IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

When is multidimensional screening a convex program?

  • Figalli, Alessio
  • Kim, Young-Heon
  • McCann, Robert J.
Registered author(s):

    A principal wishes to transact business with a multidimensional distribution of agents whose preferences are known only in the aggregate. Assuming a twist (= generalized Spence-Mirrlees single-crossing) hypothesis, quasi-linear utilities, and that agents can choose only pure strategies, we identify a structural condition on the value b(x,y) of product type y to agent type x -- and on the principal[modifier letter apostrophe]s costs c(y) -- which is necessary and sufficient for reducing the profit maximization problem faced by the principal to a convex program. This is a key step toward making the principal[modifier letter apostrophe]s problem theoretically and computationally tractable; in particular, it allows us to derive uniqueness and stability of the principal[modifier letter apostrophe]s optimal strategy -- and similarly of the strategy maximizing the expected welfare of the agents when the principal[modifier letter apostrophe]s profitability is constrained. We call this condition non-negative cross-curvature: it is also (i) necessary and sufficient to guarantee convexity of the set of b-convex functions, (ii) invariant under reparametrization of agent and/or product types by diffeomorphisms, and (iii) a strengthening of Ma, Trudinger and Wang[modifier letter apostrophe]s necessary and sufficient condition (A3w) for continuity of the correspondence between an exogenously prescribed distribution of agents and of products. We derive the persistence of economic effects such as the desirability for a monopoly to establish prices so high they effectively exclude a positive fraction of its potential customers, in nearly the full range of non-negatively cross-curved models.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL: http://www.sciencedirect.com/science/article/B6WJ3-51WD0RF-5/2/c495ce02b5ee13d26f186a052cedb769
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Article provided by Elsevier in its journal Journal of Economic Theory.

    Volume (Year): 146 (2011)
    Issue (Month): 2 (March)
    Pages: 454-478

    as
    in new window

    Handle: RePEc:eee:jetheo:v:146:y:2011:i:2:p:454-478
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

    References listed on IDEAS
    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.:

    as in new window
    1. Paulo Klinger Monteiro & Frank H. Page Jr., 1996. "Optimal Selling Mechanisms for Multiproduct Monopolists: Incentive Compatibility in the Presence of Budget Constraints," Microeconomics 9610002, EconWPA.
    2. Guesnerie, Roger & Laffont, Jean-Jacques, 1978. "Taxing price makers," Journal of Economic Theory, Elsevier, vol. 19(2), pages 423-455, December.
    3. Rochet, Jean-Charles, 1987. "A necessary and sufficient condition for rationalizability in a quasi-linear context," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 191-200, April.
    4. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
    5. David P. Baron & Roger B. Myerson, 1979. "Regulating a Monopolist with Unknown Costs," Discussion Papers 412, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    6. Carlier, Guillaume & Buttazzo, Giuseppe, 2010. "Optimal spatial pricing strategies with transportation costs," Economics Papers from University Paris Dauphine 123456789/6818, Paris Dauphine University.
    7. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
    8. 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.
    9. 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.
    10. Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
    11. Leonard J. Mirman & David Sibley, 1980. "Optimal Nonlinear Prices for Multiproduct Monopolies," Bell Journal of Economics, The RAND Corporation, vol. 11(2), pages 659-670, Autumn.
    12. McAfee, R. Preston & McMillan, John, 1988. "Multidimensional incentive compatibility and mechanism design," Journal of Economic Theory, Elsevier, vol. 46(2), pages 335-354, December.
    13. Spence, A Michael, 1980. "Multi-Product Quantity-Dependent Prices and Profitability Constraints," Review of Economic Studies, Wiley Blackwell, vol. 47(5), pages 821-41, October.
    14. Roberts, Kevin W S, 1979. "Welfare Considerations of Nonlinear Pricing," Economic Journal, Royal Economic Society, vol. 89(353), pages 66-83, March.
    Full references (including those not matched with items on IDEAS)

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:eee:jetheo:v:146:y:2011:i:2:p:454-478. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.