IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Hildenbrand Distribution Economies as Limiting Empirical Distributions of Random Economies

  • Martin Hohnisch
Registered author(s):

    The present note shows that the concept of a distribution economy (Hildenbrand (1974)) is closely related to a framework of an exchange economy in which the agents’ individual characteristics (i.e. preferences and endowments) are random (Hildenbrand (1971), Bhattacharya and Majumdar (1973), Föllmer (1974)). A random exchange economy is fully specified by the distribution of the family of random variables representing the agents’ individual characteristics. This distribution is a probability measure µ on (SA, B(S)A) with S denoting the space of individual characteristics, B(S) the Borel o-algebra generated by an appropriate topology on S and A a denumerable set of agents. The linkage between a Hildenbrand distribution economy and an ergodic random exchange economy with a countably infinite set of agents endowed with the graph topology of the integer lattice Zd is established in this paper by a convergence result for the empirical distribution of the latter. For any increasing sequence of finite subsets of A exhausting A, the associated sequence of empirical distributions converges almost everywhere on the underlying probability space to some distribution v on (S, B(S)). As far as aggregate variables of the economy, such as the mean demand or the equilibrium price system are concerned, any infinite random exchange economy with converging limiting empirical distribution v is equivalent to a Hildenbrand distribution economy characterized by the same distribution v. This relationship suggests an approach to endogenous modelling of distributions of individual characteristics in General Equilibrium Theory. Thereby, specific distributions of characteristics can be obtained from a specific stochastic microstructure of local interaction between agents affecting their individual characteristics.

    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: http://www.wiwi.uni-bonn.de/bgsepapers/bonedp/bgse28_2003.pdf
    Download Restriction: no

    Paper provided by University of Bonn, Germany in its series Bonn Econ Discussion Papers with number bgse28_2003.

    as
    in new window

    Length: 29
    Date of creation: Dec 2003
    Date of revision:
    Handle: RePEc:bon:bonedp:bgse28_2003
    Contact details of provider: Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
    Fax: +49 228 73 6884
    Web page: http://www.bgse.uni-bonn.de

    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. Evstigneev, I. & Taksar, M., 1994. "Stochastic equilibria on graphs, I," Journal of Mathematical Economics, Elsevier, vol. 23(5), pages 401-433, September.
    2. Kapteyn, A. & van der Geer, S. & van de Stadt, H. & Wansbeek, T., 1997. "Interdependent preferences : An econometric analysis," Other publications TiSEM cd68dbcd-ca9b-45bf-9ae2-b, Tilburg University, School of Economics and Management.
    3. Blume,L.E. & Durlauf,S.N., 2000. "The interactions-based approach to socioeconomic behavior," Working papers 1, Wisconsin Madison - Social Systems.
    4. Bhattacharya, Rabindra Nath & Majumdar, Mukul, 1973. "Random exchange economies," Journal of Economic Theory, Elsevier, vol. 6(1), pages 37-67, February.
    5. Kannai, Yakar, 1970. "Continuity Properties of the Core of a Market," Econometrica, Econometric Society, vol. 38(6), pages 791-815, November.
    6. Hildenbrand, Werner, 1971. "Random preferences and equilibrium analysis," Journal of Economic Theory, Elsevier, vol. 3(4), pages 414-429, December.
    7. Kapteyn, A. & Van De Ger, S. & Van De Stadt, H. & Wansbeek, T., 1989. "Interdependent Preferences: An Econometric Analysis," Papers 8954, Tilburg - Center for Economic Research.
    8. Follmer, Hans, 1974. "Random economies with many interacting agents," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 51-62, March.
    9. Hildenbrand, Werner, 1970. "On economies with many agents," Journal of Economic Theory, Elsevier, vol. 2(2), pages 161-188, June.
    10. Grodal, Birgit, 1974. "A note on the space of preference relations," Journal of Mathematical Economics, Elsevier, vol. 1(3), pages 279-294, December.
    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:bon:bonedp:bgse28_2003. 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: (BGSE Office)

    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.