Olig-1 ©2006 Chas. J. Goetz Oligopoly: Competition Among the Few Return u The Bertrand Oligopoly...
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olig- olig-1 ©2006 Chas. J. Goetz Oligopoly: Competition Among the Few Oligopoly: Competition Among the Few Return The Bertrand Oligopoly Model The Bertrand Oligopoly Model Other Oligopoly Models Other Oligopoly Models The Cournot Oligopoly Model The Cournot Oligopoly Model Assumptions for a “Hypothetical” Assumptions for a “Hypothetical”
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Transcript of Olig-1 ©2006 Chas. J. Goetz Oligopoly: Competition Among the Few Return u The Bertrand Oligopoly...
olig-olig-11©2006 Chas. J. Goetz
Oligopoly: Competition Among the FewOligopoly: Competition Among the Few
Return
The Bertrand Oligopoly ModelThe Bertrand Oligopoly Model
Other Oligopoly ModelsOther Oligopoly Models
The Cournot Oligopoly ModelThe Cournot Oligopoly Model
Assumptions for a “Hypothetical”Assumptions for a “Hypothetical”
olig-2© 2006, Chas. J. Goetz
Hypothetical Facts and Monopoly ResultHypothetical Facts and Monopoly Result
0 100 200 300 400 500 600 700 800 9000
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P = 950 - Q
MC = 50MC = 50
Monopoly Price = 500Monopoly Price = 500
MR
olig-3© 2006, Chas. J. Goetz
Monopolist’s Profit-maximizing OutputMonopolist’s Profit-maximizing Output
445 505 60 224,725 22,250 202,475446 504 58 224,784 22,300 202,484447 503 56 224,841 22,350 202,491448 502 54 224,896 22,400 202,496449 501 52 224,949 22,450 202,499450 500 50 225,000 22,500 202,500451 499 48 225,049 22,550 202,499452 498 46 225,096 22,600 202,496453 497 44 225,141 22,650 202,491454 496 42 225,184 22,700 202,484455 495 40 225,225 22,750 202,475456 494 38 225,264 22,800 202,464457 493 36 225,301 22,850 202,451458 492 34 225,336 22,900 202,436459 491 32 225,369 22,950 202,419460 490 30 225,400 23,000 202,400
Q P MR Rev Tcost Profit
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olig-olig-55©2006 Chas. J. Goetz
The Cournot Oligopoly ModelThe Cournot Oligopoly Model
Who (or What) Is “Cournot”?Who (or What) Is “Cournot”?
Premises of the Cournot ModelPremises of the Cournot Model
Mathematical Cournot ModelMathematical Cournot Model
A Topographical Cournot ModelA Topographical Cournot Model
Deriving the Reaction CurvesDeriving the Reaction Curves
The “Solution” of the ModelThe “Solution” of the Model
Efficiency Properties: The Well RevisitedEfficiency Properties: The Well Revisited
olig-6© 2006, Chas. J. Goetz
Hypothetical Facts and Monopoly ResultHypothetical Facts and Monopoly Result
Return0 100 200 300 400 500 600 700 800 900
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P = 950 - Q
MC = 50MC = 50
Monopoly Price = 500Monopoly Price = 500
MR
olig-7© 2006, Chas. J. Goetz
olig-8© 2006, Chas. J. Goetz
Regardez le Croix
d’Honneur
Recherches sur les Principes Mathématiques
de la Théorie des Richesses
(1838)
Antoine Augustin CournotAntoine Augustin Cournot (1801-1877) (1801-1877)
olig-9© 2006, Chas. J. Goetz
Premises of Cournot Oligopoly ModelPremises of Cournot Oligopoly Model
A few firms produce goods that are either perfect substitutes (homogeneous) or imperfect substitutes (differentiated).
Firms set output, as opposed to price. The market sets price where demand equals the amount supplied.
Each firm believes its rivals will hold output constant if it changes its own output.
olig-10© 2006, Chas. J. Goetz
Mathematical Approach Mathematical Approach • p = a-bQ• c(q) = cq , constant marginal cost
• Firm i’s profit : (a-b(q-i +qi))qi - cqi
• FOC: a-bq-i -2bqi - c = 0
• qi = (a-bq-i - c)/2b = R(q-i), i’s reaction• Cournot Equilibrium: qi = R(q-i) for all i.
• n equations in n unknowns.
• But all firms are alike, use symmetry: qi=q
• Reaction: q = (a-b(n-1)q - c)/2b • q = (a -c)/b(n+1) • Q = (a-c)/b n/(n+1) (a-c)/b as n . Competitive outcome!
olig-11© 2006, Chas. J. Goetz
Mathematical Approach Mathematical Approach PreferrersPreferrers
olig-13© 2006, Chas. J. Goetz
Profits of Firm #1 – 3D ViewProfits of Firm #1 – 3D View
olig-14© 2006, Chas. J. Goetz
Profits of Firm #1 – 3D View, FilledProfits of Firm #1 – 3D View, Filled
Bird’s Eye View
olig-15© 2006, Chas. J. Goetz
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Profits of Firm #1 – Birds-eye View, FilledProfits of Firm #1 – Birds-eye View, Filled
Unfilled Topographic
olig-16© 2006, Chas. J. Goetz
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Profits of Firm #1 – Birds-eye View, UnfilledProfits of Firm #1 – Birds-eye View, Unfilled
Firm #2
olig-17© 2006, Chas. J. Goetz
Profits of Firm #2 – 3D ViewProfits of Firm #2 – 3D View
Bird’s Eye View3D Firm #1
olig-18© 2006, Chas. J. Goetz
Profits of Firm #2 – Birds-eye ViewProfits of Firm #2 – Birds-eye View
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Unfilled Topographic
olig-19© 2006, Chas. J. Goetz
Profits of Firm #2 – Birds-eye View, UnfilledProfits of Firm #2 – Birds-eye View, Unfilled
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olig-20© 2006, Chas. J. Goetz
Reaction CurvesReaction Curves
Economists often use “Reaction Curves.” Where did we see this before?
In the Cournot case, the reaction curve for one firm plots its output decisions against various outputs for the other firm(s).
olig-21© 2006, Chas. J. Goetz
Profits of Firm #2 – Birds-eye View, UnfilledProfits of Firm #2 – Birds-eye View, Unfilled
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olig-22© 2006, Chas. J. Goetz
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Deriving Firm #2’s Reaction CurveDeriving Firm #2’s Reaction Curve
olig-23© 2006, Chas. J. Goetz
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Deriving Firm #1’s Reaction CurveDeriving Firm #1’s Reaction Curve
olig-24© 2006, Chas. J. Goetz
Summary: Reaction FunctionsSummary: Reaction Functions
Firm 1’s reaction (or best-response) function indicates the amount of Q1 that firm 1 should produce in order to maximize its profits for each possible quantity of Q2 produced by firm 2.
Since the products of the two firms are substitutes, an increase in firm 2’s output leads to a decrease in the profit-maximizing amount of firm 1’s product.
olig-25© 2006, Chas. J. Goetz
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Intersection of Reaction CurvesIntersection of Reaction Curves
olig-26© 2006, Chas. J. Goetz
olig-27© 2006, Chas. J. Goetz
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Adjustments Toward Equilibrium When Firm Two EntersAdjustments Toward Equilibrium When Firm Two Enters
Firm #1’s Best-Reaction Curve
Firm #1’s Best-Reaction Curve
Firm #2’s B
est-Reaction C
urve
Firm #2’s B
est-Reaction C
urve
Redo
olig-28© 2006, Chas. J. Goetz
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Stable Equilibrium, Expectations ConfirmedStable Equilibrium, Expectations Confirmed
Summary
olig-29© 2006, Chas. J. Goetz
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
olig-30© 2006, Chas. J. Goetz
QuestionsQuestions
Is the Cournot Equilibrium also a Nash Equilibrium?
Is the Cournot Equilibrium an efficient result for the firms?
Nash Equilibrium
olig-31© 2006, Chas. J. Goetz
Nash EquilibriumNash Equilibrium
this result involves output combinations at which the profits of each firm are maximized, given its expectations about output from the other firm(s);
and the outputs expected by all firms are indeed being produced by the other firm(s). That is, the expectations are validated by experience.
The intersection of the reaction curves corresponds to a Nash equilibrium because
olig-32© 2006, Chas. J. Goetz
But . . .But . . .
A Nash Equilibrium is not A Nash Equilibrium is not always an “efficient” result always an “efficient” result
for the players.for the players.
olig-33© 2006, Chas. J. Goetz
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Area to be Area to be “Zoomed”“Zoomed”
olig-34© 2006, Chas. J. Goetz
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Zoomed VersionZoomed Version
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Q1
Simplified
olig-35© 2006, Chas. J. Goetz
78.878.8 90.090.0
101.2101.2 112.4112.4
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78.8 90.0 101.2 112.4
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Simplified Diagram Showing Cournot EquilibriumSimplified Diagram Showing Cournot Equilibrium
Analogue
olig-36© 2006, Chas. J. Goetz
78.878.8 90.090.0
101.2101.2 112.4112.4
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101.2101.2 112.4
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Well Problem
Similar to the “Well Problem”Similar to the “Well Problem”
olig-37© 2006, Chas. J. Goetz
78.8 90.0
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112.4
QQ11 +Q+Q
22 =450=450
Cournot vs. Collusive ResultCournot vs. Collusive Result
Q2
Q1
Equilibrium?
olig-38© 2006, Chas. J. Goetz
78.8 90.0
101.2 112.4
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101.2101.2 112.4
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QQ11 +Q+Q
22 =450=450
Collusive Result Unstable?Collusive Result Unstable?
Q2
Q1
Monopoly Result
olig-40© 2006, Chas. J. Goetz
Nash EquilibriumNash Equilibrium
A Nash equilibrium is a set of strategies, one for each player, such that no player has an incentive to unilaterally unilaterally change her action. Players are in equilibrium if a change in strategies by any one of them would lead that player to earn less than if she remained with her current strategy.
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