387hw4sp07 - Economics 387. Dynamic Contracts. Spring 2007....

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Economics 387. Dynamic Contracts. Spring 2007. Department of Economics, University of Texas Instructor: Dean Corbae, BRB 3.134A, (o) 512-475-8530 email: corbae@eco.utexas.edu, web: www.eco.utexas.edu/˜corbae Homework #4 - Due 3/20/07 Compute the optimal contract for a version of the Thomas and Wor- rall (1990, Journal of Economic Theory ). The agent receives stochastic, nonstorable endowments { y t } which are i.i.d. drawn from a f nite time invariant set y t { y L =1 ,y H =2 } where we assume that y L <y H . Let π s = pr ( y t = y s )=1 / 2wh e r e s { L, H } The agent’s preferences E P t =0 β t u ( c t )where u ( c t )= e c t for c t [0 , )and β =0 . 9 . The princi- pal is risk neutral and has deep pockets (i.e. y is arbitrarily large). Suppose that the principal takes as given last period’s promised utility V and solves P ( V )= max { b s ,w s } S s =1 S X s =1 π s [ b s + βP ( w s )] (1)
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387hw4sp07 - Economics 387. Dynamic Contracts. Spring 2007....

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