Tag: Law of variable Proportions

The Law of Variable Proportions explains how total production changes when the quantity of one variable factor is increased while other factors remain constant. It is a short-run production law because at least one factor, such as land, machinery, or factory space, remains fixed. As additional units of labour or another variable input are combined with fixed factors, output may initially increase at an increasing rate, then at a diminishing rate, and eventually decline.

Definition of the Law

The Law of Variable Proportions states that when increasing quantities of a variable factor are combined with fixed quantities of other factors, total output initially increases at an increasing rate, then increases at a diminishing rate, and may ultimately decrease. This occurs because the proportion between fixed and variable factors changes as more units of the variable factor are employed. The law is also known as the Law.

Assumptions of the Law of Variable Proportions

1. Short-Run Production Period

The law operates in the short run, when at least one factor of production remains fixed. Factors such as land, factory space, or machinery cannot be changed immediately, while labour or raw materials may be varied. This condition allows the producer to study how changing one input affects total production while other inputs remain constant. The law therefore explains the relationship between variable and fixed factors within a limited production period.

2. One Factor is Variable

The law assumes that only one factor of production is variable, while the quantities of other factors remain unchanged. For example, a firm may increase the number of workers while keeping its machinery, building, and land constant. This assumption helps isolate the effect of the variable factor on total production. If several factors changed simultaneously, it would be difficult to identify which factor caused the change in output.

3. Fixed Factors Remain Constant

The quantities of fixed factors, such as land, machinery, buildings, and equipment, are assumed to remain unchanged throughout the analysis. The producer increases the variable factor without expanding the capacity of these fixed resources. As more variable inputs are combined with fixed factors, their proportion changes, influencing productivity. This assumption is essential for explaining why output may initially rise rapidly, later increase slowly, and eventually decline.

4. Technology Remains Unchanged

The law assumes that technology and production methods remain constant during the period of analysis. No new machinery, improved techniques, or technological innovations are introduced while the variable factor increases. If technology changes, output may rise because of improved production methods rather than the additional input. Keeping technology constant makes it possible to examine the effect of changing factor proportions on production more accurately.

5. Homogeneous Units of Variable Factor

All units of the variable factor are assumed to be homogeneous, meaning they have similar quality, efficiency, and productive capacity. For example, workers are treated as having equivalent skills and working ability. If later workers were more skilled or less efficient than earlier workers, changes in output could result from differences in worker quality. This assumption ensures that variations in production are mainly explained by changes in the quantity of the variable factor.

6. Factors Can Be Combined in Different Proportions

The law assumes that variable and fixed factors are divisible and can be combined in different proportions. A producer can add more units of labour to a given quantity of land or machinery. This flexibility allows the producer to observe how changes in the input combination affect total production. If factors could only be used in fixed proportions, it would be difficult to examine the changing productivity associated with increasing one factor while holding another constant.

7. Efficient Management and Organization

The law generally assumes that management and organizational conditions remain unchanged during the production process. The producer is expected to use available resources in a reasonably consistent manner without sudden changes in supervision, work organization, or operating practices. If management becomes significantly better or worse while inputs are changing, output may be affected by those changes. This assumption helps focus the analysis on the relationship between variable and fixed factors.

8. Output is Measurable

The law assumes that production can be measured in physical units, such as tonnes, kilograms, pieces, or units of service. This makes it possible to calculate Total Production (TP), Average Production (AP), and Marginal Production (MP) as the variable factor changes. Accurate measurement helps identify increasing returns, diminishing returns, and negative returns. The assumption is especially useful for comparing output levels under different input combinations and explaining the stages of the law clearly.

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.

• 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.

• 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.

• 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.

• 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

The law of variable proportions is universal as it applies to all fields of production. This law applies to any field of production where some factors are fixed and others are variable. That is why it is called the law of universal application.

The main cause of application of this law is the fixity of any one factor. Land, mines, fisheries, and house building etc. are not the only examples of fixed factors. Machines, raw materials may also become fixed in the short period. Therefore, this law holds good in all activities of production etc. agriculture, mining, manufacturing industries.

• Application to Agriculture

With a view of raising agricultural production, labour and capital can be increased to any extent but not the land, being fixed factor. Thus when more and more units of variable factors like labour and capital are applied to a fixed factor then their marginal product starts to diminish and this law becomes operative.

• Application to Industries

In order to increase production of manufactured goods, factors of production has to be increased. It can be increased as desired for a long period, being variable factors. Thus, law of increasing returns operates in industries for a long period. But, this situation arises when additional units of labour, capital and enterprise are of inferior quality or are available at higher cost.

As a result, after a point, marginal product increases less proportionately than increase in the units of labour and capital. In this way, the law is equally valid in industries.

Postponement of the Law

The postponement of the law of variable proportions is possible under following conditions:

(i) Improvement in Technique of Production

The operation of the law can be postponed in case variable factors techniques of production are improved.

(ii) Perfect Substitute

The law of variable proportion can also be postponed in case factors of production are made perfect substitutes i.e., when one factor can be substituted for the other.