ps9macro2sp06 - Econ 387L: Macro II Spring 2006, University...

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Econ 387L: Macro II Spring 2006, University of Texas Instructor: Dean Corbae Problem Set #9- Part I Due 4/4/06, Part II Due 4/7/06 I. The f rst problem introduces you to dynamic programming in a f nite T horizon stochastic growth model. Speci f cally, let T =1 (i.e. a two period model). Let z t Z (a f 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 .Le t 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 ,
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ps9macro2sp06 - Econ 387L: Macro II Spring 2006, University...

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