# Law of variable proportions

The Law of variable proportions or short term production function is a very important concept while studying production function and also useful for industries. The whole concept is easily explained in the article with general examples to ensure better understandability.

### Introduction

The Law of diminishing returns states that with an increase in the quantity of one input combined with other fixed factors, the marginal productivity derived first rises, then eventually falls and finally becomes negative.Here, this law is also known as the "law of variable proportions" or the "law of returns to a factor" or the "short-run production function". The reason for the name returns to a factor is that, here due to a change in one factor or

**" a factor"**i.e. variable factor our returns or marginal productivity is responding. It should be noted that in general, labour is taken as a variable factor for law because labour is the only active factor of production as other factors constitute passive nature. Similarly, it is termed as the law of diminishing returns, because due to more and more employability of the variable factor our returns tends to diminish. This law operates in the short run because, in the long run, all the factors of production are variable and hence, it is also called the short-run production function.

### Assumptions of the law

**Constant technology**: We are working with the constant state of technology because if there is any modification in technology, our production would not decline and generally improves.

**Not applicable when inputs are in fixed proportions**: Law does not hold when inputs are used in fixed proportions to yield output. For instance, while making tea we use some fixed proportion of tea leaves, sugar and milk. Now, adding more of any one substance say sugar, does not increase our output.

### Stage 1: Stage of increasing returns

In the first stage total product increases at an increasing rate, marginal product rises to the point of inflexion and average product also rises. After the point of inflexion marginal product diminishes but remains positive, due to this total product continues to rise but at a diminishing rate. When stage 1 ends, the average product reaches its maximum point.In the initial stages, the fixed factor is in excess then the employability of variable factors. Hence, the addition of more and more variable factors leads to greater, return as a fixed factor is more effectively and efficiently utilised. Now, the question arises that why the fixed factor is not taken in the quantity that suits the availability of variable factors. Here, it must be noted that only those factors which are indivisible are taken as fixed factors. Also, better coordination between fixed and variable factors in the initial stages of production leads to increased productivity.

### Stage 2: Stage of diminishing returns

The total product continues to increase at an increasing rate, but both marginal product and average product are falling but remains positive throughout the second stage of production. The second stage ends when the total product reaches its maximum point corresponding to zero marginal product. This stage has also been termed, the stage of operation.Optimum utilisation of the fixed factor results in falling marginal product when additional variable factors are employed. Also, fixed factors and variable factors are imperfect substitutes for each other. Understanding this imperfect substitutability let us take an example, that to carry a 1000 tonne box we need a crane which is a fixed factor. Now, to carry two boxes within the same time we can not employ more labour to handle one box, so it explains that the fixed factor can't be replaced by a variable factor.

### Stage 3: Stage of negative returns

In the third stage total product declines, marginal product is negative and average product is also diminishing. Due to more variable factors on limited fixed factors, it is difficult to establish coordination between fixed and variable factors and hence marginal productivity goes on diminishing.The whole law can be understood with the help of a simple example. Let us assume we have a table with a capacity of four workers. If we put one worker to work on the table then he can easily do his task. If we put one another person then both of them easily coordinate between each other and by dividing task both raise the productivity of each other. Employing one more person also raises our productivity and our aforesaid first stage continues till the fourth person is put to work on that table. Employing a fifth person reduces our productivity. More and more employment leads to diminishing returns. A stage would come when they do work in such a haphazard manner that they reduce the work done by other members. Hence, all three stages can be easily understood here.

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