Nonlinear Economic Dynamics
The present study is a preliminary draft on 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
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Nonlinear Economic Dynamics
Second, Revised and Enlarged Edition
With 64 Figures
Springer-Verlag Berlin Heidelberg N ew York London Paris Tokyo Hong Kong Barcelona
Professor Dr. T6nu Puu Department of Economics Umea University S-90l87, Umea, Sweden
ISBN -13: 978-3-642-97293-5 e- ISBN-13: 978-3-642-97291-1 DOl: 10 .1007/978-3-642-97291-1
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PREFACE
The present study is a preliminary draft on 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 Puu, "Spatial Economics" (North-Holland 1985). The monograph 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. Chapter 2 summarizes the work by the author on the structural stability of continuous spatial market equilibrium models. Chapter 3 deals with a re-fonnulation 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. The tools of analysis are basically classical perturbation methods originating with Poincare. Occasionally, more exotic beasts from the mathematical zoo are encountered, such as catastrophe, or detemlinistic chaos.
VI
It is worthwhile noting that the chaotic regime, along with quasi-periodicity and frequency locking, turns up in the most traditional multiplier-accelerator models of the business cycle, provided there is a non-linear investment function, and inter-regional t
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