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ECO 475 Homework 2
Jay H. Hong
Due: Monday, Sep 20, 2010
1
Consider the following problem.
max
{
c
t
,k
t
+1
}
∞
t
=0
∞
X
t
=0
β
t
u
(
c
t
)
subject to an initial
k
0
and a law of motion for capital
k
t
+1
=
F
(
k
t
) + (1

δ
)
k
t

c
t
.
(1)
Write down the Bellman equation.
Now assume that
u
(
c
) = log(
c
)
,F
(
k
) =
Ak
α
where
A >
0
,α
∈
(0
,
1)
,β
∈
(0
,
1) and
δ
= 1.
(2)
Let
V
0
(
k
) = 0 and derive
V
1
(
k
)
,V
2
(
k
)
,V
n
(
k
).
(3)
Derive
V
(
k
). (by
n
→ ∞
)
(4)
Let’s make a guess on the value function
V
(
k
) =
P
log(
k
) +
Q
and solve for
P,Q
by “guess and verify”. Compare the result with (3).
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Unformatted text preview: (5) Problem 2.4, SLP p. 15 2 Quadratic Utility and Linear Technology Assume that F ( k ) = Ak and u ( c ) = a + bc + dc 2 where b > 0 and d < 0. Solve for the closed form solutions for V ( k ) and decision rule. Explain why c is constant. 3 Metric Space Problem 3.3 and 3.4 from SLP p. 45 4 Completeness of ( C ,d ) Show that C the set of bounded continuous realvalued functions with the sup norm d is a complete metric space. 1...
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This note was uploaded on 09/06/2011 for the course ECO 475 taught by Professor Hong during the Fall '07 term at Rochester.
 Fall '07
 Hong

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