Oligopoly (eBook)

Preface 6
Contents 8
1 Introduction 12
Early History of Mathematical Economics 12
Cournot Oligopoly 13
Equilibrium and Other Regular Orbits 13
Multiplicity of Attractors 14
Strategy Types 16
Stackelberg Leadership 17
Stability of Cournot Equilibrium 19
Exotic Dynamics 20
Heterogeneous Commodities 22
The Hotelling Paradox 23
Agenda 24
Assumptions 25
Demand 25
Cost 26
References 26
2 Cournot Oligopoly 28
The Cournot Model 28
Example 1: Linear Demand 30
Example 2: Isoelastic Demand 32
Cournot Equilibria 34
Example 1: Linear Demand 35
Example 2: Isoelastic Demand 37
The Cournot Iterative Map 40
Formation of Expectations 41
Observing Chaotic Orbits 41
Observing Periodic Orbits 42
Stability 44
Example 1: Linear Demand 46
Example 2: Isoelastic Demand 48
References 52
3 Duopoly and Complex Dynamics 53
Introduction 53
The Cournot Model 54
Cournot Equilibrium 56
The Iterative Process 56
Stability of the Cournot Point 59
Periodic Points and Chaos: Numerical study 60
Adaptive Expectations 65
The Neimark Bifurcation 66
The Bifurcation Diagram 68
Analysis by Critical Lines 74
References 76
4 Stackelberg Leadership 78
Stackelberg and Cournot 78
Recapitulation of the Cournot Model 80
Stackelberg Equilibria 82
How to Fit Stackelberg Action in the Cournot Dynamics 85
The Combined Map 87
Numerical Study 88
The Bifurcation Plane 88
The Phase Plane 91
Learning Periodicities 95
Dynamic Stackelberg Leadership 97
Stackelberg’s Demand 97
Cournot Reaction Functions 98
Cournot Equilibrium 101
Traditional Stackelberg Equilibrium 101
Periodic Leadership 103
References 109
5 Capacity Limits 110
Stability and Capacity Limits 110
The CES Production and Cost Functions 111
Oligopoly with Capacity Limits 116
Short Run Reaction Functions 117
Long Run Reaction Functions 120
The Cournot Equilibrium 121
Stability 123
Stability in the Long Run 123
Stability in the Short Run 124
Stability of a Mixed Process 125
Investment 130
References 134
6 Multistability 135
Historical Background 135
Palander’s First Case 137
Demand and Cost Functions 137
Reaction Functions 139
Palander’s Second Case 145
Demand and Cost Functions 145
Reaction Functions 145
Instability 147
Operating Several Plants 148
The Cost Function 150
The Reaction Functions 151
The Cournot Equilibria 153
Attractors and Basins 155
References 157
7 The Hotelling Paradox 159
Spatial Oligopoly 159
A Firm Between Competitors 161
Optimal Location 164
Optimal Pricing 165
Disjoint Monopolies 167
Two Competitors on a Fixed Interval 169
Location 169
Pricing 171
Two Identical Firms on a Fixed Interval 173
Cournot Equilibrium 173
Dynamic Adjustment 176
References 178
Index 179