714s10_hw1_ans

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 - k ) + log c- 1 | {z } only place where c- 1 shows up! + 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 ) + 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 ) + W ( k ) + log ( Ak- k ) = max k ( 1 + ) log ( Ak- k ) + W ( k ) . But wait, this looks familiar. Its just the same old functional equation weve seen again and again, just multiplied by 1 + . So it better be that W ( k ) = ( 1 + ) V ( k ) = ( 1 + )( E + F log k ) , where V ( k ) solves V ( k ) = max k log ( Ak - k ) + V (...
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714s10_hw1_ans - ECON 714: MACROECONOMIC THEORY II TA: TIM...

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