IDEAS home Printed from https://ideas.repec.org/a/wly/emetrp/v90y2022i6p2795-2819.html
   My bibliography  Save this article

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, 2022. "The Converse Envelope Theorem," Econometrica, Econometric Society, vol. 90(6), pages 2795-2819, November.
  • Handle: RePEc:wly:emetrp:v:90:y:2022:i:6:p:2795-2819
    DOI: 10.3982/ECTA18119
    as

    Download full text from publisher

    File URL: https://doi.org/10.3982/ECTA18119
    Download Restriction: no

    File URL: https://libkey.io/10.3982/ECTA18119?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Matthews, Steven & Moore, John, 1987. "Monopoly Provision of Quality and Warranties: An Exploration in the Theory of Multidimensional Screening," Econometrica, Econometric Society, vol. 55(2), pages 441-467, March.
    2. Alessandro Pavan & Ilya Segal & Juuso Toikka, 2014. "Dynamic Mechanism Design: A Myersonian Approach," Econometrica, Econometric Society, vol. 82(2), pages 601-653, March.
    3. 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.
    4. Clausen, Andrew & Strub, Carlo, 2020. "Reverse Calculus and nested optimization," Journal of Economic Theory, Elsevier, vol. 187(C).
    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. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721, November.
    8. Mirrlees, J. A., 1976. "Optimal tax theory : A synthesis," Journal of Public Economics, Elsevier, vol. 6(4), pages 327-358, November.
    9. 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.
    10. 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.
    11. 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.
    12. Harold Hotelling, 1932. "Edgeworth's Taxation Paradox and the Nature of Demand and Supply Functions," Journal of Political Economy, University of Chicago Press, vol. 40(5), pages 577-577.
    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. Nicolo Cesa-Bianchi & Roberto Colomboni & Maximilian Kasy, 2023. "Adaptive maximization of social welfare," Papers 2310.09597, arXiv.org, revised Jul 2024.
    2. Mark Whitmeyer, 2022. "Making Information More Valuable," Papers 2210.04418, arXiv.org, revised Jun 2024.
    3. 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.
    4. Rahman, David M., 2024. "Detecting profitable deviations," Journal of Mathematical Economics, Elsevier, vol. 111(C).

    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, 2019. "The converse envelope theorem," Papers 1909.11219, arXiv.org, revised Jun 2022.
    2. Hellwig, Martin F., 2007. "A contribution to the theory of optimal utilitarian income taxation," Journal of Public Economics, Elsevier, vol. 91(7-8), pages 1449-1477, August.
    3. Marco Buso & Cesare Dosi & Michele Moretto, 2018. "Termination Fees and Contract Design in Public-Private Partnerships," Working Papers 2018.32, Fondazione Eni Enrico Mattei.
    4. 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.
    5. 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.
    6. 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.
    7. Marco Buso & Cesare Dosi & Michele Moretto, 2021. "Do exit options increase the value for money of public–private partnerships?," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 30(4), pages 721-742, November.
    8. repec:dau:papers:123456789/2317 is not listed on IDEAS
    9. Aloisio Pessoa_de_Araujo & Humberto L. Moreira, 2000. "Adverse Selection Problems without The Single Crossing Property," Econometric Society World Congress 2000 Contributed Papers 1874, Econometric Society.
    10. Peysakhovich, Alexander & Plagborg-Møller, Mikkel, 2012. "A note on proper scoring rules and risk aversion," Economics Letters, Elsevier, vol. 117(1), pages 357-361.
    11. Di Corato, Luca & Dosi, Cesare & Moretto, Michele, 2015. "Multidimensional auctions for long-term procurement contracts under the threat of early exit: the case of conservation auctions," Working Paper Series 2015:6, Swedish University of Agricultural Sciences, Department Economics.
    12. Schnizler, Björn & Neumann, Dirk & Veit, Daniel & Napoletano, Mauro & Catalano, Michele & Gallegati, Mauro & Reinicke, Michael & Streitberger, Werner & Eymann, Torsten, 2005. "Environmental analysis for application layer networks," Bayreuth Reports on Information Systems Management 1, University of Bayreuth, Chair of Information Systems Management.
    13. Ales, Laurence & Maziero, Pricila & Yared, Pierre, 2014. "A theory of political and economic cycles," Journal of Economic Theory, Elsevier, vol. 153(C), pages 224-251.
    14. Hao Li & Xianwen Shi, 2017. "Discriminatory Information Disclosure," American Economic Review, American Economic Association, vol. 107(11), pages 3363-3385, November.
    15. Dirk Bergemann & Alessandro Pavan, 2015. "Introduction to JET Symposium Issue on "Dynamic Contracts and Mechanism Design"," Cowles Foundation Discussion Papers 2016, Cowles Foundation for Research in Economics, Yale University.
    16. William P. Rogerson, 1987. "On the Optimality of Menus of Linear Contracts," Discussion Papers 714, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    17. Hatfield, John William & Kominers, Scott Duke, 2017. "Contract design and stability in many-to-many matching," Games and Economic Behavior, Elsevier, vol. 101(C), pages 78-97.
    18. Martin Hellwig, 2010. "Utilitarian mechanism design for an excludable public good," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(3), pages 361-397, September.
    19. Robin Boadway, 1998. "The Mirrlees Approach to the Theory of Economic Policy," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 5(1), pages 67-81, February.
    20. Lehmann, Etienne & Parmentier, Alexis & Van Der Linden, Bruno, 2011. "Optimal income taxation with endogenous participation and search unemployment," Journal of Public Economics, Elsevier, vol. 95(11), pages 1523-1537.
    21. B. Caillaud & R. Guesnerie & P. Rey & J. Tirole, 1988. "Government Intervention in Production and Incentives Theory: A Review of Recent Contributions," RAND Journal of Economics, The RAND Corporation, vol. 19(1), pages 1-26, Spring.

    More about this item

    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:wly:emetrp:v:90:y:2022:i:6:p:2795-2819. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.html .

    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.