### Chapter 9

```Managerial Economics &
Chapter 9
Basic Oligopoly Models
Oligopoly
• Relatively few firms, usually less than 10.
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Duopoly - two firms
Triopoly - three firms
• The products firms offer can be either
differentiated or homogeneous.
• Firms behave strategically
• Barriers to entry exist
• “Let’s Play Oligopoly” WSJ, 1999
Role of Strategic Interaction
• What you do affects the
• What your rival does affects
• Strategic interdependence:
You aren’t in complete
Cournot Model
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A few firms produce goods that are either
perfect substitutes (homogeneous) or
imperfect substitutes (differentiated)
Firms set output, as opposed to price.
Each firm decides “how much” given its
beliefs about the output of the other firm.
Barriers to entry exist
Example: Oil production. Each firm produces
output independently and the market price is
determined by the total amount produced.
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
given 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 profitmaximizing amount of firm 1’s product.
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 changing its own
output
Cournot Equilibrium and
Selecting Profit-Maximizing Q
• From inverse demand, find MR for each
firm
• Set MR = MC
• Solve for each firms reactions functions:
Q1(Q2) and Q2(Q1).
• Graph each firm’s reaction function (Q1 on
x-axis and Q2 on y-axis, for example).
Cournot Equilibrium and
Selecting Profit-Maximizing Q
Situation:
United Airlines and American Airlines fly passengers between
Chicago and LA. Assume no other company can enter because they
can’t get landing rights at both airports.
Facts:
Marginal Costs: MCAA = MCUA = \$147/passenger.
Market Demand: Q = 339 – P or P = 339 – Q, where Q = QAA + QUA;
Thus, P = 339 – QAA – QUA
Cournot and Profit-Maximizing Q
To maximize profits, each firm chooses Q at the level in which
MR=MC. You can either find an expression for TR for firm i, then
differentiate with respect to Qi. This will give each firm’s MR
function. Alternatively, you can use the fact that MR has twice the
slope of inverse demand function!
Marginal Costs: MCAA = MCUA = \$147/passenger.
P = 339 – QAA – QUA, so
TRAA = 339QAA – QAA2 – QUAQAA
TRUA = 339QUA – QUA2 – QAAQUA
MRAA = 339 – 2QAA – QUA and MRUA = 339 – QAA – 2QUA
For AA: 339 – 2QAA – QUA = 147 and solve for QAA.
AA Rxn Func: QAA = 96 – 0.5QUA
UA Rxn Func: QUA = 96 – 0.5QAA
Cournot Equilibrium and
Selecting Profit-Maximizing Q
To find Cournot Equilibrium (also a Nash equilibrium),
plug one firm’s rxn function into the other firm’s.
QAA = 96 – 0.5(96 - 0.5QAA), and solving for QAA = 64.
Plug QAA = 64 into UA rxn function. QUA = 64. This outcome is due
to the fact that MC are the same for both firms.
Cournot Equilibrium
QUA
192
rAA
Cournot Equilibrium
96
64
48
rUA
64
96
192
QAA
Collusion
If UA and AA collude, then see monopoly
outcome.
MR = 339 – 2Q.
Set MR=MC, 339 – 2Q = 147, Q = 96, where
UA and AA split the passengers.
P = 339 – Q, P = \$243 versus \$211 if
competing duopoly
Cournot Equilibrium
QUA
Collusion: each produce 48 & each
would earn greater profits, but
likely not sustainable.
192
rAA
Cournot Equilibrium
96
64
48
rUA
64
96
192
QAA
Stackelberg Model
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Few firms
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Barriers to entry
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The leader commits to an output before all other firms
Remaining firms are followers.
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Producing differentiated or homogeneous products
They choose their outputs so as to maximize profits, given
Example: Diamond production. DeBeers is the leader
that sets diamond production, and smaller firms
follow with their own levels of production.
Stackelberg Oligopoly
• Assume AA has first-mover advantage;
thus, picks output before UA.
• UA still has a rxn function, but AA doesn’t.
• AA plugs UA rxn function into its TR
function.
• Find AA MR function (differentiate TR)
• Set MRAA = MCAA, solve for QAA.
• Plug QAA into UA’s rxn function and get
QUA
Stackelberg Oligopoly
• Recall, UA’s rxn function is
QUA = 96 – 0.5QAA
• TRAA = 339QAA – (96 – 0.5QAA)QAA – QAA2
• MRAA = 339 – 96 + QAA – 2QAA
• MRAA = 243 – QAA
• Set MRAA = MC,
243 – QAA = 147
QAA = 96
Therefore QUA = 48 and P = \$195
Stackelberg Summary
• Leader produces more than the Cournot
equilibrium output
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Larger market share, higher profits
• Follower produces less than the Cournot
equilibrium output
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Smaller market share, lower profits
Bertrand Model
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Few firms
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Barriers to entry
Consumers enjoy
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Firms produce identical products at constant marginal
cost.
Each firm independently sets its price in order to
maximize profits
Perfect information
Zero transaction costs
Example: Competitive bidding by identical
contractors. In this case, the contractor
bidding the lowest fee will win the contract.
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
Comparing Oligopoly Models
• Cournot:
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P = \$211
Profits for each firm = \$4096 (= 211*64 – 147*64)
• Stackelberg:
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P = \$195 (lower than Cournot because Q higher)
Profits for AA = \$4608 and \$2304 for UA.
• Collusion
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P = \$243
Profits for each firm = \$4608
• Bertrand:
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P= \$147
Profits for each firm = \$0
Contestable Markets
• Key Assumptions of Contestable Markets
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Consumers respond quickly to price changes
Existing firms cannot respond quickly to entry by lowering
price
Absence of sunk costs
• Key Implications of Contestable Markets
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Threat of entry disciplines firms already in the market
Incumbents have no market power, even if there is only a
single incumbent (a monopolist)
• Note: if existing firms can respond quickly,
then may keep new entrants out.
Contestable Markets
• Video rentals: In 1998, who did you rent
movies from?
• Netflix enters 1999!
• http://digitalenterprise.org/cases/netflix.html
Summary
• Different oligopoly scenarios give rise to
different optimal strategies and different
outcomes
• Your optimal price and output depends on …
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Beliefs about the reactions of rivals
Your choice variable (P or Q) and the nature of the product
market (differentiated or homogeneous products)