# LAW OF VARIABLE PROPORTIONS

INTRODUCTION
Law of variable proportion occupies an important place in economic theory. This law also refers to input-output relation when output is increased by varying the quantity of one input.

The law of variable proportion or diminishing returns has been stated by various economists in the following manner;
As equal increments of one output are added, the inputs of other productive services being held constant, beyond a certain point the resulting increments of products will decrease i.e the marginal products will diminish (G. STIGLER)
As the proportion of one factor in the combination of factors is increased, after a point, first the marginal and then the average product of that factor will diminish.(F. BENHAM)
As increase in sum inputs relative to other fixed inputs will in a given state of technology, cause output to increase but after a point the extra output resulting from the addition of extra inputs will become less (PAUL SAMUELSON)
Marshall discussed the law of diminishing returns in relation to agriculture.
He defines the law as follows;
An increase in the capital and labour applied in the cultivation of land causes in general a less than proportionate increase in the amount of product raised unless it happens to coincide with an improvements in the arts of agriculture.
From these laws, it states that the marginal product and average product will eventually decline.
The law of variable proportion shows a particular pattern of changes in output and is a history of economics till the time of Alfred Marshall there were three laws of return, Increasing, Constant and Diminishing laws of return.

ASSUMPTIONS OF THE LAW OF VARIABLE PROPORTION
The assumptions of the law of variable proportion are given as below:
1.It is assumed that the technique of production should remain constant during production.
2.It operates in the short-run because in the long run, fixed inputs become variable.
3.Some inputs must be kept constant.
4.The various factors are not to be used in rigidly fixed proportions but the law is based upon the possibility of varying proportions. It is also called the law of proportionality.
5.It is assumed that all the units of variable factors of production are homogeneous in amount and quality.
6.It is assumed that the law operates in the short run when it is possible to vary all factor input.

DIAGRAMATICAL REPRESNTATION OF THE LAW OF VARAIBLE OF PROPORTIONS

APPLICABILITY OF THE LAW OF VARIABLE PROPORTIONS
The law of variable proportion is universal as it applies to all fields of production.
The main cause of a applicationof this law is the fixity of any factor.Land,mines,fisheries snd house buildings are not only examples of fixed factors.Machines,raw materials may also become fixed in short period.
So therefore,this law holds good in all activities of production.

• APPLICATION TO AGRICULTURE ;
With a view of raising agricultural production,Labour and capital can be increased to any extent but not the land being fixed factor.
Thus,when more and more units of variable factor like labour and capital are applied to a fixed factor then their marginal product starts to diminish.
• POSTPONEMENT OF THE LAW;
The postponement of the law of variable proportion is possible under the following conditions;
1. Improvement in technique of production
2. Perfect substitutes

• APPLICATION TO INDUSTRIES
In order to increase production of manufactured goods,factors, of production has to be increased.It can be increased as desired for a long period,being variable factors .
Thus,law of increasing returns operates in industries for a long period.but, this situation arises when additional units of labour,scapital and enterprise are of inferior quality or are available at higher cost.
As a result,after a point,marginal product increases less proportionately than increase in the units of labour and capital.

SCHEDULE
The law of variable proportion is explained with the help of the following schedule:
Units of variable factor (L) Marginal product (MPL) Total product (TPL) Average product (APL) Stages
1 2 2 2 I
2 4 6 3
3 6 12 4
4 4 16 4 II
5 2 18 3.6
6 0 18 3 III
7 -2 16 2.28
In the above schedule, units of variable factor (labor) are employed with other fixed factors of production. The marginal productivity of labor goes on increasing up to the 3rd worker. This is so because the proportion of workers to other fixed factors was at first insufficient. After 3rd worker the marginal productivity goes on falling onwards till it drops down to zero at the 6th unit of labor. The 7th worker is only a cause of obstruction to the others and is responsible in making the marginal productivity negative. The marginal productivity (MPL) and the average productivity (APL) equalize at 4the worker. Then the MPL falls more sharply