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Variations on the Theme of Scarf's Counter-Example

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Author Info
Alok Kumar
Martin Shubik

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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.

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Publisher Info
Paper provided by Santa Fe Institute in its series Working Papers with number 01-12-074.

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Date of creation: Dec 2001
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Handle: RePEc:wop:safiwp:01-12-074

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Related research
Keywords: Scarf's counter-example; price adjustment mechanism; feedback controller; multiple competitive equilibria; stability;

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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 873-75, August. [Downloadable!] (restricted)
  2. Beckmann, Martin J & Ryder, Harl E, Jr, 1969. "Simultaneous Price and Quantity Adjustment in a Single Market," Econometrica, Econometric Society, vol. 37(3), pages 470-84, July. [Downloadable!] (restricted)
  3. Herbert E. Scarf, 1959. "Some Examples of Global Instability of the Competitive Equilibrium," Cowles Foundation Discussion Papers 79, Cowles Foundation, Yale University. [Downloadable!]
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  1. Gaël Giraud, 2004. "The limit-price exchange process," Cahiers de la Maison des Sciences Economiques b04118, Université Panthéon-Sorbonne (Paris 1). [Downloadable!]
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