IDEAS home Printed from
   My bibliography  Save this paper

Linear Programming and General Equilibrium Theory


  • Louis Makowski

    (University of California)

  • Joseph M. Ostroy

    (University of California)


The general equilibrium model of market pricing and the duality theory of linear programming (LP) are paradigmatic expressions of the duality relation between quantities and prices. While LP is canonical, the market duality found in general equilibrium theory is regarded as the more comprehensive in the sense that LP models of markets are special cases of the general equilibrium model. This paper shows that by adopting an infinite-dimensional perspective, the general equilibrium model of market pricing can be formulated to fit inside LP theory. When utility is quasi-linear (transferable), LP solutions to the primal and dual coincide with market equilibria. When utility is ordinal, we show that LP theory can nevertheless be used to characterize market equilibrium through the money metric utility representation of preferences. A key feature of the LP formulation is that not only commodities, but also individuals, are ``right-hand side constraints'' of the LP problem. An implication of this feature, not explicitly found in the market equilibrium model, is the emergence of the individual as a margin of analysis and, dually, the prices of individuals. The individual as a margin of analysis is important in highlighting the properties of perfectly competitive equilibrium not emphasized in the general equilibrium model. It is also central to the relation between market equilibrium and game-theoretic concepts such as the core and the Shapley value in models with a continuum of individuals. Using the LP perspective, we demonstrate the connections among market equilibrium, the core and the Shapley value for models with both transferable and ordinal utility.

Suggested Citation

  • Louis Makowski & Joseph M. Ostroy, 2000. "Linear Programming and General Equilibrium Theory," Econometric Society World Congress 2000 Contributed Papers 1673, Econometric Society.
  • Handle: RePEc:ecm:wc2000:1673

    Download full text from publisher

    File URL:
    File Function: main text
    Download Restriction: no


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

    Cited by:

    1. Michel Le Breton & Juan Moreno-Ternero & Alexei Savvateev & Shlomo Weber, 2013. "Stability and fairness in models with a multiple membership," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 673-694, August.
    2. Peñaloza, Rodrigo, 2009. "A duality theory of payment systems," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 679-692, September.

    More about this item


    Access and download statistics


    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:ecm:wc2000:1673. 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: .

    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.