Business Cycle Dynamics

Models and Tools

herausgegeben von: Professor Dr. Tönu Puu, Dr. Iryna Sushko

Verlag: Springer Berlin Heidelberg

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

Business cycle theory has been one of the fastest growing fields in modern nonlinear economic dynamics. The book is centered around models of multiplier-accelerator type, emerging from Samuelson's seminal work, later developed into nonlinear formats by Hicks and Goodwin. These models left open ends, as the tools then available did not permit more systematic analysis. The present situation is different, due to the emergence of new methods also focusing global analysis. The focus on classical, causal or recursive models implies a deviation from current main stream business cycle theory, based on "rational expectations", which in view of the possibility of mathematical chaos becomes untenable. This book is a rejoinder to Puu and Sushko, Oligopoly Dynamics - Models and Tools, (Springer 2002).

Inhaltsverzeichnis

Frontmatter

Aims and Scope

Tönu Puu

1. Some Methods for the Global Analysis of Closed Invariant Curves in Two-Dimensional Maps

Anna Agliari, Gian-Italo Bischi, Laura Gardini

2. Center Bifurcation for a Two-Dimensional Piecewise Linear Map

Iryna Sushko, Laura Gardini

3. Short History of the Multiplier-Accelerator Model

Tönu Puu

4. Multiplier-Accelerator Models with Random Perturbations

Volker Böhm

5. Non-Autonomous Business Cycle Model

Conclusions p] In a classical model of business cycle, we introduce parameters depending on time, producing a non-autonomous linear second order difference equation, which is analyzed in the setting of non-autonomous discrete systems. Roughly speaking, one could think on a linear model whose parameters are pertubed is some way, for instance a random way.

The stability and limit set of the orbits of the non-autonomous system associated to the difference equation are studied. When all the maps of the system are contractive, then the system is stable, producing bounded orbits. in other cases, some simulations shows that when we have expansive maps in the system, unbounded orbits and some type of chaotic behaviour may appear. It must be pointed out that the chaotic behaviour appear when both, contractive and expansive maps are in the system infinitely many times.

It is an interesting question to analyze these type of “chaotic orbits”, that is: are they really chaotic in some theoretical sense?

Jose S. Cánovas Peña, Manuel Ruiz Marín

Backmatter

Titel: Business Cycle Dynamics
herausgegeben von: Professor Dr. Tönu Puu
Dr. Iryna Sushko
Verlag: Springer Berlin Heidelberg
Electronic ISBN: 978-3-540-32168-2
Print ISBN: 978-3-540-32167-5
DOI: https://doi.org/10.1007/3-540-32168-3

Springer Professional

Business Cycle Dynamics

Models and Tools

Über dieses Buch

Inhaltsverzeichnis

Frontmatter

Aims and Scope

1. Some Methods for the Global Analysis of Closed Invariant Curves in Two-Dimensional Maps

2. Center Bifurcation for a Two-Dimensional Piecewise Linear Map

3. Short History of the Multiplier-Accelerator Model

4. Multiplier-Accelerator Models with Random Perturbations

5. Non-Autonomous Business Cycle Model

6. The Hicksian Model with Investment Floor and Income Ceiling

7. Growth Cycles in a Modified Hicksian Business Cycle Model

8. Coexistence of Attractors and Homoclinic Loops in a Kaldor-Like Business Cycle Model

9. Expectations and the Multiplier-Accelerator Model

10. ‘Floors’ and/or ‘Ceilings’ and the Persistence of Business Cycles

11. A Goodwin-Type Model with Cubic Investment Function

12. A Goodwin-Type Model with a Piecewise Linear Investment Function

Backmatter