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Long Term Contracting in a Changing World

  • Alessandro Pavan

I study the properties of optimal long-term contracts in an environment in which the agent’s type evolves stochastically over time. The model stylizes a buyer-seller relationship but the results apply quite naturally to many contractual situations including regulation and optimal income-taxation. I first show, through a simple discrete example, that distortions need not vanish over time and need not be monotonic in the shock to the buyer’s valuation. These results are in contrast to those obtained in the literature that assumes a Markov process with a binary state space— e.g. Battaglini, 2005. I then show that the study of the dynamics of the optimal mechanism can be significantly simplified by assuming the shocks are independent over time. When the sets of possible types in any two adjacent periods satisfy a certain overlapping condition (which is always satisfied with a continuum of types) and some additional regularity conditions hold, then the optimal mechanism is the same irrespective of whether the shocks are the buyer’s private information or are observed also by the seller. These conditions are satisfied, for example, in the case of an AR(1) process, a Brownian motion, but also when shocks have a multiplicative effect as it is often the case in financial applications. Furthermore, the distortions in the optimal quantities are independent of the distributions of the shocks and, when the buyer’s payoff is additively separable, they are also independent of whether the shocks are transitory or permanent. Finally, I show that assuming the shocks are independent not only does it greatly simplify the analysis, it is actually without loss of generality.

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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1493.

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Date of creation: Dec 2007
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Handle: RePEc:nwu:cmsems:1493
Contact details of provider: Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014
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Web page: http://www.kellogg.northwestern.edu/research/math/
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  1. Pascal Courty & Li Hao, 1997. "Sequential screening," Economics Working Papers 224, Department of Economics and Business, Universitat Pompeu Fabra.
  2. Stephen Coate & Marco Battaglini, 2004. "Pareto Efficient Income Taxation with Stochastic Abilities," 2004 Meeting Papers 140, Society for Economic Dynamics.
  3. Péter Eső & Bal�zs Szentes, 2007. "Optimal Information Disclosure in Auctions and the Handicap Auction," Review of Economic Studies, Oxford University Press, vol. 74(3), pages 705-731.
  4. Marco Battaglini, 2005. "Long-Term Contracting with Markovian Consumers," American Economic Review, American Economic Association, vol. 95(3), pages 637-658, June.
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