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The Envelope Theorems

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Author Info
Paul Milgrom

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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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Paper provided by Stanford University, Department of Economics in its series Working Papers with number 99016.

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Handle: RePEc:wop:stanec:99016

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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.:
  1. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January. [Downloadable!] (restricted)
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  2. Jehiel, Phillipe & Moldovanu, Benny, 1999. "Efficient Design with Interdependent Valuations," Sonderforschungsbereich 504 Publications 99-74, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim. [Downloadable!]
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  3. Mirrlees, James A, 1971. "An Exploration in the Theory of Optimum Income Taxation," Review of Economic Studies, Blackwell Publishing, vol. 38(114), pages 175-208, April. [Downloadable!] (restricted)
  4. Vijay Krishna & Motty Perry, 1997. "Efficient Mechanism Design," Game Theory and Information 9703010, EconWPA, revised 28 Apr 1998. [Downloadable!]
  5. Milgrom, Paul & Roberts, John, 1988. " Communication and Inventory as Substitutes in Organizing Production," Scandinavian Journal of Economics, Blackwell Publishing, vol. 90(3), pages 275-89.
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(explanations, 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.)

  1. Hector Chade & Virginia Vera de Serio, . "Risk Aversion, Moral Hazard, and the Principal's Loss," Working Papers 2133303, Department of Economics, W. P. Carey School of Business, Arizona State University. [Downloadable!]
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