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Solutions to Problem Set 7
Econ 702, Spring 2004
Prepared by Ahu Gemici
March 24, 2004
Problem 1 (Lucas Tree Model)
Solution:
From the First Order Conditions we get:
q
i
=
β
X
j
u
c
(
c
0
)
u
c
(
c
)
Γ
ij
[
q
j
+
z
j
]
∀
i
(1)
In equilibrium, c=z,
q
i
=
β
X
j
u
c
(
z
j
)
u
c
(
z
i
)
Γ
ij
[
q
j
+
z
j
]
∀
i
(2)
The above system of equations characterizes the prices of the tree at each
state
{
q
i
}
I
i
=1
. Now we will write this system of equations in the matrix form:
q
1
..
..
q
I
=
β
Γ
11
u
0
(
z
1
)
u
0
(
z
1
)
β
Γ
12
u
0
(
z
2
)
u
0
(
z
1
)
..
β
Γ
1
J
u
0
(
z
J
)
u
0
(
z
1
)
..
β
Γ
22
u
0
(
z
2
)
u
0
(
z
2
)
..
..
..
..
..
..
β
Γ
I
1
u
0
(
z
1
)
u
0
(
z
I
)
..
..
β
Γ
IJ
u
0
(
z
J
)
u
0
(
z
I
)
q
1
..
..
q
I
+
z
1
..
..
z
I
Let q=
q
1
..
..
q
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This note was uploaded on 11/12/2010 for the course ECON 8108 taught by Professor Staff during the Spring '08 term at Minnesota.
 Spring '08
 Staff

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