Econ 387L: Macro II
Spring 2006, University of Texas
Instructor: Dean Corbae
Problem Set #10  Part I Due 4/11/06, Part II Due 4/14/06
I. A
f
rm has a production technology
y
t
=
F
(
k
t
,k
t
+1
)
where
F
:
R
+
×
R
+
→
R
+
.
Assume that
F
is continuously differentiable, increasing in
k
t
and decreasing
in
k
t
+1
(due to adjustment costs). Assume that: (i)
F
exhibits constant returns
(i.e.
F
(
λk
t
,λk
t
+1
)=
λF
(
k
t
,k
t
+1
)
,λ>
0
); (ii)
F
is strictly quasiconcave
(i.e. if
(
k
t
,k
t
+1
)
6
=(
b
k
t
,
b
k
t
+1
)
,F
(
b
k
t
,
b
k
t
+1
)
≥
F
(
k
t
,k
t
+1
)
,
and
θ
∈
(0
,
1)
,
then
F
(
k
θ
t
,k
θ
t
+1
)
>F
(
k
t
,k
t
+1
)
where
(
k
θ
t
,k
θ
t
+1
)=
θ
(
k
t
,k
t
+1
)+(1
−
θ
)(
b
k
t
,
b
k
t
+1
);
and (iii)
F
is such that the marginal adjustment cost becomes arbitrarily high as the reate of growth
of capital approaches
α>
0
(i.e.
lim
k
t
+1
→
(1+
α
)
k
t
∂F
(
k
t
,k
t
+1
)
∂k
t
+1
→−∞
). Let
δ
∈
(0
,
1)
be
the depreciation rate and
q
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 Spring '07
 CORBAE
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