The functional relationship between physical input and physical output of a firm with a given state of technology is known as Production Function. A production function is a mathematical statement used to describe the technological relationship between input and output in physical terms. In its general form, it tells that production of a commodity depends on certain specific inputs. It presents the quantitative relationship between input and output. Besides, the production function represents the technology of a firm, of an industry, and of the economy as a whole. A production function may take the form of a schedule or table, a graphed line or curve, an algebraic equation or a mathematical model. But each of these forms of a production function can be converted into its other forms.

Definition of Production Function
The concept of production has been differently defined by different economists as stated below:

1. In words of Alfa. C. Chiang, “Function is a group of combination for variables (independent and dependent) in a specific order. The specialty of this function is that any value of X determines a unique value of Y.”

2. 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 unchanging technology”.

3. 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, T) are used, then we will write the Production function as:
Y = f (Ld, L,K,0, T)”

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

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

Features of Production Function

Production function has the following main features:

1. It indicates a functional relationship between physical input and physical output of a firm.
2. The production function is always in context to a period of time.
3. The production function can specify either the maximum output that can be produced from a given set of inputs or the minimum quantity of inputs required to produce a given level of output.
4. Production function is purely a technical relationship. It has no reference to cost of inputs or costs of products.
5. Output in the production function is the result of combined use of factors of production.
6. The production function includes all the technically efficient methods of production.

Assumptions of Production Function

1. It presumes a fixed given technology.
2. The costs of means of production remain the same.
3. Production function presumes a definite time period.
4. Combinations of factors of productions can be changed to an extent only.
5. Factors of production are homogenous, i.e., labour = labour and capital = capital.
6. Factors of production are variable.
7. Substitutability of factors of production is upto a limited extent.
8. The objective of firm is output maximization.