2 Important Approaches to Study the Law of Variable Proportions

The law of variable proportions is one of the most important, fundamental and unchallenged law of production. This law is also termed as return to a factor, as under it one factor is varied, while keeping all other factors fixed.

With these variations in the quantity of one factor, keeping the quantity of other factors constant, the ratio of employment of the variable factor to that of the fixed factor keeps on changing. As we study the effects of variations in factor proportions under this law, this is called the law of variable proportions. There are two important approaches available to study this law:

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1. Classical Approach:

The law of variable proportions is the new name for the famous ‘Law of Diminishing Returns’ of classical economists like Adam Smith, Ricardo, Malthus, etc. But, the real credit goes to Marshall for providing a logical and scientific basis of the law, which was confined to agriculture only. He defines the law as follows:

“An increase in the capital and labour applied in the cultivation of land causes in general a less than proportionate increase in the amount of product raised unless it happens to coincide with an improvement in the arts of agriculture”.

The following table explains the operation of the law of diminishing returns;

The above table shows that cultivator employs more and more units of labour to get more produce. One unit of labour gives a total product of 20 quintals. When two units of labour are employed, the total product rises to 30 quintals. The marginal product (i.e., addition to total product with employment of one additional factor) in this case is 10 quintals.

When one additional unit of labour is further employed, the marginal product becomes 8 quintals, which is less than the marginal product in the previous situation. With each successive increase in the units of labour, the total product increases, but, at a decreasing rate.

In other words, the marginal product diminishes with employment of additional units of labour. Fig. 8.1 depicts the operation of the law of diminishing returns. Curve AB in the figure has a negative slope. Thus, more units of labour (variable factor) provide diminishing marginal product.


Law of diminishing returns assumes static technology. That is why it is more often applicable to agriculture, where there is very little scope for improvement in the technology. However, improvements in the art of agriculture cannot be perfectly assumed away. This law is subject to a number of limitations.

(a) Improvements in Methods of Cultivation:

The law assumes away any improvement in the arts of agriculture. Marshall has clarified it by inserting the phrase “… unless it happens to coincide with an improvement in the arts of agriculture” in his definition of this law. If this assumption is relaxed, i.e., scientific or improved methods of cultivation (use of better seeds, better agriculture implements, etc.) are adopted, the returns are bound to increase and the law will no longer hold true.

However, there is some limit to the improvement in the methods of production. Hence, sooner or later, the law of diminishing returns is bound to operate. Similarly, if a virgin soil is brought under cultivation, the additional return from each successive dose of labour and capital may cause increasing returns initially.

(b) Variable Factors Working with Fixed Factors:

This law will not operate, if it is not possible to keep some factor fixed (say, land).

(c) Hetrogenous Variable Factors:

All the units of variable factors are assumed to be homogenous or identical. In other words, diminishing marginal returns are not due to the use of inferior units of the variable factor. However, in real world various factor units are hetrogenous.

(d) Inadequate Units of Variable Factor:

The operation of the law of diminishing returns is also held up for sometimes, if the units of variable factors, i.e., labour and capital applied to a certain fixed piece of land is insufficient to cultivate to the full capacity of that piece of land.


Alfred Marshall gave a fairly satisfactory explanation of the law of diminishing returns. He discussed the law in relation to agriculture. Applicability of the law to agriculture can be advocated on several grounds:

(i) Overdependence of agriculture on unpredictable natural factors like rainfall, climate and weather conditions, particularly in less developed countries.

(ii) Little scope for the use of implements, machines and other improved methods of production.

(iii) Seasonal unemployment in agriculture reduces the productivity of agriculture labour.

(iv) Effective supervision is not possible due to scattered agricultural operations over a vast area and over a number of months.

(v) Quantity of land remains fixed.

(vi) Last, but the most important reason is that fertility of the soil gradually falls. So, the use of additional units of labour and capital will result in less than proportionate increase in output.

The law is equally applicable to the mines, forests and fisheries, which get exhausted as more and more are taken out of them. Hence, same quantities of labour and capital produce or extract lesser and lesser quantity of final product.

For instance, in the beginning, coal is found near the surface of earth. Gradually, one has to go deeper and deeper into the bowels of the earth to get the same amount of coal and fish in the two cases respectively.

Marshall’s law of diminishing returns applies not only to agriculture (for which it was originally developed), but also to extractive industries and to other industries, where land or other natural resources are important.

However, there is little scope of applicability of this law for most of the other manufacturing industries, which enjoy the advantages of large scale production through specialisation by machinery, men and management.

But, this is possible only temporarily. Ultimately, the tendency to diminishing returns is bound to appear. In brief, the law has been found to be applicable in agricultural production more quickly than in industrial production, because in the former a natural factor (i.e., land) plays a predominant role, while in the latter, manmade factors play the major role.

2. Modern Approach:

Law of diminishing returns enunciated by the classical and neo-classical economists like Marshall was peculiar to agriculture. Modern economists have given universal law which applies to all lines of production and in all sectors of the economy-agriculture, manufacturing and service sector.

This law again assumes presence of some fixed factor (not necessarily land) and one or more variable factors (say labour, capital). Moreover, modern economists believe that diminishing, constant and increasing returns are not three different laws, but they are three phases of one general law of variable proportions.

The law of variable proportions states that as we use more and more units of some factors of production to work with one or more fixed factors, the total product will increase at an increasing rate, then at a constant rate and finally at a diminishing rate. In other words, the marginal, average and total product will rise up to a certain stage and then will decline. The law has been stated by various economists in the following words:

“As equal increments of one input are added; the inputs of other productive service being held constant, beyond a certain point the resulting increments of product will decrease, i.e., the marginal products will diminish”.

“As the proportion of one factor in a combination of factors is increased, after a point first the marginal and then the average product of that factor will diminish”.

“An increase in some inputs relative to other fixed inputs will, in a given state of technology, cause output to increase; but after a point the extra output resulting from the same additions of extra inputs will become less and less”.

K.E. Boulding avoids the use of loose expression, ‘diminishing returns’, which can be variously interpreted. He rather names the law as ‘The Law of Eventually Diminishing Marginal Physical Productivity’ and defines it; “As we increase the quantity of any one input which is combined with a fixed quantity of the other inputs the marginal physical productivity of the variable input must eventually decline”.

The views of Alfred Marshall (stated under classical approach), GStigler, F. Benham, P.A. Samuelson and K.E. Boulding on this law are fundamentally the same. The only difference is that whereas according to Benham, the law operates when both MP and AP begin to diminish. But, this is not so with other economists. According to them, the law must be stated in terms of marginal product rather than average product as the former is more important.

It is obvious from the above definitions of the law of variable proportions (or the law of diminishing returns) that it refers to the behaviour of output as the quantity of one factor is increased, keeping the quantity of other factors fixed. It further states that the marginal product and average product will decline eventually, as more and more quantities of variable factor are combined with (at least) one constant factor.

Law of variable proportions is based upon the following assumptions:

(i) The state of technology is given and remains constant. If there is improvement in technology, then marginal and average products may rise instead of diminishing.

(ii) Quantity of at least one factor input is constant and one factor input is variable. It is only in this way that the firm can alter the factor proportions and know its effects on output.

(iii) Effect of changing units of a variable factor on output can be estimated correctly.

(iv) The law is based upon the possibility of varying the proportions in which the various factors can be combined to produce a product. The law does not apply in those situations, where the factors must be used in fixed proportions to yield a product.

In such situations, increase in one factor would not lead to any increase in output, i.e., the marginal product of the factor will be zero and not diminishing. For example, two drivers cannot drive the same vehicle at the same time. However, such situations are very uncommon.

(v) All the units of variable factor are homogenous, i.e., equal in efficiency.

(vi) Input prices remain unchanged,

(viii) Output is measured in physical units.