Econ 387L: Macro II
Spring 2006, University of Texas
Instructor: Dean Corbae
Problem Set #9 Part I Due 4/4/06, Part II Due 4/7/06
I. The
f
rst problem introduces you to dynamic programming in a
f
nite
T
horizon
stochastic growth model. Speci
f
cally, let
T
=1
(i.e. a two period model). Let
z
t
∈
Z
(a
f
nite and time independent set) denote an exogenous technology shock in period
t
and
π
(
z
t
,z
t
−
1
)
denote the probability of being in state
z
t
conditional on being in state
z
t
−
1
.
Let capital holdings at the beginning of period
t
be denoted
k
t
∈
X
and the state variable
be denoted
s
t
=(
k
t
,z
t
)
∈
X
×
Z
.Le
t
y
(
s
t
)=
z
t
f
(
k
t
)
denote output in state
s
t
where
f
(0) = 0
,f
0
>
0
,f
00
<
0
,c
(
s
t
)
denote consumption in state
s
t
,and
k
t
+1
(
s
t
)
denote
capital chosen in state
s
t
used for production next period. Households start with
k
0
units of
capital. Households are expected utility maximizers with preferences that satisfy
u
0
(
c
)
>
0
,
u
00
(
c
)
<
0
,
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 Spring '07
 CORBAE
 Dynamic Programming, Probability theory, Stochastic process, Markov chain, Convex function

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