The law of variable proportions is one of the important laws of economics. It is a new name of the Law of Diminishing Returns. The economists like Marshall. Benham, Samuelson, and Mrs. Joan Robinson have contributed to the development of this law. This law shows the short-run relation. The gist of this law is that if the quantity of a factor is increased, keeping constant the quantity of other factors, eventually the marginal and average product decline.

 

According to C.E. Ferguson —“As the amount of variable input is increased, the amount of other inputs held constant, a point is reached beyond which marginal product declines”.

 

Likewise, in the words of W.J. Baumol more and more of some input is employed, all other input quantities being held constant, eventually a point will be reached where additional quantities of input will yield diminishing marginal contribution to total product”.

 

The clear example of this law can be found in agriculture production. In agriculture, if we keep the quantities of land fixed and go on increasing the quantity of labour, eventually the marginal product declines.

 

Assumptions of Law of Variable Proportions

 

This law is based on the following assumptions:

 

1. The state of technology is given and constant.
2.  The quantity of at least one factor should be kept fixed. From this it is easier to vary factor proportion and its effects on production can be seen.
3. The ratio in which different factors are combined should be liable to vary.

 

This law can be illustrated by the help of a table and a figure. Suppose that the quantity of fixed factor, capital is kept fixed. The increase in quantity of the variable factor, labour, to increase output the production (hypothetical) will be as shown in the table.

Units of Labour	Total Product	Average Product	Marginal Product
1 2 3 4 5 6 7 8	10 24 39 52 61 66 66 64	10.0 12.0 13.0 13.0 12.2 11.0 9.4 8.0	- 14 15 13 9 5 0 -2

 

There are three stages of production as shown in the fable.

 

First Stage

 

The total product and the average product increase rapidly in this stage. The marginal product is maximum when 3 units of labour is used and diminishes thereafter. The average product is maximum when 4 units of labour are used. The average product is maximum when marginal product and average product are equal. The first stage ends when the average product is maximum. This stage is called the stage of increasing.

 

The reasons for increase in production in this stage are:

 

1. There is enough fixed capital. Hence. more use of variable factor leads to the efficient use of fixed factor.
2. The more use of variable factor increases its own efficiency. Because more use of variable factor leads to specialization and division of labour. This, in turn, leads to an increase in production. A

 

Second Stage

 

In this stage, the total product continues to increase in diminishing rate. The average and marginal product both decline. This stage ends when the total product is maximum and the marginal product is zero. In table this happens when seventh unit of labour is used. This stage is called the stage of diminishing returns.

 

The reasons for the decrease in production in this stage are:-

 

1. The fixed factor is overutilised and becomes inadequate. The variable factor cannot substitute the fixed factor. According to Mrs. Joan Robinson the returns diminish because the factors are imperfect substitutes of each other.
2.  The production decline because of the indivisibility of the fixed factor. According to Bober “Let divisibility enter through the door, law of variable production rushes out of the window”.

 

Third Stage

 

In this stage, the total product and average product both decline. The marginal product is negative.

 

The reason for the marginal product being zero is that the variable factor is very large in this stage. They disturb each other. This makes management and coordination difficult. “Too many cooks spoil the broth” comes to be true. Consequently, the marginal product becomes negative.

 

The law has been illustrated in the figure below.

 

 

It is seen in the figure that, the total product curve rises in increasing rate in the beginning and increases at diminishing rate after point F. The total product declines after point G.

 

The average and marginal product also increases in the beginning and decline after reaching the maximum point. At point J, average product is maximum. Here, average product and marginal product are equal. When the total product is maximum at point G, the marginal product is zero and becomes negative thereafter.