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Solutions Homework #1
Exercise 1:
i) The present value of her lifetime earnings is:
T
X
t
=1
β
t
h
t
k
t
=
T
X
t
=1
β
t
φ
±
k
t
+1
k
t
¶
k
t
ii)  The state variable is:
k
t
, the current human capital stock.
 The control variable is:
h
t
the number of hours worked. Alternatively, because we
have a onetoone relationship between
h
t
and
k
t
+1
when
k
t
is known, it is equivalent
to have the next period human capital stock as a control variable. We keep the second
formulation which is slightly more convenient.
iii) The equation of motion is:
(1

δ
)
k
t
≤
k
t
+1
≤
(1 +
λ
)
k
t
iv) The dynamic optimization problem writes:
max
{
k
t
+1
}
T

1
t
=1
T
X
t
=1
β
t
k
t
φ
±
k
t
+1
k
t
¶
s.t.
(1

δ
)
k
t
≤
k
t
+1
≤
(1 +
λ
)
k
t
∀
t
and
k
1
>
0
given
Exercise 2:
i) In stage 1, there are 2 options in stage 1 and 3 options in stages 2 and 3, resulting in
a total of 18 possible routes.
ii) Intuitive method: we start at the beginning point, A.
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This note was uploaded on 02/19/2010 for the course ECON 831 taught by Professor Antoine during the Fall '09 term at Simon Fraser.
 Fall '09
 Antoine
 Economics

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