IDEAS home Printed from https://ideas.repec.org/p/sce/scecf0/266.html
   My bibliography  Save this paper

Undecidable Economic Dynamics

Author

Listed:
  • K. Vela Velupillai

    (University of Trento)

Abstract

In a recent paper (Velupillai, 1999) I discussed the following two propositions (in reverse order):Proposition 1: Assume that the (individual) market excess-demand functions are restricted to be defined on the domain of computable reals. Suppose also that we have an arbitrary exchange economy satisfying (i)~(iii): (i). Market excess-demand functions are homogeneous of degree zero in prices: z(lp) = z(p), l Î Â+ where, z: the vector of market excess-demands p: the vector of prices (ii). Market excess-demand functions satisfy the Walras Law: p.z(p) = 0 (iii). Market excess-demand functions are continuous over their (appropriately dimensioned) domain of definition: and a p*. Then, given any algorithm, initialised at the configuration of the given arbitrary exchange economy, it is undecidable whether it will terminate at p*.Proposition 2: Assume that the market excess-demand functions are computable and, therefore, continuous (hence satisfying (iii), above), on a suitable subset of Sn+ ´ T (T: time axis). Then, there exist exchange economies such that the solution to the associated tŸtonnement process: is uncomputable inside a nontrivial domain of z(p(t),t). These propositions were stated without detailed proofs; only some broad hints were provided. In this paper an attempt is made to provide detailed proofs for the above two propositions. The constructions underlying the detailed proofs makes it possible to seek a closer connection between constructive and computable analysis. In a concluding section I speculate on the possibility that intuitionistic logic may also lie at the foundations of computable analysis.

Suggested Citation

  • K. Vela Velupillai, 2000. "Undecidable Economic Dynamics," Computing in Economics and Finance 2000 266, Society for Computational Economics.
  • Handle: RePEc:sce:scecf0:266
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    More about this item

    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:sce:scecf0:266. 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: (Christopher F. Baum). General contact details of provider: http://edirc.repec.org/data/sceeeea.html .

    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.

    We have no references for this item. You can help adding them by using 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.