Consider the following data: z s n United States 1 0.2 0.01 Canada 0.86 0.25 0.0
ID: 1169550 • Letter: C
Question
Consider the following data:
z
s
n
United States
1
0.2
0.01
Canada
0.86
0.25
0.012
Argentina
0.45
0.14
0.014
Thailand
0.23
0.21
0.015
Cameroon
0.05
0.1
0.028
Assume that d = 0.075 across all countries.
Given the production function: Y=zK^(1/3) N^(2/(3 ))Y
1. What is the steady-state output per worker in the United States, Canada, Argentina, Thailand and Cameroon?
2. Given the information in question (1), now suppose each country had the same total factor productivity as the United States. What would be the new output per worker in Canada, Argentina, Thailand, and Cameroon?
z
s
n
United States
1
0.2
0.01
Canada
0.86
0.25
0.012
Argentina
0.45
0.14
0.014
Thailand
0.23
0.21
0.015
Cameroon
0.05
0.1
0.028
Explanation / Answer
Y = z K1/3 N2/3
y = f(k) = Y / N = z (K / N)1/3
or, y = z (k)1/3
where k = K / N
in steady state,
s / (d + n) = k / f(k)
or, s / (d + n) = (k)1/3 / z
or,
k = [z x s / (d + n)]3 [Output per worker]
(1) calculating k for:
a. US: k = [1 x 0.2 / (0.01 + 0.075)]3 = 13.03
b. Canada: k = [0.86 x 0.25 / (0.012 + 0.075)]3 = 15.09
c: Argentina: k = [0.45 x 0.14 / (0.014 + 0.075)]3 = 0.35
d. Thailand: k = [0.23 x 0.21 / (0.015 + 0.075)]3 = 0.15
e. Cameroon: k = [0.05 x 0.1 / (0.028 + 0.075)]3 = 0.0001
(2) z = 1 for all countries. Then, calculating k for:
a. US: k = [1 x 0.2 / (0.01 + 0.075)]3 = 13.03
b. Canada: k = [1 x 0.25 / (0.012 + 0.075)]3 = 23.73
c: Argentina: k = [1 x 0.14 / (0.014 + 0.075)]3 = 3.89
d. Thailand: k = [1 x 0.21 / (0.015 + 0.075)]3 = 2.33
e. Cameroon: k = [1 x 0.1 / (0.028 + 0.075)]3 = 0.92
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