When is multidimensional screening a convex program?
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.
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- Monteiro, Paulo K. & Page Jr., Frank H., 1998.
"Optimal selling mechanisms for multiproduct monopolists: incentive compatibility in the presence of budget constraints,"
Journal of Mathematical Economics,
Elsevier, vol. 30(4), pages 473-502, November.
- KLINGER MONTEIRO , Paulo & PAGE, Frank H. Jr., 1997. "Optimal selling mechanisms for multiproduct monopolists : incentive compatibility in the presence of budget constraints," CORE Discussion Papers 1997011, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- 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.
- Baron, David P & Myerson, Roger B, 1982.
"Regulating a Monopolist with Unknown Costs,"
Econometric Society, vol. 50(4), pages 911-30, July.
- 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.
- Roberts, Kevin W S, 1979. "Welfare Considerations of Nonlinear Pricing," Economic Journal, Royal Economic Society, vol. 89(353), pages 66-83, March.
- Guesnerie, Roger & Laffont, Jean-Jacques, 1978.
"Taxing price makers,"
Journal of Economic Theory,
Elsevier, vol. 19(2), pages 423-455, December.
- 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.
- repec:dau:papers:123456789/6818 is not listed on IDEAS
- J. A. Mirrlees, 1971. "An Exploration in the Theory of Optimum Income Taxation," Review of Economic Studies, Oxford University Press, vol. 38(2), pages 175-208.
- Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
- McAfee, R. Preston & McMillan, John, 1988. "Multidimensional incentive compatibility and mechanism design," Journal of Economic Theory, Elsevier, vol. 46(2), pages 335-354, December.
- Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
- 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.
- Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
- A. Michael Spence, 1980. "Multi-Product Quantity-Dependent Prices and Profitability Constraints," Review of Economic Studies, Oxford University Press, vol. 47(5), pages 821-841.
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