Law of Variable Proportions

Law of Variable Proportions is an important law of production in micro economics. It explains the relationship between variable factors and output when other factors remain constant. According to this law, as more units of a variable factor like labour are combined with fixed factors like land or machinery, total output first increases at an increasing rate, then increases at a diminishing rate, and finally decreases. This law operates in the short run because at least one factor of production remains fixed. It helps firms understand how output changes with variation in input. In Indian industries and agriculture, this law explains productivity and efficient use of labour and capital.

Assumption of Law of Variable Proportions:

1. One Factor is Variable and Others are Fixed

The law of variable proportions assumes that one factor of production is variable while other factors remain fixed. Usually, labour is taken as the variable factor, and land or capital is fixed. In the short run, firms cannot change all factors due to time limitation. For example, a factory may increase labour but machinery remains fixed. This assumption is necessary to study how output changes when only one input is varied. Without fixed factors, the law cannot operate properly.

2. Technology Remains Constant

It is assumed that the state of technology does not change during the operation of the law. If technology improves, output may increase even without increasing the variable factor. For example, use of modern machines or improved methods can raise production. To clearly study the effect of changing variable input on output, technology must remain constant. This assumption helps isolate the relationship between variable factor and output and keeps the analysis simple.

3. Factors are Homogeneous

The law assumes that all units of the variable factor are homogeneous or identical in quality. This means each unit of labour has the same skill, efficiency, and productivity. If labour quality differs, output change may be due to difference in skill rather than quantity of labour. In India, labour skills vary, but for theoretical analysis, homogeneity is assumed. This helps in accurately measuring the effect of additional units of variable factor on output.

4. Production is Measured in Physical Units

It is assumed that both input and output are measured in physical units and not in monetary terms. For example, labour is measured in number of workers and output in units of goods. This avoids the effect of price changes on output measurement. By using physical units, the law focuses only on technical relationship between inputs and output. This assumption ensures clarity and correctness in production analysis.

5. Short Run Operation

The law of variable proportions operates only in the short run. In the short run, at least one factor remains fixed. In the long run, all factors can be changed, and this law does not apply. For example, a factory can increase labour quickly but cannot expand building or machinery in short period. This assumption highlights time element and explains why the law is relevant only for short run production decisions.

6. Efficient Use of Fixed Factors

It is assumed that fixed factors are efficiently and optimally used. If fixed factors are underutilized or poorly managed, output may not increase properly. In India, inefficient use of machinery or land can reduce productivity. This assumption ensures that changes in output are due to change in variable factor and not due to inefficiency of fixed factors.

Graphic Presentation:

In fig. 1, on OX axis, we have measured number of labourers while quantity of product is shown on OY axis. TP is total product curve. Up to point ‘E’, total product is increasing at increasing rate. Between points E and G it is increasing at the decreasing rate. Here marginal product has started falling. At point ‘G’ i.e., when 7 units of labourers are employed, total product is maximum while, marginal product is zero. Thereafter, it begins to diminish corresponding to negative marginal product. In the lower part of the figure MP is marginal product curve.

Up to point ‘H’ marginal product increases. At point ‘H’, i.e., when 3 units of labourers are employed, it is maximum. After that, marginal product begins to decrease. Before point ‘I’ marginal product becomes zero at point C and it turns negative. AP curve represents average product. Before point ‘I’, average product is less than marginal product. At point ‘I’ average product is maximum. Up to point T, average product increases but after that it starts to diminish.

Three Stages of the Law:

1. First Stage

First stage starts from point ‘O’ and ends up to point F. At point F average product is maximum and is equal to marginal product. In this stage, total product increases initially at increasing rate up to point E. between ‘E’ and ‘F’ it increases at diminishing rate. Similarly marginal product also increases initially and reaches its maximum at point ‘H’. Later on, it begins to diminish and becomes equal to average product at point T. In this stage, marginal product exceeds average product (MP > AP).

2. Second Stage

It begins from the point F. In this stage, total product increases at diminishing rate and is at its maximum at point ‘G’ correspondingly marginal product diminishes rapidly and becomes ‘zero’ at point ‘C’. Average product is maximum at point ‘I’ and thereafter it begins to decrease. In this stage, marginal product is less than average product (MP < AP).

3. Third Stage

This stage begins beyond point ‘G’. Here total product starts diminishing. Average product also declines. Marginal product turns negative. Law of diminishing returns firmly manifests itself. In this stage, no firm will produce anything. This happens because marginal product of the labour becomes negative. The employer will suffer losses by employing more units of labourers. However, of the three stages, a firm will like to produce up to any given point in the second stage only.

In Which Stage Rational Decision is Possible

To make the things simple, let us suppose that, a is variable factor and b is the fixed factor. And a₁, a₂ , a₃….are units of a and b₁ b₂b₃…… are unit of b.

Stage I is characterized by increasing AP, so that the total product must also be increasing. This means that the efficiency of the variable factor of production is increasing i.e., output per unit of a is increasing. The efficiency of b, the fixed factor, is also increasing, since the total product with b₁ is increasing.

The stage II is characterized by decreasing AP and a decreasing MP, but with MP not negative. Thus, the efficiency of the variable factor is falling, while the efficiency of b, the fixed factor, is increasing, since the TP with b₁ continues to increase.

Finally, stage III is characterized by falling AP and MP, and further by negative MP. Thus, the efficiency of both the fixed and variable factor is decreasing.

Rational Decision

Stage II becomes the relevant and important stage of production. Production will not take place in either of the other two stages. It means production will not take place in stage III and stage I. Thus, a rational producer will operate in stage II.

Suppose b were a free resource; i.e., it commanded no price. An entrepreneur would want to achieve the greatest efficiency possible from the factor for which he is paying, i.e., from factor a. Thus, he would want to produce where AP is maximum or at the boundary between stage I and II.

If on the other hand, a were the free resource, then he would want to employ b to its most efficient point; this is the boundary between stage II and III.

Obviously, if both resources commanded a price, he would produce somewhere in stage II. At what place in this stage production takes place would depend upon the relative prices of a and b.

Condition or Causes of Applicability:

There are many causes which are responsible for the application of the law of variable proportions.

1. Under Utilization of Fixed Factor

In initial stage of production, fixed factors of production like land or machine, is under-utilized. More units of variable factor, like labour, are needed for its proper utilization. As a result of employment of additional units of variable factors there is proper utilization of fixed factor. In short, increasing returns to a factor begins to manifest itself in the first stage.

2. Fixed Factors of Production

The foremost cause of the operation of this law is that some of the factors of production are fixed during the short period. When the fixed factor is used with variable factor, then its ratio compared to variable factor falls. Production is the result of the co-operation of all factors. When an additional unit of a variable factor has to produce with the help of relatively fixed factor, then the marginal return of variable factor begins to decline.

3. Optimum Production

After making the optimum use of a fixed factor, then the marginal return of such variable factor begins to diminish. The simple reason is that after the optimum use, the ratio of fixed and variable factors become defective. Let us suppose a machine is a fixed factor of production. It is put to optimum use when 4 labourers are employed on it. If 5 labourers are put on it, then total production increases very little and the marginal product diminishes.

4. Imperfect Substitutes

Mrs. Joan Robinson has put the argument that imperfect substitution of factors is mainly responsible for the operation of the law of diminishing returns. One factor cannot be used in place of the other factor. After optimum use of fixed factors, variable factors are increased and the amount of fixed factor could be increased by its substitutes.

Such a substitution would increase the production in the same proportion as earlier. But in real practice factors are imperfect substitutes. However, after the optimum use of a fixed factor, it cannot be substituted by another factor.

Applicability of the Law of Variable Proportions:

1. Applicability in Agriculture

The law of variable proportions is highly applicable in agriculture. In agriculture, land is a fixed factor while labour, seeds, and fertilizers are variable factors. When more labour and inputs are applied to a fixed piece of land, output initially increases at a faster rate due to better use of land. After a point, output increases at a diminishing rate because land becomes overcrowded. Finally, excessive use of labour reduces output. In India, small land holdings clearly show this law. Farmers experience diminishing returns when too many workers are employed on the same land.

2. Applicability in Industrial Production

This law is also applicable in industrial production in the short run. In factories, machinery and building remain fixed, while labour is variable. When more workers are employed, production increases due to specialization and better division of work. After optimum use of machinery, additional workers cause congestion and inefficiency, leading to diminishing and negative returns. In Indian small scale industries, this law helps managers decide the optimum number of workers for maximum output. It helps in avoiding wastage of resources and controlling production cost.

3. Applicability in Short Run Decision Making

The law of variable proportions is applicable only in the short run, where at least one factor of production is fixed. It helps firms take short run production decisions such as how many workers to employ with given machinery. Indian firms often face short run constraints like limited capital and space. This law helps them understand stages of production and select the best level of output. It guides managers to stop production before negative returns begin, ensuring efficient use of resources and higher profitability.

Postponement of the Law:

1. Improvement in Technology

Improvement in technology helps in postponing the law of variable proportions. When better machines, tools, and production methods are used, fixed factors become more efficient. As a result, additional units of variable factor like labour can be used more productively for a longer time. Output continues to increase without facing diminishing returns quickly. In India, use of modern farming equipment and improved irrigation postpones diminishing returns in agriculture. Technological improvement increases productivity and allows better use of resources, delaying the stage of diminishing and negative returns.

2. Better Organisation and Management

Efficient organisation and management help in postponing the law of variable proportions. Proper planning, supervision, and coordination improve the use of fixed and variable factors. When workers are well managed, wastage is reduced and productivity increases. In Indian industries, better management practices like proper scheduling and training help firms use labour more effectively with existing machinery. Good organisation ensures smooth production flow and avoids congestion. This delays the point where additional labour becomes less productive and postpones diminishing returns.

3. Improvement in Quality of Variable Factors

Improvement in the quality of variable factors such as skilled labour, better seeds, and quality raw materials postpones the law of variable proportions. Skilled workers can produce more output with the same fixed factors. In Indian agriculture, use of high quality seeds and fertilizers increases output even when land remains fixed. Better quality inputs increase efficiency and productivity. As a result, diminishing returns appear at a later stage, allowing firms to produce more output before reaching inefficiency.

4. Proper Combination of Factors

Proper combination of factors of production helps in postponing the law of variable proportions. When variable and fixed factors are combined in correct proportion, resources are fully utilized. Overcrowding and underutilization are avoided. In Indian factories, correct labour machine ratio improves productivity. Balanced use of inputs ensures smooth production and higher output. This delays the stage where extra units of labour reduce efficiency. Thus, optimum factor combination postpones diminishing returns and increases overall production efficiency.