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Optimal insurance with adverse selection

  • Schlee, Edward

    ()

    (Department of Economics, Arizona State University)

  • Chade, Hector

    ()

    (Department of Economics, Arizona State University)

We solve the principal-agent problem of a monopolist insurer selling to an agent whose riskiness (loss chance) is private information, a problem introduced in Stiglitz's (1977) seminal paper. For an \emph{arbitrary} type distribution, we prove several properties of optimal menus, such as efficiency at the top and downward distortions elsewhere. We show that these results extend beyond the insurance problem we emphasize. We also prove that the principal always prefers an agent facing a larger loss, and a poorer one if the agent's risk aversion decreases with wealth. For the standard case of a continuum of types and a smooth density, we show that, under the mild assumptions of a log-concave density and decreasing absolute risk aversion, the optimal premium is \emph{backwards-S shaped} in the amount of coverage, first concave, then convex. This curvature result implies that quantity discounts are consistent with adverse selection in insurance, contrary to the conventional wisdom from competitive models.

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Article provided by Econometric Society in its journal Theoretical Economics.

Volume (Year): 7 (2012)
Issue (Month): 3 (September)
Pages:

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Handle: RePEc:the:publsh:671
Contact details of provider: Web page: http://econtheory.org

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  13. Bennardo, Alberto & Chiappori, Pierre-André, 2002. "Bertrand and Walras Equilibria Under Moral Hazard," CEPR Discussion Papers 3650, C.E.P.R. Discussion Papers.
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  18. Pierre‐André Chiappori & Bruno Jullien & Bernard Salanié & François Salanié, 2006. "Asymmetric information in insurance: general testable implications," RAND Journal of Economics, RAND Corporation, vol. 37(4), pages 783-798, December.
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  28. Jewitt, Ian, 1987. "Risk Aversion and the Choice between Risky Prospects: The Preservation of Comparative Statics Results," Review of Economic Studies, Wiley Blackwell, vol. 54(1), pages 73-85, January.
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