Answer :
a. The annual growth rate for each variable are 200%, 300% and 200%
b. Based on the given information, the productivity growth for this country is approximately 0.587 or 58.7%.
How to calculate the annual growth rate
To calculate the annual growth rate for each variable, we can use the formula:
Growth rate = (New value - Old value) / Old value * 100
Let's calculate the annual growth rate for each variable:
a) Output per worker:
Growth rate of output per worker = ((6 - 2) / 2) * 100 = 200%
b) Physical capital per worker:
Growth rate of physical capital per worker = ((60 - 15) / 15) * 100 = 300%
c) Human capital per worker:
Growth rate of human capital per worker = ((21 - 7) / 7) * 100 = 200%
Now, let's calculate the productivity growth for this country. The productivity growth can be calculated by taking the geometric mean of the growth rates of output per worker, physical capital per worker, and human capital per worker, raised to the power of alpha (1/3 in this case).
Productivity growth = ((1 + Growth rate of output per worker) * (1 + Growth rate of physical capital per worker) * (1 + Growth rate of human capital per worker))^(alpha) - 1
Productivity growth = ((1 + 2) * (1 + 3) * (1 + 2))^(1/3) - 1 = (3 * 4 * 3)^(1/3) - 1 = 36^(1/3) - 1 ≈ 1.587 - 1 ≈ 0.587
Therefore, the productivity growth for this country is approximately 0.587 or 58.7%.
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