IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1909.11219.html
   My bibliography  Save this paper

The converse envelope theorem

Author

Listed:
  • 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.

Suggested Citation

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

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1909.11219
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    3. Mirrlees, J. A., 1976. "Optimal tax theory : A synthesis," Journal of Public Economics, Elsevier, vol. 6(4), pages 327-358, November.
    4. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    5. Spence, Michael, 1974. "Competitive and optimal responses to signals: An analysis of efficiency and distribution," Journal of Economic Theory, Elsevier, vol. 7(3), pages 296-332, March.
    6. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    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.
    9. Morand, Olivier & Reffett, Kevin & Tarafdar, Suchismita, 2015. "A nonsmooth approach to envelope theorems," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 157-165.
    10. Silberberg, Eugene, 1974. "A revision of comparative statics methodology in economics, or, how to do comparative statics on the back of an envelope," Journal of Economic Theory, Elsevier, vol. 7(2), pages 159-172, February.
    11. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Gregorio Curello & Ludvig Sinander, 2024. "The Comparative Statics of Persuasion," CRC TR 224 Discussion Paper Series crctr224_2024_564, University of Bonn and University of Mannheim, Germany.
    2. Bíró, Anikó & Prinz, Dániel & Sándor, László, 2022. "The minimum wage, informal pay, and tax enforcement," Journal of Public Economics, Elsevier, vol. 215(C).
    3. Rahman, David M., 2024. "Detecting profitable deviations," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    4. Nicolo Cesa-Bianchi & Roberto Colomboni & Maximilian Kasy, 2023. "Adaptive maximization of social welfare," Papers 2310.09597, arXiv.org, revised Jul 2024.
    5. Mark Whitmeyer, 2022. "Making Information More Valuable," Papers 2210.04418, arXiv.org, revised Jun 2024.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ludvig Sinander, 2022. "The Converse Envelope Theorem," Econometrica, Econometric Society, vol. 90(6), pages 2795-2819, November.
    2. X. Ruiz del Portal, 2012. "Conditions for incentive compatibility in models with multidimensional allocation functions and one-dimensional types," Review of Economic Design, Springer;Society for Economic Design, vol. 16(4), pages 311-321, December.
    3. Golosov, M. & Tsyvinski, A. & Werquin, N., 2016. "Recursive Contracts and Endogenously Incomplete Markets," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 725-841, Elsevier.
    4. Mishra, Debasis & Pramanik, Anup & Roy, Souvik, 2014. "Multidimensional mechanism design in single peaked type spaces," Journal of Economic Theory, Elsevier, vol. 153(C), pages 103-116.
    5. Marimon, Ramon & Werner, Jan, 2021. "The envelope theorem, Euler and Bellman equations, without differentiability," Journal of Economic Theory, Elsevier, vol. 196(C).
    6. Araujo, Aloisio & Moreira, Humberto, 2010. "Adverse selection problems without the Spence-Mirrlees condition," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1113-1141, May.
    7. Noldeke,G. & Samuelson,L., 2004. "Decomposable principal-agent problems," Working papers 14, Wisconsin Madison - Social Systems.
    8. Noldeke, Georg & Samuelson, Larry, 2007. "Optimal bunching without optimal control," Journal of Economic Theory, Elsevier, vol. 134(1), pages 405-420, May.
    9. David Martimort & Jérôme Pouyet & Carine Staropoli, 2020. "Use and abuse of regulated prices in electricity markets: “How to regulate regulated prices?”," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 29(3), pages 605-634, July.
    10. Olivier Morand & Kevin Reffett & Suchismita Tarafdar, 2018. "Generalized Envelope Theorems: Applications to Dynamic Programming," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 650-687, March.
    11. Hector Chade, 2017. "Disentangling Moral Hazard and Adverse Selection," 2017 Meeting Papers 1537, Society for Economic Dynamics.
    12. Frongillo, Rafael M. & Kash, Ian A., 2021. "General truthfulness characterizations via convex analysis," Games and Economic Behavior, Elsevier, vol. 130(C), pages 636-662.
    13. Ruiz del Portal, X., 2009. "A general principal-agent setting with non-differentiable mechanisms: Some examples," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 262-278, March.
    14. repec:dau:papers:123456789/2317 is not listed on IDEAS
    15. Dassiou, Xeni & Glycopantis, Dionysius, 2017. "A note on the envelope theorem," Economics Letters, Elsevier, vol. 150(C), pages 77-82.
    16. Zou, Liang, 1992. "Threat-based incentive mechanisms under moral hazard and adverse selection," Journal of Comparative Economics, Elsevier, vol. 16(1), pages 47-74, March.
    17. Paweł Dziewulski, 2011. "On Time-to-Build Economies with Multiple-Stage Investments," Gospodarka Narodowa. The Polish Journal of Economics, Warsaw School of Economics, issue 9, pages 23-49.
    18. 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.
    19. M. Yenmez, 2014. "Pricing in position auctions and online advertising," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(1), pages 243-256, January.
    20. Castro-Pires, Henrique & Moreira, Humberto, 2021. "Limited liability and non-responsiveness in agency models," Games and Economic Behavior, Elsevier, vol. 128(C), pages 73-103.
    21. Hanming Fang & Peter Norman, 2014. "Toward an efficiency rationale for the public provision of private goods," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 375-408, June.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    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:arx:papers:1909.11219. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.