Question

Economic development question

1. Suppose 75% of national income goes to labor and 25% goes to capital. Capital stock grows by 3%, labor force grows by 4%, and output grows by 4%.

1. Is the growth rate of output fully explained by the growth rates of the factors of production?

                  No the growth rate of productivity or a=0.0025 or 0.25%

2. What percent of the growth rate of output can be explained by the growth rate of capital?

                  18.75%

3. What percent of the growth rate of output can be explained by the growth rate of labor?

                  75%

4. What percent of the growth rate of output can be explained by the growth rate of productivity?

6.25%

I have attached the answer to this question, so please show all the steps and the reason why, thanks a lot!

Answer 1

We are given that 75% of national income goes to labor (labor share = 0.75) and 25% goes to capital (capital share = 0.25). Capital stock grows by 3% (gK), labor force grows by 4% (gL), and output grows by 4% (gY)

We use growth accounting for Cobb-Douglas production function Y = AK^0.25L^0.75 which gives

gY = capital share x gK + labor share x gL + gA (growth rate of TFP)

a) Is the growth rate of output fully explained by the growth rates of the factors of production?

Lets see. We have 4% = 0.25*3% + 0.75*4% + gA

We can see that 0.25*3% + 0.75*4% is 3.75% and gY is 4% which means 0.25% growth is not explained by labor or capital. This implies that it is the TFP that grows at 0.25%.

b) What percent of the growth rate of output can be explained by the growth rate of capital?

This is equivalent to capital share x gK/gY = 0.25*3% / 4% = 18.75%

c) What percent of the growth rate of output can be explained by the growth rate of labor?

This is equivalent to labor share x gL/gY = 0.75*4% / 4% = 75%

d) What percent of the growth rate of output can be explained by the growth rate of productivity?

This is equivalent to gA/gY = 0.25% / 4% = 6.25%