Intermediate Microeconomic Analysis

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Intermediate Microeconomic Analysis (Fall
2009) Lecture 10 Oligopoly Models
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Oligopoly A market structure with a few,
relatively large firms. Between 2 and 10
firms There is Market Power No longer Price
Takers.
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Managing in Oligopolies The manager of any
firm must consider the impact of that firms
decisions on the decisions of other
firms The decisions of other firms will impact
the managers firm
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Basic Models of Oligopolies Sweezy raises
price, other firms will not raise lowers
price, other firms will lower Cournot
change own output, other firms will not
react. Stackelberg one firm is a market
leader and can act first, other firms
will react. Bertrand price competition to
get consumers, who have perfect information
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Sweezy Oligopoly Each firm considers two
possible demand curves. D1 other firm
changes its prices D2 other firm does not
change its prices
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D1 Relatively Inelastic Other Firm Matches
Price D2 Relatively Elastic Other Firm Does Not
Match Price
P
Start Here
D2
MR2
D1
Q
MR1
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Demand is more ELASTIC if the other firm does
not match price Firm believes that if it lowers
its price, the other firm will lower its price
too The firm believes that if it raises its
price, the other firm will not raise its price
Raise price face a relatively Elastic
Demand. Lower price faces a relatively
Inelastic Demand.
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If Firm Lowers its Price Other Firms
Match Follow D1 IF Firm Raises its Price Other
Firms Do Not Match Follow D2
P
Follow MR with the Associated Demand Curve
D2
Dsw
MR2
D1
Q
Q
MR1
MRsw
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Oligopolists want to maximize profits.
where MRMC. A Sweezy Oligopolist has a
wide range of MCMR spots where Quantity will
not increase will not always increase output
in response to a lower of marginal
cost. keeps society from getting the benefits
of decreased MC
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MC1
P
MC2
MC3
MC4
Dsw
Q
MRsw
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Cournot Oligopoly Firm doesnt believe the other
firms pay much attention to it. Decides how
much it should produce itself in order to
maximize profits. Profit level of one firm will
depend on the quantity it produces, and the
quantity the other firm produces. The firm would
like to produce most of the industry
outputhigher profits.
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Reaction Function A function that defines
the profit-maximizing level of output for a
firm for all possible output levels of the
other firm. Reaction Function for Firm 1
Q1r1(Q2) Reaction Function for Firm 1
Q2r2(Q1)
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Q2
Firm 1 Produces Less Firm 2 Produces Some Firm 1
Makes Less Profits Than Before
Firm Makes More Profits in This Direction
Firm 1 a Monopoly
r1
Q1
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Reaction Function A function that defines
the profit-maximizing level of output for a
firm for all possible output levels of the
other firm. Reaction Function for Firm 1
Q1r1(Q2) Reaction Function for Firm 1
Q2r2(Q1) Some points about Reaction
Functions If the other firm produces
nothing, the given firm is a
Monopolist. If the other firm starts to
produce, the given firm produces less. The
two products are substitutes.
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Iso-Profit Curve A function that defines
the combinations of outputs produced by all
firms that yield a given firm the same level of
profits.
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Q2
Iso-Profit Curve
Reaches High Point as it crosses the r1
If Firm 1 Produces More, Firm 2 Must Produce
Less For Firm1 to make the Same Profits
If Firm 1 Produces Less, It will Make Less
Profits Unless Firm 2 Also Cuts Back Production
r1
Q1
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Q2
Reaction Function and Iso-Profit Curve for Firm 2
Reaches High Point (to right) as it crosses the
r2
r2
Q1
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Iso-Profit Curve A function that defines
the combinations of outputs produced by all
firms that yield a given firm the same level of
profits. Some Points about Iso-profit
curves Every point on an iso-profit curve
yields the same profits. Iso-profit curves
closer to a firms monopoly output level will
give that firm Larger profits. Iso-profit
curves will reach their peaks where they
intersect the reaction functions. Iso-profit
curves never intersect each other.
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Cournot Equlibrium A situation in which
neither firm has an incentive to change its
output given the other firms output.
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• Assume Firm 1 Produces at Green Dot, Q11
• Firm 2 would, want to Produce at Q21
• Knowing this Firm 1 Moves to Q12
• And so on
• Until you reach Equilibrium

Q2
Equilibrium
Q21
r2
Q1
r1
Q11
Q12
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Cournot Equlibrium A situation in which
neither firm has an incentive to change its
output given the other firms output. A firm
experiencing a reduction in Marginal cost will
end up providing more to the market.
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Q2
If MC1 Decreases, Firm 1s Reaction Function Will
Shift Right Changes Equilibrium, Firm 1 will
Produce More
r2
Q1
r1
r1
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A lens (of the Iso-Profit Curves) Shows
possible production points where both firms
can increase their profits (by firms
restricting output).
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Q2
At Equlibrium Look at Firm 1s Iso-Profit
Curve, Look at Firm 2s Iso-Profit Curve Both
Firms Better Off by moving into Lens
r2
Monopoly Profits Split By the Firms
Potential for Collusion
Q1
r1
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This lens is possible production points where
both firms can increase their profits (by
firms restricting output). Collusion Each
firm has the incentive to cheat and move to the
reaction function. But this is only a short
run gain
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Reaction Function Example Assume 2 Firms in An
Industry. Face Demand p280-2(Q1Q2) Costs
are C1 3Q1 C2 2Q2
1. Find the Marginal Function Revenue for Each
Firm TR1 P Q1 280-2(Q1Q2)Q1 MR1 280 -4Q1
-2Q2 TR2 P Q2 280-2(Q1Q2)Q2 MR2 280 -4Q2
-2Q1
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Reaction Function Example Assume 2 Firms in An
Industry. Face Demand p280-2(Q1Q2) Costs
are C1 3Q1 C2 2Q2
2. Find the Reaction Function for Each Firm You
know Profit Maximization Occurs with MRMC,
so MR1MC1 280 -4Q1 -2Q2 3 Solve for
Q1 r1 Q1 69.25 -.5Q2 MR2 MC2 280 -4Q2 -2Q1
2 Solve for Q2 r2 Q2 69.5 - .5Q1
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Reaction Function Example Assume 2 Firms in An
Industry. Face Demand p280-2(Q1Q2) Costs
are C1 3Q1 C2 2Q2
3. Find Out the Output Each Firm will Produce in
Equilibrium Substitute Q2 into Q1 Q1 69.25
-.5 (69.5 - .5Q1) So Q1 46 And Q2 69.5 -
.5(46) 46.5
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Stackelberg Oligopoly An industry leader and a
few followers. Leader first mover The
leader will NOT decide to produce along the
reaction function Followers maximize profits
after the leader moves.
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Q2
The Leader, Firm 1, will produce where It can
Maximize Profits, Knowing Firm 2 will Produce on
its own Iso-Profit Curve Will chose
curve Just Tangent to the r2
Q2
r2
r1
Q1
Q1
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Typical Stackelberg Sequence Leader Maximizes
Profits knowing followers stay along their own
reaction functions. This leader will consider
its own iso-profit curves. Maximization occurs
at the highest iso-profit curve. Best Point
where one iso-profit curve is
just-tangent to the followers reaction
function. Follower takes the Leaders
production as given and maximizes profits.
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Results Leader more output and more
profits than in Cournot Follower less
output and less profits than in Cournot
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Bertrand Oligopoly Very Similar Products and
Firms Engage in Price Competition Consumers
have Perfect Information They will always
buy from the firm with the lowest
price. Leads to a spiral of lower
prices. Same result as Perfect Competition
(P1P2MC) and P 0.