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The Envelope Theorems

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  • Paul Milgrom

Abstract

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.

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  • Paul Milgrom, "undated". "The Envelope Theorems," Working Papers 99016, Stanford University, Department of Economics.
    • Handle: RePEc:wop:stanec:99016
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    File URL: http://www-econ.stanford.edu/faculty/workp/swp99016.pdf
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    References listed on IDEAS

    as
    1. J. A. Mirrlees, 1971. "An Exploration in the Theory of Optimum Income Taxation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(2), pages 175-208.
    2. Vijay Krishna & Motty Perry, 1997. "Efficient Mechanism Design," Game Theory and Information 9703010, University Library of Munich, Germany, revised 28 Apr 1998.
    3. repec:bla:scandj:v:90:y:1988:i:3:p:275-89 is not listed on IDEAS
    4. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    5. Jehiel, Philippe & Moldovanu, Benny, 2001. "Efficient Design with Interdependent Valuations," Econometrica, Econometric Society, vol. 69(5), pages 1237-1259, September.
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