The Law of Variable Proportions

The Law of variable proportions states that as more and more of the variable factor is combined with the fixed factor, the marginal product of the variable factor may initially rise, but eventually a situation must come when the marginal product of the variable factor starts declining. In fact, a stage may come when the marginal product becomes zero or even negative.

If the input of one factor is increasing while all other factors remain constant, then the proportion between the factors is changed. Supposing, there are two factors of production, i.e., land and Labour.  

The land is a fixed factor and labour is a variable factor. Supposing,  you have land measuring 2 hectares. You grow tomatoes on it with the help of one unit of labour.

Accordingly, the proportion between labour and land will be 1: 2. If the units of labour are increased to 2 then the new proportion between labour and land will be 2: 2. In other words, if there were 2 hectares of land per unit of labour previously, now there will be 1 hectare of land per unit of labour.

On account of change in the proportion of factors, there will also be a change in total output, but at different rates. Initially, when more labour is employed on the fixed land, the total output may increase at an increasing rate.

But, eventually, a stage must come when as a matter of law,  total output will increase only at a diminishing rate. This is popularly known as the law of variable proportions or the law of diminishing returns.

Tabular and Diagrammatic Presentation of the Law

Units of LandUnits of Labour Total ProductMarginal Product
1
1
1
1
1
1
1
1
1
2
3
4
5
6
7
8
2
5
9
12
14
15
15
14
2
3
4
3
2
1
0
-1
Increasing MP implies increasing returns to a factor

Diminishing MP implies diminishing returns to a factor

Negative MP implies negative returns to a factor

Diagrammatic Presentation of the law

Stage I is between O to K on the curve TP. In this zone, MP is increasing and TP is increasing at an increasing rate.

Stage II is between K to T. In this zone, MP is decreasing and TP is increasing at a decreasing rate.

Stage III is beyond point T. Now TP starts declining because MP is negative.

K is a point of inflexion where TP stops increasing at the increasing rate and instead starts increasing at the decreasing rate.

The table shows that as more and more units of labour are used, the marginal product tends to rise 3 units of labour are employed. In this situation, the total product increases at an increasing rate.

This is a situation of increasing returns to the factor. But with the application of the 4th unit of labour situation of diminishing returns sets in MP starts decreasing and TP increases only at the decreasing rate.

Diminishing  MP reduces to zero. Total output is maximum when marginal output is zero.  Eventually, the marginal product may be negative.  Now output TP starts declining when the 8th unit of labour is employed.

Causes of Increasing Returns to a Factor

Increasing returns to factor occur because of the following factors :

1. Fuller Utilisation of the Fixed Factor: In the initial stages fixed factor remains underutilised. Its fuller utilisation calls for greater application of the variable factor. Hence, initially, additional units of the variable factor add more and more to the total output or marginal product of the variable factor tends to increase.

2. Division of labour and increase in efficiency: Additional application of the variable factor enables process-based division of labour. Specialised workers may be used for different processes of production. This increases the efficiency or productivity of the variable factor. Accordingly, marginal productivity tends to rise.

3. Better coordination between the factors: So long as the fixed factor remains underutilised, an additional application of the variable factor tends to improve the degree of coordination between the fixed and variable factors. As a result, marginal product increases and total product increases at an increasing rate.

Causes of diminishing returns to a factor

Diminishing returns to a factor or the law of diminishing returns may be explained in terms of the following factors :

1. Fixity of the factor: Fixity of the factors is the principal cause behind the law of diminishing returns. As more and more units of the variable factor are combined with the fixed factor the latter gets excessively utilised. It suffers greater wear and Tear and loses its efficiency. Hence, the diminishing returns.

2. Imperfect factor Substitutbility: Factors of production are imperfect substitutes for each other. More and more labour cannot be continuously used in place of capital. Accordingly, diminishing returns are bound to set in if only the variable factor is increased to increase output.

3. Poor coordination between the factors: increasing application of the variable factor eventually disturbs the ideal factor ratio. This results in poor coordination between the fixed and variable factors. Hence, the diminishing returns.

Assumptions of the Law

The Law of variable proportion is based on certain assumptions these are as follows :

  • Ratio in which factors of production are combined can be changed.
  • Units of the variable factor are homogeneous or equally efficient, and are increased one by one. Thus, the law of diminishing returns sets in not because latter units of the variable factors are less efficient than the former ones. It sets in because the ideal factor ratio is disturbed or because the availability of the fixed factor reduces per unit of the variable factor
  • State of technology does not change.

Postponement of the Law

Postponement of the law of variable proportions is possible under two situations as under :

  • When there is improvement in technology used in the process of  production. So that greater output is achieved with the same inputs.
  • When some substitute of the fixed factor  is discovered. So that the constraint of the fixed factor is removed. However, such a situation is very rare, if not possible.

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