Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Managerial Economics &
Business Strategy
Chapter 9
Basic Oligopoly Models
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Overview
I,Conditions for Oligopoly?
II,Role of Strategic Interdependence
III,Profit Maximization in Four Oligopoly
Settings
? Sweezy (Kinked-Demand) Model
? Cournot Model
? Stackelberg Model
? Bertrand Model
IV,Contestable Markets
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Oligopoly
? Relatively few firms,usually less than 10,
? Duopoly - two firms
? Triopoly - three firms
? The products firms offer can be either
differentiated or homogeneous,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Role of Strategic Interaction
? What you do affects
the profits of your
rivals
? What your rival does
affects your profits
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
An Example
? You and another firm sell differentiated
products
? How does the quantity demanded for your
product change when you change your
price?
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
P
Q
D1
P0
Q0
PL
D2 (Rival matches your price change)
PH
(Rival holds its
price constant)
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
P
Q
D1
P0
Q0
D2 (Rival matches your price change)
(Rival holds its
price constant)
D
Demand if Rivals Match Price
Reductions but not Price Increases
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Key Insight
? The effect of a price reduction on the quantity
demanded of your product depends upon whether
your rivals respond by cutting their prices too!
? The effect of a price increase on the quantity
demanded of your product depends upon whether
your rivals respond by raising their prices too!
? Strategic interdependence,You aren’t in complete
control of your own destiny!
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Sweezy (Kinked-Demand)
Model
? Few firms in the market
? Each producing differentiated products,
? Barriers to entry
? Each firm believes rivals will match (or
follow) price reductions,but won’t match
(or follow) price increases,
? Key feature of Sweezy Model
? Price-Rigidity
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Sweezy Marginal Revenue
P
Q
D1
P0
Q0
D2 (Rival matches your price change)
(Rival holds its
price constant)
MR1
MR2
D
MR
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Sweezy Profit-Maximization
P
Q
P0
Q0
D
MR
MC
MCH
MCL
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Cournot Model
? A few firms produce goods that are either
perfect substitutes (homogeneous) or
imperfect substitutes (differentiated)
? Firms set output,as opposed to price
? Each firm believes their rivals will hold
output constant if it changes its own output
(The output of rivals is viewed as given or
“fixed”)
? Barriers to entry exist
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Reaction Functions
? Suppose two firms produce homogeneous products,
? Firm 1’s reaction (or best-response) function is a
schedule summarizing the amount of Q1 firm 1
should produce in order to maximize its profits for
each quantity of Q2 produced by firm 2,
? Since the products are substitutes,an increase in
firm 2’s output leads to a decrease in the profit-
maximizing amount of firm 1’s product,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Graphically
Q2
Q1
(Firm 1’s Reaction Function)
Q1M
Q2*
Q1*
r1
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Cournot Equilibrium
? Situation where each firm produces the
output that maximizes its profits,given the
the output of rival firms
? No firm can gain by unilaterally changing
its own output
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Cournot Equilibrium
Q2*
Q1*
Q2
Q1 Q1
M
r1
r2
Q2M Cournot Equilibrium
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Summary of Cournot
Equilibrium
? The output Q1* maximizes firm 1’s profits,
given that firm 2 produces Q2*
? The output Q2* maximizes firm 2’s profits,
given that firm 1 produces Q1*
? Neither firm has an incentive to change its
output,given the output of the rival
? Beliefs are consistent,
? In equilibrium,each firm,thinks” rivals will stick to
their current output -- and they do!
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Firm 1’s Isoprofit Curve
? The combinations of outputs of the two
firms that yield firm 1 the same level of
profit
Q1 Q1M
r1
A
B C
?1 = $100
?1 = $200
Increasing
Profits for
Firm 1
D
Q2
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Another Look at
Cournot Decisions,
Q2
Q1 Q1M
r1
Q2*
Q1*
Firm 1’s best response to Q2*
? 1 = $100
? 1 = $200
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Another Look at
Cournot Equilibrium
Q2
Q1 Q1M
r1
Q2*
Q1*
Firm 1’s Profits
Firm 2’s Profits
r2
Q2M Cournot Equilibrium
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Stackelberg Model
? Few firms
? Producing differentiated or homogeneous products
? Barriers to entry
? Firm one is the leader
? The leader commits to an output before all other firms
? Remaining firms are followers,
? They choose their outputs so as to maximize profits,
given the leader’s output,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Stackelberg Equilibrium
Q1 Q1M
r1
Q2*
Q1*
r2
Q2
Q1S
Q2S
Follower’s Profits Decline
Leader’s Profits Rise
Stackelberg Equilibrium
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Stackelberg Summary
? Stackelberg model illustrates how
commitment can enhance profits in strategic
environments
? Leader produces more than the Cournot
equilibrium output
? Larger market share,higher profits
? First-mover advantage
? Follower produces less than the Cournot
equilibrium output
? Smaller market share,lower profits
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Bertrand Model
? Few firms
? Firms produce identical products at constant marginal cost,
? Each firm independently sets its price in order to maximize
profits
? Barriers to entry
? Consumers enjoy
? Perfect information
? Zero transaction costs
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Bertrand Equilibrium
? Firms set P1 = P2 = MC! Why?
? Suppose MC < P1 < P2
? Firm 1 earns (P1 - MC) on each unit sold,while
firm 2 earns nothing
? Firm 2 has an incentive to slightly undercut
firm 1’s price to capture the entire market
? Firm 1 then has an incentive to undercut firm
2’s price,This undercutting continues..,
? Equilibrium,Each firm charges P1 = P2 =MC
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Contestable Markets
? Key Assumptions
? Producers have access to same technology
? Consumers respond quickly to price changes
? Existing firms cannot respond quickly to entry by
lowering price
? Absence of sunk costs
? Key Implications
? Threat of entry disciplines firms already in the market
? Incumbents have no market power,even if there is only
a single incumbent (a monopolist)
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Summary
? Different oligopoly scenarios give rise to
different optimal strategies and different
outcomes
? Your optimal price and output depends on …
? Beliefs about the reactions of rivals
? Your choice variable (P or Q) and the nature of the product
market (differentiated or homogeneous products)
? Your ability to commit
Managerial Economics &
Business Strategy
Chapter 9
Basic Oligopoly Models
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Overview
I,Conditions for Oligopoly?
II,Role of Strategic Interdependence
III,Profit Maximization in Four Oligopoly
Settings
? Sweezy (Kinked-Demand) Model
? Cournot Model
? Stackelberg Model
? Bertrand Model
IV,Contestable Markets
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Oligopoly
? Relatively few firms,usually less than 10,
? Duopoly - two firms
? Triopoly - three firms
? The products firms offer can be either
differentiated or homogeneous,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Role of Strategic Interaction
? What you do affects
the profits of your
rivals
? What your rival does
affects your profits
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
An Example
? You and another firm sell differentiated
products
? How does the quantity demanded for your
product change when you change your
price?
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
P
Q
D1
P0
Q0
PL
D2 (Rival matches your price change)
PH
(Rival holds its
price constant)
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
P
Q
D1
P0
Q0
D2 (Rival matches your price change)
(Rival holds its
price constant)
D
Demand if Rivals Match Price
Reductions but not Price Increases
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Key Insight
? The effect of a price reduction on the quantity
demanded of your product depends upon whether
your rivals respond by cutting their prices too!
? The effect of a price increase on the quantity
demanded of your product depends upon whether
your rivals respond by raising their prices too!
? Strategic interdependence,You aren’t in complete
control of your own destiny!
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Sweezy (Kinked-Demand)
Model
? Few firms in the market
? Each producing differentiated products,
? Barriers to entry
? Each firm believes rivals will match (or
follow) price reductions,but won’t match
(or follow) price increases,
? Key feature of Sweezy Model
? Price-Rigidity
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Sweezy Marginal Revenue
P
Q
D1
P0
Q0
D2 (Rival matches your price change)
(Rival holds its
price constant)
MR1
MR2
D
MR
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Sweezy Profit-Maximization
P
Q
P0
Q0
D
MR
MC
MCH
MCL
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Cournot Model
? A few firms produce goods that are either
perfect substitutes (homogeneous) or
imperfect substitutes (differentiated)
? Firms set output,as opposed to price
? Each firm believes their rivals will hold
output constant if it changes its own output
(The output of rivals is viewed as given or
“fixed”)
? Barriers to entry exist
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Reaction Functions
? Suppose two firms produce homogeneous products,
? Firm 1’s reaction (or best-response) function is a
schedule summarizing the amount of Q1 firm 1
should produce in order to maximize its profits for
each quantity of Q2 produced by firm 2,
? Since the products are substitutes,an increase in
firm 2’s output leads to a decrease in the profit-
maximizing amount of firm 1’s product,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Graphically
Q2
Q1
(Firm 1’s Reaction Function)
Q1M
Q2*
Q1*
r1
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Cournot Equilibrium
? Situation where each firm produces the
output that maximizes its profits,given the
the output of rival firms
? No firm can gain by unilaterally changing
its own output
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Cournot Equilibrium
Q2*
Q1*
Q2
Q1 Q1
M
r1
r2
Q2M Cournot Equilibrium
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Summary of Cournot
Equilibrium
? The output Q1* maximizes firm 1’s profits,
given that firm 2 produces Q2*
? The output Q2* maximizes firm 2’s profits,
given that firm 1 produces Q1*
? Neither firm has an incentive to change its
output,given the output of the rival
? Beliefs are consistent,
? In equilibrium,each firm,thinks” rivals will stick to
their current output -- and they do!
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Firm 1’s Isoprofit Curve
? The combinations of outputs of the two
firms that yield firm 1 the same level of
profit
Q1 Q1M
r1
A
B C
?1 = $100
?1 = $200
Increasing
Profits for
Firm 1
D
Q2
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Another Look at
Cournot Decisions,
Q2
Q1 Q1M
r1
Q2*
Q1*
Firm 1’s best response to Q2*
? 1 = $100
? 1 = $200
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Another Look at
Cournot Equilibrium
Q2
Q1 Q1M
r1
Q2*
Q1*
Firm 1’s Profits
Firm 2’s Profits
r2
Q2M Cournot Equilibrium
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Stackelberg Model
? Few firms
? Producing differentiated or homogeneous products
? Barriers to entry
? Firm one is the leader
? The leader commits to an output before all other firms
? Remaining firms are followers,
? They choose their outputs so as to maximize profits,
given the leader’s output,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Stackelberg Equilibrium
Q1 Q1M
r1
Q2*
Q1*
r2
Q2
Q1S
Q2S
Follower’s Profits Decline
Leader’s Profits Rise
Stackelberg Equilibrium
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Stackelberg Summary
? Stackelberg model illustrates how
commitment can enhance profits in strategic
environments
? Leader produces more than the Cournot
equilibrium output
? Larger market share,higher profits
? First-mover advantage
? Follower produces less than the Cournot
equilibrium output
? Smaller market share,lower profits
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Bertrand Model
? Few firms
? Firms produce identical products at constant marginal cost,
? Each firm independently sets its price in order to maximize
profits
? Barriers to entry
? Consumers enjoy
? Perfect information
? Zero transaction costs
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Bertrand Equilibrium
? Firms set P1 = P2 = MC! Why?
? Suppose MC < P1 < P2
? Firm 1 earns (P1 - MC) on each unit sold,while
firm 2 earns nothing
? Firm 2 has an incentive to slightly undercut
firm 1’s price to capture the entire market
? Firm 1 then has an incentive to undercut firm
2’s price,This undercutting continues..,
? Equilibrium,Each firm charges P1 = P2 =MC
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Contestable Markets
? Key Assumptions
? Producers have access to same technology
? Consumers respond quickly to price changes
? Existing firms cannot respond quickly to entry by
lowering price
? Absence of sunk costs
? Key Implications
? Threat of entry disciplines firms already in the market
? Incumbents have no market power,even if there is only
a single incumbent (a monopolist)
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Summary
? Different oligopoly scenarios give rise to
different optimal strategies and different
outcomes
? Your optimal price and output depends on …
? Beliefs about the reactions of rivals
? Your choice variable (P or Q) and the nature of the product
market (differentiated or homogeneous products)
? Your ability to commit
