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Recursive Contracts, Lotteries and Weakly Concave Pareto Sets

  • Harold Cole

    ()

    (Department of Economics, University of Pennsylvania)

  • Felix Kubler

    ()

    (University of Zurich and Swiss Finance Institute)

Marcet and Marimon (1994, revised 1998) developed a recursive saddle point method which can be used to solve dynamic contracting problems that include participation, enforcement and incentive constraints. Their method uses a recursive multiplier to capture implicit prior promises to the agent(s) that were made in order to satisfy earlier instances of these constraints. As a result, their method relies on the invertibility of the derivative of the Pareto frontier and cannot be applied to problems for which this frontier is not strictly concave. In this paper we show how one can extend their method to a weakly concave Pareto frontier by expanding the state space to include the realizations of an end of period lottery over the extreme points of a .at region of the Pareto frontier. With this expansion the basic insight of Marcet and Marimon goes through .one can make the problem recursive in the Lagrangian multiplier which yields significant computational advantages over the conventional approach of using utility as the state variable. The case of a weakly concave Pareto frontier arises naturally in applications where the principal’s choice set is not convex but where randomization is possible.

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File URL: http://economics.sas.upenn.edu/system/files/working-papers/10-038.pdf
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Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 10-038.

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Length: 31 pages
Date of creation: 10 Dec 2010
Date of revision:
Handle: RePEc:pen:papers:10-038
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  1. Thomas Cooley & Ramon Marimon & Vincenzo Quadrini, 2003. "Aggregate Consequences of Limited Contract Enforceability," NBER Working Papers 10132, National Bureau of Economic Research, Inc.
  2. Edward C Prescott & Robert M Townsend, 1997. "General Competitive Analysis in an Economy with Private Information," Levine's Working Paper Archive 1578, David K. Levine.
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  4. Aubhik Khan & Robert G. King & Alexander L. Wolman, 2001. "Optimal monetary policy," Working Papers 01-5, Federal Reserve Bank of Philadelphia.
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  8. Matthias Messner & Nicola Pavoni, 2004. "On the Recursive Saddle Point Method," Working Papers 255, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  9. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, June.
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  17. Edward C Prescott & Robert M Townsend, 2010. "Pareto Optima and Competitive Equilibria With Adverse Selection and Moral Hazard," Levine's Working Paper Archive 2069, David K. Levine.
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