The Cobb – Douglas Production Function:

The simplest and the most broadly employed production function in economics is the Cobb-Douglas production function. This is a statistical production function specified by professors C.W. Cobb and P.H. Douglas.

The Cobb-Douglas production function can be defined as:

Q = b L^a C^1-a 

Here,

Q = Actual output
L = Labor
C = Capital
b = number of units of Labor
a = Exponent of labor
1-a = Exponent of Capital

According to the above production function, when both factors of production (i.e., labor and capital) are raised by one percent, the output (i.e., total product) will raise by the sum of the exponents of capital and labor that is, by (a+1-a). As a+1-a =1, according to the equation, whenever the input is raised by one percent, the output too increases by one percent. Therefore the Cobb Douglas production function elucidates only constant returns to scale. This is mostly since the addition of,

Q = b L^a C^b

In above production function, the summation of the exponents exhibits the degree of “returns to scale” in production function.

a + b >1: Increasing returns to scale
a + b =1: Constant returns to scale
a + b <1: Decreasing returns to scale

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