ps8macro2sp08 - 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 #8- Due 4/3/08 This question comes from 5.1 (The One-Sector Model of Optimal Growth) of Stokey and Lucas (1989). In Chapter 2, Stokey and Lucas introduced the problem of optimal growth in a one-good economy: max { x t +1 } t =0 X t =0 β t U ( f ( x t ) x t +1 ) (1) s.t. 0 x t +1 f ( x t ) ,t =0 , 1 , ... given x 0 0 This problem is defined by the parameter β, the functions U : R + R and U : R + R , and the initial capital stock x 0 . The assumptions we will use for preferences are: (U1) β (0 , 1) (U2) U is continuous (U3) U is strictly increasing (U4) U is strictly concave (U5) U is continuously differentiable For the technology we assume that (T1) f is continuous (T2) f (0) = 0 ;forsome x> 0 , we have x f ( x ) x for all x X =[0 , x ] and f ( x ) <x for all x (T3) f is strictly increasing (T4) f is (weakly) concave (T5) f is continuously differentiable Note that X is the set of maintainable capital stocks and that U3 and T3 justify the assumption, implicit in (1) that free disposal is never used. Corresponding to the problem in
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This note was uploaded on 08/06/2008 for the course ECON 387 taught by Professor Corbae during the Spring '07 term at University of Texas at Austin.

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ps8macro2sp08 - Econ 387L: Macro II Spring 2008, University...

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