Adverse selection problems without the Spence-Mirrlees condition

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.jet.2010.02.010 Byline: Aloisio Araujo (a)(b), Humberto Moreira (a) Keywords: Spence-Mirrlees condition; Global incentive compatibility; U-shaped condition; Discrete pooling Abstract: This paper studies a class of one-dimensional screening problems where the agent's utility function does not satisfy the Spence-Mirrlees condition (SMC). The strength of the SMC for hidden information problems is to provide a full characterization of implementable contracts using only the local incentive compatibility (IC) constraints. These constraints are equivalent to the monotonicity of the decision variable with respect to the agent's unobservable one-dimensional parameter. When the SMC is violated the local IC constraints are no longer sufficient for implementability and additional (global) IC constraints have to be taken into account. In particular, implementable decisions may not be monotonic and discretely pooled types must have the same marginal utility of the decision (or equivalently, get the same marginal tariff). Moreover, at the optimal decision, the principal must preserve the same trade-off between rent extraction and allocative distortion measured in the agent's marginal rent unit. In a specific setting where non-monotone contracts may be optimal we fully characterize the solution. Author Affiliation: (a) Graduate School of Economics, Getulio Vargas Foundation, Praia de Botafogo, 190, Rio de Janeiro, RJ 22250900, Brazil (b) Instituto Nacional de Matematica Pura e Aplicada, Estrada Dona Castorina, 110, Rio de Janeiro, RJ 22460902, Brazil Article History: Received 3 October 2003; Revised 8 August 2009; Accepted 3 October 2009 Article Note: (footnote) [star] We acknowledge CNPq and FAPERJ of Brazil for financial support. Preliminary versions of this paper were presented at the Universite de Toulouse 1, Pompeu Fabra (Barcelona), IMPA, PUC-Rio, EPGE/FGV, University of Chicago, Universite de Paris 1, the Nineteenth Meeting of the Brazilian Econometric Society, the 2000 World Congress of the Econometric Society (Seattle), 2006 Latin American Meeting of the Econometric Society (Cidade de Mexico) and the 2006 Stony Brook Game Theory Festival. We are grateful to A. Chassagnon, P.-A. Chiappori, D. Gottlieb, J.-J. Laffont, G. Maggi, A. Mas-Colell, J.-C. Rochet, J. Scheinkman, L. Stole, J. Tirole, an associate editor, and a referee for helpful discussions and suggestions. We would like to thank Caio Almeida for helping us with the numerical implementation of the example of the previous version of the paper and Marcos Tsuchida for important comments. Finally, we are in debt with Sergei Vieira who did a careful revision of the proofs and checked some of them numerically.