The production of any good is obtained through a combination of various factors of production like land, labour, capital etc. The good produced under the production process is termed as ‘Output’ and the factors used for production are termed as ‘Input’. There is some relation between quantities of inputs used and output produced. This functional relationship is known as the ‘**Production Function**‘. Thus, production function is a relationship between physical input and physical output of a firm for a given state of technology. It describes how and in how much volume the output will change when the quantity of inputs is changed in a given period of time.

## Characteristics Of Production Function

(1) Production function expresses a functional relationship between quantities of inputs and output.

(2) It represents technical relationship between inputs and output.

(3) Output is the result of a joint use of factors of production, so, the physical productivity of one factor can be measured only in context of this factor being used in conjunction with other factors.

(4) It expresses a flow of inputs resulting in a flow of output in a specific period of time.

(5) Production function is determined by the state of technology Any change in technology will mean shift in production function.

(6) Advancement in technology will result in a larger output from a given combination of the factors of production.

(7) Production function is not related with money price. It does not have any monetary significance. In other words, it is related with physical quantity.

## TYPES OF PRODUCTION FUNCTION

Several forms of production function can be prepared to explain the relationship between output and inputs. There are two types of production function.

#### (A) Short Run Production Function

Short-run is that time period in which production can be increased by changing variable factors of production only. In other words, in short run, it is possible to increase the units of one input while keeping the units of other inputs constant in order to have more output. This aspect of the production function is known as the ‘Law of Variable Proportions’. Law of variable proportions refers to the effect of change in factor ratio on the output. This law is also named as ‘Returns to a Variable Factor’. The law of variable proportions states that with an increase in a variable factor, keeping other factors constant, total production increases initially at increasing rate and then, it increases at diminishing rate and finally, it starts declining.

Since, it is related to short-run, so, it is called a short-run production function. Thus, law of variable proportions is related to the short-run production function in which keeping some factors of production constant, the quantity of one factor of production is varied. Therefore, proportion between the fixed factors and variable factor undergoes a change. In other words, law of variable proportions studies the effect of this variation in proportion of factors on the output. It is also known as ‘Returns to a Factor’. There are three aspects of law of returns to a factor which are given here-as:

**(i) Increasing Returns to a Factor:** Law of increasing returns to a factor states that total production increases at increasing rate when more of the variable factor is combined with the fixed factors of production. It means marginal production of variable factor increases.

**(ii) Constant Returns to a Factor:** Law of constant returns to a factor states that total production increases at constant rate when more of variable factor is combined with fixed factors of production i.e. marginal product of variable factor is constant.

**(iii) Diminishing Returns to a Factor:** Law of diminishing returns to a factor states that when more of variable factor is employed with fixed factors. then total production increases at a diminishing rate i.e. marginal production of variable factor goes on diminishing.

#### Long Run Production Function

In long-run, all factors of production are variable. In long-run, it is possible for a firm to change all inputs according to its scale. This is known as ‘Returns to Scale’. The concept of returns to scale is related to the fixed proportion production function in which all factors of production are used in fixed proportion. Thus, returns to scale show the relationship between output and scale of inputs in long-run when all variable factors are increased in the same proportion. Since, it is related to long period, it is called ‘Long-run Production Function‘. In long period, when all the factors are increased in fixed proportion and the scale of production is expanded, then the behaviour of output shows following three aspects of returns to scale :

**(i) Increasing Returns to Scale :** Increasing returns to scale occur when output increases in a larger proportion than the increase in all inputs.

**(ii) Constant Returns to Scale :** Constant returns to scale occur when output increases in the same proportion as the increase in all inputs.

**(iii) Diminishing Returns to Scale:** Diminishing returns to scale occur when output increases in a smaller proportion than the increase in all inputs. Learn more about Demand.

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