IDEAS home Printed from
   My bibliography  Save this paper

The Envelope Theorems


  • Paul Milgrom


December 19, 1999 (Revised) At least three different "envelope theorems" have proved useful for economic analysis. One applies to unconstrained optimization problems with parameterized objectives and unique solutions, a second to constrained, smooth concave maximization problems in which both the objective and constraint are parameterized, and a third, which had not previously been given a general statement, to problems with parameterized objectives and any number of solutions. We state and prove the third theorem, generalize the first, and develop the precise relationship among the three.

Suggested Citation

  • Paul Milgrom, "undated". "The Envelope Theorems," Working Papers 99016, Stanford University, Department of Economics.
  • Handle: RePEc:wop:stanec:99016

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Jehiel, Philippe & Moldovanu, Benny, 2001. "Efficient Design with Interdependent Valuations," Econometrica, Econometric Society, vol. 69(5), pages 1237-1259, September.
    2. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    3. J. A. Mirrlees, 1971. "An Exploration in the Theory of Optimum Income Taxation," Review of Economic Studies, Oxford University Press, vol. 38(2), pages 175-208.
    4. Vijay Krishna & Motty Perry, 1997. "Efficient Mechanism Design," Game Theory and Information 9703010, EconWPA, revised 28 Apr 1998.
    5. Milgrom, Paul & Roberts, John, 1988. " Communication and Inventory as Substitutes in Organizing Production," Scandinavian Journal of Economics, Wiley Blackwell, vol. 90(3), pages 275-289.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. Hector Chade & Virginia N. Vera de Serio, 2002. "Risk aversion, moral hazard, and the principal's loss," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(3), pages 637-644.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:


    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:wop:stanec:99016. 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: (Thomas Krichel). 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.

    If CitEc recognized a 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.

    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.