The present study deals with nonlinear economic dynamics, with which the author has been concerned the last years. It grew out from the joint work by Professor Martin Beckmann and the present author on nonlinear statics in spatial economics, Beckmann and Pull, "Spatial Economics" (N orth-Holland 1985), later followed by its companion, Beckmann and Puu "Spatial Structures" (Springer-Verlag 1990). The first mono graph mentioned contains sections on price waves and business cycles, but in a linear format. The rest is static theory. The author has finally come to the conviction that linear dynamic modelling has very little to yield. This is due to the poor set of alternatives -decay or explosion of motion -pertinent to linear models. Therefore, the present work centres on non-linearity. Another distinction is that only purely causal models are dealt with, as those formatted as inter-temporal equilibria hardly belong to the more restricted field of dynamics. The spatial origin is visible in the choice of models. Chapters 1 and 2 summarize the work by the author on the structural stability of continuous spatial market eqUilibrium models. Chapter 3 deals with a re-formulation of the ingenious population growth and diffusion model invented by the young Hotelling in 1921. Chapter 4 is a detailed digression on business cycle models in a continuous spatial format with inter-regional trade.
Auflage
3rd, rev. and enlarged ed.
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Editions-Typ
Illustrationen
1 s/w Tabelle
93 illustrations, 1 table
Maße
Höhe: 23.5 cm
Breite: 15.5 cm
Gewicht
ISBN-13
978-3-540-56145-3 (9783540561453)
DOI
10.1007/978-3-642-97450-2
Schweitzer Klassifikation
- Nonlinear Economic Dynamics.- 1 Dynamics Versus Equilibrium Analysis.- 2 Linear Versus Nonlinear Modelling.- 3 The Tools of Analysis.- 3.1 Perturbation Methods.- 3.2 Structural Stability and Catastrophe.- 3.3 Chaos and Fractals.- 4 The Choice of Models.- 1 - Spatial Pattern Formation.- 1 Scientific Explanations.- 1.1 Spatial Patterns.- 1.2 Types of Scientific Explanation.- 1.3 Teleological Explanation as Shorthand for Causal.- 1.4 The Case of Minimal Action.- 1.5 Hexagonal Cell Formation.- 2 Optimal Patterns.- 2.1 Tessellations.- 2.2 The Isoperimetric Problem.- 2.3 Average Distance.- 3 Structurally Stable Patterns.- 3.1 Dangers of Optimality.- 3.2 Structural Stability of Cell Aggregates.- 3.3 Structural Stability of Flows.- 3.3.1 The Flow Model.- 3.3.2 The Structure of Flow Portraits.- 3.3.3 Perturbations.- 3.3.4 Topological Equivalence.- 3.3.5 Structural Stability.- 3.3.6 The Character of Stable Flows.- 3.3.7 Economic Interpretation.- 3.4 Transitions Between Stable Patterns.- 4 Conclusion.- 2 - The Genesis of Economic Centres.- 1 One Dimension.- 2 Two Dimensions: Circular Markets.- 3 Two Dimensions: Triangles, Squares, Hexagons.- 4 Changing Population Density.- 5 Conclusion.- 3 - Population Dynamics.- 1 The Original Hotelling Model.- 1.1 Stationary Solutions.- 1.2 Stability.- 1.3 Discrete Case.- 2 Growth.- 2.1 Production.- 2.2 Pure Growth: Stationary Solutions.- 2.3 Pure Growth: Stability.- 3 Diffusion.- 4 Growth and Diffusion.- 4.1 Stationary Solutions in One Dimension.- 4.2 Amplitude and Period.- 4.3 Stability.- 4.4 Dynamics.- 5 Structural Stability.- 5.1 Stabilizing the Original Hotelling Model.- 5.2 Stabilizing the Model with Production.- 6 Conclusion.- 7 Appendix: Model with Endogenous Capital.- 7.1 Dynamics of Capital and Labour.- 7.2 Bifurcations: Geometric Aspects.- 7.3 Bifurcations: Computational Aspects.- 7.4 Diffusion.- 4 - Business Cycles: Continuous Time.- 1 The Multiplier-Accelerator Model.- 1.1 The Original Model.- 1.2 Nonlinear Investment Functions and Limit Cycles.- 1.2.1 Limit Cycles: Existence.- 1.2.2 Limit Cycles: Asymptotic Approximation.- 1.2.3 Limit Cycles: Transients and Stability.- 2 Spatial Models.- 2.1 Interregional Trade.- 2.2 The Linear Model.- 2.3 Coordinate Separation.- 2.3.1 Example: Square Region.- 2.3.2 Example: Circular Region.- 2.3.3 Example: Spherical Region.- 2.4 Nonlinear Spatial Model.- 2.4.1 Example: Dispersive Waves.- 2.4.2 Example: Standing Waves.- 5 - Business Cycles: Discrete Space.- 1 The Two-Region Model.- 1.1 The Persistence of Cycles.- 1.2 Perturbation Analysis.- 1.3 The Unstable Zero Equilibrium.- 1.4 Other Fixed Points.- 1.5 Properties of Fixed Points.- 1.6 The Arbitrary Phase Angle.- 1.7 Stability.- 2 The Forced Oscillator.- 2.1 The World Market.- 2.2 The Small Open Economy.- 2.3 Stability.- 2.4 Catastrophe.- 2.5 Quasiperiodic Motion.- 3 Relaxation Cycles.- 3.1 Relaxation Oscillations: The Autonomous Model.- 3.2 Relaxation Oscillations: The Forced System.- 4 Three Identical Regions.- 4.1 On the Existence of Periodic Solutions.- 4.2 Stability.- 4.3 Quasiperiodicity and Chaos.- 6 - Business Cycles: Discrete Time.- 1 First Discrete Model.- 1.1 Investments.- 1.2 Consumption.- 2 The Cubic Iterative Map.- 2.1 Fixed Points, Cycles, and Chaos.- 2.2 Formal Analysis of Chaotic Dynamics.- 2.2.1 Co-ordinate Transformation.- 2.2.2 The Three Requisites of Chaos.- 2.3 Symbolic Dynamics.- 3 Brownian Random Walk.- 4 Digression on Order and Disorder.- 5 The General Model.- 5.1 Relaxation Cycles.- 5.2 Other Cycles.- 5.3 The Slow Feed Back.- 5.3.1 Changes of the Fixed Points.- 5.3.2 Response of the Chaotic Process.- 6 Conclusion.- 7 Appendix: Digression on The Rationale of the Cubic.- 7 - Cournot Duopoly.- 1 Duopoly.- 2 The Cournot Model.- 3 Adjustment by Taking Turns.- 4 Simultaneous Adjustment.- 5 Conclusion.- References.
