ECN 713 Spring 2010
Natalia Kovrijnykh
Problem Set 2: Due on Thursday, February 11 in class
(100 points total)
Write a MATLAB code for the following stochastic growth model. The state of a rep
resentative agent is de°ned by his capital stock,
k
, and a productivity shock,
z
. The shock
can take two values,
z
L
=
:
9
and
z
H
= 1
:
1
, and follows a °rstorder Markov process with
transition matrix
Q
(
z; z
0
)
, where the transition probabilities of staying at either value is
:
8
.
The agent is endowed with one unit of time each period and maximizes his expected
discounted utility of consumption,
E
1
P
t
=0
°
t
u
(
c
t
)
,
where
u
(
c
) = log (
c
)
and
°
=
:
9
. (The agent does not care about leisure.) The output from
the CobbDouglas production technology,
y
t
=
z
t
k
°
t
l
1
°
°
t
, where
±
=
:
3
, is divided between
consumption and investment into the capital stock. The capital stock depreciation is
²
=
:
1
.
Use the interval
K
=
°
k
;
°
k
±
with
N
equally spaced points as your grid for the capital
stock with
k
=
:
01
. You will need to experiment with setting
°
k
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 Spring '10
 natalia
 Economics, Markov chain, Andrey Markov, Capital accumulation

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