The Law of Variable Proportions or Returns to a Factor plays an important role in the study of the Theory of Production. In this article, we will look at the meaning, explanation, stages, significance, and reasons behind the operation of the Law of Variable Proportions.

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## Law of Variable Proportions or Returns to a Factor

This law exhibits the short-run production functions in which one factor varies while the others are fixed.

Also, when you obtain extra output on applying an extra unit of the input, then this output is either equal to or less than the output that you obtain from the previous unit.

The Law of Variable Proportions concerns itself with the way the output changes when you increase the number of units of a variable factor. Hence, it refers to the effect of the changing factor-ratio on the output.

In other words, the law exhibits the relationship between the units of a variable factor and the amount of output in the short-term. This is assuming that all other factors are constant. This relationship is also called returns to a variable factor.

The law states thatÂ keeping other factors constant, when you increase the variable factor, then the total product initially increases at an increases rate, then increases at a diminishing rate, and eventually starts declining.

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**Why is it called the Law of Variable Proportions?**

As one input varies and all others remain constant, the factor ratio or the factor proportion varies. Let’s look at an example to understand this better:

Let’s say that you have 10 acres of land and 1 unit of labour for production. Therefore, the land-labour ratio is 10:1. Now, if you keep the land constant but increase the units of labour to 2, the land-labour ratio becomes 5:1.

Therefore, as you can see, the law analyses the effects of a change in the factor ratio on the amount of out and hence called the Law of Variable Proportions.

**Law of Variable Proportions Explained**

Let’s understand this law with the help of another example:

In this example, theÂ land is the fixed factor and labour is the variable factor. The table shows the different amounts of output when you apply different units of labour to one acre of land which needs fixing.

The following diagram explains the law of variable proportions. In order to make a simple presentation, we draw a Total Physical Product (TPP) curve and a Marginal Physical Product (MPP) curve as smooth curves against the variable input (labour).

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**Three Stages of the Law**

The law has three stages as explained below:

**Stage I**– The TPP increases at an increasing rate and the MPP increases too. The MPP increases with an increase in the units of the variable factor. Therefore, it is also called the stage of increasing returns. In this example, the Stage I of the law runs up to three units of labour (between the points O and L).**Stage II**– The TPP continues to increase but at a diminishing rate. However, the increase is positive. Further, the MPP decreases with an increase in the number of units of the variable factor. Hence, it is called the stage of diminishing returns. In this example, Stage II runs between four to six units of labour (between the points L and M). This stage reaches a point where TPP is maximum (18 in the above example) and MPP becomes zero (point R).**Stage III**– Now, the TPP starts declining, MPP decreases and becomes negative. Therefore, it is called the stage of negative returns. In this example, Stage III runs between seven to eight units of labour (from the point M onwards).

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**Significance of the three stages**

**Stage I**

A producer does not operate in Stage I. In this stage, the marginal product increases with an increase in the variable factor.

Therefore, the producer can employ more units of the variable to efficiently utilize the fixed factors. Hence, the producer would prefer to not stop in Stage I but will try to expand further.

**Stage III**

Producers do not like to operate in Stage III either. In this stage, there is a decline in total product and the marginal product becomes negative.

In order to increase the output, producers reduce the amount of variable factor. However, in Stage III, he incurs higher costs and also gets lesser revenue thereby getting reduced profits.

**Stage II**

Any rational producer avoids the first as well as third stages of production. Therefore, producers prefer Stage II – the stage of diminishing returns. This stage is the most relevant stage of operation for a producer according to the law of variable proportions.

**Law of Variable Proportions in terms of TPP and MPP**

The explanation is as follows:

**Law of Variable Proportions – in terms of TPP**

We know that the law of variable proportions shows the relationship between units of a variable factor and the total physical product.

Also, if we keep other factors constant and increase the units of the variable factor, then the TPP initially increases at an increasing rate, then at a diminishing rate, and finally declines. Therefore, it has three clear stages:

- I – TPP increasing at an increasing rate
- II – TPP increasing at a diminishing rate
- III – TPP declining

**Example of Law of Variable Proportion in terms of TPP**

**Diagram ofÂ ****Law of Variable Proportion in terms of TPP**

**Law of Variable Proportions in terms of MPP**

The Law also states that if we keep all other factors constant and increase the units of a variable factor, then the marginal physical product initially increases, then decreases, and finally becomes negative. Therefore, it has three stages:

- I – MPP increasing
- II – MPP decreasing but remaining positive
- III – MPP continuing to decrease and becoming negative

**Reason for the Operation of the Law**

- In the short-term, we cannot vary all factors of production.
- In this case, there is only one variable factor while others are fixed.
- All other factors combine optimally to produce the maximum output.
- Before the point of optimum combination, if the units of a variable factor increase, then the factor proportion becomes more suitable and it leads to more efficient utilization of the fixed factors. Therefore, the marginal physical product increases.
- During the initial stages, the total product tends to rise at an increasing rate when the producer employs more units of a variable factor to the fixed factors.
- Subsequently, beyond the point of optimum combination, if the producer employs more units of the variable factor, then the factor proportion becomes inefficient. Therefore, the marginal product of that variable factor declines.
- Also, the producer sees a fall in the quantity of the fixed factor input per unit of the variable as he increases the units of the variable factor.
- Therefore, successive units of the variable input add decreasing amounts to the total output as they have less fixed inputs to work with.

## Questions on Law of Variable Proportions

**Q1. What is the law of variable proportions?**

Answer: The law of variable proportions is as follows:

“If a producer increases the units of a variable factor while keeping other factors fixed, then initially the total product increases at an increasing rate, then it increases at a diminishing rate, and finally starts declining.”

Hi,

In the first table where you have mentioned the ‘Law of Variable Proportions Explained’, there is a small typo error that needs to be corrected. Instead of Variable factor ‘Labour’, it is written as ‘Land’ in the heading of second column. Please correct it.

The overall explanation of the ‘Law of Variable Proportions’ is quite interesting and anyone can easily understand. The change in proportions (or ratio) (Land-Labour ratio here) of the factor inputs is well explained.

Thanks for the efforts.

Regards.

Gaurav

why the marginal product became negative?

In stage-3 ,Why the marginal product became negative?

As more and more of variable input (labour) is employed marginal product starts to fall. Finally after a certain point marginal product become negative

it is similar to too many cooks spoil the broth

Also it becomes a case of disguised unemployment