Manipulation of the Cobb Douglas Equation gives us expression for output per working age person:
growth rate of (Y/N)=[1/(1-alpha)*growth rate of TFP]+[(alpha/(1-alpha))*growth rate of (K/Y)]+ [growth rate of (L/N)]
N is the working age population
K is capital stock
L is labor quantity
TFP is total factor productivity
Why is this equation useful?
What are the main determinants of K/Y and L/N
The Cobb Douglas equation is used to calculate the productivity of factors, growth rate of output by using the ratio of labor to total population and the ratio of capital to the total income in a country at a point of time.
K/Y is the ratio between capital and total income and L/N is the ratio between the labor force and the total population of the nation at a point of time.
The determinants of K/Y are :
1.
Investment: The level of investment in capital goods affects the stock of capital. Higher levels of investment lead to an increase in capital stock, which in turn increases the K/Y ratio.
2. Depreciation: The rate of depreciation of capital also influences the K/Y ratio. Higher depreciation rates result in a decrease in the capital stock, leading to a lower K/Y ratio.
3. Technological advancements: Advances in technology can increase the productivity of capital, allowing for more output to be produced with the same amount of capital. This leads to a higher K/Y ratio.
4. Efficiency: The efficiency with which capital is utilized also affects the K/Y ratio. Higher efficiency means that more output can be produced with the available capital, resulting in a higher K/Y ratio.
The determinants of L/N are:
1. Birth and death rates: The birth and death rates of a population affect the size of the labor force. Higher birth rates and lower death rates lead to an increase in the labor force, resulting in a higher L/N ratio.
2. Immigration and emigration: The movement of people into and out of a country can affect the size of the labor force. Immigration increases the labor force, while emigration decreases it, thus impacting the L/N ratio.
3. Labor force participation rate: The percentage of the working-age population that is actively participating in the labor force affects the L/N ratio. A higher labor force participation rate increases the numerator (labor force), while a lower rate decreases it, thus altering the L/N ratio.
4. Education and skills: The level of education and skills of the labor force is also an important determinant of the L/N ratio. Higher levels of education and skills can lead to higher labor productivity, resulting in a higher L/N ratio.
Overall, the Cobb Douglas equation and its components provide a framework for analyzing the contribution of different factors (capital, labor, and total factor productivity) to the growth of output per working-age person. It helps to understand the key determinants of economic growth and identify areas for policy interventions to improve productivity and living standards.