# Law of variable Proportions

The law of variable proportions is also named as the laws of returns or the laws of returns to a variable factor.

The law states that as the quantity of a variable impute is increased by equal doses, keeping the quantities of other inputs constant, total product will increase, but after a point, at diminishing rate. This principle can also be defined thus, when more units of variable factors are used having the quantities of fixed factors constant, a point is reached beyond which the marginal product, then the average and finally the total product will diminish.’

According to Prof. Watson, “The law of variable proportions, also known as the law of diminishing returns, can be stated as follows: when total output or production of a commodity is increased by adding units of a variable input while the quantities of other inputs are held constant then increase in total production becomes, after some point, smaller.”

In simple words, the law of variable proportions (or returns to a variable factor) states that with the increase in variable factor, keeping other factors constant, the marginal product after rising to some extent becomes smaller and smaller.

Why is it called the Law of variable proportions?

It is because of two reasons:

(i)   The factor: proportion (or factor-ratio) varies as one input varies and others are held constant. This can be understood with the help of an example. Suppose in the beginning 10 Ropani of land and 1 unit of labor are taken for production, hence the land- labor ratio was: 10 1. Now if the land remains the same but the unit of labor increases to 2, now the land- labor ratio would become 5: 1. Thus law analyses the effects of change in factor-proportions on the amount of output and therefore called the law of variable proportions:

(ii)  The return also varies non-proportionally with the change in factor-ratio: It means when one factor is varied keeping other factors constant, the input-output ratio also undergoes a change. For example, if 10 Ropani of land and 1 unit of labor give the output of 20 quintals of wheat then the ratio between labor (variable factor) and output of what is 1:20? Now if with 2 units of labor, the output increases to 30 quintals then the labor-output ratio would become 1: 15. Thus, the ratio between the variable factor and the output change and that is why it is termed as the law of variable proportions.

Assumptions

(i)   One is variable factor and others are the fixed factors.

(ii)  It is possible to make chances in the factor-proportions.

(iii) No change in technique of production and organization.

(iv) All units of the variable factors are homogeneous

Causes of the Operation of the Law:

(i)   In the short period all factors of production cannot be varied i.e. some are fixed factors in the short-run.

(ii)  Factor of productions is not perfect substitutes.

(iii) Factors of production are scarce in relation to their demand.

Explanation of Law

This law of variable proportion can be illustrated with the help of the following example and diagram. In this example, we have presumed that land is a fixed factor and labor is a variable factor.

Example

 Fixed factor land (Ropani) Variable Factor Labor (VF) (Units) TP (Qnt.) AP=TP/VF (Qnt.) MP (Qnt.) 1 0 0 0 – 1 1 4 4 4 1 2 12 6 8 1 3 24 8 12 1 4 32 8 8 1 5 36 7.2 4 1 6 36 6 0 1 7 28 4 -8

In this example we have assumed that sand is the fixed factor and labor is a variable factor. The table shows the different amounts of output obtained by applying different units of labor to one acre of labor to one Ropani of land, which is fixed.

Three stages of the Law

The relation between variable factor and physical output has three stages that are shown in the example as well as in the diagram. These are known as the three stages of the law

Stage I.

In this stage total product increases at an increasing rate and the average product of labor (AP) also increases. In the beginning of this stage marginal product (MP) also increased but increases but after a point it starts to decline. Average product continues to increase till marginal product is greater than the average product. But when marginal product becomes equal to average product, the increase in average product is withheld and this is the outer limit of the first stage. In our example, the first stage, of the law runs up to four units are labor and this limit is shown by point A in the diagram. Since in this stage average product increases with the increases in the units the variable factor, it is called the stage of increasing returns.

Why does the law of increasing return operate? Following are given its main reasons:

(i)   Indivisibility of Factors. There are some factors that cannot be purchased in parts. For example, if no generator is available in the market less than the size of 15-horse power then we have to purchase and use this generator. If at present we are not using this generator to its full capacity then with the increase in production marginal cost will decline.

(ii)  Increase in Efficiency. If the efficiency of fixed factor increases with the increase in the quantities of variable factor, the law of increasing returns will apply.

(iii)            Fixed Factors. The cost of fixed factors is also fixed. Hence, with the increase in output per unit fixed cost will decline which in turn will lower the over all average cost also up to a certain limit.

(iv) Division of Labor. If the increase in the units of labor brings greater division of labor and specialization in the production, it will also create the conditions of increasing returns.

(v)  Optimum combination. If to achieve optimum combination of various factors of production, the increase in the quantities of a particular factor is required it will also bring increasing returns.

Stage II.

In this stage also the total product continues to increase but at a diminishing rate. This stage goes to the point when total product reaches the maximum and marginal product becomes zero. In this stage average product goes on diminishing. It means there is decline in the efficiency of labor. In our example second stages runs between 5 units and 6 units of labor and in the diagram it is between point A and point M. In this stage both average product and marginal product decline but remains positive. This stage is known as the stage of diminishing returns also. Why does the law of diminishing returns operate? Following are given its main reasons:

(i)   Fixed Factor. The quantity of the fixed factor-input per unit of the variable input flls as more and more of the later is put to use successive units of the variable input, therefore, must add decreasing amounts to the total output as they have less of the fixed input to work e.g. land is a fixed factor.

(ii)  Scarcity of Factors. Factors of production are scarce and limited in supply. If factors had not been limited, this law would also not have come into existence.

(iii)            Imperfect Substitutes. Factors of production cannot be substituted fully. For example, labor or capital cannot be substituted in place of land.

(iv) Optimum Combination. These are an optimum combination pf different factors that gives the maximum output. When we increase a particular factor of production beyond this optimum combination, marginal product of that variable factor declines naturally.

Importance

Samuelson has regarded the law of diminishing returns as a natural Law. Since this law is applicable in all the fields of production, it is called as the universal law of production. Many principles of economics such as the Malthusian theory of population, Ricardian theory of rent, marginal productivity theory of distribution are based on the assumption of the law of diminishing returns. Though this law is applicable in all fields yet it is more applicable in the fields of agriculture. The main reason behind this is that in agriculture nature plays a greater role than the man. In the words of Wick steed the law of diminishing returns ” is as universal as the law of life itself.” The universal applicability of this law has transcended economics to the realm of science. Above all, it is of fundamental importance for understanding the problems of under developed countries.

Stage III.

In the third stage total product starts to decline and marginal product becomes negative. That is why total product curve starts to decline and marginal product curve goes below the X-axis. In our example this stage comes when 7Th and 8th units of labor are employed and according to diagram this stage starts when more than OM units of labor are employed. This stage is called the stage of negative returns.

Possibility of operation

The law of variable proportions guides us about the possibility of operation. A rational producer will never choose first and third stage for its production he will always operate in the second stage, i.e. the stage of diminishing returns. The producer will not produce in the first and the third stages because in the first stage the fixed factor of production i.e. capital is underutilized and its marginal return is negative and in third stage the variable factor of production i.e. labor is over utilized and thus its marginal return becomes negative. In other words, the marginal return of fixed factor and variable factor is negative in first stage and third stage respective. It is the second stage where the return on both the fixed factors and variables though diminishing is positive. The producer will always produce in second stage.

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