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Incentive Compatibility And Pricing Under Moral Hazard

  • Belén Jerez

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We study a simple insurance economy with moral hazard, in which random contracts overcome the non-convexities generated by the incentive-compatibility constraints. The novelty is that we use linear programming and duality theory to study the relation between incentive compatibility and pricing. Using linear programming has the advantage that we can impose the incentive-compatibility constraints on the agents that are uninformed (the insurance firms). In contrast, most of the general equilibrium literature imposes them on the informed agents (the consumers). We derive the two welfare theorems, establish the existence of a competitive equilibrium, and characterize the equilibrium prices and allocations. Our competitive equilibrium has two key properties: (i) the equilibrium prices reflect all the relevant information, including the welfare costs arising from the incentive-compatibility constraints; (ii) the equilibrium allocations are the same as when the incentive-compatibility constraints are imposed on the consumers.

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Paper provided by Universidad Carlos III, Departamento de Economía in its series Economics Working Papers with number we035722.

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Date of creation: Oct 2003
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Handle: RePEc:cte:werepe:we035722
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  1. Bennardo, Alberto & Chiappori, Pierre-André, 2002. "Bertrand and Walras Equilibria Under Moral Hazard," CEPR Discussion Papers 3650, C.E.P.R. Discussion Papers.
  2. Greenwald, Bruce C & Stiglitz, Joseph E, 1986. "Externalities in Economies with Imperfect Information and Incomplete Markets," The Quarterly Journal of Economics, MIT Press, vol. 101(2), pages 229-64, May.
  3. Belen Jerez, 2000. "General Equilibrium with Asymmetric Information: A Dual Approach," Econometric Society World Congress 2000 Contributed Papers 1497, Econometric Society.
  4. Bel? Jerez, 2001. "A Dual Characterization of Incentive Efficiency," UFAE and IAE Working Papers 494.01, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  5. Mas-Colell, Andreu & Zame, William R., 1991. "Equilibrium theory in infinite dimensional spaces," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 34, pages 1835-1898 Elsevier.
  6. Wilson, Charles, 1977. "A model of insurance markets with incomplete information," Journal of Economic Theory, Elsevier, vol. 16(2), pages 167-207, December.
  7. Richard Arnott & Bruce Greenwald & Joseph E. Stiglitz, 1993. "Information and Economic Efficiency," NBER Working Papers 4533, National Bureau of Economic Research, Inc.
  8. Feldman, Mark & Gilles, Christian, 1985. "An expository note on individual risk without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 35(1), pages 26-32, February.
  9. Rothschild, Michael & Stiglitz, Joseph E, 1976. "Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information," The Quarterly Journal of Economics, MIT Press, vol. 90(4), pages 630-49, November.
  10. Bisin, Alberto & Gottardi, Piero, 1999. "Competitive Equilibria with Asymmetric Information," Journal of Economic Theory, Elsevier, vol. 87(1), pages 1-48, July.
  11. Gretsky, Neil E. & Ostroy, Joseph M. & Zame, William R., 1999. "Perfect Competition in the Continuous Assignment Model," Journal of Economic Theory, Elsevier, vol. 88(1), pages 60-118, September.
  12. Alberto Bisin & Piero Gottardi, 2000. "Decentralizing Incentive Efficient Allocations of Economies with Adverse Selection," Econometric Society World Congress 2000 Contributed Papers 0855, Econometric Society.
  13. Prescott, Edward C & Townsend, Robert M, 1984. "Pareto Optima and Competitive Equilibria with Adverse Selection and Moral Hazard," Econometrica, Econometric Society, vol. 52(1), pages 21-45, January.
  14. Prescott, Edward C & Townsend, Robert M, 1984. "General Competitive Analysis in an Economy with Private Information," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(1), pages 1-20, February.
  15. Timothy J. Kehoe & David K. Levine & Edward Prescott, 2000. "Lotteries, Sunspots and Incentive Constraints," Levine's Working Paper Archive 1974, David K. Levine.
  16. Rogerson, William P, 1985. "Repeated Moral Hazard," Econometrica, Econometric Society, vol. 53(1), pages 69-76, January.
  17. Sun, Yeneng, 1998. "A theory of hyperfinite processes: the complete removal of individual uncertainty via exact LLN1," Journal of Mathematical Economics, Elsevier, vol. 29(4), pages 419-503, May.
  18. Pradeep Dubey & John Geanakoplos & Martin Shubik, 1988. "Default and Efficiency in a General Equilibrium Model with Incomplete Markets," Cowles Foundation Discussion Papers 879R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1989.
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