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CHAPTER 9
Basic Oligopoly Models
CHAPTER OUTLINE

Cournot oligopoly (Collusion)

Stackelberg oligopoly

Bertrand oligopoly
Chapter Overview
9-2
INTRODUCTION


Conditions for Oligopoly
Oligopoly market structures are characterized by
only a few firms, each of which is large relative to the
total industry.
Common Characteristics:
Typical number of firms is between 2 and 10.
 Products can be identical or differentiated.
 The outcome for one firm depends on what other firms in
the industry do

9-3
EXAMPLES

Conditions for Oligopoly
Auto Industry
9-4
EXAMPLES

Conditions for Oligopoly
Credit card networks industry
9-5
INTRODUCTION

Conditions for Oligopoly
Duopoly: An oligopoly market composed of two firms
Competition between Airbus and Boeing has been
characterized as a duopoly in the large jet airliner market
since the 1990s
----Airlines Industry Profile: United States,
Datamonitor, November 2008, pp. 13–14
9-6
INTRODUCTION

Conditions for Oligopoly
Oligopoly settings tend to be the most difficult to
manage since managers must consider the likely
impact of his or her decisions on the decisions of other
firms in the market.
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9.1 COURNOT OLIGOPOLY
The number of firms in the industry:
Few firms
 The degree of homogeneity of the product:
Differentiated or identical products
 The ease of entry and exit:
Barriers to entry exist
 Each firm believes rivals will hold their output
constant if it changes its output

Profit Maximization in Four
Oligopoly Settings
9.1 COURNOT OLIGOPOLY

Consider a Cournot duopoly. Each firm makes an
output decision under the belief that its rival will hold
its output constant when the other changes its output
level.

.
Implication: Each firm’s marginal revenue is impacted by
the other firms output decision.
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Profit Maximization in Four
Oligopoly Settings
9.1 COURNOT OLIGOPOLY
2) Best –response function (Reaction function)
 A function that defines the profit-maximizing
level of output for a firm given the output levels of
another firm
9-
Profit Maximization in Four
Oligopoly Settings
9.1 COURNOT OLIGOPOLY
2) Best –response function (Reaction function)
 Conditions:
• Two firms
• Product produced by the two firms is homogeneous
• Firms choose output
• Firms compete with each other and make their
production decision simultaneously
• No potential entrants
9-
9.1 COURNOT OLIGOPOLY
B. Given a linear (inverse) demand function: 𝑃𝑃 = 𝑎𝑎 − 𝑏𝑏 𝑄𝑄1 + 𝑄𝑄2
C. Cost functions: 𝐶𝐶1 𝑄𝑄1 = 𝑐𝑐1 𝑄𝑄1 and 𝐶𝐶2 𝑄𝑄2 = 𝑐𝑐2 𝑄𝑄2
D. So Marginal cost functions: 𝑀𝑀𝑀𝑀1 𝑄𝑄1 = 𝑐𝑐1 and 𝑀𝑀𝑀𝑀2 𝑄𝑄2 = 𝑐𝑐2
How to derive their reaction functions?
Profit Maximization in Four
Oligopoly Settings
9.1 COURNOT OLIGOPOLY

Given a linear (inverse) demand function
𝑃𝑃 = 𝑎𝑎 − 𝑏𝑏 𝑄𝑄1 + 𝑄𝑄2
and cost functions, 𝐶𝐶1 𝑄𝑄1 = 𝑐𝑐1 𝑄𝑄1 and 𝐶𝐶2 𝑄𝑄2 = 𝑐𝑐2 𝑄𝑄2 ,
the reactions functions are:
𝑎𝑎 − 𝑐𝑐1 1
− 𝑄𝑄2
𝑄𝑄1 = 𝑟𝑟1 𝑄𝑄2 =
2
2𝑏𝑏
𝑎𝑎 − 𝑐𝑐2 1
− 𝑄𝑄1
𝑄𝑄2 = 𝑟𝑟2 𝑄𝑄1 =
2
2𝑏𝑏
9-
Profit Maximization in Four
Oligopoly Settings
9.1 COURNOT OLIGOPOLY

Cournot Equilibrium: a situation in which neither
firm has an incentive to change its output given the
other firm’s output
9-
9.1 COURNOT OLIGOPOLY
Profit Maximization in Four
Oligopoly Settings
Quantity2
𝑄𝑄2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑄𝑄2
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶
Firm 1’s Reaction Function
𝑄𝑄1 = 𝑟𝑟1 𝑄𝑄2
C
Cournot equilibrium
A
D
B
𝑄𝑄1 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶
𝑄𝑄1 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
Firm 2’s Reaction Function
𝑄𝑄2 = 𝑟𝑟2 𝑄𝑄1
Quantity1
9-
Profit Maximization in Four
Oligopoly Settings
9.1 COURNOT OLIGOPOLY

Suppose the inverse demand function in a Cournot
duopoly is given by
𝑃𝑃 = 10 − 𝑄𝑄1 + 𝑄𝑄2
and their marginal costs are 2.



What are the reaction functions for the two firms?
What are the Cournot equilibrium outputs?
What is the equilibrium price?
9-
Profit Maximization in Four
Oligopoly Settings
9.1 COURNOT OLIGOPOLY

The reaction functions are:
𝑄𝑄1 = 𝑟𝑟1 𝑄𝑄2 =


𝑄𝑄2 = 𝑟𝑟2 𝑄𝑄1 =
8
1
− 2 𝑄𝑄2
2
8
1
−
𝑄𝑄
2
2 1
Equilibrium output is found as:
1
1
8
𝑄𝑄1 = 5 −
4 − 𝑄𝑄1 ⟹ 𝑄𝑄1 =
2
2
3
8
Since the firms are symmetric, 𝑄𝑄2 = 3.
Total industry output is
8
8
𝑄𝑄 = 𝑄𝑄1 + 𝑄𝑄2 = 3 + 3 =
16
3
So, the equilibrium price is: 𝑃𝑃 = 10 −
16
3
=
14
.
3
9-
STEPS FOR FINDING COURNOT
EQUILIBRIUM
Step 1: Firm 1: MR1=MC1=> Q1=R(Q2)
 Step 2: Firm 2: MR2=MC2=> Q2=R(Q1)
or using Symmetry
 Step 3: Solve Q1 and Q2 by reaction function
 Step 4: Q=Q1+Q2
 Step 5: Solve P by market demand function:
P=a-bQ
 Step 6: Profit of firm 1= P*Q1-C1(Q1)
Profit of firm 2= P*Q2-C2(Q2)

Note: Step 1 & Step 2 also could be solved using reaction functions by
plugging numbers
Profit Maximization in Four
Oligopoly Settings
9.1 COURNOT OLIGOPOLY
3) Cournot Oligopoly: Collusion

Def: Markets with only a few dominant firms can
coordinate to restrict output to their benefit at the
expense of consumers
Restricted output leads to higher market prices.
 Collusion, however, is prone to cheating behavior.
 Since both parties are aware of these incentives, reaching
collusive agreements is often very difficult.

9-
Profit Maximization in Four
Oligopoly Settings
9.1 COURNOT OLIGOPOLY
•
EX2: Suppose the inverse demand function in a Cournot
duopoly is given 𝑃𝑃 = 10 − 𝑄𝑄1 + 𝑄𝑄2 and their marginal
costs are 2. Suppose they decide to collude, then
a. What are the equilibrium outputs of each firm?
b. What is the equilibrium price?
c. What is the equilibrium profits for each firm?
d. Compared to the profit in example1, which profit is
higher?
9-
9.2 STACKELBERG OLIGOPOLY
1) Characteristics:
• The number of firms in the industry:
Few firms
• The degree of homogeneity of the product:
Either differentiated or homogeneous products
• The ease of entry and exit:
Barriersto entry exist
9.2 STACKELBERG OLIGOPOLY
1) Characteristics:
• 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 leader’s output
Profit Maximization in Four
Oligopoly Settings
9.2 STACKELBERG OLIGOPOLY

Given a linear (inverse) demand function
𝑃𝑃 = 𝑎𝑎 − 𝑏𝑏 𝑄𝑄1 + 𝑄𝑄2
and cost functions 𝐶𝐶1 𝑄𝑄1 = 𝑐𝑐1 𝑄𝑄1 and 𝐶𝐶2 𝑄𝑄2 = 𝑐𝑐2 𝑄𝑄2 .


The follower sets output according to the reaction function
𝑄𝑄2 = 𝑟𝑟2 𝑄𝑄1
The leader’s output is
𝑄𝑄1 =
𝑎𝑎 − 𝑐𝑐2 1
− 𝑄𝑄1
=
2𝑏𝑏
2
𝑎𝑎 + 𝑐𝑐2 − 2𝑐𝑐1
2𝑏𝑏
9-
Profit Maximization in Four
Oligopoly Settings
9.2 STACKELBERG OLIGOPOLY

Suppose the inverse demand function for two firms in
a homogeneous-product, Stackelberg oligopoly is given
by
𝑃𝑃 = 50 − 𝑄𝑄1 + 𝑄𝑄2
and their costs are:
𝐶𝐶1 𝑄𝑄1 = 2𝑄𝑄1
𝐶𝐶2 𝑄𝑄2 = 2𝑄𝑄2
Firm 1 is the leader, and firm 2 is the follower.




What is firm 2’s reaction function?
What is firm 1’s output?
What is firm 2’s output?
What is the market price?
9-
Profit Maximization in Four
Oligopoly Settings
9.2 STACKELBERG OLIGOPOLY



1
The follower’s reaction function is: 𝑄𝑄2 = 𝑟𝑟2 𝑄𝑄1 = 24 − 2 𝑄𝑄1 .
The leader’s output is: 𝑄𝑄1 =
50+2−4
2
= 24.
1
The follower’s output is: 𝑄𝑄2 = 24 − 2 24 = 12.
The market price is: 𝑃𝑃 = 50 − 24 + 12 = $14.
=>First-mover advantage: the leader produces more
than the follower

9-
9.2 STACKELBERG OLIGOPOLY
“Quantity-setting” Oligopoly Model
 Cournot
 Collusion
 Stackelberg
“Price-setting” Oligopoly Model
 Bertrand
9.3 BETRAND OLIGOPOLY
1) Characteristics:
• The number of firms in the industry:
Few firms
• The degree of homogeneity of the product:
Identical products
• The ease of entry and exit:
Barriers to entry exist
9.3 BERTRAND OLIGOPOLY
1) Characteristics:
• Firms engage in price competition and react
optimally to prices charged by competitors
• Consumers have perfect information and there
are no transaction cost
9.3 BERTRAND OLIGOPOLY
2) Bertrand Oligopoly: equilibrium
EX4: Consider a Bertrand oligopoly consisting of four firms
that produce an identical product at a marginal cost of $100.
The inverse market demand for this product is P = 500 - 2Q.
a. Determine the equilibrium market price.
b. Determine the equilibrium level of output in the market.
c. Determine the profits of each firm.
CHAPTER 9

EX5: The table below compares and contrasts the
output levels and profits for the Cournot, Stackelberg,
Bertrand and Collusion models. Fill in the table
assuming that there are two firms in the market, the
market demand is given by Q=150-1/10 P, each firm
has a marginal cost of $20, an average variable cost of
20, and fixed costs of zero.
CHAPTER 9
Firm One's Firm Two's Total Market Firm One's Firm Two's
Profit
Output
Output
Output Price
Profit
a. Cournot
b.Stackelberg (leader)
c. Bertrand
d. Collusion
(follower)
CHAPTER 9
Firm One's Firm Two's Total Market Firm One's Firm Two's
Profit
Output
Output
Output Price
Profit
a. Cournot
49.33
b.Stackelberg (leader)
74
c. Bertrand
74
d. Collusion
37
49.33
98.66
513.33 $24,338
$24,338
(follower)
37
111
390
$27,380
$13,690
74
148
20
$0
$0
37
74
760
$27,380
$27,380
SUMMARY OF FOUR MARKET STRUC
# of firms
Perfect
Competition
Monopolistic
Competition
Oligopoly
Monopoly
Very many
many
few
One
idential or
differentiated
unique
(no close
substitutes)
Product
identical
differentiated (but highly
substituable)
Entry/Exit
Profit max
rule
Easy
Easy
difficult
Nearly impossible
MR=MC(or P=MC)
MR=MC
MR=MC
MR=MC
π<, > or =0
π<, >, or =0
π<, > or =0
π<, > or =0
π=0
π=0
π> or =0
π> or =0
Short run
profit
Long run
profit
Price(P)
Quantity(Q)
Ppc<Pmc<Po<Pm
Qpc>Qmc>Qo>Qm