simpleDP - ECON 714: MACROECONOMIC THEORY II TA: TIM LEE...

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Unformatted text preview: ECON 714: MACROECONOMIC THEORY II TA: TIM LEE FEBRUARY 5, 2010 Dynamic Programming Lets use the simple growth example from class: W ( k ) = max { c t , k t + 1 } t = t = t log ( c t ) s.t. c t + k t + 1 Ak t t . We already know from class how to use the guess and verify" technique to solve for the value function instead: V ( k ) = max k [ 0, Ak ] log ( Ak - k ) + V ( k ) , with the guess of E + F log k , so that E = ( 1- )- 1 log ( 1- ) A + 1- log A F = 1- g ( k ) = Ak where k 0* = g ( k ) is the policy function. Note that we cant say V ( k ) W ( k ) yet, this is the subject of next weeks lectures. For now take for granted that it holds in this case, and Ill use this example throughout to highlight some other facts. 1. Iterating the value function: Although in this case we can just solve out for the value and policy functions pretty easily, usually we will be exploiting the Contrac- tion Mapping Theorem to get an approximation to the value function. Suppose we use this technique using...
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This note was uploaded on 06/19/2011 for the course ECON 714 taught by Professor Staff during the Spring '08 term at Wisconsin.

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simpleDP - ECON 714: MACROECONOMIC THEORY II TA: TIM LEE...

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