IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v34y2010i6p1077-1091.html
   My bibliography  Save this article

Convergence of iterative tâtonnement without price normalization

Author

Listed:
  • Kitti, Mitri

Abstract

This paper presents global convergence conditions for a non-normalized fixed-point iteration in computing the equilibria of exchange economies. The usual conditions for the stability of Walras' tâtonnement are obtained as a limiting case from these conditions. The iteration leads to an equilibrium under a strengthened form of the weak axiom of revealed preferences introduced in the paper. Results for economies with global gross substitutability and no trade at equilibrium are also presented. Furthermore, it is shown that a rather general class of non-normalized iterations converges under the same conditions as the fixed-point iteration.

Suggested Citation

  • Kitti, Mitri, 2010. "Convergence of iterative tâtonnement without price normalization," Journal of Economic Dynamics and Control, Elsevier, vol. 34(6), pages 1077-1091, June.
    • Handle: RePEc:eee:dyncon:v:34:y:2010:i:6:p:1077-1091
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165-1889(10)00012-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702, September.
    2. Day, Richard H. & Pianigiani, Giulio, 1991. "Statistical dynamics and economics," Journal of Economic Behavior & Organization, Elsevier, vol. 16(1-2), pages 37-83, July.
    3. Debreu, Gerard, 1972. "Smooth Preferences," Econometrica, Econometric Society, vol. 40(4), pages 603-615, July.
    4. Day, Richard H. & Pianigiani, Giulio, 1991. "Statistical Dynamics and Economics," Working Paper Series 293, Research Institute of Industrial Economics.
    5. Debreu, Gerard, 1976. "Smooth Preferences: A Corrigendum," Econometrica, Econometric Society, vol. 44(4), pages 831-832, July.
    6. M. Kitti & H. Ehtamo, 2009. "Adjustment of an Affine Contract with a Fixed-Point Iteration," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 477-497, March.
    7. Anjan Mukherji, 1999. "A simple example of complex dynamics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(3), pages 741-749.
    8. Yves Balasko, 2007. "Out-of-equilibrium price dynamics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(3), pages 413-435, December.
    9. Tuinstra, Jan, 2000. "A discrete and symmetric price adjustment process on the simplex," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 881-907, June.
    10. Saari, Donald G, 1985. "Iterative Price Mechanisms," Econometrica, Econometric Society, vol. 53(5), pages 1117-1131, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mathieu Moslonka-Lefebvre & Herv'e Monod & Christopher A. Gilligan & Elisabeta Vergu & Jo~ao A. N. Filipe, 2013. "Epidemics in markets with trade friction and imperfect transactions," Papers 1310.6320, arXiv.org.
    2. Shu-Heng Chen & Bin-Tzong Chie & Ying-Fang Kao & Ragupathy Venkatachalam, 2019. "Agent-Based Modeling of a Non-tâtonnement Process for the Scarf Economy: The Role of Learning," Computational Economics, Springer;Society for Computational Economics, vol. 54(1), pages 305-341, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kaizoji, Taisei, 2010. "Multiple equilibria and chaos in a discrete tâtonnement process," Journal of Economic Behavior & Organization, Elsevier, vol. 76(3), pages 597-599, December.
    2. Hommes, Cars & Huang, Hai & Wang, Duo, 2005. "A robust rational route to randomness in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 29(6), pages 1043-1072, June.
    3. Tamotsu Onozaki, 2018. "Nonlinearity, Bounded Rationality, and Heterogeneity," Springer Books, Springer, number 978-4-431-54971-0, March.
    4. Ahmad K. Naimzada & Serena Sordi, 2018. "On controlling chaos in a discrete†time Walrasian tâtonnement process," Metroeconomica, Wiley Blackwell, vol. 69(1), pages 178-194, February.
    5. Cavalli, Fausto & Naimzada, Ahmad, 2015. "A tâtonnement process with fading memory, stabilization and optimal speed of convergence," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 116-129.
    6. Hommes, C.H. & Huang, H. & Wang, D., 2002. "A Robust Rational Route to in a Simple Asset Pricing Model," CeNDEF Working Papers 02-08, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    7. Anjan Mukherji, 2003. "Competitive Equilibria: Convergence, Cycles or Chaos," ISER Discussion Paper 0591, Institute of Social and Economic Research, The University of Osaka.
    8. Ahmad K. Naimzada & Serena Sordi, 2016. "On controlling chaos in a discrete tâtonnement process," Department of Economics University of Siena 729, Department of Economics, University of Siena.
    9. van der Laan, G. & Talman, A.J.J., 2002. "Dynamic Adjustment of Supply Constrained Disequilibria to Walrasian Equilibrium," Other publications TiSEM 8c5d443d-92c8-4e82-bcef-3, Tilburg University, School of Economics and Management.
    10. Herings, Jean-Jacques & van der Laan, Gerard & Talman, Dolf & Venniker, Richard, 1997. "Equilibrium adjustment of disequilibrium prices," Journal of Mathematical Economics, Elsevier, vol. 27(1), pages 53-77, February.
    11. Rui Pascoa, Mario & Ribeiro da Costa Werlang, Sergio, 1999. "Determinacy of equilibria in nonsmooth economies," Journal of Mathematical Economics, Elsevier, vol. 32(3), pages 289-302, November.
    12. Goeree, Jacob K. & Hommes, Cars & Weddepohl, Claus, 1998. "Stability and complex dynamics in a discrete tatonnement model," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 395-410, January.
    13. Herings, Jean-Jacques & van der Laan, Gerard & Venniker, Richard, 1998. "The transition from a Dreze equilibrium to a Walrasian equilibrium1," Journal of Mathematical Economics, Elsevier, vol. 29(3), pages 303-330, April.
    14. Zhou, Yuqing, 1997. "The structure of the pseudo-equilibrium manifold in economies with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 27(1), pages 91-111, February.
    15. Hayashi, Takashi, 2008. "A note on small income effects," Journal of Economic Theory, Elsevier, vol. 139(1), pages 360-379, March.
    16. Stahn, Hubert, 1998. "On monopolistic equilibria with incomplete markets: the case of an exchange economy," Journal of Mathematical Economics, Elsevier, vol. 29(1), pages 83-107, January.
    17. João Correia-da-Silva & Carlos Hervés-Beloso, 2014. "Irrelevance of private information in two-period economies with more goods than states of nature," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(2), pages 439-455, February.
    18. P. Jean-Jacques Herings & Herakles Polemarchakis, 2006. "Pareto Improving Price Regulation when the Asset Market is Incomplete," Studies in Economic Theory, in: Christian Schultz & Karl Vind (ed.), Institutions, Equilibria and Efficiency, chapter 12, pages 225-244, Springer.
    19. Yves Balasko & Mich Tvede, 2010. "General equilibrium without utility functions: how far to go?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 201-225, October.
    20. Predtetchinski, Arkadi & Herings, P. Jean-Jacques & Peters, Hans, 2002. "The strong sequential core for two-period economies," Journal of Mathematical Economics, Elsevier, vol. 38(4), pages 465-482, December.

    More about this item

    Keywords

    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:dyncon:v:34:y:2010:i:6:p:1077-1091. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jedc .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.