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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.

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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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  1. Jehiel, Phillipe & Moldovanu, Benny, 1999. "Efficient Design with Interdependent Valuations," Sonderforschungsbereich 504 Publications 99-74, Sonderforschungsbereich 504, Universit├Ąt Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  2. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
  3. Milgrom, Paul & Roberts, John, 1988. " Communication and Inventory as Substitutes in Organizing Production," Scandinavian Journal of Economics, Wiley Blackwell, vol. 90(3), pages 275-89.
  4. Vijay Krishna & Motty Perry, 1997. "Efficient Mechanism Design," Game Theory and Information 9703010, EconWPA, revised 28 Apr 1998.
  5. Mirrlees, James A, 1971. "An Exploration in the Theory of Optimum Income Taxation," Review of Economic Studies, Wiley Blackwell, vol. 38(114), pages 175-208, April.
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