IDEAS home Printed from https://ideas.repec.org/a/kap/compec/v55y2020i2d10.1007_s10614-019-09904-z.html
   My bibliography  Save this article

Approximating Walrasian Equilibria

Author

Listed:
  • Aad Ruiter

    (University of Amsterdam)

Abstract

This paper proposes a price adjustment process that converges globally for a set of pure exchange economies, in which each agent has a Constant Elasticity of Substitution utility function. In this process, the auctioneer approximates demand schedules by assuming that each trader has a Cobb–Douglas utility function. The process generates prices that cannot be represented by linear combinations of previous prices, and hence precludes cycles. In the so-called unstable Scarf economies, prices spiral towards the Walrasian equilibrium in the same direction as found by Scarf. Simulation in large scale Scarf economies suggests that the speed of convergence may be polynomial in the size of the economy.

Suggested Citation

  • Aad Ruiter, 2020. "Approximating Walrasian Equilibria," Computational Economics, Springer;Society for Computational Economics, vol. 55(2), pages 577-596, February.
    • Handle: RePEc:kap:compec:v:55:y:2020:i:2:d:10.1007_s10614-019-09904-z
    DOI: 10.1007/s10614-019-09904-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10614-019-09904-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10614-019-09904-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jean-Jacques Herings, P., 1997. "A globally and universally stable price adjustment process," Journal of Mathematical Economics, Elsevier, vol. 27(2), pages 163-193, March.
    2. Alok Kumar & Martin Shubik, 2004. "Variations on the Theme of Scarf's Counter-Example," Computational Economics, Springer;Society for Computational Economics, vol. 24(1), pages 1-19, August.
    3. Smale, Steve, 1976. "A convergent process of price adjustment and global newton methods," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 107-120, July.
    4. Van Der Laan, G. & Talman, A. J. J., 1987. "A convergent price adjustment process," Economics Letters, Elsevier, vol. 23(2), pages 119-123.
    5. Sonnenschein, Hugo, 1973. "Do Walras' identity and continuity characterize the class of community excess demand functions?," Journal of Economic Theory, Elsevier, vol. 6(4), pages 345-354, August.
    6. Jean-Jacques Herings, P., 2002. "Universally converging adjustment processes--a unifying approach," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 341-370, November.
    7. Mantel, Rolf R., 1974. "On the characterization of aggregate excess demand," Journal of Economic Theory, Elsevier, vol. 7(3), pages 348-353, March.
    8. Goeree, Jacob K. & Lindsay, Luke, 2016. "Market design and the stability of general equilibrium," Journal of Economic Theory, Elsevier, vol. 165(C), pages 37-68.
    9. Anderson, Christopher M. & Plott, Charles R. & Shimomura, K.-I.Ken-Ichi & Granat, Sander, 2004. "Global instability in experimental general equilibrium: the Scarf example," Journal of Economic Theory, Elsevier, vol. 115(2), pages 209-249, April.
    10. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, December.
    11. Mantel, Rolf R., 1976. "Homothetic preferences and community excess demand functions," Journal of Economic Theory, Elsevier, vol. 12(2), pages 197-201, April.
    12. Herbert E. Scarf, 1967. "The Approximation of Fixed Points of a Continuous Mapping," Cowles Foundation Discussion Papers 216R, Cowles Foundation for Research in Economics, Yale University.
    13. Herbert Gintis, 2007. "The Dynamics of General Equilibrium," Economic Journal, Royal Economic Society, vol. 117(523), pages 1280-1309, October.
    14. Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
    15. Saari, Donald G & Simon, Carl P, 1978. "Effective Price Mechanisms," Econometrica, Econometric Society, vol. 46(5), pages 1097-1125, September.
    Full references (including those not matched with items on IDEAS)

    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. Joosten, Reinoud & Talman, Dolf, 1998. "A globally convergent price adjustment process for exchange economies," Journal of Mathematical Economics, Elsevier, vol. 29(1), pages 15-26, January.
    2. Paul Oslington, 2012. "General Equilibrium: Theory and Evidence," The Economic Record, The Economic Society of Australia, vol. 88(282), pages 446-448, September.
    3. Herings,P. Jean-Jacques, 2000. "Universally Stable Adjustment Processes - A Unifying Approach -," Research Memorandum 006, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    4. W D A Bryant, 2009. "General Equilibrium:Theory and Evidence," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6875.
    5. Jean-Jacques Herings, P., 2002. "Universally converging adjustment processes--a unifying approach," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 341-370, November.
    6. Anjan Mukherji, 2012. "The second fundamental theorem of positive economics," International Journal of Economic Theory, The International Society for Economic Theory, vol. 8(2), pages 125-138, June.
    7. Jean-Jacques Herings, P., 1997. "A globally and universally stable price adjustment process," Journal of Mathematical Economics, Elsevier, vol. 27(2), pages 163-193, March.
    8. Arkit, Aleksandra, 2003. "Globally stable price dynamics," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 27-38, February.
    9. Rabani, Yuval & Schulman, Leonard J., 2021. "The invisible hand of Laplace: The role of market structure in price convergence and oscillation," Journal of Mathematical Economics, Elsevier, vol. 95(C).
    10. Yuval Rabani & Leonard J. Schulman, 2016. "The Invisible Hand of Laplace: the Role of Market Structure in Price Convergence and Oscillation," Papers 1602.07628, arXiv.org.
    11. Herings, P.J.J., 1994. "A globally and universally stable quantity adjustment process for an exchange economy with price rigidities," Other publications TiSEM 6f90d995-9065-4ad8-bd04-2, Tilburg University, School of Economics and Management.
    12. Colander, David & Rothschild, Casey, 2010. "Sins of the Sons of Samuelson: Vision, pedagogy, and the zig-zag windings of complex dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 74(3), pages 277-290, June.
    13. Sean Crockett & Daniel Friedman & Ryan Oprea, 2021. "Naturally Occurring Preferences And General Equilibrium: A Laboratory Study," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 62(2), pages 831-859, May.
    14. Chiappori, P. A. & Ekeland, I., 2004. "Individual excess demands," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 41-57, February.
    15. Jugal Garg & Ruta Mehta & Vijay V. Vaziranic, 2018. "Substitution with Satiation: A New Class of Utility Functions and a Complementary Pivot Algorithm," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 996-1024, August.
    16. Gaël Giraud, 2004. "The limit-price exchange process," Cahiers de la Maison des Sciences Economiques b04118, Université Panthéon-Sorbonne (Paris 1).
    17. Joosten, Reinoud, 1995. "Evolution, dynamics, and fixed points," Research Memorandum 005, Maastricht University, Maastricht Economic Research Institute on Innovation and Technology (MERIT).
    18. Crockett, Sean & Friedman, Daniel & Oprea, Ryan, 2017. "Aggregation and convergence in experimental general equilibrium economies constructed from naturally occurring preferences," Discussion Papers, Research Professorship Market Design: Theory and Pragmatics SP II 2017-501, WZB Berlin Social Science Center.
    19. Gerard Ballot & Antoine Mandel & Annick Vignes, 2015. "Agent-based modeling and economic theory: where do we stand?," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 10(2), pages 199-220, October.
    20. Chiappori, Pierre-Andre & Ekeland, Ivar & Browning, Martin, 2007. "Local disaggregation of negative demand and excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 43(6), pages 764-770, August.

    More about this item

    Keywords

    Walrasian equilibrium; Scarf examples; CES preferences; Computation; Complexity;
    All these keywords.

    JEL classification:

    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

    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:kap:compec:v:55:y:2020:i:2:d:10.1007_s10614-019-09904-z. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.