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homework2 - (5 Problem 2.4 SLP p 15 2 Quadratic Utility and...

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ECO 475 Homework 2 Jay H. Hong Due: Monday, Sep 20, 2010 1 Value Function Iteration & Guess and Verify Consider the following problem. max { c t ,k t +1 } t =0 X t =0 β t u ( c t ) subject to an initial k 0 and a law of motion for capital k t +1 = F ( k t ) + (1 - δ ) k t - c t . (1) Write down the Bellman equation. Now assume that u ( c ) = log( c ) , F ( k ) = Ak α where A > 0 , α (0 , 1) , β (0 , 1) and δ = 1. (2) Let V 0 ( k ) = 0 and derive V 1 ( k ) , V 2 ( k ) , V n ( k ). (3) Derive V ( k ). (by n → ∞ ) (4) Let’s make a guess on the value function V ( k ) = P log( k ) + Q and solve for P, Q by “guess and verify”. Compare the result with (3).
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Unformatted text preview: (5) Problem 2.4, SLP p. 15 2 Quadratic Utility and Linear Technology Assume that F ( k ) = Ak and u ( c ) = a + bc + dc 2 where b > 0 and d < 0. Solve for the closed form solutions for V ( k ) and decision rule. Explain why c is constant. 3 Metric Space Problem 3.3 and 3.4 from SLP p. 45 4 Completeness of ( C ,d ) Show that C the set of bounded continuous real-valued functions with the sup norm d is a complete metric space. 1...
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