Economics 302
Spring 2008
Answers to Homework #4
Homework will be graded for both content and neatness.
This homework requires the
use of Microsoft Excel.
Please put your section number or discussion section meeting
time on the front page when turning in your homework.
1) Consider the Solow Growth model without population growth or technological change.
The parameters of the model are as described in the table below:
Year
s
δ
k
y
c
i
depreciation
change in k
1
0.2
0.05
20
where s is the saving rate, δ is the depreciation rate, k is the capital stock per worker, y is
output per worker, c is consumption per worker, and i is investment per worker.
a) Assume that our production function is given by
3
/
2
3
/
1
L
K
Y
=
.
Rewrite this
production function in terms of output per worker as a function of capital per worker.
We divide both sides by L to get output per worker on the left hand side, so we have:
3
/
1
3
/
1
3
/
1
3
/
2
3
/
1
k
L
K
L
L
K
L
Y
y
=
=
=
=
b) With the production function in a), fill out the first row of the table above.
We fill in the table as follows:
3
/
1
k
y
=
, i = sy, c = y – i, depreciation =
δ*
k, change in k = i –depreciation.
This yields the values below.
Year
s
δ
k
y
c
i
depreciation
change in k
1
0.2
0.05
20
2.714418
2.171534
0.542884
1
0.457116477
c) Again using the production function from a), find the steady state level of capital in
this economy.
We know that at steady state, the change in the capital stock must be 0.
Thus, looking at
the formulas above, we set i = depreciation, so
k
k
k
sy
i
05
.
0
20
.
0
3
/
1
=
⇒
=
=
δ
.
Solving
this equation for k gives us
3
/
1
05
.
0
20
.
0
k
k
=
, so
3
/
2
4
k
=
, so k = 8 in steady state.
d) Use Excel to fill out the above table for years 110.
Then extend the table until the
level of capital per worker is within 1 of the steady state value.
In which year does k
reach this point?
(Note: you need only turn in the first 10 years of the table).
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '07
 GOLD
 Economics, Macroeconomics, Steady State, Quodium

Click to edit the document details