Law of Variable Proportions


Production is an important topic in economics as it is directly related to the well-being of societies. We can understand the health of an economy from its production values of it. Production is not only important for survival but prosperity is also brought to economies by it. Productions include variable and fixed factors and by differentiating the factors various observations can be made. The law of variable proportions is one such laws that is related to production.

What is the Law of Variable Proportions?

The Law of variable proportion states that when only one production element is allowed to increase keeping all other elements constant, the production firstly increases, then the output will decrease and finally there will be a negative production.

This law is also known as the law of equality. According to this law when the dynamic value goes up, it can lead to a negative product value of a third-party product.

When the dynamic factor increases while all other factors remain constant, initially the price of the product will rise. However, in subsequent phases, there will be a decrease in output. Finally, with additional input of dynamic factor, there will be a negative output of production.


There are some assumptions that must be considered while considering the law of variable proportions.

These assumptions are as follows:

  • Continuous technological improvement − It is assumed that the technological infrastructure will remain the same and with improvements in technology, production will improve.

  • Flexible estimates of characters − The law assumes that production characteristics will vary. The law is not applicable when production features remain constant.

  • Homogenous units of factors − The law indicates that all output products are the same in nature. Their attributes, prices, and other features are all the same.

  • Short-run − The production is considered to be of a short duration during which all features of the product cannot be changed.

Three Phases of the Law: Increasing, Diminishing, and Negative Returns

First Stage: Increasing Return to a Factor

In the first stage, the addition of every additional variable factor adds more value to the output. Therefore, the production of goods increases with an increase in the additional variable input. This means that total product (TP) increases at a quicker rate and the marginal product (MP) of each variable factor goes up.

More efficient use of fixed factors and an increase in efficiency of variable factors due to specialization are the main reasons for the increase in output.

Second Stage: Diminishing Returns to a Factor

In the following stage, additional inputs of every unit result in a lesser and lesser amount of output. The total product increases at a lower rate while the marginal product falls with the increase in the variable factors. The breakdown of a combination of fixed and variable factors is responsible for diminishing returns to a factor.

Third Stage: Negative Returns to a Factor

The addition of units of variable factors causes negative returns. The TP declines with the addition of each unit of the additional variable factor. As production declines in this phase, it is known to be a phase of negative returns. Poor coordination between fixed and variable factors causes negative returns in the third stage.

Reasons for the Law of Variable Proportions

There are various reasons for the law of variable proportions that can be discussed for each phase of the law. Here are the reasons for each phase.

Reasons for increasing returns to a factor

  • Better use of the fixed factor − In the first phase of the production function, the supply of fixed factors is huge. Therefore, the fixed factor remains under-utilized. When variable factors are introduced to fixed factors, the underutilized fixed factors are included in the production process which increases the overall efficiency of production leading to increasing returns.

  • Increased efficiency of variable factors − When variable factors are increasingly combined with fixed factors, the variable factors are used in a more efficient manner. Moreover, better cooperation and higher degrees of specialization are observed in the case of variable factor which helps to increase production.

  • Indivisibility of fixed factor − The fixed factors that are combined with variable factors are usually indivisible. When large and increasing amounts of variable factors are added to indivisible fixed factors, production increases until the optimum level of combination between variable and fixed factors is reached.

Reasons for diminishing returns to a factor

  • Optimum combination − There is an optimum combination of fixed and variable factors where the total product (TP) value is maximum. After having the maximum use of fixed factors, the marginal product return of variable factors starts to diminish. This leads to a diminishing return to a factor.

  • Imperfect substitution − The variable factors can be used as a substitute for one another up to a certain limit. When this limit is crossed, the availability of substitutes is no more accessible. This reduces production and leads to diminishing returns.

Reasons for a negative return to a factor

  • Limits of fixed factor − Some factors of production are always fixed in nature. These factors cannot be increased with an increase in variable factors which results in a negative return to a factor.

  • Poor coordination between fixed and variable factors − Too excessive amount of variable factors in comparison to fixed factors obstructs production. Therefore, the addition of variable factors beyond a limit leads to poor coordination between the two, leading to negative returns to a factor. The outcome is a fall in the output instead of an increase.

  • Decrease in the efficiency of variable factors − The advantages related to the specialization of a variable and its division of labor start to go down with a continuous increment of variable factors. This causes negative returns to take place.


The law of variable proportion is an important and widely used law in economics. IT not only paves the path for controlled production but also shows the producers why their productions may have halted. The law also offers insight into the optimal amount of inputs that are required to control a given amount of output.

The producers of goods and services can be benefited from the use of this law. As it offers the idea of variables that must be altered to get the desired amount of output, producers can use this law on their behalf. Moreover, in the case of two variable productions, producers can realize the points of increasing, diminishing, and negative outputs. Thereby they can limit the wastage of resources and increase the output to the maximum level.


Qns 1. What is an important assumption regarding the variable factors in the law of variable proportions?

Ans. An assumption related to variable factors, in the case of the law of variable proportions, different units of variable factors can be combined with fixed factors.

Qns 2.What do factors of production become beyond a certain limit according to the law of variable proportions?

Ans. According to the law of variable proportions, factors of production become imperfect substitutes for each other beyond a certain point of production.

Qns 3.What is the assumption regarding technology in the case of the law of variable proportions?

Ans. According to the assumptions of the law of variable proportions, the state of technology should remain constant during the operation of the law.


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