IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this paper

Power Method Tâtonnements for Cobb-Douglas Economies

Listed author(s):
  • V. Shikhman
  • Nesterov
  • Victor Ginsburgh

We consider an economy with consumers maximizing Cobb-Douglas utilities from the algorithmic perspective. It is known that in this case nding equilibrium prices reduces to the eigenvalue problem for a particularly structured stochastic matrix. We show that the power method for solving this eigenvalue problem can be naturally interpreted as a t^atonnement executed by an auctioneer. Its linear rate of convergence is established under the reasonable assumption of pairwise connectivity w.r.t. commodities within submarkets. We show that the pairwise connectivity remains valid under suciently small perturbations of consumers' tastes and endowments. Moreover, the property of pairwise connectivity holds for almost all Cobb-Douglas economies.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: https://dipot.ulb.ac.be/dspace/bitstream/2013/248466/3/2017-09-SHIKHMAN_NESTEROV_GINSBURGH-power.pdf
File Function: Œuvre complète ou partie de l'œuvre
Download Restriction: no

Paper provided by ULB -- Universite Libre de Bruxelles in its series Working Papers ECARES with number ECARES 2017-09.

as
in new window

Length: 19 p.
Date of creation: Mar 2017
Publication status: Published by:
Handle: RePEc:eca:wpaper:2013/248466
Contact details of provider: Postal:
Av. F.D., Roosevelt, 39, 1050 Bruxelles

Phone: (32 2) 650 30 75
Fax: (32 2) 650 44 75
Web page: http://difusion.ulb.ac.be

More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as
in new window


  1. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-392, May.
  2. Du, Ye & Lehrer, Ehud & Pauzner, Ady, 2015. "Competitive economy as a ranking device over networks," Games and Economic Behavior, Elsevier, vol. 91(C), pages 1-13.
  3. 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.
  4. Bonnisseau, Jean-Marc, 2003. "Regular economies with non-ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 39(3-4), pages 153-174, June.
  5. Jean-Marc Bonnisseau & Michael Florig & Alejandro Jofré, 2001. "Continuity and Uniqueness of Equilibria for Linear Exchange Economies," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00265684, HAL.
  6. Eaves, B. Curtis, 1976. "A finite algorithm for the linear exchange model," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 197-203, July.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:eca:wpaper:2013/248466. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Benoit Pauwels)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.