# Production Function

Contents in the Article

Production Function- Meaning, Features, Types

### Meaning

Production function expresses the technological relationship between physical inputs and physical quantities of output.

In other words “it shows that with a given state of technological knowledge and during a particular period of time how much can be produced with given amount inputs.

To generalize, if Q is the output per period of time of a firm and Labour (L), Capital (C) and Land (N) are the required inputs to produce Q, output over the same period, the production function may be expressed as:

Q = f (L, C, N)

Apparently the expression on the right hand side can be expanded to include as many inputs as are used in the production of the output Q.

### Definition

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

1. L. R. Klein, “The production function is a technical or engineering relation between input and output. As long as the natural laws of technology remain unchanged, the production function remains unchanged.”
2. Prof. George J. Stigler, “Production function is the relationship between inputs of productive services per unit of time and outputs of product per unit of time.”
3. Watson, “The relationship between a firm’s physical production (output) and the material factors of production (input) are referred to as production functions.”

Thus from the above definitions, we can conclude that production function is the technical relationship between the quantity of goods produced (output) and the factors of production (inputs) necessary to produce it.

### Features of Production Function

1. It indicates a functional relationship between physical inputs and physical output of a firm.
2. The production function is always in relation 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. It is purely a technical relationship. It has no reference to money price.
5. Output in the production function is the result of joint use of factors of production.
6. The production function includes all the technically efficient methods of production. ‘

Thus production function describes the law of production, i.e., the transformation of factor inputs into outputs (products) at any particular period of time.

### Explanation

A production function is an economic summary or description of technological possibilities; it is the framework the economist uses to record what he needs to know about the physical aspects of the production process.

Although technology (methods of combining resources) may change rapidly, at any particular time it can be taken as given. The producer surveys production possibilities within the limits of available technical knowledge. A function can be presented as a schedule or san an algebraic function with output dependent on possible input combinations. In the second case, production Function describes the relation between physical inputs and physical outputs of a firm. The laws of production are a study of the production function.

Algebraically, production function can be written as

Q = f (A, B, C, D,..) where, Q = quantity of output

A, B, C, D…. = quantities of the factor a, b, c, d…..

### Types of Production Functions

Business economics looks to two kinds of input-output relations in production function. These are as follows:

1. Input-output relation where some inputs are fixed while quantities of other inputs vary (or short-run).
2. Input-output relation where all the inputs are variable (or long-run production function).

#### Short Run or Short Period Production Function

Short run is defined as that period of time in which one or more factors of production or inputs are fixed and others are variable: Therefore, changes in output must be accomplished exclusively by changes in the use of variable inputs. In other words, in the short run there are both variable inputs and fixed inputs. Thus if producers wish to expand output in the short run, they must do so by using more raw materials, hours of labour service with the existing plant and equipment.

The distinguishing characteristics of short run is that certain factor-inputs are fixed in character, while other factor inputs are variable in nature only. The level of production can be changed: The scale of production cannot be changed.

The behaviour of output when one input is varied and other is held constant is studied under the ‘Law of variable proportions’. It is also known as the ‘Law of Diminishing returns’ and the ‘Law of non-proportional returns’.

#### Long Run or Long Period

Long period or long run is defined as that period of time in which all factors of production or inputs are variable. Distinction between fixed and variable inputs obtains only in the short run. In the long run all inputs become variable, i.e., the scale of production itself can be changed by installing new plant and equipment and hiring more labour and other factor inputs. The behaviour of output when all inputs are varied in study under the ‘Law of Returns to Scale’. 