homework4 - ECO 475 Homework 4 Jay H. Hong Due: Oct 4, 2010...

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Unformatted text preview: ECO 475 Homework 4 Jay H. Hong Due: Oct 4, 2010 1 Neoclassical Growth Model Consider the following problem. max { c t ,k t +1 } ∞ t =0 ∞ X t =0 β t u ( c t ) (1) subject to an initial k and a law of motion k t +1 + c t = F ( k t ) + (1- δ ) k t . Assume that k t ≥ ,c t ≥ 0 for all t . Feel free to make any assumption you may need. (1) Solve the above infinite horizon maximization problem by dynamic programming technique. We want to write the above problem into v ( x ) = max a ∈ Γ( x ) { U ( x,a ) + βv [ f ( x,a )] } . Let’s use c as our control variable. (Remember we use k as the control variable in class). What is your state variable? Rewrite U, Γ ,f,x,a using u,F,k,c,δ . (2) Derive the Euler equation when c is used as a control variable. Make appropriate assumptions as you need to derive the Euler equation but specify those. (3) Let k ≡ g k ( k ) = F ( k ) + (1- δ ) k- g c ( k ) where g c ( k ) is the consumption policy you obtained from (2). Verify that g k ( k ) = α ( k ) where α ( k ) is the policy function we studied in class by using k as a control variable. Show thatvariable....
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This note was uploaded on 09/06/2011 for the course ECO 475 taught by Professor Hong during the Fall '07 term at Rochester.

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homework4 - ECO 475 Homework 4 Jay H. Hong Due: Oct 4, 2010...

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