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Unformatted text preview: where d (0 , 1). Using your Euler equation derive 1 ( k ) and show that 1 ( k ) = 1 + d Ak . (3) Derive 2 ( k ) , n ( k ) and ( k ) (by n ). (4) Discuss whether we need d (0 , 1) or not. Why? (5) Discuss whether n ( k ) ( k ) is pointwise convergence or uniform convergence. Why? (Hint: Theorem 3.8 SLP) 3 Habit Persistance Utility Consider the following problem. max { c t ,k t +1 } t =0 X t =0 t [log( c t ) + B log( c t1 )] subject to an initial k and c1 and a law of motion k t +1 = Ak tc t , where A > , (0 , 1) , (0 , 1) and B > 0. Formulate and solve the recursive problem. What are your control variable and state variables? Derive the closed form solutions for the value function V and the policy function . 1...
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 Fall '07
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