Production Function

The functional relation that exists between input and output is called production function. The relation described in the production function is a technical relation. The minimum of inputs required to produce a given output technologically determined. There is no question of propensity or pattern of human behaviour as we find in case of consumption. In terms of mathematical equation, the relationship can be expressed as follows:

Q = f (L,k)

Where Q = output, L and k are labour and capital respectively. Besides labour and capital, we can add other factor inputs in the right side of the equation. But for the sake of simplicity, we have taken two factor inputs. Here the factor inputs are independent variable and output is the dependent variable. Output can only change when there is a change in inputs, given the state of technology.

Production function is divided into short-run production function and long-run production function. In the short-run it is not possible to change all factors of production to change the output of a firm. We can keep some factors constant and vary others to study is effect on output. In the long-run all factors can he changed to study its effects on output.

The short-run production function refers to the law of variable proportions and the long-run production function refers to the law of returns to scale.

As we have already discussed, in the short-run some factors are fixed while others are variable. Therefore before discussing the law of variable proportions let us first discuss the meaning of short-run, production function exhibits the Law of Variable factors.

Short-Run

Short-run refers an operational time period in which the output of a firm can be varied by changing all factors. In the long-run all factors are variable. In the long-run, production function is subject to the Law of Returns to Scale.