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Law of Variable Proportions

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The law of variable proportions was propounded by economists like Joan Robinson, Alfred Marshall, P.A. Samuelson, etc. This law is also known as the law of diminishing returns. This law is also known as law of diminishing returns. This law concerns with short-um production function. It plays an important role in economic theory.

The law of variable proportions states that as the quantity of one factor is increased, keeping the other factors fixed, the marginal product of that factor will eventually decline. This means that up to the use of a certain amount of variable factor, marginal product of the factor may increase and after a certain stage it starts diminishing. When the variable factor becomes relatively abundant, the marginal product may become negative. 

Assumptions:
The law of variable proportion is based on the following assumptions:
1. The state of technology is assumed to be given or unchanged.
2. At least, one facto of production should be fixed.
3. There must be possibility of varying the proportion of factors of production.

On the basis of the above mentioned assumptions, the law of variable proportions can be explained with the help of the table below:

Land(Ld) ( In Ropanies)Units of Labour(L)Total Product (TP)Average Product(AP)Marginal Product(MP)Stages of Production
100000First Stage
101101010First Stage
10
2301520First Stage
10
3602030First Stage
10
4802020First Stage
10
5901810Second Stage
10
690150Second Stage
10
78011.4-10Third Stage

In the table above, land is fixed factor and labour is a variable factor. As the units of labour are increased keeping land fixed, TP first increases at an increasing rate up to the 3rd unit of labour and then increases at a decreasing rate up to the 5th unit of labour. It is maximum at the 5th unit of labour. It becomes stable at the 6th unit of labour. Thereafter, it decreases.

MP first increases, then becomes maximum at the 3rd unit of labour, and thereafter declines. At the 6th unit of labour, it is zero and thereafter it is negative.

AP also first increases, then becomes maximum at the 3rd unit of labour, and at 4th unit of labour, it is stable. After this, AP is decreasing. At the 4th unit of labour, AP and MP are equal.

This law is presented diagrammatically in the figure below:



Stages of the Law

The law of variable proportions can be divided into three stages. These three stages are as follows:
Stage I ( Stage of Increasing Returns)
In this stage, total product increases at an increasing rate upto a certain point and then increases but at the decreasing rate. In the figure, TP is increasing at the increasing rate up to the point A and then has started to increase at the diminishing rate. MP is increasing up to the point G and then it is decreasing. AP is decreasing up to the point H and at the point E, it is stable. This stage ends at the point E where AP and MP are equal, i.e. AP=MP 

Stage II ( Stage of Decreasing Returns)
This stage begins from the point B of TP. In this stage, total product continues to increase at the diminishing rate until it reaches at the point C. It remains stable at the point D, where the second stage ends. In this stage, AP is continuous decreasing, MP is also continuously decreasing and it is zero at the point F.

Stage III ( Stage of Negative Returns)
This stage begins from the point D. In this stage, TP is declining, AP is also declining and MP is negative o below X-axis. AP never becomes zero and negative. 

Stage of Operation 
A rational producer will never choose to produce in the stage III when marginal product of variable factor is negative. Even if the variable factor is free, a rational producer will not produce in the stage III because the total product declines in this stage.
A rational producer also does not choose to produce in the stage I although TP increases and MP of variable factor is positive. Thus, there is an opportunity of increasing production by increasing quantity of variable factor where AP continues to rise throughout the stage I. Thus, it is clear that a rational producer will produce in the stage II where both MP and AP of variable factors are diminishing. The answer of at which particular point in this stage the producer will decide to produce depends upon the prices of factors. 

Application of the Law

The law of variable proportions specially applies to agriculture. There are several reasons why agriculture is subject to this law. These reasons are:
1. The agricultural operations are spread out over a wide area and consequently supervision cannot be very effective.
2. Scope for the use of specialized machinery is also very limited.
3. There are further limitations arising from the seasonal nature of the industry, Agricultural operations are likely to be interrupted by rainfall and other climatic change.