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Existence of an exact Walrasian equilibrium in nonconvex economies

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  • D'Agata, Antonio

Abstract

The existence of an exact Walrasian equilibrium in nonconvex economies is still a largely unexplored issue. This paper shows that such an equilibrium exists in nonconvex economies by following the nearby economyapproach introduced by Postlewaite and Schmeidler (Approximate Walrasian Equilibrium and Nearby Economies, 1981) for convex economies. More precisely, the paper shows that any equilibrium price of the convexified version of a nonconvex economy is an equilibrium price also for a set of perturbed economies with the same number of agents. It shows that in this set there are economies that differ from the original economy only as regards preferences or initial endowments.

Suggested Citation

  • D'Agata, Antonio, 2012. "Existence of an exact Walrasian equilibrium in nonconvex economies," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy, vol. 6, pages 1-16.
    • Handle: RePEc:zbw:ifweej:201212
    DOI: 10.5018/economics-ejournal.ja.2012-12
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    References listed on IDEAS

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    1. Smale, S., 1974. "Global analysis and economics IIA : Extension of a theorem of Debreu," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 1-14, March.
    2. Felix Kubler & Karl Schmedders, 2003. "Approximate Versus Exact Equilibria," Discussion Papers 1382, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Felix Kubler & Karl Schmedders, 2008. "Approximate Versus Exact Equilibria in Dynamic Economies," Lecture Notes in Economics and Mathematical Systems, in: Computational Aspects of General Equilibrium Theory, pages 135-163, Springer.
    4. Robert M. Anderson & M. Ali Khan & Salim Rashid, 1982. "Approximate Equilibria with Bounds Independent of Preferences," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(3), pages 473-475.
    5. Hildenbrand, Werner & Schmeidler, David & Zamir, Shmuel, 1973. "Existence of Approximate Equilibria and Cores," Econometrica, Econometric Society, vol. 41(6), pages 1159-1166, November.
    6. Felix Kubler, 2008. "Approximate Generalizations and Computational Experiments," Lecture Notes in Economics and Mathematical Systems, in: Computational Aspects of General Equilibrium Theory, pages 109-133, Springer.
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    Keywords

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    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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