Problem Set 2
FE312 Fall 2007
Rahman
Partial Answer Key
1)
Assume that production is a function of capital and
labor, and that the rate of savings,
depreciation, population growth, and are all constant, as described in Chapter 7’s version
of the Solow Model.
Further, assume that the production per effective worker can be
described by the function:
2
1
2
1
L
K
Y
where
K
is capital and
L
is labor.
a
. What is the perworker production function
y=f(k)
?
Show your work.
2
/
1
2
/
1
2
/
1
k
y
L
L
L
K
L
Y
b
.
If the saving rate (
s
) is 0.4, what are capital per worker, production per worker,
and consumption per worker in the steady state?
(Note:
you need to set Δ
k
= 0, to
get an equation in
s
,
δ
,
n
,
and
k
, and then solve for
k
).
2
2
*
4
.
0
n
n
s
k
n
n
s
y
4
.
0
*
n
n
n
s
s
y
s
c
ss
24
.
0
4
.
0
4
.
0
1
1
1
*
c
.
Solve for steadystate capital per worker, production per worker, and consumption
per worker with
s
= 0.8.
2
*
8
.
0
n
k
n
y
8
.
0
*
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Problem Set 2
FE312 Fall 2007
Rahman
n
n
c
16
.
0
8
.
0
8
.
0
1
*
d.
Is it possible to save too much?
Why?
Yes, it is possible to save too much, in the sense that longrun consumption could
actually be higher if you saved less.
Indeed, s = 0.8 appears to be too high a savings
rate, since steady state consumption per person is definite smaller with s = 0.8 than
with s = 0.4.
Notice that we can conclude this even without knowing what the
population growth rate or the depreciate rate for the economy are.
By the way, could we figure out what the actual “best” savings rate is, based on just
the information given?
Yes, with a bit of deductive reasoning.
The golden rule level
of capital is where MPK = n + δ…
2
2
/
1
5
.
0
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 Summer '09
 Steady State, Stock and flow, Capital accumulation

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