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Variations on the Theme of Scarf's Counter-Example

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  • Alok Kumar
  • Martin Shubik

Abstract

In this paper we study the relationship between the stability of a competitive equilibrium (CE) and the price adjustment mechanism used to attain that equilibrium point. Using two specific examples, a three- commodity exchange economy with a unique competitive equilibrium (Scarf's global instability example) and a two-commodity, two-trader type exchange economy with multiple competitive equilibria, we show that the stability of a CE depends critically upon the dynamics of the price adjustment mechanism. A particular CE may be unstable under one price adjustment mechanism but stable under another. The joint dynamics of the chosen price adjustment mechanism and the given economy determines the overall stability of its competitive equilibrium. Our results suggest that context-rich studies of economic systems which focus on a specific price adjustment mechanism may provide insights into the dynamics and stability of economic systems that are often not revealed through a context-independent analysis.

Suggested Citation

  • Alok Kumar & Martin Shubik, 2001. "Variations on the Theme of Scarf's Counter-Example," Working Papers 01-12-074, Santa Fe Institute.
    • Handle: RePEc:wop:safiwp:01-12-074
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    References listed on IDEAS

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    1. Shapley, Lloyd S & Shubik, Martin, 1977. "An Example of a Trading Economy with Three Competitive Equilibria," Journal of Political Economy, University of Chicago Press, vol. 85(4), pages 873-875, August.
    2. Herbert E. Scarf, 1959. "Some Examples of Global Instability of the Competitive Equilibrium," Cowles Foundation Discussion Papers 79, Cowles Foundation for Research in Economics, Yale University.
    3. Beckmann, Martin J & Ryder, Harl E, Jr, 1969. "Simultaneous Price and Quantity Adjustment in a Single Market," Econometrica, Econometric Society, vol. 37(3), pages 470-484, July.
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    Cited by:

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    2. Mandel, Antoine & Gintis, Herbert, 2016. "Decentralized Pricing and the equivalence between Nash and Walrasian equilibrium," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 84-92.
    3. Leimbach, Marian & Edenhofer, Ottmar, 2007. "Technological spillovers within multi-region models: Intertemporal optimization beyond the Negishi approach," Economic Modelling, Elsevier, vol. 24(2), pages 272-294, March.
    4. Mandel, Antoine & Gintis, Herbert, 2014. "Stochastic stability in the Scarf economy," Mathematical Social Sciences, Elsevier, vol. 67(C), pages 44-49.
    5. Gaël Giraud, 2004. "The limit-price exchange process," Cahiers de la Maison des Sciences Economiques b04118, Université Panthéon-Sorbonne (Paris 1).
    6. Huber, Juergen & Shubik, Martin & Sunder, Shyam, 2010. "Three minimal market institutions with human and algorithmic agents: Theory and experimental evidence," Games and Economic Behavior, Elsevier, vol. 70(2), pages 403-424, November.
    7. Marian Leimbach & Klaus Eisenack, 2009. "A Trade Algorithm for Multi-Region Models Subject to Spillover Externalities," Computational Economics, Springer;Society for Computational Economics, vol. 33(2), pages 107-130, March.
    8. Sakane, Hirokazu, 2016. "Asymptotic stability of a general equilibrium under perfect and monopolistic competition," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 21-26.
    9. Chen, Guo & Korpeoglu, C. Gizem & Spear, Stephen E., 2017. "Price stickiness and markup variations in market games," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 95-103.
    10. Emanuela Randon & Peter Simmons, 2017. "A top dog tale with preference complementarities," Journal of Economics, Springer, vol. 120(1), pages 47-63, January.

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