2. A country has the per-worker production function where yt is output per worke
ID: 1121070 • Letter: 2
Question
2. A country has the per-worker production function where yt is output per worker and kt is the capital-labor ratio. The savings function is given as follows S = 0.2% where S is the total national savings and Yt is total national output. (a) What is the steady-state value of the capital-labor ratio? Express k as a function of the capital depreciation rate d and the population growth rate n. (b) Assuming the capital depreciation rate is given as 0.05, complete the following table, where s is the savings rate and c is the steady state consumption per worker Table 2 0.05 0.10 0.15 0.20 0.25 0.30Explanation / Answer
We know that in steady-state kt = 0
10skt0.5 – (n+d)*kt = 0
10s/(n+d) =(kt)0.5
[10s/(n+d)]2 = kt
b)
s
d
n
k
y
c
0.2
0.1
0.1
20.0
44.7
35.8
0.2
0.1
0.1
13.3
36.5
29.2
0.2
0.1
0.2
10.0
31.6
25.3
0.2
0.1
0.2
8.0
28.3
22.6
0.2
0.1
0.3
6.7
25.8
20.7
0.2
0.1
0.3
5.7
23.9
19.1
s
d
n
k
y
c
0.2
0.1
0.1
20.0
44.7
35.8
0.2
0.1
0.1
13.3
36.5
29.2
0.2
0.1
0.2
10.0
31.6
25.3
0.2
0.1
0.2
8.0
28.3
22.6
0.2
0.1
0.3
6.7
25.8
20.7
0.2
0.1
0.3
5.7
23.9
19.1
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