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The converse envelope theorem

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  • Ludvig Sinander

Abstract

I prove an envelope theorem with a converse: the envelope formula is equivalent to a first-order condition. Like Milgrom and Segal's (2002) envelope theorem, my result requires no structure on the choice set. I use the converse envelope theorem to extend to general outcomes and preferences the canonical result in mechanism design that any increasing allocation is implementable, and apply this to selling information.

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  • Ludvig Sinander, 2019. "The converse envelope theorem," Papers 1909.11219, arXiv.org, revised Jun 2022.
    • Handle: RePEc:arx:papers:1909.11219
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    References listed on IDEAS

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    1. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    2. Benveniste, L M & Scheinkman, J A, 1979. "On the Differentiability of the Value Function in Dynamic Models of Economics," Econometrica, Econometric Society, vol. 47(3), pages 727-732, May.
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    7. Oyama, Daisuke & Takenawa, Tomoyuki, 2018. "On the (non-)differentiability of the optimal value function when the optimal solution is unique," Journal of Mathematical Economics, Elsevier, vol. 76(C), pages 21-32.
    8. Guesnerie, Roger & Laffont, Jean-Jacques, 1984. "A complete solution to a class of principal-agent problems with an application to the control of a self-managed firm," Journal of Public Economics, Elsevier, vol. 25(3), pages 329-369, December.
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    Cited by:

    1. Bíró, Anikó & Prinz, Dániel & Sándor, László, 2022. "The minimum wage, informal pay, and tax enforcement," Journal of Public Economics, Elsevier, vol. 215(C).
    2. Mark Whitmeyer, 2022. "Making Information More Valuable," Papers 2210.04418, arXiv.org, revised Dec 2023.

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