## Law of Variable Proportions

The law of variable proportion is one of the fundamental laws of economics. The law of variable proportion is the study of short run production function with some factors fixed and some factors variable.

As the quantity of different units of only one factor input is increased to a given quantity of fixed factors, beyond a particular point, the marginal, average and total output eventually decline.

The law of variable proportions is the new name for the famous “Law of Diminishing Returns” of classical economists. This law is stated by various economists in the following manner –

According to Prof. Benham, “As the proportion of one factor in a combination of factors is increased, after a point, first the marginal and then the average product of that factor will diminish”.

In the words of Prof. Marshall “An increase in the quantity of a variable factor added to fixed factors, at the end results in a less than proportionate increase in the amount of product, given technical conditions.”

The change in factor proportion and its effect on output forms the subject- matter of the law of variable proportions.

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.

**Assumptions of the Law:**

- The state of technology is assumed be given and unchanged.
- The law specially operates in the short run because some factors are fixed and the proportion between factors is disturbed.
- Variable factor units are homogeneous or identical in amount and quality.
- The law is based on the possibility of varying the proportions in which the various factors can be combined to produce a product.
- The law will hold good for short and given period.
- Input prices remain unchanged.
- Output is measured in physical units.
- Factors are indivisible in nature.

**Explanation of the law: **The law can be explained with an example. Supposing there are two factors-land and labor.

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.

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, total 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 at increasing rate. In this stage MP is increasing and reaches its maximum point and same is the case with AP, It is also increasing and reaches the point of maximum.

**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.

**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. As **MP is negative this stage is also known as the stage of negative return**.

In this stage the proportion of variable factor (labour) is very much relative higher to the fixed factor. Which leads to inappropriate proportion between both the factors of production.

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