Answer to Question #221598 in Macroeconomics for Phil

Question

What are the special properties of Cobb- Douglas production function and how can the function be used to calculate the sources of growth

Answer 1

Cobb- Douglas production function is a particular functional form of the production function widely used to represent the technological relationship between the amounts of two or more inputs (particularly capital and labor) and the amount of output that can be produced by those inputs.

The production function is:

$Q=(L,K)=AL^\alpha K^\beta$

The special properties are;

• Q - this is the total production( the real value of all goods produced in a year).
• L- labor input (the total number of persons-hours worked in a year).
• K- capital input (a measure of all machinery ,equipment and buildings. The value of capital input divided by the price of capital).
• A- Total factor productivity.
• $\alpha$ and $\beta$ - output elasticities of capital and labor respectively. These values are constants determined by the available technology.

The Cobb- Douglas production function measures returns to scale by the sum of its exponents:

• If $\alpha+\beta=1$ , returns to scale are constant.
• If $\alpha+\beta>1,$ returns to scale are increasing.
• If $\alpha+\beta<1$ , returns to scale are decreasing.

The exponents of labor and capital in Cobb-Douglas production function give a measure of output elasticities of labor and capital respectively.