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A Hicksian Multiplier-Accelerator Model with Floor Determined by Capital Stock and Tongues of Periodicity in a Family of Two-dimensional Discontinuous Maps of Real Möbius Type
Umeå University, Faculty of Social Sciences, Centre for Regional Science (CERUM).
Dep. of Economics, University of Urbino, Italy.
Institute of Mathematics, National Academy of Sciences of Ukraine, Kiev, Ukraine.
2003 (English)Report (Other academic)
Abstract [en]

A Hicksian Multiplier-Accelerator Model

This article reconsiders the Hicksian multiplier-accelerator model with the "floor" related to the depreciation on actual capital stock. Through the introduction of the capital variable a growth trend is created endogenously by the model itself, along with growth rate oscillations around it. The "ceiling" can be dispensed with altogether. As everything is growing in such a model, a variable transformation is introduced to the end of focusing relative dynamics of the income growth rate and the actual capital output ratio.

Tongues of Periodicity in a Family of Two-dimensional Discontinuous Maps of Real Möbius Type

In this paper we consider a two-dimensional piecewise-smooth discontinuous map representing the so-called "relative dynmics" of an Hicksian business cycle model. The main features of the dynamics occur in the parameter region in which no fixed points at finite distance exist, but we may have attracting cycles of any periods. The bifurcations associated with the periodicity tongues of the map are studied making use of the first return map on a suitable segment of the phase plane. The bifurcation curves bounding the periodicity tongues in the parameter plane are related with saddle-node and border-collision bifurcations of the first-return map. Moreover, the particular "sausages structure" of the bifurcation tongues is also explained.

Place, publisher, year, edition, pages
2003. , 30 p.
, CERUM Working Paper, ISSN 1404-5362 ; 65
National Category
URN: urn:nbn:se:umu:diva-24675OAI: diva2:227108
Centrum för regionalvetenskap (CERUM), 90187, Umeå
In part published in Chaos, Solitons and Fractals ISSN 0960-0779 2004 vol 21 no 2 pp 403-412 doi:10.1016/j.chaos.2003.12.012 In part bublished in Journal of Economic Behavior and Organization ISSN 0167-2681 2005 vol 56 no 3 pp 331-348 doi:10.1016/j.jebo.2003.10.008 Elsevier. Changes may have been made to these works since it was submitted for publication.Available from: 2009-07-13 Created: 2009-07-09 Last updated: 2012-03-14

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