A given output can be produced with many different combinations of factors of production (land, labor, capital and organization) or inputs. The output, thus, is a function of inputs. The functional relationship that exists between physical inputs and physical output of a firm is called production function.
In abstract term, production function is written in the form of formula:
Q = f (x1, x2, ……., xn)
Q is the maximum quantity of output and x1, x2 and xn are quantities of various inputs. The functional relationship between inputs and output is governed by the laws of returns.
The laws of returns are categorized into two types.
(i) The law of variable proportion seeking to analyze production in the short period.
(ii) The law of returns to scale seeking to analyze production in the long period.