Production function explains the relationship between factor inputs and output, which means the relation between factors of production, their productivity, and final outcome. It may also be defined as the technological relationship between inputs and outputs.

According to Prof. Watson "Production function is the relation between a firm's physical production (output) and the material factors of production (inputs).”

Production may be defined as the conversion of physical inputs into physical output. As output depends upon input so we can say output is a function of inputs.

There is a direct relationship between the number of inputs and the production of output. The production function is nothing other than a tool used to show this relationship.

The production function is given as -

Q = f (L,K,D...)

Where –

Q stands for - Output of the firm

f stands for function

L, K, D stands for the physical quantity of Labour (L), Capital (K) and Land (D) used.

Suppose we say that a firm uses two inputs - capital and labour, then the production function will indicate the physical relationship between these two inputs and output of the firm. It will be represented as

Q = f (L,K)

Where –

Q stands for - Output of the firm

f stands for function

L, K stands for the physical quantity of labour and capital used.