5. (Based on Chapter 3)In a certain country, the production fiunction is The fra
ID: 1137491 • Letter: 5
Question
5. (Based on Chapter 3)In a certain country, the production fiunction is The fraction of output invested, s, is 0.25. The depreciation rate 0.03 and population growth is n = 0.02. A, the overall productivity parameter, and h the human capital per worker both equal 1. (e) What are the steady state levels of capital per worker, k, and output er worker, y? (b) In year 1, the level of capital per worker, k, is 16. Complete a table like the one below showing how capital and output change over time (the beginning is filled in as a demonstration). Continue the table upto year 8. Note that k/k is the growth rate of k and Ay/y is the growth rate of y. You need to use the following growth rate rule to go from k to y : Hints: . Also note that I have not calculated the growth rates for the first year (because we do not have values for anything preceding it). . Capital per worker in the second year will be capital per worker in the first year plus the change in capital in the first year. Yenr Capital pw Output pw Investment Depreciation kchange k srowth y growth 16 0.8 0.2 N/A N/AExplanation / Answer
Production function per capita terms: y = Ak1/2h1/2
Put A=1 and h = 1. Y= k1/2.
At steady state k =0.
k = sy – (n+)k
k = s* k1/2 – (n+)k
s* k1/2 – (n+)k =0. Solve for k
k* = [s/(n+)]2
k* = [0.25/(0.03+0.02)]2
k* = 25
y* = 5 are the steady state level of capital per capita and output per capita.
Year
Capital pw
output pw
Investment
Depreciation
kchange
kgrowth
ygrowth
k
y
sy
k
k
k/k
y/y
1
16.000
4.000
1.000
0.800
0.200
2
16.200
4.025
1.006
0.810
0.196
0.012
0.006
3
16.396
4.049
1.012
0.820
0.192
0.012
0.006
4
16.589
4.073
1.018
0.829
0.189
0.012
0.006
5
16.778
4.096
1.024
0.839
0.185
0.011
0.006
6
16.963
4.119
1.030
0.848
0.182
0.011
0.006
7
17.144
4.141
1.035
0.857
0.178
0.010
0.005
8
17.322
4.162
1.040
0.866
0.174
0.010
0.005
Year
Capital pw
output pw
Investment
Depreciation
kchange
kgrowth
ygrowth
k
y
sy
k
k
k/k
y/y
1
16.000
4.000
1.000
0.800
0.200
2
16.200
4.025
1.006
0.810
0.196
0.012
0.006
3
16.396
4.049
1.012
0.820
0.192
0.012
0.006
4
16.589
4.073
1.018
0.829
0.189
0.012
0.006
5
16.778
4.096
1.024
0.839
0.185
0.011
0.006
6
16.963
4.119
1.030
0.848
0.182
0.011
0.006
7
17.144
4.141
1.035
0.857
0.178
0.010
0.005
8
17.322
4.162
1.040
0.866
0.174
0.010
0.005
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