I study the properties of optimal long-term contracts in an environment in which the agents 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 rst show, through a simple example, that distortions need not vanish over time and need not be monotonic in the shock to the buyers 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 when the sets of possible types in any two adja- cent periods satisfy a certain overlapping condition (which is always satis ed with a continuum of types), then the dynamics of the optimal mechanism can be signi cantly simpli ed by as- suming the shocks are independent over time. Under certain regularity conditions, the optimal mechanism is then the same irrespective of whether the shocks are the buyers private informa- tion or are observed also by the seller. These conditions are satis ed, for example, in the case of an AR(1) process, a Brownian motion, but also when shocks have a multiplicative e¤ect as it is often the case in nancial applications. Furthermore, the distortions in the optimal quantities are independent of the distributions of the shocks and, when the buyers valuation 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 greatly simpli es the analysis but is actually without loss of generality with a continuum of types.
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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
1456.
Length: Date of creation: Dec 2007 Date of revision: Handle: RePEc:nwu:cmsems:1456
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Find related papers by JEL classification: D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance
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