a
To calculate:Solow residual for year 2015 and 2016 and growth rate
a

Answer to Problem 5NP
The growth rate of Solow residual between 2015 and 2016 is
Explanation of Solution
Given Information:
Capital stock = 30
Employed Labor = 100
For 2015:
Substituting values in above formula:
Therefore, the Solow residual in2015 is 1.437.
For 2016:
Y = 105
Capital stock = 30
Employed Labor = 100
Therefore, the Solow residual in the year 2016 is 1.509.
The growth rate of Solow Residual between the two years is calculated as follows:
Therefore, the growth rate of Solow residual between 2015 and 2016 is
Introduction:
Solow residual is a numerical expression which shows growth of output due to factor inputs. It is usually calculated in chronological manner on yearly basis.
Y = Total output
K = Capital Stock
N= Labor employed
b)
Relationship between growth in 2015 and 2016.
b)

Explanation of Solution
After including the utilization rate of the factor inputs for interpreting the Solow Residual, the formula for Solow Residual can be written as follows:
Where,
The Solow residuals, calculated in part (a), are the residuals without taking into consideration the utilization rate of the factors of input. Those residuals are now the value ofA(productivity) for the respective years. If the utilization rate of the factor inputs (capital and labor) remains unchanged during 2015-16, then there is no difference in the growth rate of productivities and the growth rate of Solow Residuals for the two years. This can be shown as follows:
Since,
Introduction:
Steady state is a situation at which investment is equal to depreciation. It implies all the investment done is used to replace the
c)
Relationship between growth in 2015 and 2016 when utilization of labor increases by 3%.
c)

Explanation of Solution
Under the assumption that the utilization of labor (
Therefore, the growth rate of Solow residuals is 7.2% after incorporating the increase in utilization rate of labor. The growth rate of Solow residuals is more than the productivity growth. This is so because there has been a growth in utilization rate of labor by 3%.
Introduction:
Steady state is a situation at which investment is equal to depreciation. It implies all the investment done is used to replace the depreciating capital.
d)
Relationship between growth in 2015 and 2016 when utilizationof labor and capital is increased by 3%.
d)

Explanation of Solution
If the utilization rates of labor and capital both increase by 3% between 2015 and 2016 then the growth rate of Solow Residual increases further. The growth rate can be calculated as follows:
Therefore, the growth rate of Solow Residuals is 8.16% after incorporating the increase in utilization rates of both labor and capital. We have a higher growth rate of Solow Residuals as compared to the growth rate of productivity. This is so because we observed an increase of 3% each in the utilization rate of labor and capital between the years 2015 and 2016.
Introduction:
Steady state is a situation at which investment is equal to depreciation. It implies all the investment done is used to replace the depreciating capital.
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