# Concept of Production Function

In an economy, both consumers and producers are needed for a smooth functioning. A producer makes use of various inputs for production of goods and services. Production is an important activity as it enhances the utility of the product by changing it in the form needed by the consumers. Therefore it is very important to understand the concept of production function.

## Production Function

Production refers to transformation of inputs into outputs. There exists some relation between inputs and outputs of a firm. In Economics, such a relationship is known as production function. Production function is an expression of the technological relation between physical inputs and outputs of a good. A production function can be an equation, table or graph showing a maximum amount of a commodity that a firm can produce from a given set of inputs during a period of time.

The concept of production function describes the ways in which a firm uses its factors of production and combines them to produce different level of outputs. It shows the minimum set of inputs required to produce a given level of output or it shows the maximum level of output that can be produced with the given level of inputs. Production function can be symbolically written as,

OX = f (i1, i2, i3 …….in)

Where,

OX = Output of commodity X
f = Functional relation
i1, i2, i3 …….in = Inputs needed for OX

Suppose a firm is manufacturing chairs by using two inputs -labour and capital. The production function can be written as,

OChairs = f(L,K)

The concept of production function defines the maximum number of chairs which can be produced with the given labour and capital. If the production function is given as 250 = (7L,2K), it means that 7 units of labour and 2 units of capital can produce a maximum of 250 chairs.

A production function either specifies the maximum outputs that can be produced with the given amount of inputs or the minimum inputs required to produce a given level of output. It establishes a technical relationship between inputs and outputs. The production function only includes technically efficient methods of production and no rational consumer will use inefficient methods.

## Short Run and Long Run Production Function

Before we move on to short run and long run production function, we need to first take a look at the two types of factors of production – variable factors and fixed factors.

1. Variable Factors – Variable factors refer to those factors which can be changed in the short run. They vary directly with the level of output. As output increases, requirement for variable factors also rises and vice versa. Variable factors are not required in case of zero output. For example, raw material, casual labour, power, fuel etc.
2. Fixed Factors – Fixed factors refer to those factors which cannot be changed in the short run. The quantity of fixed factors remain the same in the short run irrespective of the level of output. They do not change whether the level of output rises, falls or becomes zero. For example, plant and machinery, building, land etc.

Let us now understand what is meant by short run and long run production function.

### Short Run Production Function

Short run refers to a period in which output can be changed by changing only variable factors. In the short run, fixed factors like plant, machinery, building etc. cannot be changed. Therefore production can be raised only by increasing variable factors, but till the extent of the capacity of the fixed factors.

For example, if a producer wants to increase output in the short run, he can do so by using more raw materials or increasing the number of workers with the existing factory building, plant and equipment. One cannot immediately expand factory building, additional plant and equipment. So, in the short run, some factors are fixed and some are variable and fixed factors cannot be changed during such a short span of time.

The period of short run is not a fixed time span. The period is a rather functional concept, which depends on production conditions. It varies from firm to firm and industry to industry.

The short run production function studies the effect on output due to change in variable inputs, assuming that there is no change in other factors. As there is change in variable input only, the ratio between different inputs tends to change at different levels of output.

### Long Run Production Function

Long run refers to a time period in which output can be changed by changing all factors of production. In long run, there are no fixed factors as all factors can be varied. Long run is a period long enough for the firm to adjust all its inputs according to change in the conditions. In the long run, a firm can change its factory size, switch to new techniques of production, purchase new machinery etc. All factors are variable in the long run.

Therefore, if a producer wants to increase his output in the long run, he can do so by changing any of the factors of production, including factory building, plants machinery etc.

The long run production function studies the effect on output due to change in all the factors inputs. As all inputs are variable in the long run, the ratio between different inputs tend to remain the same at different levels of output.