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Border Collision Bifurcations in Boom and Bust Cycles

  • Ingrid Kubin


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

  • Laura Gardini


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

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.

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Paper provided by Vienna University of Economics and Business, Department of Economics in its series Department of Economics Working Papers with number wuwp137.

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Date of creation: Mar 2012
Date of revision:
Handle: RePEc:wiw:wiwwuw:wuwp137
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  1. Currie, Martin & Kubin, Ingrid, 1995. "Non-linearities and partial analysis," Economics Letters, Elsevier, vol. 49(1), pages 27-31, July.
  2. Fabio Tramontana & Laura Gardini & Tönu Puu, 2008. "Cournot Duopoly when the Competitors Operate Multiple Production Plants," Working Papers 0809, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2008.
  3. Athanasiou, George & Karafyllis, Iasson & Kotsios, Stelios, 2008. "Price stabilization using buffer stocks," Journal of Economic Dynamics and Control, Elsevier, vol. 32(4), pages 1212-1235, April.
  4. David Besanko & Ulrich Doraszelski, 2002. "Capacity Dynamics and Endogenous Asymmetries in Firm Size," Computing in Economics and Finance 2002 196, Society for Computational Economics.
  5. Mark Paich & John D. Sterman, 1993. "Boom, Bust, and Failures to Learn in Experimental Markets," Management Science, INFORMS, vol. 39(12), pages 1439-1458, December.
  6. 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.
  7. 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.
  8. Yuanzhu Lu & Sougata Poddar, 2004. "Mixed oligopoly and the choice of capacity," CEMA Working Papers 495, China Economics and Management Academy, Central University of Finance and Economics.
  9. Gardini, Laura & Sushko, Iryna & Naimzada, Ahmad K., 2008. "Growing through chaotic intervals," Journal of Economic Theory, Elsevier, vol. 143(1), pages 541-557, November.
  10. Roberto Dieci & Frank Westerhoff, 2010. "Interacting cobweb markets," Post-Print hal-00849411, HAL.
  11. 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.
  12. 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.
  13. 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.
  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. 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.
  16. Saari, Donald G, 1985. "Iterative Price Mechanisms," Econometrica, Econometric Society, vol. 53(5), pages 1117-31, September.
  17. 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.
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