BUS 525: Managerial Economics Lecture 12 Pricing Strategies for Firms with Market Power
BUS 525: Managerial Economics Lecture 9 Basic Oligopoly Models
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Transcript of BUS 525: Managerial Economics Lecture 9 Basic Oligopoly Models
BUS 525: Managerial Economics
Lecture 9
Basic Oligopoly Models
OverviewOverviewI. Conditions for Oligopoly?II. Role of Strategic InterdependenceIII. Profit Maximization in Four Oligopoly Settings
– Sweezy (Kinked-Demand) Model– Cournot Model– Stackelberg Model – Bertrand Model
IV. Contestable Markets
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Oligopoly EnvironmentOligopoly EnvironmentA market structure there are only a fewFirms, each of which is large relative the totalindustry• Relatively few firms, usually less than 10.
– Duopoly - two firms– Triopoly - three firms
• The products firms offer can be either differentiated or homogeneous.
• Firms’ decisions impact one another.• Many different strategic variables are modeled:
– No single oligopoly model.
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Role of Strategic InteractionRole of Strategic Interaction• Your actions affect the profits of
your rivals.• Your rivals’ actions affect your
profits.• How will rivals respond to your
actions?
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An ExampleAn Example• You and another firm sell
differentiated products.• How does the quantity demanded for
your product change when you change your price?
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P
Q
D2 (Rival holds itsprice constant)
P0
PL
D1 (Rival matches your price change)
PH
Q0 QL2 QL1QH1 QH2
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B
P
Q
D1
P0
Q0
D2 (Rival matches your price change)
(Rival holds itsprice constant)
D2
Demand if Rivals Match Price Reductions but not Price Increases
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Note that demand is more inelastic when rivals match a price change than when they do notReason: For a given price reduction, a firm will sell more if rivals do not cut their prices D2 than it will if they lower their prices D1
Key InsightKey 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!
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Sweezy (Kinked-Demand) Sweezy (Kinked-Demand) Model EnvironmentModel Environment
• Few firms in the market serving many consumers.
• Firms produce 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.
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Sweezy Demand and Sweezy Demand and Marginal RevenueMarginal Revenue
P
Q
P0
Q0
D1(Rival holds itsprice constant)
MR1
D2 (Rival matches your price change)
MR2
DS: Sweezy Demand
MRS: Sweezy MR
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Sweezy Profit-Maximizing Sweezy Profit-Maximizing DecisionDecision
P
Q
P0
Q0
DS: Sweezy DemandMRS
MC1MC2
MC3
D2 (Rival matches your price change)
D1 (Rival holds price constant)
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A
C
E
Sweezy Oligopoly SummarySweezy Oligopoly Summary
• Firms believe rivals match price cuts, but not price increases.
• Firms operating in a Sweezy oligopoly maximize profit by producing where
MRS = MC.– The kinked-shaped marginal revenue curve
implies that there exists a range over which changes in MC will not impact the profit-maximizing level of output.
– Therefore, the firm may have no incentive to change price provided that marginal cost remains in a given range.
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Cournot Model Cournot Model EnvironmentEnvironment
• A few firms produce goods that are either perfect substitutes (homogeneous) or imperfect substitutes (differentiated).
• Firms’ control variable is output in contrast 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.
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Inverse Demand in a Cournot Inverse Demand in a Cournot DuopolyDuopoly
• Market demand in a homogeneous-product Cournot duopoly is
• Thus, each firm’s marginal revenue depends on the output produced by the other firm. More formally,
212 2bQbQaMR
121 2bQbQaMR
21 QQbaP
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Best-Response FunctionBest-Response Function• Since a firm’s marginal revenue in a
homogeneous Cournot oligopoly depends on both its output and its rivals, each firm needs a way to “respond” to rival’s output decisions.
• Firm 1’s best-response (or reaction) 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.
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Best-Response Function for a Best-Response Function for a Cournot DuopolyCournot Duopoly
• To find a firm’s best-response function, equate its marginal revenue to marginal cost and solve for its output as a function of its rival’s output.
• Firm 1’s best-response function is (c1 is firm 1’s MC)
• Firm 2’s best-response function is (c2 is firm 2’s MC)
21
211 21
2Q
bcaQrQ
12
122 21
2Q
bcaQrQ
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Graph of Firm 1’s Best-Graph of Firm 1’s Best-Response FunctionResponse Function
Q2
Q1
(Firm 1’s Reaction Function)
Q1M
Q2
Q1
r1
(a-c1)/b Q1 = r1(Q2) = (a-c1)/2b - 0.5Q2
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Cournot EquilibriumCournot 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 to improve its profit.– A point where the two firm’s best-
response functions intersect.
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Graph of Cournot EquilibriumGraph of Cournot Equilibrium
Q2*
Q1*
Q2
Q1
Q1M
r1
r2
Q2M
Cournot Equilibrium
(a-c1)/b
(a-c2)/b
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AB
CE
Summary of Cournot Summary of Cournot EquilibriumEquilibrium
• 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!
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The Isoprofit CurveThe Isoprofit Curve
Firm 1’s Isoprofit CurveFirm 1’s Isoprofit Curve• The combinations of outputs of the two firms
that yield firm 1 the same level of profit
Q1Q1M
r1
0 = $100
1 = $200
Increasing Profits for
Firm 1D
Q2
A
B C
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2 = $300E
Another Look at Cournot Another Look at Cournot DecisionsDecisions
Q2
Q1Q1M
r1
Q2*
Q1*
Firm 1’s best response to Q2*
1 = $200 2 = $300
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0 = $100A B CD
QA QB QD
Another Look at Cournot Another Look at Cournot EquilibriumEquilibrium
Q2
Q1Q1M
r1
Q2*
Q1*
Firm 1’s Profits
Firm 2’s Profits
r2
Q2M Cournot Equilibrium
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Collusion Incentives in Collusion Incentives in Cournot OligopolyCournot Oligopoly
Q2
Q1
r1
Q2M
Q1M
r2
Cournot2
Cournot1
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Impact of Rising Costs on the Impact of Rising Costs on the Cournot EquilibriumCournot Equilibrium
Q2
Q1
r1**
r2
r1*
Q1*
Q2*
Q2**
Q1**
Cournot equilibrium prior to firm 1’s marginal cost increase
Cournot equilibrium after firm 1’s marginal cost increase
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Price Leadership ModelPrice Leadership Model• In a price leadership model, one dominant firm takes
reactions of all other firms into account in its output and pricing decisions
• Competitive fringe: A group of firm that act as a price taker in a market dominated by a price leader
• A dominant firms demand curve is the residual demand curve that shows what it can sell after accounting for sales by other firms
• Other firms accept whatever price is set by the dominant firm and produce an output where P=MC
• Note that P>MC for dominant firm, total industry output is less than competitive output
Dominant Firm Dominant Firm ModelModel
Fig : Equilibrium in the Dominant Firm Model
Stackelberg Model Stackelberg Model EnvironmentEnvironment
• Few firms serving many consumers.• Firms produce 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.
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The Algebra of the Stackelberg The Algebra of the Stackelberg ModelModel
• Since the follower reacts to the leader’s output, the follower’s output is determined by its reaction function
• The Stackelberg leader uses this reaction function to determine its profit maximizing output level, which simplifies to
12
122 5.02
QbcaQrQ
bccaQ
22 12
1
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Stackelberg SummaryStackelberg 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.
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Bertrand Model Bertrand Model EnvironmentEnvironment
• Few firms that sell to many consumers.• Firms produce identical products at
constant marginal cost.• Each firm independently sets its price in
order to maximize profits (price is each firms’ control variable).
• Barriers to entry exist.• Consumers enjoy
– Perfect information. – Zero transaction costs.
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Bertrand EquilibriumBertrand 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.
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Contestable MarketsContestable Markets• Key Assumptions
– Producers have access to same technology.– Consumers respond quickly to price changes.– Existing firms cannot respond quickly to deter 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).
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ConclusionConclusion• 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 credibly commit prior to your rivals.
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..Basic modelBasic model
Q2 - 120Q P.Q have we
120
120
costs, zero Assuming
caseMonopoly
QP
PQ
3600 PQ
60 P
thereforeand,
60 Qor
0 2Q - 120 dQd
0 /dQdπ settingby found bemay profits Maximum
Duopoly case
0 2Q - Q - dQdQQ - 120
dQdπ
0 Q - dQdQQ - 2Q - 120
dQdπ
2Q - QQ - 120Q P.Q π
QQ2 Q 120Q P.Q π
Q (Q - 120 P
212
11
2
2
21
211
1
1
221222
211111
2121 Q Q Q , )
2Q - 120 Q
2Q - 120 Q
0 2Q - Q - 120 dQd
0 Q - 2Q - 120 dQdπ
0 dQdQ
dQdQ
SolutionCournot
12
21
21
2
2
211
1
2
1
1
2
]profit)oly 3600(monop3200profit [Cournot 1600 PQ 1600 PQ
40 80 - 120 )Q (Q - 120 P
402Q - 120 Q
40 Q
Q 120 Q4
]Q of valuengsubstituti[by 2)/2Q - (120- 120
2Q- 120 Q
22
11
21
12
1
11
212
1
process in the erodedseriously been hasprofit s2' Firm reaction. s2' firm of knowledge its usingby profit its increase toablebeen has 1 Firm 900 PQ
1800 PQ 30 90 - 120 )Q (Q - 120 P
30 Q60 Q
32 - 80 Q
0 Q Q21 2Q - 120
dd
21 -
dQdQ
suppose function,reaction rivals its discovered has firm Onesolution gStackelber
22
11
21
2
1
21
2111
1
1
2
Q
Q
...
2Q - 120 Q: R 2
11
120
60
40
060 120
40
Equilibrium
Q = 120 - P
120
60
40
60 80 120
Price
Q per period
0
60
60Q
0 120
120
P
P
Q
Zero cost monopoly
Cournot solution Stackelberg solutionMR
Q = 120 - P
2Q - 120 QR 1
2 2 :
Monopoly
Cournot
Stackelberg