# Law of Variable Proportions.

The law of variable proportions examines the production function assuming one factors as variable and others as fixed. According to this law, if additional units of variable inputs are added, keeping the quantities of fixed factors constant, then beyond a certain point, additions to the total product i.e., the marginal product shall go on diminishing.

This law is the improved form of the law of diminishing returns. The law of diminishing returns also states the same that is, if increasing quantities of a variable factor (Labour) are applied to a given quantity of a fixed factor (Capital), then the marginal product and the average product, of the variable factor will eventually decrease.

This law is consistent with the marginal and average product curves and their relationship, given the total product curve. This law of diminishing, returns is also called ‘the law of variable proportions’, because it predicts the consequences of varying the proportions in which inputs of different types are used. In other words, by using every additional unit of a variable factor, the factor proportions between fixed and variable factor varies. This saw is based on the following assumptions.

- Technology is assumed to be given and unchanged.
- Some inputs
*r*e assumed be fixed only for the short run, therefore, the law applies only yo the short run. - This law assumes that it is possible to change factor proportions.

**Given these assumptions, there are three stages of production. They are explained below with the help of a diagram.**

**First Stage:** In this stage, the total product (TP) increases at an increasing rate and correspondingly both average product (AP) and marginal product (MP) increase to begin with.

The AP continues increasing throughout the first stage as a result of applying more and more units of the variable factor (L) to given fixed factor (K). However, the marginal product starts declining as the rate of increase of TP declines after A in the diagram. Corresponding to that we have the maximum point of MP denoted as A. So first stage is until the point where AP_{L} is the maximum. It is called^{.} the stage of increasing, average.

**Second Stage:** This is the stage of diminishing returns. In this stage, TP increases but at a decreasing rate, with the result that both average and marginal product decline. This stage starts from the point where AP is the maximum and MP cuts it from above, *i.e., *MP = AP at point B’ in the diagram This stage continues till the point where TP is the maximum and the marginal product becomes zero.

Third Stage. This is the stage of negative returns. This stage starts when TP is maximum and MP_{L} is zero. During this stage, as more and more of variable factor is employed beyond level, TP declines and MP_{L} becomes negative. Accordingly this is not an efficient region to operate on by a rational firm.

In which stage a producer should operate. Every producer would like to operate in the second stage. In the first stage, AP is increasing at every level of output. AP is increasing, at every level of output, therefore, it is worthwhile for the firm to expand and continue with the production by increasing/adding the variable factor in the short run.

So question of stopping at any point during this stage does not arise. In the third stage, however, total product declines as a result of employing an additional unit of variable factor, hence it is not possible for the producers to operate here at all. Therefore, a rational producer will always operate in second stage.