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A pitchfork bifurcation in the tatonnement process

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  • Venkatesh Bala

    (Department of Economics, McGill University, 855 Sherbrooke St. W., Montreal, CANADA H3A 2T7)

Abstract

This note extends the example of Gale (1963) by considering the continuous time tatonnement process for a class of two agent, two commodity exchange economies, parametrized by a number µ∈(0,1). We demonstrate that as the parameter passes a threshold value µ* the unique, globally stable competitive equilibrium loses local stability while two new locally stable equilibria appear. Intuitively, as µ increases the income effect become increasingly more important relative to substitution effect, and eventually overwhelms the latter. As the parameter µ approaches 1, the economy tends to the example considered by Gale, as does the limiting behavior of the tatonnement.

Suggested Citation

  • Venkatesh Bala, 1997. "A pitchfork bifurcation in the tatonnement process," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(3), pages 521-530.
    • Handle: RePEc:spr:joecth:v:10:y:1997:i:3:p:521-530
    Note: Received: February 28, 1996; revised version August 5, 1996
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    Cited by:

    1. He, Yijun & Barnett, William A., 2006. "Singularity bifurcations," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 5-22, March.
    2. Anjan Mukherji, 2012. "The second fundamental theorem of positive economics," International Journal of Economic Theory, The International Society for Economic Theory, vol. 8(2), pages 125-138, June.
    3. Anjan Mukherji, 2003. "Competitive Equilibria: Convergence, Cycles or Chaos," ISER Discussion Paper 0591, Institute of Social and Economic Research, Osaka University.
    4. Mukherji, Anjan, 2010. "Stability of the Market Economy in the Presence of Diverse Economic Agents," Working Papers 8, JICA Research Institute.
    5. William A. Barnett & Yijun He, 2002. "Bifurcations in Macroeconomic Models," Macroeconomics 0210006, University Library of Munich, Germany.
    6. Jan Tuinstra & Claus Weddepohl, 1999. "On the equivalence between the overlapping-generations model and cyclical general-equilibrium models," Journal of Economics, Springer, vol. 70(2), pages 187-207, June.

    More about this item

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General

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