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Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter

Introduction

Nonlinear Economic Dynamics
Abstract
Dynamic analysis in economics is as old as economics itself. A glance at the subject index in Schumpeter (1954) is sufficient to convince you about this. Even dynamic mathematical models are fairly old. The cobweb model of price adjustments for instance dates back to 1887.
Tönu Puu

Chapter 1. Spatial Pattern Formation

Abstract
The formation of spatial patterns in economics is in substance similar to pattern formation in matter, living or dead, as dealt with in biology or physics. Spatial patterns in the two- and three-dimensional world, such as beehives or foams of soap bubbles, have fascinated mankind from antiquity to present times. There exist parallels in biology, physics, and economics in the field of pattern formation so as to make it a good prototype for the comparison of various philosophies on scientific modelling.
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Chapter 2. The Genesis of Production Centres

Abstract
In Chapter 1 we applied stability considerations to the formation of spatial economic structures. Presently we will take a look at optimality as the working principle and consider the mesh size rather than the shape of the spatial configuration.
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Chapter 3. Population Dynamics

Abstract
Hotelling (1921) proposed a model for the growth and spatial dispersion of populations. Growth was modelled on Malthusian principles as a logistic process, whereas Fourier’s heat diffusion was the source of inspiration for migratory processes in space. A saturation density of population was assumed, if the actual density was higher, population decreased, if the actual density’ was lower, population increased. The reason for spatial diffusion stated was that people move from more to less densely populated regions when per capita output decreases with increasing population (=labour force), as it does under decreasing returns.
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Chapter 4. Business Cycles: Continuous Time

Abstract
The invention by Samuelson (1939) of the business cycle machine, combining the multiplier and the accelerator, certainly was a major event. That two such simple forces as consumers spending a given fraction of their incomes on consumption and producers keeping a fixed ratio of capital stock to output (=real income) combined to produce cyclical change was simple, surprising and convincing at the same time. This model if any qualifies for the attribute of scientific elegance. In passing it should be stressed that the Keynesian macroeconomic outlook was an essential background.
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Chapter 5. Business Cycles: Discrete Space

Abstract
In the preceding discussion the parameters of the model, s, v, and m, were supposed to be spatial invariants. Thus the natural frequencies of oscillation are equal for all locations and no incompatibilities for synchronization are present. This prevents the dynamics from displaying the more spectacular phenomena known in modern systems theory.
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Chapter 6. Business Cycles: Discrete Time

Abstract
Although we for reasons given prefer to work with continuous models it must be admitted that there are certain advantages in displaying the details of chaos for discrete models. This is so because, before the tools of analysis, like symbolic dynamics, can be applied to such models we need to construct the return map on the Poincaré section for the orbit investigated. This, however, means that we first have to integrate the system over a complete “cycle”. The details of such an integration can become much too complex.
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Chapter 7. Cournot Duopoly

Abstract
Economics recognizes two opposite market forms: competition and monopoly. In the first case the firms are very numerous and thus small in comparison to the size of the total market. In consequence they consider market price as being given independently of any action they can take alone with regard to their supply. In the second case one single firm supplies the whole market. Its supply influences market price appreciably, and it is able to increase its profits by limiting supply and establishing a monopoly price.
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Backmatter

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