Production function is the physical or quantitative relation between production and the means which contribute in production. 

Following are the definitions of production function-

1. In words of Henderson and Quandt, “Production function is an engineering concept which explains the relationship between input and output. This relation is quantitave and assumes a fixed, given technology”.

2. As per Dr Balwant Kandoi, “If quantity of production is Q and the factors of production like labour, capital, land, management and technique (Ld, L, K, O) are used, then we will write the Production function as:
Y = f (Ld, L, K, O)”

3. According to the N Gregory Mankiw, “Relationship between physical quantity factors of production or inputs and the production is production function”.

4. According to Watson, “The relationship between a firm’s physical production (output) and the material factors of production (inputs) necessary to produce it is called production function”.

On the basis of the above definitions, production function can be defined in simple terms as follows :

Production Function is the physical relation between Input and Output.

General characteristics of Production Function

1. Production Function is cost independent- Production Function has no relation with the price of produced goods and the cost of means used to produce them. Its relation is mainly with the physical quantities of production. Although, each producer, at the time of deciding the level of production or selecting the combination of means, always keeps the price of goods and means in his mind.

2. Production Function is an Engineering concept, not an economic concept- The task of Production Function is to interpret the relation between the means of production and the physical level of production. Therefore, it is considered as an Engineering concept, not on economic concept.

3. Production Function is a time dependent concept- The relation of production function is with a specific time period. It does not have any meaning if the time period is changed. That is why it is considered as a time dependent concept.

4. Production Function accepts the substitution possibilities of means – The concept of Production function accepts that the substitution possibilities of means of production exist, meaning one means can be used in place of another. Example- capital can be used in place of labour.

5. Production Function accepts the complete divisibility of means- Production Function accepts the complete divisibility of means; that means, it accepts that every mean of production can be divided.

6. Production Function is related to a definite given technique- The technique of production must not vary, it is based on the single technique. When the technique is of lower grade, without even decreasing the level of means, the production can be decreased.

7. Production Function is the subject of static economics- The concept of Production Function is the subject of static economics because under this, cost of means, level of technical knowledge and the timeline is considered to be constant.

8. Production Function is short-term or long-term on the basis of time period- Production Function is categorised as short-term or long-term on the basis of time period. There is a difference between these two types of production functions on the basis of proportion of means. In short-term, the ratio of varied and constant means keeps on changing with the production, while in long term, the ratio of every means remains equal.