ECON 401
Hartman
Autumn 2010
PROBLEM SET VII
(for Thursday, December 2)
1.
In each period a firm uses capital to produce output according to the production function
()
tt
Yf
K
where
Y
t
is output in period
t
and
K
t
is the capital input in that period.
The firm
makes changes in the level of capital through investment.
If
I
t
denotes investment in period
t
,
then capital accumulates according to
K
I
K
t
1
1
where
is the depreciation rate.
(Note
that investment in a period does not affect the capital stock until the next period.)
The output ptice
for period
t
is
t
p
, and the purchase price for a unit of the investment good in period
t
is
t
q
.
The
firm maximizes the net present value of its cash flows,
0
(1
)
ttt
t
t
t
pfK
qI
r
where
K
0
is fixed by
past decisions and
r
is the interest rate.
Substitute for
I
t
, and derive the first order conditions for
the choice of
K
t
for some typical time period
t
.
Interpret this condition.
What is the user cost of
capital for period
t
?
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This note was uploaded on 04/04/2011 for the course ECON 401 taught by Professor Staff during the Spring '08 term at University of Washington.
 Spring '08
 Staff
 Macroeconomics

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