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.

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.

The variation in the ratio of the inputs causes a change in the size of production at various rates. The law of variable proportions or diminishing returns has been stated by Benham in the following manner.

"As the proportion of one factor in a combination of factors is increased, after a point, first the marginal and then the average production of that factor will diminishing”.

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**Assumptions of the Law: **

**(i) **The state of technology is assumed be given and unchanged.

**(ii)**The law specially operates in the short run because some factors are fixed and the proportion between factors is disturbed.

**(iii)**Variable factor units are homogeneous or identical in amount and quality.

(Iv) The law is based on the possibility of varying the proportions in which the various factors can be combined to produce a product.

**Explanation of the law:**

The law can be explained with help of a table. The behaviour of output as a result of change in the proportion of variable factors to the fixed factor can be studied through three stages. The table given below explains the short run production function of a firm with some factors variable.

Any change of variable factor to the fixed factor changes the output. The changes due to change in Win in the factors on the total product, average. Product and the marginal product are shown in the table. As the number of laborers increases from 1 to 2, marginal as well as the average product increases. But with the further addition of labour units the average product falls and the marginal falls more speedily.

Average and marginal product continue to fall as more men are put to work. The 7th labour unit adds nothing to total production. After the 7th unit of labour, the eighth labour causes the total product to diminish. In other words the marginal productivity of 8th labour is negative.

**Diagrammatic Representation**

Measures quantity of variable factors. Oy-axis measures output. In the diagram quantity of the variable factor is increased. Total product rises at first, remains constant at point N, and then starts falling. Average product and marginal product curves are represented by AP and MP. AP and MP curve also rise and decline. MP curve starts declining earlier than the AP curve. The behaviour of these total, average and marginal products of the variable factor as a result of the increase in its amount is generally divided into three stages.

**Stage-I (Increasing Return)**

Total product increases at an increasing rate to the point F. corresponding to the point F marginal product increases up to this level. From the point F total product goes on rising at a diminishing rate and marginal product starts falling -but is still higher than average product and the AP continues to rise. 1st stage ends where MP curve cuts AP curve from above.

**Stage-II (Diminishing Return)**

The second stage begins from the point of intersection of AP and MP curves and ends at that point where" MP is zero. At this stage both MP and AP go on falling and both of them are positive. The total product goes on rising at a diminishing rate. This stage is known as the stage of diminishing return. This is stage where a firm wishes to operate.

**Stage-Ill (Negative Return)**

In the third stage marginal product of variable factor is zero. MP curve cuts the OX-axis at point M. In this stage the total product starts diminishing. Total product continues to decline. As MP is negative this stage is also known as the stage of negative return.

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