Cobb-Douglas Production Function

The best known production function in economics, is the Cobb-Douglas production function.   It is named after its pioneer Douglas who fitted a function suggested by Cobb on the basis of the statistical data pertaining to the entire business of manufacturing in U.S.A.   The Cobb-Douglas Production Function is a linear homogeneous production function implying Constant Returns to Scale.

It takes the following form:

Q = A.K^α.L^1-α

Where,

• Q Stands for the Output.
• L and K are inputs
• A is a positive constant
• α  is a positive fraction i.e.  Î± < 1.

In the above formula if L and K are increased in equal proportion i.e. if L becomes gL and K becomes gK, then the output Q will become gQ.

Thus the Cobb-Douglas Production function indicates constant Returns to scale.   The Cobb-Douglas Production function also shows that Elasticity of Substitution equals One.   Further it hints that if one of the inputs is zero the output will also be zero.   The Cobb-Douglas production function strengthens the validity of Euler’s Theorem, which states that if factors of production are paid according to their marginal product then the total product will be exhausted.

Criticism of the Cobb-Douglas Production function

1. The Cobb-Douglas production function only considers two factor inputs viz, Labour and Capital.   Besides Cobb-Douglas production function were often used for manufacturing sector alone.
2. The Cobb-Douglas production function assumes only constant Returns to scale, and thus it would be difficult to explain diminishing returns in process of production in the long-run.
3. It is easier to calculate labor input in terms of number of men employed or hours of work, but it is difficult to measure capital input, more so because it depreciates over a period of time.
4. The Cobb-Douglas production function assumes the prevalence of perfect competition in the market.
5. All the units of labour are assumed to be homogeneous.

Modified Cobb-Douglas production function

Several studies were made in 1920’s and 1930’s which assured that Cobb Douglass production function was highly reliable.   But in 1937, David Durand proposed that the restricted function of the equation, Q = A.K^α.L^1-α , needed modification.   According to Durand, the use of  Î± and 1-α restricted the model to Constant Returns alone; because the sum of the exponents  Î±+1-α would always be equal to one.   Thus to enable the exponent of capital to be independently determined the Cobb-Douglas Production function was slightly modified to be read as follows:

Q = A.K^α.L^β

In this Production function, the sum of the exponent shows the type of Returns to Scale.

• If  Î± + β = 1 then it represents Constant Returns.
• If  Î± +  Î² > 1 then it indicates Increasing Returns.
• If  Î± +  Î² < 1 then it indicates Decreasing Returns.

Returns to scale refers to a technical property of production that examines changes in output subsequent to a proportional change in all inputs (where all inputs increase by a constant factor). If output increases by that same proportional change then there are constant returns to scale, sometimes referred to simply as returns to scale. If output increases by less than that proportional change, there are decreasing returns to scale. If output increases by more than that proportion, there are increasing returns to scale.

Despite criticism levied against the Cobb-Douglass Production function it continues to remain, even today, perhaps the most popularly used production function.