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ps7macro2sp08

# ps7macro2sp08 - Econ 387L Macro II Spring 2008 University...

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Econ 387L: Macro II Spring 2008, University of Texas Instructor: Dean Corbae Problem Set #7- Due 3/25/08 I. The fi rst problem introduces you to dynamic programming in a fi nite T horizon stochastic growth model. Speci fi cally, let T = 1 (i.e. a two period model). Let z t Z (a fi nite and time independent set) denote an exogenous technology shock in period t and π ( z t , z t 1 ) denote the probability of being in state z t conditional on being in state z t 1 . Let capital holdings at the beginning of period t be denoted k t X and the state variable be denoted s t = ( k t , z t ) X × Z . Let y ( s t ) = z t f ( k t ) denote output in state s t where f (0) = 0 , f 0 > 0 , f 00 < 0 , c ( s t ) denote consumption in state s t , and k t +1 ( s t ) denote capital chosen in state s t used for production next period. Households start with k 0 units of capital. Households are expected utility maximizers with preferences that satisfy u 0 ( c ) > 0 , u 00 ( c ) < 0 , discount the future at rate β , and have a uniform prior before period 0 of π ( z i 0 , ) = μ for all z i 0 Z .

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ps7macro2sp08 - Econ 387L Macro II Spring 2008 University...

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