Disequilibrium Economics: Oligopoly, Trade, and Macrodynamics
by Tönu Puu (Author)

About the Author
Tönu Puu is a Swedish econo-mist of Estonian descent. He worked as acting full professor of economics at Uppsala University from 1963-1970, where he received his Ph.D., and was appointed ordinary professor of economics at Umeå University in 1971. Since 2001, when he became an emeritus professor, he has been working as a senior professor at the Centre for Regional Science (CERUM). In 2014 he was awarded the Doctor Jubilaris of Uppsala University. Puu has published over 20 books and more than 120 scholarly articles on economics, philosophy and mathematics. Topics studied include portfolio selection, investment and production, philosophy of science (in collaboration with Sir Karl Popper), spatial economics, economics of the arts, nonlinear dynamic processes, oligopoly and business cycles.
Puu was founder and director of the Nordic Baroque Music Festival from 1987 to 2001 and in this capacity received the Prize for Extraordinary Promotion of Culture, awarded by the county government. Other musical interests include playing the viola da gamba and being a "luthier", making his own instruments.

About this book
This book discusses mathematical models for various applications in economics, with a focus on non-linear dynamics. Based on the author’s over 50 years of active work in the field, the book has been inspired by models from the period between 1920 and 1950. Following a brief introduction to economics for mathematicians and other modelers, it assembles a repository of useful specific functions for global dynamic modeling. Furthermore, twelve “research stubs” – outlined research agendas that have not yet been fully worked on – are suggested for further study and could even be expanded to entire research projects. The book is a valuable resource, particularly for young scientists who are skilled in mathematical and computational techniques and are looking for applications in economics.

Brief contents
Part I Introductory Matter
1 Utility and Demand. 3
    1.1 The Paradox of Value 3
        1.1.1 Indifference 4
        1.1.2 Altruism. 5
    1.2 Utility and Demand Functions 5
        1.2.1 Linear Demand 5
        1.2.2 Cobb-Douglas Utility. 7
        1.2.3 Cobb-Douglas Coefficients and Advertising 9
    1.3 Lancaster’s New Demand Theory 10
        1.3.1 Properties and Commodities 10
        1.3.2 Optimum 11
        1.3.3 “Shadow” Property Prices 12
        1.3.4 Demand Functions.. 13
        1.3.5 Product Design. 14
        1.3.6 Inverse Demand and Revenue.. 15
    References. 15
2 Elements of Production 17
    2.1 Inputs, Output, and the Production Function 18
        2.1.1 Decreasing Returns 18
        2.1.2 The CES Function 20
        2.1.3 Cost and Capacity Limits 26
    2.2 Returns to Scale 32
    2.3 Fixed Costs 36
    References. 37
Part II Models
3 Cournot I: Constant Returns 41
    3.1 Introduction.. 42
        3.1.1 Biographical 42
        3.1.2 Cournot’s Contribution. 42
        3.1.3 Cournot’s Heritage. 43
    3.2 Formal Model 47
        3.2.1 Iso-Elastic Demand. 47
    3.3 The Iterative Process 50
    3.4 Stability of the Cournot Point. 52
    3.5 Periodic Points and Chaos 53
    3.6 Adaptive E
    3.7 The Neimark Bifurcation 57
    3.8 Critical Lines and Absorbing Area 64
    3.9 Conclusion. 66
    3.10 Computer Programs 66
    References. 71
4 Cournot II: Returns to Scale and Stability 73
    4.1 Introduction.. 74
        4.1.1 The “Theocharis Problem” 74
        4.1.2 Capacity Limits 75
    4.2 Duopoly with Capacity Limits. 75
        4.2.1 Production and Cost 75
        4.2.2 Long Run Cost 76
        4.2.3 Reaction Functions 78
        4.2.4 Numerics. 80
    4.3 Increasing Competition 81
        4.3.1 Production and Cost Functions 83
        4.3.2 Reaction Functions 84
    4.4 Equilibrium and Its Stability 85
        4.4.1 Cournot Equilibrium 85
        4.4.2 Cost Structure in Cournot Equilibrium 87
        4.4.3 Stability of Cournot Equilibrium 88
    4.5 Capital and Investment. 90
        4.5.1 Equilibrium with Identical Firms 90
        4.5.2 Some Numerics. 91
        4.5.3 Endogenous Investment Decisions. 93
        4.5.4 The Cournot Agenda 96
    References. 96
5 Bertrand 97
    5.1 Some History 98
        5.1.1 Biographical 98
        5.1.2 Bertrand’s Argument 98
    5.2 Introduction.. 99
        5.2.1 Substitutes 100
    5.3 A Solution: Lancaster 101
        5.3.1 Properties and Commodities 102
        5.3.2 Utility 103
        5.3.3 Budget Constraint 103
        5.3.4 Optimization 104
        5.3.5 Demand Functions.. 105
        5.3.6 Inverse Demand. 105
    5.4 Duopoly.. 107
        5.4.1 Amoroso Formulas 107
    5.5 Reaction Functions. 108
        5.5.1 Approximating the Reaction Functions.. 110
        5.5.2 Fixed Point Destabilization 112
    5.6 Numerical Results 114
        5.6.1 ComputationModel 114
    5.7 Product Design 117
        5.7.1 Introduction 117
    5.8 The Model 118
        5.8.1 The Production Possibility Frontier 118
        5.8.2 Optimum Design 118
        5.8.3 Design Update Rule 121
    5.9 The Design Update Map 122
    References. 123
6 Stackelberg 125
    6.1 Some History 126
        6.1.1 Biographical 126
        6.1.2 Stackelberg Leadership. 126
        6.1.3 The Stackelberg Model 127
        6.1.4 Digression.. 128
    6.2 Unifying Cournot and Stackelberg 130
        6.2.1 Agenda 130
    6.3 Model Setup 131
        6.3.1 Cournot Action 131
        6.3.2 Digression on Profits 133
        6.3.3 Stackelberg Action 134
    6.4 A Proposed Map. 136
        6.4.1 Profit Considerations 136
    6.5 The Map 136
        6.5.1 The Parameter Plane. 137
    6.6 Numerics. 140
        6.6.1 Parameter Space: Attractors and Bifurcations.. 140
        6.6.2 The Phase Plane: Attractors and Basins 144
        6.6.3 Rational Expectations 152
    References. 153
7 Hotelling Duopoly 155
    7.1 Introduction.. 156
        7.1.1 Biographical 156
        7.1.2 Some History 157
        7.1.3 Digression About Space 158
    7.2 The Model 163
        7.2.1 Assumptions and Notation 163
        7.2.2 Total Demand and Profits 165
        7.2.3 Market Area Endpoints. 165
        7.2.4 Interpretation of the Cases 166
        7.2.5 Demand and Optimal Location 167
        7.2.6 Profit Maximization and Mill Price 173
    7.3 Summary for the Cases 176
    7.4 Equilibria 177
        7.4.1 Duopoly. 178
        7.4.2 Monopolies 180
    7.5 Further Issues 181
        7.5.1 Different Time Scales 182
        7.5.2 Different Pricing Policies 182
    References. 182
8 Disequilibrium Trade and Pricing of Durable Commodities 183
    8.1 Introduction.. 184
    8.2 Assumptions 186
        8.2.1 Notation. 186
        8.2.2 Budget Constraints 186
        8.2.3 Utility Functions 187
        8.2.4 Individual Optima 188
        8.2.5 Trade 189
        8.2.6 Excess Demand. 190
        8.2.7 Tatonnement 191
    8.3 The Model 191
    8.4 Numerical Analysis and Graphics 191
        8.4.1 The Phase Plane 191
        8.4.2 Bifurcation Diagrams. 197
    8.5 Summary.. 199
    References. 200
9 Macroeconomics and the Trade Cycle 201
    9.1 Background. 201
        9.1.1 Flows 202
        9.1.2 The MONIAC. 204
        9.1.3 Protagonists. 205
        9.1.4 The Multiplier-Accelerator Model 206
    9.2 The Models 208
        9.2.1 The Original Samuelson–Hicks Model 209
        9.2.2 Digression on Technology 211
    9.3 Floor Only 212
        9.3.1 The Formal Model 212
        9.3.2 Stationary Relative Dynamics. 217
        9.3.3 Periodicity 221
        9.3.4 Absolute and Relative Variables 223
    9.4 Ceiling Included. 226
        9.4.1 Exponential Decay and Half-Life 226
        9.4.2 Tying the Ceiling to Capital Stock 226
        9.4.3 The Relative System. 231
        9.4.4 Numerical Results 236
    References. 238
Part III Model Stubs
10 Introduction to the Stubs 243
11 CAUDEX PRIMUS. 245
    11.1 A Formal Model 246
        11.1.1 Demand 246
        11.1.2 Cost and Profit 247
        11.1.3 Reaction Functions 248
    11.2 Capacity Limits. 248
    Reference. 249
12 CAUDEX SECUNDUS. 251
    12.1 Hotelling in 2D 251
13 CAUDEX TERTIUS. 255
    13.1 The Open Economy 255
    13.2 Addendum: Small and Big Economies. 258
    Reference. 258
14 CAUDEX QUARTUS 259
    14.1 Dynamic Stackelberg.. 259
    Reference. 261
15 CAUDEX QUINTUS 263
    15.1 Product Design 263
16 CAUDEX SEXTUS 267
    16.1 Migration 267
    References. 270
17 CAUDEX SEPTIMUS 271
    17.1 Advertising 271
18 CAUDEX OCTAVUS. 275
    18.1 Interregional Trade 275
    18.2 The Static Model 276
    18.3 The Dynamic Model 278
    18.4 Discretizing 278
    18.5 Price Dynamic Alone 280
    18.6 Suggested Agenda. 282
    References. 284
19 CAUDEX NONUS 285
    19.1 Business Cycle Diffusion 285
    References. 287
20 CAUDEX DECIMUS 289
    20.1 Disequilibrium Trade: Several Agents 289
21 CAUDEX UNDECIMUS 293
    21.1 Disequilibrium Trade: Several Commodities 293
    21.2 Some Geometry 294
        21.2.1 Digression on the Preparation of Solid Box Picture 295
    21.3 Bilateral Deals 297
        21.3.1 Bilateral Deal x, y 299
        21.3.2 Bilateral Deal x, z 300
    21.4 Trade Maps 300
    21.5 Arbitrary Numbers of Traders and Commodities. 301
22 CAUDEX DUODECIMUS 303
    22.1 Duopolists with Multiple Plants 303
    References. 307

Pages: 306 pages
Publisher: Springer; 1st ed. 2018 edition (April 3, 2018)
Language: English
ISBN-10: 3319744143
ISBN-13: 978-3319744148