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Rebecca Chapman
Econ 302
Spring 2008
Homework #4
Discussion 303
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
_
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.
Y=K^(1/3) L^(2/3)
Y/L=y
=(K^(1/3) L^(2/3)) /L
=K^(1/3) L^(1/3)
=(K^(1/3))/(L^(1/3))
=k^(1/3)=f(k)
Output per worker y, depends on the amount of capital per worker (k)
b) With the production function in a), fill out the first row of the table above.
year
s
δ
k
y
c
I
deprec
change k
1
0.2
0.05
20
2.72
2.18
0.54
1
0.46
c) Again using the production function from a), find the steady state level of capital
in this economy.
k*/f(k*)=s/
δ
k*/k^(1/3)=0.2/0.05
(k*/(k^1/3))^(3)=(4)^3
(k*^(3)/(k*))=64
sq. root of (k*)^(2)=sq. root of 64
k*=8
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View Full Document 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).
year
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This note was uploaded on 10/03/2008 for the course ECON 302 taught by Professor Gold during the Spring '07 term at Wisconsin.
 Spring '07
 GOLD
 Macroeconomics

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