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markovchain

# markovchain - E CON 714 M ACROECONOMIC T HEORY II TA T IM L...

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E CON 714: M ACROECONOMIC T HEORY II TA: T IM L EE F EBRUARY 12, 2010 Outline to HW Solutions 1. Habit Persistence 1. States : ( k , c - 1 ) , Control: k 0 . Bellman Equation: Z ( k , c - 1 Z ( k , c - 1 ) = max k 0 log ( Ak α - k 0 ) + γ log c - 1 | {z } only place where c - 1 shows up! + β Z ( k 0 , Ak - k 0 ) 2. 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 0 log ( Ak - k 0 ) + β W ( k 0 ) + βγ log ( Ak - k 0 ) = max k 0 ( 1 + βγ ) log ( Ak - k 0 ) + β W ( k 0 ) . But wait, this looks familiar. It’s just the same old functional equation we’ve seen

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markovchain - E CON 714 M ACROECONOMIC T HEORY II TA T IM L...

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