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Hicks’ trade cycle revisited: cycles and bifurcations
Department of Economics, Universita Politecnica delle Marche, Italy.
Department of Economics, University of Urbino, Italy.
Umeå University, Faculty of Social Sciences, Centre for Regional Science (CERUM).
Institute of Mathematics, National Academy of Sciences of Ukraine, Ukraine.
2003 (English)In: Mathematics and Computers in Simulation, ISSN 0378-4754, E-ISSN 1872-7166, Vol. 63, no 6, 505-527 p.Article in journal (Refereed) Published
Abstract [en]

In the Trade Cycle, Hicks introduced the idea that endogenous fluctuations could be coupled with a growth process via nonlinear processes. To argue for this hypothesis, Hicks used a piecewise-linear model. This paper shows the need for a reinterpretation of Hicks’ contribution in the light of a more careful mathematical investigation. In particular, it will be shown that only one bound is needed to have non explosive outcome if the equilibrium point is an unstable focus. It will also be shown that when the fixed point is unstable the attracting set has a particular structure: It is a one-dimensional closed invariant curve, made up of a finite number of linear pieces, on which the dynamics are either periodic or quasi-periodic. The conditions under which the model produces periodic or quasi-periodic trajectories and the related bifurcations as a function of the main economic parameters are determined.

Place, publisher, year, edition, pages
2003. Vol. 63, no 6, 505-527 p.
Keyword [en]
Business cycle models, Piecewise-linear maps, Tongues of periodicity, Bifurcation diagram
National Category
Economics
Identifiers
URN: urn:nbn:se:umu:diva-24523DOI: 10.1016/S0378-4754(03)00060-0OAI: oai:DiVA.org:umu-24523DiVA: diva2:226630
Available from: 2009-07-02 Created: 2009-07-02 Last updated: 2017-12-13

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