11 | OligopolyCournot model, Stackelberg model, Isoprofit curves
ECO217 Microeconomics I
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OligopolyOligopoly – market organization in which are few sellers of a commodity
Seller side is few big participants – oligopolists
Demand side – many participants – none of them can influence price
Oligopolists can compete with homogenous good – like steel, aluminum, cement or with heterogeneous good – automobiles, tires, television sets etc.
Supply side participants has full information about number of competitors and their sales. Information about other competitors price can be full or partial
Oligopoly usually generate high profit and has strategies to deter other from coming into market
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OligopolyActions of each seller will affect other sellers
Reactions of other firms are unknown
Since cannot construct one definite demand curve, oligopoly have indeterminate solutions
Each behavioral assumption will have different solution
No general theory of oligopoly exist
Duopoly – market organization where are two firms selling product
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In Cournot model each firmassumes that other firm willkeep output constantCournot model
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Cournot model
Firm 1 and firm 2 choose quantity simultaneouslyand after both firms have chosen their outputs,the price of good on the market and the profits ofboth firms are determined
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Reaction functionReaction function – functionthat specifies a firms optimalchoice for some variable such asoutput, given choices of itscompetitors
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Reaction function; Quantity CompetitionAssume that firms compete by choosing output levels.
If firm 1 produces y1 units and firm 2 produces y2 units, total quantity supplied is y1 + y2.
The market price will be p(y1+ y2) that is depends from both outputs - y1 and y2
Suppose firm 1 takes firm 2’s output level choice y2 as given. Then firm 1 sees its profit function as
Given y2, what output level y1 maximizes firm 1’s profit?
1 1 2 1 2 1 1 1( ; ) ( ) ( ).y y p y y y c y
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Quantity Competition; An Example
( ; ) ( ) .y y y y y y1 2 1 2 1 1260
For given y2, firm 1’s profit function is
Given y2, firm 1’s profit-maximizing output level solves
y
y y y1
1 2 160 2 2 0 .
Firm 1’s best response to y2 is
y R y y1 1 2 215 14
( ) .
Market inverse demand function is = 60 −the firms’ total cost functions are= = 15 +
y2
y1
60
15
Firm 1’s “reaction curve”
y R y y1 1 2 215 14
( ) .
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Quantity Competition; An Example
( ; ) ( ) .y y y y y y y2 1 1 2 2 2 2260 15
Similarly, given y1, firm 2’s profit function is
So, given y1, firm 2’s profit-maximizing output level solves
y
y y y2
1 2 260 2 15 2 0 .
Firm 2’s best response to y1 is
y R y y2 2 1
1454
( ) .
y2
y1
Firm 2’s “reaction curve”
445)( 1
122yyRy
45/4
45
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Quantity Competition; An Example
An equilibrium is when each firm’s output level is a best response to the other firm’s output level, for then neither wants to deviate from its output level.
A pair of output levels (y1*,y2*) is a Cournot-Nash equilibrium if
y1* = R1(y2*) and y2* = R2(y1*)
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Quantity Competition; An Exampley R y y1 1 2 215 1
4* * *( ) y R y y
2 2 1145
4* *
*( ) . and
y y y11
115 14
454
13**
*
y245 13
48* .
The Cournot-Nash equilibrium is
( , ) ( , ).* *y y1 2 13 8
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Quantity Competition; An Exampley2
y1
Firm 2’s “reaction curve”
48
60
Firm 1’s “reaction curve”
y R y y1 1 2 215 14
( ) .
8
13
Cournot-Nash equilibrium
y y1 2 13 8* *, , .
y R y y2 2 1
1454
( ) .
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Iso-Profit Curves
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y2
y1
Iso-Profit Curves for Firm 1
With y1 fixed, firm 1’s profitincreases as y2 decreases.
Increasing profitfor firm 1. For firm 1, an iso-profit curve contains
all the output pairs (y1,y2) giving firm 1 the same profit level P1.
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y2
y1
Iso-Profit Curves for Firm 1
If firm 2 chooses y2 = y2’, where along the line y2 = y2’ is the output level that maximizes firm 1’s profit?
The point attaining the highest iso-profit curve for firm 1. y1’ is firm 1’s best response to y2 = y2’.
y2’
y1’
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y2
y1
y2’
y2”
R1(y2”) R1(y2’)
Firm 1’s reaction curve passes through the “tops” of firm 1’s iso-profit curves.
Iso-Profit Curves for Firm 1
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y2
y1
Iso-Profit Curves for Firm 2
Increasing profitfor firm 2.
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y2
y1
Iso-Profit Curves for Firm 2
Firm 2’s reaction curve passes through the “tops” of firm 2’s iso-profit curves.
y2 = R2(y1)
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Collusiony2
y1y1*
y2*
Are there other output level pairs (y1,y2) that give higher profits to both firms?
(y1*,y2*) is the Cournot-Nash equilibrium.
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Collusiony2
y1y1*
y2*
y2m
y1m
(y1m,y2
m) denotes the output levelsthat maximize the cartel’s total profit.
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Stackelberg – sequentialcompetition in quantitieswhere on firm acts as aquantity leader, choosingquantity first, with other firmacting as follower
Stackelberg model
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Stackelberg model
y2
y1y1*
y2*
(y1*,y2*) is the Cournot-Nashequilibrium.
Higher 2
Higher 1
Follower’sreaction curve
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Stackelberg modely2
y1y1*
y2*
(y1*,y2*) is the Cournot-Nash equilibrium. (y1
S,y2S) is the Stackelberg equilibrium.
y1S
Follower’sreaction curve
y2S
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A model of oligopolisticcompetition where firmscompete by setting pricesBertrand model
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Bertrand model
One firm can just slightly lower its price and sell to all the buyers (capture all market), thereby increasing its profit. Firm with higher price will sell nothing
The only common price which prevents undercutting is c. This is the only Nash equilibrium
Bertrand paradox
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Sweezy model
If one firm increases price others will not try tomatch it (elastic demand curve above price $20).
If once firm lowers price others will match price cut
Strong incentive for oligopolists not to changeprice
Engagement in gaining greater market share onbasis of quality, advertisement etc.
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Cartel model
Cartel – formal organization of producers withinindustry that determines policies for all members
Cartel’s MC is horizontal sum of all members MC
Cartel maximizes profit similarly to monopoly.
Profit is distributed between members accordingto their agreement.
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Oligopoly models summary
Competition in Productdifferentiation
Acting Assumptions
Cournot quantities homogeneous simultaneous Hard to adjust capacity, capacity competition
Stackelberg quantities homogeneous sequence Leader sets quantity first, others follow
Bertrand prices homogeneous simultaneous Can adjust capacity easy, can capture all market
Sweezy prices differentiated simultaneous Rivals will not rise prices in response to price increase