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The computation of a continuum of constrained equilibria

Author

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  • Herings, P.J.J.

    (Tilburg University, School of Economics and Management)

  • Talman, A.J.J.

    (Tilburg University, School of Economics and Management)

  • Yang, Z.F.

    (Tilburg University, School of Economics and Management)

Abstract

The equilibria of a model of an exchange economy with price rigidities are called constrained equilibria. A simplicial algorithm on the unit cube is proposed to compute an approximation of a continuum of zero points of the excess demand correspondence of such an economy. This continuum of zero points corresponds to a continuum of constrained equilibria of the economy, linking the two so-called trivial equilibria. Moreover, the convergence properties of the algorithm and the accuracy of the approximate constrained equilibria obtained by the algorithm are discussed. Finally, an example is given as an illustration.
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Suggested Citation

  • Herings, P.J.J. & Talman, A.J.J. & Yang, Z.F., 1996. "The computation of a continuum of constrained equilibria," Other publications TiSEM ba4c6d83-befb-4a25-8477-c, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:ba4c6d83-befb-4a25-8477-ccd85c62156d
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    References listed on IDEAS

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    1. Kaneko, Mamoru & Yamamoto, Yoshitsugu, 1986. "The existence and computation of competitive equilibria in markets with an indivisible commodity," Journal of Economic Theory, Elsevier, vol. 38(1), pages 118-136, February.
    2. Cornielje, O. J. C. & Van Der Laan, G., 1986. "The computation of quantity-constrained equilibria by virtual taxes," Economics Letters, Elsevier, vol. 22(1), pages 1-6.
    3. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    4. Herings, P.J.J., 1992. "On the structure of constrained equilibria," Other publications TiSEM 4c64f078-57cf-43ea-aee2-f, Tilburg University, School of Economics and Management.
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    Citations

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    Cited by:

    1. Dolf Talman & Zaifu Yang, 2012. "On a Parameterized System of Nonlinear Equations with Economic Applications," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 644-671, August.
    2. Talman, A.J.J. & Yamamoto, M., 2001. "Contiuum of Zero Points of a Mapping on a Compact Convex Set," Discussion Paper 2001-56, Tilburg University, Center for Economic Research.
    3. Kazuya Kamiya & So Kubota & Kayuna Nakajima, 2011. "Efficient estimation and particle filter for max-stable processes," CIRJE F-Series CIRJE-F-792, CIRJE, Faculty of Economics, University of Tokyo.
    4. Herings, P. Jean-Jacques & van der Laan, Gerard & Talman, Dolf, 2009. "Equilibria with coordination failures," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 23-37, January.
    5. Talman, A.J.J. & Yang, Z.F., 2003. "On the Connectedness of Coincidences and Zero Points of Mappings," Other publications TiSEM b061dd09-2b7f-4fe3-af6e-d, Tilburg University, School of Economics and Management.
    6. Herings, P.J.J. & Talman, A.J.J. & Yang, Z.F., 1999. "Variational Inequality Problems With a Continuum of Solutions : Existence and Computation," Other publications TiSEM 73e2f01b-ad4d-4447-95ba-a, Tilburg University, School of Economics and Management.
    7. Andersson, Tommy & Yang, Zaifu & Zhang, Dongmo, 2015. "How to efficiently allocate houses under price controls?," Economics Letters, Elsevier, vol. 130(C), pages 97-99.
    8. Kazuya Kamiya & Takashi Shimizu, 2005. "A New Technique for Proving the Existence of Monetary Equilibria in Matching Models with Divisible Money," CARF F-Series CARF-F-037, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    9. Herings, P. Jean-Jacques & van den Elzen, Antoon, 2002. "Computation of the Nash Equilibrium Selected by the Tracing Procedure in N-Person Games," Games and Economic Behavior, Elsevier, vol. 38(1), pages 89-117, January.
    10. Xiaotie Deng & Qi Qi & Amin Saberi & Jie Zhang, 2011. "Discrete Fixed Points: Models, Complexities, and Applications," Mathematics of Operations Research, INFORMS, vol. 36(4), pages 636-652, November.
    11. Talman, A.J.J. & Yang, Z.F., 2008. "A dynamic auction for differentiated items under price rigidity," Other publications TiSEM dbce61c1-07fd-4e95-a9c1-4, Tilburg University, School of Economics and Management.
    12. Kazuya Kamiya & Takashi Shimizu, 2004. "Real Indeterminacy of Stationary Equilibria in Matching Models with Media of Exchange," CIRJE F-Series CIRJE-F-167, CIRJE, Faculty of Economics, University of Tokyo.
    13. Herings, P.J.J. & van der Laan, G. & Talman, A.J.J., 1998. "Price-Quantity Adjustment in a Keynesian Economy," Discussion Paper 1998-118, Tilburg University, Center for Economic Research.
    14. Talman, Dolf & Yang, Zaifu, 2008. "A dynamic auction for differentiated items under price rigidities," Economics Letters, Elsevier, vol. 99(2), pages 278-281, May.
    15. Babenko, R. & Talman, A.J.J., 2006. "Quantity Constrained General Equilibrium," Other publications TiSEM 393bf7c1-3045-4a3b-b3c3-5, Tilburg University, School of Economics and Management.
    16. P. J. J. Herings & G. A. Koshevoy & A. J. J. Talman & Z. Yang, 2004. "General Existence Theorem of Zero Points," Journal of Optimization Theory and Applications, Springer, vol. 120(2), pages 375-394, February.
    17. P. J. J. Herings & A. J. J. Talman, 1998. "Intersection Theorems with a Continuum of Intersection Points," Journal of Optimization Theory and Applications, Springer, vol. 96(2), pages 311-335, February.
    18. Kamiya, Kazuya & Talman, Dolf, 2009. "Matching models with a conservation law: The existence and global structure of the set of stationary equilibria," Journal of Mathematical Economics, Elsevier, vol. 45(5-6), pages 397-413, May.
    19. van den Elzen, Antoon & Kremers, Hans, 2006. "An adjustment process for nonconvex production economies," Journal of Mathematical Economics, Elsevier, vol. 42(1), pages 1-13, February.
    20. van den Elzen, Antoon, 1997. "An adjustment process for the standard Arrow-Debreu model with production," Journal of Mathematical Economics, Elsevier, vol. 27(3), pages 315-324, April.
    21. Zaifu Yang & Dongmo Zhang, 2013. "On a Fundamental Property of Talman-Yang's Auction under Price Control," Discussion Papers 13/06, Department of Economics, University of York.

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