# Law of Variable Proportion Meaning, Assumptions, Three Stages, Casues of Applicability

## Micro Economics B.Com Notes

### Law of Variable Proportion Meaning

The law of variable proportion is one of the fundamental laws of economics. It is also known as the ‘Law of Diminishing Marginal Returns’ or the ‘Law of Diminishing Marginal Productivity.’ This Law of variable proportion shows the input-output relationship or production function with one variable factor, i.e., a factor, which can be changed, while other factors of production are kept constant.

In short-period when the output of a good is sought to be increased by way of additional application of the variable factor, law of variable proportions comes into operation. When the number of one factor is increased while all other factors remain constant, then the proportion between the factors is altered. On account of change in the proportion of factors there will also be a change in total output at different rates.

In economics, this tendency is called Law of Variable Proportions. The law states that as the proportion of factors is changed, the total production at first increases more than proportionately, then equi-proportionately and finally less than proportionately.

According to Samuelson, “The law states than an increase in some inputs relative to other fixed input will, in a given state of technology, cause total output to increase, but after a point the extra output resulting from the same addition of extra inputs is likely to become less and less.”

### Law of Variable Proportion Assumptions

The law of variable proportions functions is based on following assumptions:

1. Constant technology: The technology is assumed to be constant because technological changes will result into rise of marginal and average product.

2. Short-run: The law operates in the short-run because it is a well-known fact that some factors are fixed and others are variable. In the long-run, all factors are variable.

3. Homogeneous input: The variable input employed is homogeneous or identical in amount and quality.

4. Use of varying amount of variable factor: It is possible to use various amounts of a variable factor on the fixed factors of production.

### Explanation of the Law of Variable Proportion with the help of an example

Law of variable proportion can be explained with the help of following table and diagram:

 Units of Land Units of Labour Total Product Marginal Product Average Product 1 1 2 2 2 1 2 5 3 2.5 1 3 9 4 3 1 4 12 3 3 End of the first State Beginning of the Second Stage 1 5 14 2 2.8 1 6 15 1 2.5 1 7 15 0 2.1 End of the Second Stage Beginning of the Third Stage 1 8 14 -1 1.7

Explanation:

From the above Table and Diagrams drawn on the assumption that production obeys the law of variable proportions, one can easily understand three stages of production. These are elucidated in the following table:

### Three Stages of Production

 Stages Total Product Marginal Product Average Product 1st Stage Initially it increases at an increasing rate. Later at diminishing rate. Initially increases and reaches the maximum point. The starts decreasing. Increases and reaches its maximum point 2nd Stage Increases at diminishing rate and reaches its maximum point. Decreases and becomes zero. After reaching its maximum begins to decrease. 3rd Stage Begins to fall Becomes Negative. Continues to diminish.

### Causes of Applicability of Law of Variable Proportion

Main causes accounting for the application of the law of variable proportions are as follows:

1. Under-utilization of Fixed Factor: In the initial stage of production, fixed factor of production like land or machine is under-utilized. More units of variable factor, like labour are needed for its proper utilization. Thus, as a result of employment of additional units of variable factor there is proper utilization of fixe factor. Consequently, total production begins to increase.

2. Fixed Factors of production: The principal cause of the operation of this law is that some of the factors of production are fixed during the short period. When the fixed factor is used with variable factor, then its ratio if compared to variable factor falls. Production is the result of the cooperation of all factors. Consequently, marginal return of the variable factor begins to diminish.

3. Optimum Production: After making the optimum use of a fixed factor if it is combined with increasing units of variable factor, then the marginal return of such variable factor begins to diminish.

4. Imperfect Substitute: It is the imperfect substitution of factors that is mainly responsible for the operation of the law of diminishing returns. One factor cannot be used in place of the other factor. Consequently, when fixed and variable factors are not combined in an appropriate ratio, the marginal return of the variable factors begins to diminish.

### Postponement of the Law of Variable Proportion

Postponement of the law of variable proportions is possible under the following conditions:

1. Improvement in Technique of Production: Operation of the law can be postponed if along with the increase in variable factors technique of production is improved.

2. Perfect Substitute: The law can also be postponed if factors of production are made perfect substitutes, i.e. when one factor can be substituted for the other.

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