714s10_hw1_ans - ECON 714 MACROECONOMIC THEORY II TA TIM...

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Unformatted text preview: ECON 714: MACROECONOMIC THEORY II TA: TIM LEE FEBRUARY 18, 2010 Outline to HW1 Solutions Mind you, I might be wrong...open to any disputes! 1. Habit Persistence (a) States : ( k , c- 1 ) , Control: k . Bellman Equation: Z ( k , c- 1 ) Z ( k , c- 1 ) = max k log ( Ak α- k ) + γ log c- 1 | {z } only place where c- 1 shows up! + β Z ( k , Ak- k ) (b) We got to make a good guess. But since c- 1 shows up only where I said it does, it better be that Z ( k , c- 1 ) = W ( k ) + γ log c- 1 , where W ( k ) is some function of only k . Plugging this guess in we get W ( k ) = max k log ( Ak- k ) + β W ( k ) + βγ log ( Ak- k ) = max k ( 1 + βγ ) log ( Ak- k ) + β W ( k ) . But wait, this looks familiar. It’s just the same old functional equation we’ve seen again and again, just multiplied by 1 + βγ . So it better be that W ( k ) = ( 1 + βγ ) V ( k ) = ( 1 + βγ )( E + F log k ) , where V ( k ) solves V ( k ) = max k log ( Ak α- k ) + β V (...
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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 University of Wisconsin.

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714s10_hw1_ans - ECON 714 MACROECONOMIC THEORY II TA TIM...

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