ECO 610
Fall 2010
Assignment 2
The due date for this assignment is Tuesday March 22.
1. (Capital Utilization) Consider an economy in which each individual ranks consumption
sequence according to the functional
∞
X
t
=0
β
t
u
(
c
t
)
,
0
<β<
1
where the function
u
is increasing, di
f
erentiable and strictly concave. This economy
imports investment goods. Assume that the international price of the investment good
is
p
k
≥
1
. Thus, the feasiblility constraint faced by the planner is
c
t
+
p
k
x
t
≤
f
(
k
e
t
)
,
where
k
e
t
denotes e
f
ective units of capital per worker (to be de
f
ned). The planner
chooses that intensity of use of the capital stocks. Let intensity of use be denoted
ν
,
where
0
≤
ν
≤
1
. If the economy has available
k
units of capital and it is used at
intensity
ν
,thee
f
ective supply of capital is
k
e
=
νk
. In this case the depreciation rate
is
δ
(
ν
)=
ν
1+
λ
,
λ>
0
and
0
≤
ν
≤
1
.
In this economy there are installation costs. If
x
units of investment goods are allocated
to the production of new capital, they produce
G
(
x, a
)
units of new capital goods.
Thus, the aggregate law of motion of capital is
k
t
+1
=(1
−
δ
(
ν
t
))
k
t
+
G
(
x
t
,a
)
,
where
a
is a factor of
f
xed supply.
. The function
G
is assumed increasing in each
argument, di
f
erentiable and concave. One interpretation of
G
is that it represents
installation costs that are necessary to make capital goods productive. Assume that
the production function is given by
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 Spring '10
 C.Subramanian
 Economics, ln Ct, equilibrium price function, ln ct−1, function ln ct

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