It is a functional relationship between physical output and physical inputs. It shows how output responds to different levels of inputs. It is a technical relationship, not any economic relationship. It may be expressed as under:
Often, L is taken as a variable factor and K as a fixed factor, and throughout our analysis we shall follow this practice.
On the basis of time period, production function is categorised as :
(i) Short Run Production Function, and
(ii) Long Run Production Function.
Details are as under:
Short Run Production Function
Short run is the time period in which output can be varied only by changing the variable inputs, like labour. The inputs that remain fixed are called fixed inputs or fixed factors.
Short run production function is a relation between inputs and output for a given technology in which output can be varied by changing one factor (say labour) only. All other factors remain fixed. Mathematically Q = f (L) i.e., output is a function of labour. Or,
, i.e., output is a function of labour keeping capital constant.
Long Run Production Function
Long run is the time period in which distinction between fixed and variable inputs disappears. All inputs are variable. So output can be varied by changing all the inputs simultaneously.
Long run production function is a relation between inputs output for a given technology in which output can be varied by altering all factor inputs simultaneously. Here, factor ratio remains constant.
Distinction between Short Run Production Function (SRPF) and Long Run Production Function (LRPF)
Following are the points of distinction:
1. In SRPF, output changes are accompanied by changes in factor proportions whereas in LRPF, factor proportion does not change whatever may be the level of output.
2. In SRPF, output is varied by altering one factor of production whereas in LRPF, output is sought to be increased by altering all the inputs.
3. The scale of output does not change with change in level of output in case of SRPF. However in case of LRPF, the scale of output changes when there is change in level of output.
Note : Scale of output refers to production capacity of the firm. Often it is measured in terms of size of the plant/machinery installed by the firm. It is a fixed factor during the short period. Short period is a period of time during which fixed factors (or size of the plant or scale of production) cannot be changed. In the long period, all factors are variable including the plant /machinery. Accordingly, during the long period, scale of production tends to change.