ECN 713 Spring 2010
Natalia Kovrijnykh
Problem Set 7: Due on Tuesday, April 27, in class
(100 points total)
Lucas and Prescott (1974).
1. [15 points] Consider the operator corresponding to the Bellman equation we studied
in class:
T
(
v
) (
x; z
) = max
f
(
x; z
) + min
±
Z
v
(
x; z
0
)
Q
(
z; dz
0
)
±±
.
Show that
T
is a contraction.
2. [60 points] Let the island economy we studied in class have a productivity shock that
takes on two possible values,
f
z
L
; z
H
g
with
0
< z
L
< z
H
constant from one period to another with probability
²
2
(
:
5
;
1)
, and its productivity changes
to the other possible value with probability
1
²
. These symmetric transition probabilities
imply a stationary distribution where half of the islands experience a given
z
at any point
in time. Let
N
labor force has two possible values,
f
x
1
; x
2
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '10
 natalia
 Recursion, Optimization, Probability theory, Bellman equation, Markov decision process

Click to edit the document details