# Law of Variable Proportion, and Returns to Scale with diagram

**Definition of the Law of Variable Proportion:**

The Law of variable proportion has great importance and applicability in the field of economics. According to this law ‘*with the increment in the units of variable factors i.e., labor or capital, and the fixed factor being constant, the marginal product first tends to increase, becomes constant and finally diminishes’ *the law is mostly applicable in the short run in which some of the factors are fixed and the other factor is variable. The marginal product increases more proportionately in the first stage, then it decreases in the second stage and falls to negative in the third stage. This law is also known as the law of non-proportional return.

**Assumptions of the law:**

There are certain assumptions of the law which must be taken care of otherwise, the law will not hold if we violate any of the assumptions of the law.

**Technology must be kept constant**

The technology must be kept constant during the process because if there was an improvement in the technology then the law will not hold. Because improvement in the technology will lead to an increase in the marginal product. That is why technology and techniques of production should remain constant.

**Homogeneity of the factor units**

The unit of variable factors is the same in terms of quality and in the case of labor all laborers are equally efficient.

**Short-run**

The law functions only in the short run where some factors are fixed and only labor is variable. Whereas, in the long run, all the factors are variable.

**Table of Contents**show

**Explanation of the law of variable proportion:**

To understand the law of variable proportion let’s follow the table below; suppose that land is a fixed factor i.e. 12 acres and the labor is being used on it. Hence, the total product, marginal product, and of course the average product will go under the following changes.

From the table above it is quite clear that there are three stages of this law (Law of variable proportion). The first stage includes an increasing trend with each additional unit of labor (the variable factor). In the first stage, the marginal product, the total product, and also the average product increases. Both marginal product and average product increase up to the 3^{rd} unit after which both start decreasing. This is the end of the first stage.

The first stage ends when Mp becomes exactly equal to Ap. Whereas, this is the start of the second stage. In this stage, both average and marginal product start decreasing. The rate at which marginal product falls is greater than the fall in the average product. You can also look at the total product in the above table. The total product increases with the diminishing rate. The total product is maximum when the marginal product becomes zero.

The 6th unit is the point where the third stage starts. In this stage, the total product starts falling and the marginal product becomes negative and the average product also falls.

**Graphical Representation of the law of variable proportion:**

As it is visible from the graph that units of labor are taken on the OX axis whereas total, average and marginal product is taken on the axis OY. You can observe in the graph that at first total, the average and the marginal product starts increasing. The marginal product increases at a rate faster than Ap, i.e., Mp > Ap. However, the third unit is the point where Mp is exactly equal to the average product i.e. Mp = Ap. This is the end of the first stage.

The second stage starts after the completion of the first stage. Initially, Mp < Ap in this stage, and at the fifth unit, the marginal product becomes zero. This is the point where total production is maximum. The stage ends here and if we start increasing the variable factor when marginal has already become zero. We will face a loss because MP becomes negative, Ap also falls and total product also starts falling. So, a rational producer will always stop where the production is maximum and that is the point where marginal product is zero.