Production is a process involving the use of different physical inputs. In fact it is the result of the inputs. Factors of production are also called ‘inputs’. The product obtained from the inputs is known as ‘output’. Production function explains the functional relationship between physical inputs and physical output.
Production function shows how maximum output is secured with the combination of different inputs in a given time and with a given technology, managerial ability etc.
Definition of Production Function:
Professor Stigler defined the function as “the name given to the relationship between the rates of input of productive service and the rates of output of the product“.
Production Function Formula :
Production function may be explained by the following formula or equation:
P = f(a, b, c, ……n)
Where P denotes the rate of output; a, b, c, …..n denote different factors and services used per unit of time.; f denoted the function. This equation shows that P is the function of the different factors of production used as inputs. It may be remembered that production function is not same for all the firms. It differs from firm to firm. Production function is different in the case of different firms because of the differences in technical knowledge and managerial efficiency of the firms.
Linear Homogeneous Function :
This function shows constant returns enjoyed by a firm. It is expressed as follows
mP = F (mX, mY)
Where P is the total product. X and Y are the two factors of production. This equation shows that when factors of production of ‘X’ and ‘Y’ are increased ‘m’ times, production also increases by ‘m’ times.
Characteristics of Production Function :
The function has the following characteristics
1) Production function always relates to a particular period.
2) It shows maximum output secured by combining the available technical knowledge with the factors of production.
3) It reveals all the possibilities of combination of different factors needed for the purpose of production. Production function is necessary for a producer for knowing the quantity of different factors and their prices.
4) It explains about the relationship between physical inputs and physical output only. It did not mention the prices of these units.
5) The method of utilizing the inputs in production depends on the technical knowledge.
6) The nature of production is determined by whether the factors of production are completely divisible or indivisible. Constant returns does not arise when the factors of production are divisible.