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Unformatted text preview: 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 . Bellman Equation: Z (k, c−1 Z (k, c−1 ) = max log( Akα − k ) +
γ log c−1
k + β Z (k , Ak − k ) only place where c−1 shows up! 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 log( Ak − k ) + βW (k ) + βγ log( Ak − k )
k = max (1 + βγ) log( Ak − k ) + βW (k ) .
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 log( Akα − k ) + βV (k)
k and we already know what E and F are. 2. Habit Persistence
1. 3. Habit Persistence
1 4. Habit Persistence
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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.
- Spring '08