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Border Collision Bifurcations in Boom and Bust Cycles

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  • Ingrid Kubin

    (Department of Economics, Vienna University of Economics and Business)

  • Laura Gardini

    (Department of Economics, Society and Politics, University of Urbino)

Abstract

Boom and bust cycles are widely documented in the literature on industry dynamics. Rigidities and delays in capacity adjustment in combination with bounded rational behavior have been identified as central driving forces. We construct a model that features only these two elements and we show that this is indeed sufficient to reproduce some stylized facts of a boom and bust cycle. The bifurcation diagrams summarizing the dynamic behavior reveal complex cycles and in particular also abrupt changes in the nature of these cycles. We apply new insights from the mathematical theory of piecewise smooth dynamic systems - in particular, results from the theory of border collision bifurcations - and show that the very existence of borders such as capacity constraints or nonnegativity constraints may lie behind abrupt changes in the dynamic behavior of economic variables.

Suggested Citation

  • Ingrid Kubin & Laura Gardini, 2012. "Border Collision Bifurcations in Boom and Bust Cycles," Department of Economics Working Papers wuwp137, Vienna University of Economics and Business, Department of Economics.
    • Handle: RePEc:wiw:wiwwuw:wuwp137
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    Cited by:

    1. Tuinstra, Jan & Wegener, Michael & Westerhoff, Frank, 2014. "Positive welfare effects of trade barriers in a dynamic partial equilibrium model," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 246-264.
    2. Schmitt, Noemi & Tuinstra, Jan & Westerhoff, Frank, 2017. "Side effects of nonlinear profit taxes in an evolutionary market entry model: Abrupt changes, coexisting attractors and hysteresis problems," Journal of Economic Behavior & Organization, Elsevier, vol. 135(C), pages 15-38.
    3. Agliari, Anna & Pecora, Nicolò & Szuz, Alina, 2022. "Appearance of closed invariant curves in a piecewise Cournot model with advertising," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    4. Tuinstra, Jan & Wegener, Michael & Westerhoff, Frank, 2013. "Positive welfare effects of trade barriers in a dynamic equilibrium model," BERG Working Paper Series 91, Bamberg University, Bamberg Economic Research Group.
    5. Roberto Cellini & Fabio Lamantia, 2015. "Quality competition in markets with regulated prices and minimum quality standards," Journal of Evolutionary Economics, Springer, vol. 25(2), pages 345-370, April.
    6. Ingrid Kubin & Laura Gardini, 2022. "On the significance of borders: the emergence of endogenous dynamics," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 17(1), pages 41-62, January.
    7. Zhusubaliyev, Zhanybai T. & Mosekilde, Erik, 2015. "Multistability and hidden attractors in a multilevel DC/DC converter," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 109(C), pages 32-45.

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    More about this item

    Keywords

    Boom and bust cycle; cobweb dynamics; piecewise smooth system; border collision bifurcation.;
    All these keywords.

    JEL classification:

    • B52 - Schools of Economic Thought and Methodology - - Current Heterodox Approaches - - - Historical; Institutional; Evolutionary; Modern Monetary Theory;
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D41 - Microeconomics - - Market Structure, Pricing, and Design - - - Perfect Competition

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