Sar Sopheap
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Transcript of Sar Sopheap
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Sar Sopheap Cambodia Mekong University
Chapter 9Basic Oligopoly Models
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Overview
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I. 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 Environment
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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 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 Example
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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
D1 (Rival holds itsprice constant)
P0
PL
D2 (Rival matches your price change)
PH
Q0 QL2 QL1QH1 QH2
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P
Q
D1
P0
Q0
D2 (Rival matches your price change)
(Rival holds itsprice constant)
D
Demand if Rivals Match Price Reductions but not Price Increases
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Key Insight
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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) Model Environment
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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 Marginal Revenue
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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 Decision
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P
Q
P0
Q0
DS: Sweezy DemandMRS
MC1MC2
MC3
D2 (Rival matches your price change)
D1 (Rival holds price constant)
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Sweezy Oligopoly Summary
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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 Environment
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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 Duopoly
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
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21 QQbaP
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Best-Response Function
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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 Cournot 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)
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211 21
2Q
bcaQrQ
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122 21
2Q
bcaQrQ
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Graph of Firm 1’s Best-Response Function
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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 Equilibrium
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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 Equilibrium
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Q2*
Q1*
Q2
Q1
Q1M
r1
r2
Q2M
Cournot Equilibrium
(a-c1)/b
(a-c2)/b
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Summary of Cournot Equilibrium
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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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Firm 1’s Isoprofit Curve The combinations of outputs of the two firms
that yield firm 1 the same level of profit
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Q1Q1
M
r1
1 = $100
1 = $200
Increasing Profits for
Firm 1D
Q2
A
BC
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Another Look at Cournot Decisions
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Q2
Q1Q1
M
r1
Q2*
Q1*
Firm 1’s best response to Q2*
1 = $100
1 = $200
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Another Look at Cournot Equilibrium
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Q2
Q1Q1
M
r1
Q2*
Q1*
Firm 1’s Profits
Firm 2’s Profits
r2
Q2M Cournot Equilibrium
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Impact of Rising Costs on the Cournot Equilibrium
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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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Collusion Incentives in Cournot Oligopoly
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Q2
Q1
r1
Q2M
Q1M
r2
Cournot2
Cournot1
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Stackelberg Model Environment
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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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Stackelberg Equilibrium
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Q1Q1
M
r1
Q2C
Q1C
r2
Q2
Q1S
Q2S
Follower’s Profits Decline
Stackelberg Equilibrium
πLS
π1C
πFS
π2C
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The Algebra of the Stackelberg Model 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 Summary
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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 Environment
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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 Equilibrium
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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 Markets
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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).
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Conclusion
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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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