This law examines the production function assuming one factor as variable and other as fixed. In reality, this law is the improved form of the law of decreasing returns because that law also explains as to how returns would be affected assuming one factor as variable and others as fixed.

According to the law of variable proportions, if units of variable factor are added keeping the quantities of fixed factors constant, then beyond a certain point, additions to the total product (marginal product) shall go on diminishing.

In other words, after a certain point total product increases at a decreasing rate which additional units of a variable factor are used keeping the quantities of other factors as fixed.

In the words of Benham, “An the proportion of one factor in a combination of factors is ‘increased, after a point first the marginal and then the overall product of the factor will diminish. “

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This law is called as the law of variable proportions because by using every additional unit of a variable factor, the factor proportion between fixed and variable factors varies. The law of variable proportions is the new name of the law of the diminishing returns which was propounded by Marshall and other classical economists.

Assumptions:

This law holds well under the following conditions:

(i) Technology is assumed to be given and unchanged:

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This law will not apply, if there is an improvement in the technology because in that case average and marginal products may rise instead of declining. In reality, the law of diminishing returns does not apply under modern conditions because of the constant improvement in the technology.

(ii) There should be some inputs whose quantities remain fixed:

If all the factors are vari­able, this law will not apply because production will keep on increasing. Inputs are fixed only for the short period; therefore, this law is applicable in the short period only.

(iii) This law assumes that it is possible to change factor proportion:

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Such production func­tion, where factor proportion is fixed, this law does not apply. For example, on the typewriter, only one person can work, therefore in this example, we cannot treat typewriter as fixed and typist as variable.

(iv) This law applies only in the short period.