Law of variable proportion

By Kamna Sharma ECE

THE LAWS OF VARIABLE PROPORTIONS

The law of variable proportion is one of the fundamental laws of economics. It is the generalized form of Law of Diminishing marginal return. The law of variable proportion is the study of short run production function with some factors fixed and some factors variable.                                                                                                         

 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 upto 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.

                      

In the short run the volume of production can be changed by altering variable factors only. In the study of production function (variable proportion) the effect on output is examined by varying factor proportions. When we increase the quantity of variable factors to the combination of fixed factor, the proportion between fixed and variable factors change. The change in factor proportion and its effect on output forms the subject- matter of the law of variable proportions.

The ratio of variable factor to the fixed factor changes as the variable factors are increased in the combination. Thus the main thing to be noted is the break of proportion between fixed and variable factors of production. With disproportionate combination of factors, the returns may initially increase then remain constant for sometime and ultimately diminishes.

Therefore, the law of variable proportion is called non-proportional returns. The law can be explained with an example. Supposing there are two factors-land and labor. Land is fixed and labor is variable factor. Further we have one acre of land and 2 laborers. The ratio of land to labor is 1:2. To increase the production 3 labors are employed with the same plot of land. The new ratio will be 1:3.

Assumptions: The law of variable proportions holds good under the following conditions:

Constant State of Technology: First, the state of technology is assumed to be given and unchanged. If there is improvement in the technology, then the marginal product may rise instead of diminishing.

Fixed Amount of Other Factors: Secondly, there must be some inputs whose quantity is kept fixed. It is only in this way that we can alter the factor proportions and know its effects on output. The law does not apply if all factors are proportionately varied.

       

Possibility of Varying the Factor proportions: Thirdly, the law is based upon the possibility of varying the proportions in which the various factors can be combined to produce a product. The law does not apply if the factors must be used in fixed proportions to yield a product. 

Illustration of the Law: The law of variable proportion is illustrated in the following table and figure. Suppose there is a given amount of land in which more and more labour (variable factor) is used to produce wheat.

Units of Labour	Total Product	Marginal Product	Average Product
1	2	2	2
2	6	4	3
3	12	6	4
4	16	4	4
5	18	2	3.6
6	18	0	3
7	14	-4	2
8	8	-6	1

It can be seen from the table that upto the use of 3 units of labour, total product increases at an increasing rate and beyond the third unit total product increases at a diminishing rate. This fact is shown by the marginal product which  is the addition made to Total Product as a result of increasing the variable factor i.e. labour.

It can be seen from the table that the marginal product of labour initially rises and beyond the use of  three units of labour, it starts diminishing. The use of six units of labour does not add anything to the total production of wheat. Hence, the marginal product of labour has fallen to zero. Beyond the use of six units of labour, total product diminishes and therefore marginal product of labour becomes negative. Regarding the average product of labour, it rises up to the use of third unit of labour and beyond that it is falling throughout. 

Three Stages of the Law of Variable Proportions: These stages are illustrated in the following figure where labour is measured on the X-axis and output on the Y-axis.

Stage 1. Stage of Increasing Returns: In this stage, t

otal product increases at an increasing rate up to a point. This is because the efficiency of the fixed factors increases as additional units of the variable factors are added to it. In the figure, from the origin to the point F, slope of the total product curve TP is increasing i.e. the curve TP is concave upwards upto the point F, which means that the marginal product MP of labour rises. The point F where the total product stops increasing at an increasing rate and starts increasing at a diminishing rate is called the point of inflection. Corresponding vertically to this point of inflection marginal product of labour is maximum, after which it diminishes. This stage is called the stage of increasing returns because the average product of the variable factor increases throughout this stage. This stage ends at the point where the average product curve reaches its highest point.

Stage 2. Stage of Diminishing Returns: In this stage, total product continues to increase but at a diminishing rate until it reaches its maximum point H where the second stage ends. In this stage both the marginal product and average product of labour are diminishing but are positive. This is because the fixed factor becomes inadequate relative to the quantity of the variable factor. At the end of the second stage, i.e., at point M marginal product of labour is zero which corresponds to the maximum point H of the total product curve TP. This stage is important because the firm will seek to produce in this range. There is always an optimum combination of factors of production at which cost per unit is minimum. Too less or too much of the variable factors leads to cost increases. The law speaks about three stages of production. The first stage goes from origin to the point where the average output is maximum. When a firm expands output by increasing the quantity of variable factors in proportion to fixed it moves towards optimum combination of factors of production. In this stage the law of increasing return maybe said to operate and marginal product begins to fall i.e. law of diminishing returns sets in.

The second stage goes from the point where the average output is maximum to thepoint where the marginal output is zero. After having attained the optimum.Combination of the fixed inputs and the variable input, if the firm increases stillfurther the quantity of the variable input, the per unit output of the variable inputfalls. In this stage, total output rises but only at a diminishing rate.

Stage 3. Stage of Negative Returns: In stage 3, total product declines and therefore the TP curve slopes downward. As a result, marginal product of labour is negative and the MP curve falls below the X-axis. In this stage the variable factor (labour) is too much relative to the fixed factor.

The third stage covers the range over which the marginal output is negative and total output naturally falls. No producer will operate at this stage, even if he can procure the variable input at zero price. The first and the third stages are known as stages are known as stages of economic absurdity or economic non-sense. A producer will always seek to operate in the second stage. At which point the producer will operate in this stage will depend upon the prices of the factor inputs. In the following figures we have drawn TP and units of variable inputs in one figure and AP and MP and units of variable inputs in the other figure. In both the table and the graphic representation, we see that both average and marginal products first increase reach the minimum and eventually decline.

Importance and Applicability of the Law of Variable Proportion:

The Law of Variable Proportion has universal applicability in any branch of production. It forms the basis of a number of doctrines in economics. The Malthusian theory of population stems from the fact that food supply does not increase faster than the growth in population because of the operation of the law of diminishing returns in agriculture.

Ricardo also based his theory of rent on this principle. According to him rent arises because the operation of the law of diminishing return forces the application of additional doses of labour and capital on a piece of land. Similarly the law of diminishing marginal utility and that of diminishing marginal physical productivity in the theory of distribution are also based on this theory.

The law is of fundamental importance for understanding the problems of underdeveloped countries. In such agricultural economies the pressure of population on land increases with the increase in population. This leads to declining or even zero or negative marginal productivity of workers. This explains the operation of the law of diminishing returns in LDCs in its intensive form. Ragnar Nurkse have suggested ways to make use of these disguisedly unemployed labour by withdrawing them and putting them in those occupations where the marginal productivity is positive.

The application of the law is subject to the following assumptions:-

1.       Techniques of production remain unchanged.

2.       Prices of inputs is given and don’t change.

3.       Units of variable factors are homogeneous.

4.       Factor proportion can be altered.

The diminishing return stage of the law is almost universal. This, generally, applicable to every productive activity.