# Law of Variable Proportions

## Law of Variable Proportion Definition

The Law of variable proportion occupies an essential place in economics and is also known as the law of proportionality. The law explains the production function keeping the one-factor variable and others fixed. In the short run, when the output of commodities has increased, the law of variable proportion comes into operation.

It is mainly concerned with the changes in output that take place when there is an increase or decrease in units of a variable proportion.

For Instance: There are two factors of production, namely land and labour. The land is a fixed factor and labour being variable. Suppose we have land measuring 5 hectares. Wheat is grown in it with the help of variable factors (labour). Looking into this, the proportion of land and labour will be 1:5. If we increase the number of labour to 2., the ratio set will be 2:5. Due to this increase in the proportion of factors, there will also emerge in the change in total output. This tendency is known as the law of variable proportion.

The law of variable proportion is also defined as - “An increase in some inputs relative to other fixed inputs will be in a given state of technology cause output to increase, but after a point, the extra output resulting from the same additions of extra inputs will become less and less”.

### Assumptions of Law of Variable Proportions

These are the following assumptions on which the Law of variable proportions is based:

1. Factor Proportions are Variable:

If factors of production are combined in fixed numbers, the law has no validity. The law assumes factors of production to be proportional.

1. Constant Technology:

The status of technology is assumed to be constant. If there is improved technology, the production is said to move upwards.

1. Short-Run:

The law operates in the short-run as it is not possible to vary all factor inputs.

1. Homogenous Factor Inputs:

The units of variable factors are identical. Each unit added is homogenous in quality and amount.

To get a clear picture of the stages of variable proportion, we take the example of agriculture. Let us assume land and labour are the only factors of production in a given area. Keeping land as a fixed factor, the production of variable factor can be shown with the help of the following table:

## Stages of Law of Variable Proportion

 Units of Land Units of Labour Total Production Average Production Marginal Production 10 Acres 0 - - - “ 1 20 20 20 “ 2 50 25 30 “ 3 90 30 40 “ 4 120 30 30 “ 5 140 28 20 “ 6 150 25 10 “ 7 150 21.3 0 “ 8 140 17.5 -10

There are three stages of the law of variable proportion. In the first stage, due to more capital employed with fixed factors average production increases. In the table, we are able to analyze that total product, marginal product, and the average product is increasing. But average products and marginal products have increased up to 40 units and are decreasing after that. This is because the proportion of labour is insufficient for a given fixed land.

The second stage starts where the average product is equal to the marginal product. From here on, both are falling and the marginal rate falls at a faster rate. Here the total product is increasing at a diminishing rate. In the table, it is also found that the marginal product becomes 0 whereas it is not possible for the average product to be 0 or negative.

The third stage starts in the 8th unit. The marginal product is negative, the total product falls but the average product remains positive.

With the discussion of stages of Law of variable proportions, here comes on what are the causes of the law of variable proportion. The causes of the law of variable proportion mainly depend on the following:

1. Underutilization of fixed factors of production.

2. Optimum production.

3. Imperfect substitutes.

### What is the Importance of the Three Stages in the Law of Variable Proportions?

In stage one, the producer does not operate. In this stage, the marginal product increases with the increase in variable factors. Therefore, the producer can employ more units of the variable to efficiently use fixed factors.

Producers do not like to operate in stage three as there is a decline in total product and also the marginal product falls to negative. In order to increase output, the producer reduces the number of variable factors. The producer here incurs higher costs and less revenue-making profits lower.

Any producer will avoid the first and third stages of production. Producers prefer the second stage - The stage of diminishing returns. Which is considered the most relevant stage of operation for a producer.

Q1. What is the Importance of the Law of Variable Proportion? How is it Different From Returns to Scale?

Ans. The law occupies an important place in the economic world. The diminishing returns phase of the law of variable proportion has universal application in the field of production. Many economic principles are derived from the law of variable proportion. This law applies as much to the agriculture sector as to industries.

Whereas the returns to scale applications in the long run and all factors are increased simultaneously. There is no difference between fixed and variable factors of production. There are 3 stages namely, increased returns, constant returns, and decreasing returns, and no stage is considered best for the long run.

Q2. State the Law of Variable Proportion with its Assumptions.

Ans. The law of variable proportion applies to all fields of production namely agriculture, industry, etc. This law applies to every field where some factors are fixed and another variable. The law states that up to the use of a certain amount of variable factor, the marginal product may increase and after a certain stage, it starts diminishing. The law of variable proportion holds good under the following conditions:

1. The fixed amount of other factors.

2. The constant state of technology.

3. Possibility of varying the factor proportion.