Law of Variable Proportion and Law of Diminishing Marginal Product

The Law of Diminishing Marginal Product and the Law of Variable Proportions are both models of economic theories. Such theories involve an advanced level of abstraction, which is a compact representation of any system that removes several layers of detail to capture the underlying structure and function of the concerned system. 

Economic theories, based on which these two laws are published, are conceptual, abstract models which rest upon several assumptions. With the help of these models, it is easier to find the fundamental issues of the economy with substantial justifications.

Both these laws of diminishing marginal product or productivity and variable proportions help to identify such issues faster and deal with them accordingly for betterment of the economy of a system.

What is the Law of Diminishing Marginal Product?

The Law of Diminishing Marginal Product depicts a specific system, where an increase in any one production variable while keeping other variables constant, will initially increase the overall production of the system. However, a further increase in that particular variable will generate lesser returns.

In simple terms, as per the law of diminishing marginal product or productivity, increasing only one factor of production for a particular unit will bring in more returns but only past a certain point of increase. This law does not always imply that addition of production variables will decrease overall productivity in the long run, but it is usually the case. 

For example, an agricultural company is hiring labourers to increase their production of crops. However, they are on a fixed budget, and their profits are used to keep these work hands on the payroll. A graph is illustrated below to see the outcome of the returns. 

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From this example, it can be determined that with an increase in new labours, there was a certain increase in both output and productivity. However, with the addition of the 5th and 6th labourer, overall productivity started to decline. Here, diminishing returns are taking place on exceeding 4 labourers for this agricultural company. 

So, with the help of this example of the law of variable proportion definition, it is clear that the law of diminishing marginal productivity affects all types of businesses that make alterations in their inputs to yield a higher output. The occurrence of this phenomenon suggests that this company cannot make use of the maximum labourers or machinery it can afford in order to improve efficiency. So, every company, which aims to be as much cost-efficient as possible, is required to know when Diminishing Marginal Productivity will affect their business.

What is the Law of Variable Proportions Definition?

Also referred to as the Law of Proportionality, the Law of Variable Proportion in economics concerns itself with how the output of a system alters with an increase in the number of units of a production variable, thus expressing the features of a changing factor-ratio proportion of the concerned output.

In simple terms, this law exhibits a propionate increase of variable factors of a system in relation to its generated output during shorter terms. The most important criteria for conducting such analysis is keeping all other factors a system constant. So, this relationship between the input and output is also considered as Returns to the Variable Factor. 

Assumptions in the Law of Variable Proportions

The law of variable proportions is based on these following assumptions –

• Constant Technology

It is assumed that the state of technology is constant and is not improving or degrading during alterations of production variables. 

If there is an improvement or degradation in the technology adopted by a company for its production unit, it will be impossible to get a clear understanding how a change in the production variables are affecting the overall output. 

• Variable Factors

As per this law, production factors are assumed to be variable. If all production variables are considered as a fixed proportion in relation to the output, this will be invalid. 

• Homogenous Units

All the units of the variable factor are regarded as homogenous. This indicates that each and every unit is of identical quality and quantity and amount to an identical figure. 

• Short-Run

The law of variable proportions only works for systems operating short-term where it is not feasible to alter every production input.

Three Stages of the Law of Variable Proportion

The three stages of this law require an example for an easier explanation. Let us assume that an agricultural company has 100 acres of land and 10 units of labour for production. So, the land to labour ratio is currently at 10:1. However, increasing the units of labour to 20, this ratio now becomes 5:1.

In the diagram below, the objective is to find TPP or Total Physical Product and MPP, which is the Marginal Physical Product. 

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From this example, it can be determined that –

1. During Stage 1, both TPP and MPP are increasing at a given rate on increase in the variable inputs, i.e. the units of labour for the given acre of land. 

2. On Stage 2, TPP is found to increase but at a diminishing rate. In case of the MPP, it decreases with an increase in the number of labour units. At a certain period during this stage, TPP will reach its maximum value while MPP is about to hit 0. 

3. During Stage 3, TPP will carry on decreasing while MPP will decrease further and become negative.

So, it can be concluded that, the law of variable proportion states that successive units of variable input will lead to a decreased overall output as there will be fewer input variables to work with. 

Causes for the Operation of the Law of Variable Proportion

• Firstly, in the short-term duration, it is difficult to change all factors of production. In such cases, we maintain only one variable factor while others remain fixed/ static.

• All other factors when combined optimally can generate the maximum output. There can be increased marginal production if the units of a variable factor are increased prior to the point of optimum combination, as the factor proportion becomes more suitable leading to much better utilization of the fixed factors.

• During the initial stages, it has been observed that the total product tends to improve in value at an increasing rate if the producer puts in more units of a variable factor in comparison to the fixed factors.

• Subsequently, beyond the point of optimum combination, if the producer still continues the use of more units of the variable factor, then it counteracts and the factor proportion becomes inefficient. This causes the marginal product of that variable factor to declining.

• A steep rise in the quantity of the fixed factor input per unit of the variable is also observed if the producer keeps on increasing the units of the variable factor. Therefore, it is important to add successive units of the variable input alongside decreasing amounts to the total output as they have less fixed inputs to work with.

Following are the Reasons that can Improve/ Increase Returns to a Factor :

1.  During the initial stages, there can be much better utilization of the fixed factor if there is the increased application of variable factor input leading to an increase in total output.

2.  An efficient application of the variable factor causes process-based division of labour which further improves the efficiency of the factor. Accordingly, the marginal product of the factor tends to increase.

Following are the Factors that can Deteriorate Returns to a Factor:

1.  There can be stagnancy and over utilisation of the fixed factor if more & more units the variable factor is continuously combined with the fixed factor. This can cause diminishing returns post process.

2.  One must remember that factors of production are imperfect substitutes for each other. One can not repeatedly use more & more labour in place of additional capital.

Applications of the Law of Variable Proportion

The applicability of this law is diverse as Law of variable proportions applies to all fields of production, like agriculture, industry, etc. Since all the fields of production consist of some factors that are static while others vary, it is known as the law of universal application.

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