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Border collision bifurcations in boom and bust cycles

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  • Ingrid Kubin

    ()

  • Laura Gardini

    ()

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. Copyright Springer-Verlag Berlin Heidelberg 2013

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Bibliographic Info

Article provided by Springer in its journal Journal of Evolutionary Economics.

Volume (Year): 23 (2013)
Issue (Month): 4 (September)
Pages: 811-829

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Handle: RePEc:spr:joevec:v:23:y:2013:i:4:p:811-829

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Keywords: Boom and bust cycle; Cobweb dynamics; Piecewise smooth system; Border collision bifurcation; B52; C61; C62; C63; D41;

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  1. Gardini, Laura & Merlone, Ugo & Tramontana, Fabio, 2011. "Inertia in binary choices: Continuity breaking and big-bang bifurcation points," Journal of Economic Behavior & Organization, Elsevier, vol. 80(1), pages 153-167.
  2. Anna Agliari & Pasquale Commendatore & Ilaria Foroni & Ingrid Kubin, 2011. "Border Collision Bifurcations in a Footloose Capital Model with First Nature Firms," Computational Economics, Society for Computational Economics, vol. 38(3), pages 349-366, October.
  3. Gardini, Laura & Sushko, Iryna & Naimzada, Ahmad K., 2008. "Growing through chaotic intervals," Journal of Economic Theory, Elsevier, vol. 143(1), pages 541-557, November.
  4. Fabio Tramontana & Laura Gardini & Frank Westerhoff, 2011. "Heterogeneous Speculators and Asset Price Dynamics: Further Results from a One-Dimensional Discontinuous Piecewise-Linear Map," Computational Economics, Society for Computational Economics, vol. 38(3), pages 329-347, October.
  5. Currie, Martin & Kubin, Ingrid, 1997. "Investment in Fixed Capital and Competitive Industry Dynamics," Oxford Economic Papers, Oxford University Press, vol. 49(4), pages 521-42, October.
  6. Tramontana, Fabio & Gardini, Laura & Puu, Tönu, 2009. "Cournot duopoly when the competitors operate multiple production plants," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 250-265, January.
  7. Lu, Yuanzhu & Poddar, Sougata, 2005. "Mixed oligopoly and the choice of capacity," Research in Economics, Elsevier, vol. 59(4), pages 365-374, December.
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  10. Jean-Michel Grandmont & P, A, Pintus & R, De Vilder, 1997. "Capital-Labor Substitution and Competitive Nonlinear Endogenous Business Cycles," Working Papers 97-28, Centre de Recherche en Economie et Statistique.
  11. Sushko, Iryna & Gardini, Laura & Puu, Tönu, 2010. "Regular and chaotic growth in a Hicksian floor/ceiling model," Journal of Economic Behavior & Organization, Elsevier, vol. 75(1), pages 77-94, July.
  12. David Besanko & Ulrich Doraszelski, 2002. "Capacity Dynamics and Endogenous Asymmetries in Firm Size," Computing in Economics and Finance 2002 196, Society for Computational Economics.
  13. Fabio Tramontana & Frank Westerhoff & Laura Gardini, 2010. "On the complicated price dynamics of a simple one-dimensional discontinuous financial market model with heterogeneous interacting traders," Working Papers 1005, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2010.
  14. John D. Sterman & Rebecca Henderson & Eric D. Beinhocker & Lee I. Newman, 2007. "Getting Big Too Fast: Strategic Dynamics with Increasing Returns and Bounded Rationality," Management Science, INFORMS, vol. 53(4), pages 683-696, April.
  15. Saari, Donald G, 1985. "Iterative Price Mechanisms," Econometrica, Econometric Society, vol. 53(5), pages 1117-31, September.
  16. Currie, Martin & Kubin, Ingrid, 1995. "Non-linearities and partial analysis," Economics Letters, Elsevier, vol. 49(1), pages 27-31, July.
  17. Dieci, Roberto & Westerhoff, Frank, 2010. "Interacting cobweb markets," Journal of Economic Behavior & Organization, Elsevier, vol. 75(3), pages 461-481, September.
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Cited by:
  1. 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.

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