Best Response Function) of Firm 1

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Q2

r1(Q2)

Note: The x-axis depicts the quantity produced by Firm 1 and the y-axis depicts the quantity produced by Firm 2.

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Reaction Functions of Firm 1 and Firm 2

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Q2

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 firm’s output.

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Cournot Equilibrium: Q1=26.67 and Q2=26.67

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Q2

r1(Q2)

r2(Q1)26.67

26.67

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Profits from Cournot Equilibrium: Q1=26.67 and Q2=26.67 so Q=Q1+Q2=53.3

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53.33

46.66

=AVC=ATC

Firm 1 Profits=46.66*26.67-20*26.67= 713

Firm 2 Profits=46.66*26.67-20*26.67= 713

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Cournot Equilibrium compared to Perfect Collusion Cournot Equilibrium

Q1=26.67 , Firm 1 Profits = 713

Q2=26.67 , Firm 2 Profits = 713

Perfect Collusion

Q1=20 , Firm 1 Profits = 800

Q2=20 , Firm 2 Profits = 800

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Why can’t achieve Perfect Collusion with Q1=20 and Q2=20?

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Q2

r1(Q2)

r2(Q1)

Both Firms have incentive to cheat!!

Note that we are assuming the firms interact just once.

26.67

26.67

Cournot: Q1=Q2=26.67 and Profits of both firms are 713.

Perfectly Collude at Q1=Q2=20 results in profits of 800 for each firm.

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Industry Characteristics that Facilitate Collusion1. Repeated Interaction

Suppose Firm 1 thinks Firm 2 won’t deviate from Q2=20 if Firm 1 doesn’t deviate from collusive agreement of Q1=20 and Q2=20. 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 Q1=20 and Q2=20.

Firm 1’s profits from not cheating

Firm 1’s profits from cheating (by producing Q1=30 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

2. Stable Industry

3. Few Number of Firms

4. If a firm cheats on a collusive agreement, the probability the firm is “caught” is high.

5. Ability to Credibly Punish in a Severe Manner.

6. Industry demand is growing.

7. 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 Oligopoly1. Few firms in market serving many

customers.2. Firms produce either differentiated or

homogeneous products.3. A single firm (the leader) chooses an

output before all other firms choose their outputs.

4. All other firms (the followers) take as given the output of the leader and choose outputs that maximize profits given the leader’s output.

5. 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?

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Q2

r1(Q2)

r2(Q1)

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.

In this example, Firm 1 will produce Q1=40 so Firm 2 produces Q2=20. Firm 1’s profits are 40*40-20*40=800 and Firm 2’s profits are 40*20-20*20=400.

FIRST MOVER ADVANTAGE!!

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Bertrand Oligopoly

1. Few firms in market serving many customers.

2. Firms produce a homogeneous product at a constant marginal cost (need not actually be the case).

3. Firms engage in price competition and react optimally to prices charged by competitors.

4. Consumers have perfect information and there are no transaction costs.

5. 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?

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MCQ

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)