Question 16 — Explain the Law of Variable Proportions along with its Reasons of Applicability.

Introduction

The theory of production studies the relationship between inputs (factors of production) and output. In the short run, some factors (like plant, machinery, land, building etc.) are fixed, while others (such as labour, raw material, power etc.) are variable. When output is increased or decreased by changing only the quantity of the variable factor, keeping other factors constant, the behaviour of output is explained by the Law of Variable Proportions.

In the PU B.Com Semester I syllabus, following T.R. Jain & V.K. Ohri, Microeconomics, the law of variable proportions is treated as a fundamental short-run law of production. It is also known in older literature as the Law of Diminishing Marginal Returns.

Meaning of Law of Variable Proportions

Suppose land and machinery (capital) are fixed, and the producer varies the units of labour employed. As more and more units of labour are applied to a given fixed factor, total output first rises at an increasing rate, then at a diminishing rate, and eventually may even start declining. This systematic pattern is summarized in the Law of Variable Proportions.

Thus, as the proportion between the variable factor and the fixed factor changes, the productivity behaviour passes through three distinct stages, which are very important for a producer’s decision-making.

Assumptions of the Law of Variable Proportions

The law operates under certain standard assumptions, as presented in your prescribed text:

1. Short-run situation: At least one factor is fixed (e.g., land, plant size), while one factor is variable (e.g., labour). Thus, factor proportions are changeable.
2. Homogeneous units of variable factor: All units of the variable factor are identical in quality and efficiency, i.e., one unit of labour is the same as another unit of labour.
3. Constant technology: The technique of production remains unchanged. Any change in output is only due to change in factor proportions, not due to improvements in technology.
4. Divisibility of factors: The variable factor can be increased or decreased in small units.
5. Perfect divisibility of product: Output can be measured and divided into units conveniently.
6. Rational behaviour: The producer is rational and aims at maximising profit or at least maximising output for a given cost.
7. Applicable to agriculture and industry: The law is of general applicability and is not confined only to agriculture, although classical economists first discussed it in the context of agriculture.

Illustrative Schedule of Total, Average and Marginal Product

The operation of the law can be shown with the help of a hypothetical schedule. Consider land (fixed) and labour (variable). As more units of labour are employed on the same land, total product (TP), marginal product (MP) and average product (AP) behave as follows:

From the schedule we observe:

• TP rises at an increasing rate up to 3 units of labour (MP rising).
• TP continues to rise but at a diminishing rate from 4th to 7th unit (MP falling but still positive).
• TP reaches a maximum at 7 units, and then declines when the 8th unit is employed (MP becomes negative).
• AP rises initially, reaches its maximum, and then declines.
• MP initially rises, then falls, and ultimately becomes negative.

Diagrammatic Explanation: TP, MP and AP Curves

The behaviour of total, average and marginal product of the variable factor can be expressed by smooth curves derived from the above schedule.

Three Stages of the Law of Variable Proportions

Stage I – Increasing Returns to the Variable Factor

In Stage I, as the variable factor (labour) is increased:

• TP rises at an increasing rate.
• MP rises and is greater than AP.
• AP rises and reaches its maximum at the end of Stage I.

This stage starts from the origin where the first unit of labour is employed and continues up to the point where AP is maximum. Economically, this stage reflects improved utilisation of fixed factors. Initially, the fixed factor (e.g., land, machine) is underutilised; as more labour is added, specialisation and better division of labour become possible, resulting in increasing returns.

Stage II – Diminishing Returns to the Variable Factor

In Stage II:

• TP continues to increase, but at a diminishing rate.
• MP is positive but declining.
• AP is also falling, but remains positive.
• This stage lies between the point where AP is maximum and the point where MP becomes zero.

Stage II is the economically rational stage of production. A producer will operate in this region because in Stage I, fixed factors are still underutilised, and in Stage III, marginal product becomes negative. In Stage II, both factors are utilised in an economically meaningful way and the firm can adjust the optimum combination of fixed and variable factors.

Stage III – Negative Returns to the Variable Factor

In Stage III:

• TP declines with the addition of further units of the variable factor.
• MP becomes negative.
• AP continues to fall.

This stage begins where MP becomes zero and continues as MP turns negative. Economically, Stage III is an irrational region of production, because the producer is adding units of variable factor which actually reduce total output. In a competitive environment, no rational producer will voluntarily operate in this stage.

Reasons of Applicability of the Law (Causes of Operation)

The question specifically asks for the reasons of applicability of the law of variable proportions. That is, why does this pattern of increasing, diminishing and negative returns generally appear in the short run? The main reasons, as discussed in T.R. Jain & V.K. Ohri, can be grouped as follows:

1. Indivisibility and Better Utilisation of Fixed Factors

Many fixed factors such as machines, land, buildings, management, etc., are indivisible. They cannot be used in very small fractions. When only a few units of the variable factor are combined with a large indivisible fixed factor, that fixed factor remains underutilised.

As more units of the variable factor are employed, the fixed factor is used more intensively and efficiently. Consequently, TP increases at an increasing rate and MP rises, giving increasing returns in the initial stage. Thus, indivisibility and fuller utilisation of fixed factors explain the existence of Stage I.

2. Increased Specialisation and Division of Labour

In the beginning, when only a small number of workers are employed, each worker may have to perform many different tasks and cannot become highly specialised in any one task. As more workers are added:

• Work can be divided into smaller tasks.
• Each worker can specialise in a particular operation.
• Coordination between workers and fixed equipment improves.

This leads to higher efficiency and higher productivity per unit of labour, contributing to the increasing returns part of the law. After a point, however, the scope for further specialisation is exhausted.

3. Fixity of at Least One Factor and Crowding of Variable Factor

The essence of the law of variable proportions is that, in the short run, some factors are fixed. When more and more units of the variable factor are applied to the same fixed factor, a situation of overcrowding or over-utilisation arises.

For example, if too many workers are put to work on the same machine or the same piece of land:

• Each worker gets less fixed capital or land to work with.
• Workers may get in each other’s way, causing disruption and inefficiency.
• Management and supervision become more difficult.

Beyond the optimum proportion, additional units of the variable factor contribute less and less to output, leading to diminishing marginal returns and, eventually, negative returns. This explains Stage II and Stage III.

4. Imperfect Substitutability of Factors

In real life, factors of production are not perfect substitutes for each other. More and more units of labour, for instance, cannot indefinitely compensate for a limited amount of land or machinery. Due to this imperfect substitutability:

• Initially, some substitution between factors is possible, contributing to rising MP.
• Beyond a point, additional labour without additional capital or land cannot be properly absorbed.

Hence, as the variable factor is increased while fixed factors remain constant, diminishing and negative returns are bound to set in sooner or later. This limited substitutability of factors supports the universal applicability of the law in the short run.

5. Optimal Factor Proportion and Economic Rationality

For every given technology, there is an optimum factor proportion at which the combination of fixed and variable factors yields the best possible productivity. When the firm employs less than this optimum amount of the variable factor, fixed factors are underutilised and productivity rises as variable factor is added. Once the optimum is reached, any further increase in the variable factor disturbs this optimal balance and reduces efficiency.

Therefore, the law of variable proportions reflects the movement towards and away from this optimum factor combination. It is “applicable” because producers in the real world typically operate with a fixed capacity in the short run and must decide how much variable input to add to it.

6. Short-run Nature of Production Decisions

In the long run, firms can vary all factors; they can change the size of the plant, acquire more land, or install additional machinery. In such a long-run setting, the Law of Returns to Scale is more relevant. But in the short run, firms necessarily make decisions by varying only some factors while others remain fixed.

Because short-run production is a universal feature of economic life, the law of variable proportions becomes widely applicable. Most real-world production decisions—especially in agriculture, small-scale industry and services—show the pattern predicted by this law.

Importance of the Law of Variable Proportions

The applicability of the law is also clear from its practical importance in economics and business:

Conclusion

To conclude, the Law of Variable Proportions is a fundamental short-run law of production. It describes how output responds when the quantity of one factor is varied while other factors are kept fixed. Total product first increases at an increasing rate, then at a diminishing rate, and ultimately falls, giving rise to three distinct stages of production. The law is widely applicable because in the short run at least one factor remains fixed, factors are imperfect substitutes, and producers face the problem of choosing an optimum combination of fixed and variable inputs. Its careful treatment in your prescribed text by T.R. Jain & V.K. Ohri makes it an important, frequently asked question in B.Com Semester I examinations.