Labour, L :
Output, Q :
Factors other than labour are all fixed. Units of capital available are 4. When units of labour are increased as shown in the table, the total output increases initially at a slow pace. It picks up thereafter and reaches its maximum of 60 units when 6 units of labour input are employed.
If additional units of labour be employed, particularly the 7th unit, total product remains unchanged at 60 units indicating that the 7th unit of labour has contributed nothing to the total product. If 8th unit of labour be employed, the total product declines from 60 to 56 units indicating that the 8th unit of labour has contributed negative units to the total product.
This implies that the 8th worker has caused a damage to the total product of the earlier 7 workers. Let us define average and the marginal products before proceeding any further.
Average Product (AP) of labour is defined as output per unit of labour and may be given as
AP = Q / L
AP increases from 8 units per worker to a maximum of 12 units per worker. Thereafter it declines steadily to 7 units per worker. Marginal product is defined as the addition to the total product per additional unit of labour employed. It can also be given as the ratio of the change in total output to a change in number of units of labour employed. Thus
MP = Change in total product / Change in labour units employed
= ? (TP) / ?L = ?Q / ?L = dQ / dL
Marginal product increases from 8 units per worker (at L = 1) to a maximum of 16 units per worker (at L = 3) only to decline subsequently to -4 units per worker when 8th unit of labour is employed.
Diagrammatically, TP, AP and MP for this illustration are portrayed in Figure. 4.1.
Nature of TP, AP and MP curves reveals three stages in production as described in Figure 4.1. In stage I, the average product steadily rises as successive unit of labour input are employed. The stage is characterised as the stage of increasing returns to the variable factor labour.
This implies that the average product of the variable factor labour has an increasing tendency in stage I. The marginal product also rises in this stage but before the end of the stage, it begins to decline to meet the average product curve at the point where average product is maximum.
The point of intersection of MP and AP marks the end of the first stage and also that of the increasing returns to the variable factor labour. Average product, after this stage, falls steadily but the marginal product falls faster. It reduces to zero at the point where the total product is maximum.
Stage II is characterised as the stage of the diminishing returns to the variable factor labour. In this stage, MP falls but keeps below the AP curve and is non-zero. This stage is also characterised as the stage in which total product increases but at a diminishing rate.
The point where MP is zero or TP is maximum, marks the end of the second stage. In the third stage, marginal product of labour is negative and the total product develops a declining trend. This stage is characterised as the stage of negative returns to the variable factor labour. Every additional unit of labour, if employed, leads to a decrease in total output.
Returns to variable factor labour imply outputs realised in return to the increasing doles of labour input. As factors other than labour are all fixed, the proportion of labour to the fixed factors varies with additional units of labour employed.
Returns to the variable factor labour, thus, are also known as the returns to variable proportions. Increasing, diminishing and negative returns to variable proportions taken together comprise the law of diminishing returns. Different economists have defined the law of diminishing returns in the following manner.
In the language of G.J. Stigler, “As equal increments of one input are added; the inputs of other productive services being held constant, beyond a certain point the resulting increments of product will decrease, i.e., the marginal products will diminish.”
According to F. Benham, “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.”
According to P.A. Samuelson, “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 is of the view that the expression ‘diminishing returns’ is a loose one because it can be variously interpreted. He, therefore, avoids the use of the expression and names it “the Law of Eventually Diminishing Marginal Physical Productivity “and defines it thus—”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.”
Whatever the terminology, the law of diminishing returns to variable proportions can be stated as ‘the law of initial increasing returns to a variable input followed by steadily decreasing returns to its successively increasing units employed with fixed quantities of collaborating factors of production.’ The law, anyhow, remains a combination of the stages of increasing, diminishing and negative returns to a variable input, given that other inputs remain unchanged.
The reasons of increasing, diminishing and negative returns to variable proportions are explained in the following paragraphs.
The main reason for the increasing returns to variable proportions is the indivisibility of certain fixed factors of production. Such factors can’t be had in smaller quantities to suit the smaller size of the variable factor.
As the size of the variable inputs rises, it tends to approach the optimal proportion of combination of the two. This leads to fuller utilisation of the fixed factor. That is the reason for the increasing returns to variable proportions in the initial stage of production.
To illustrate, suppose a machine requires 10 workers to operate it at its full capacity; if only two workers be employed, they won’t be able to exploit its full capacity and the total as well as the average product will both be small.
As the number of workers is increased, the machine moves towards its fuller utilisation and marginal product of the variable factor rises. In consequence, the average product of the variable factor rises until it reaches its maximum at an employment of the requisite number of the workers which is 10 in this case.
The reason for decreasing returns to variable proportions is partly the overcrowding of the fixed factor by the variable factor and partly, the non-homogeneity of the additional units of the variable factor.
The additional units of the variable factor fail to match the earlier units in their productivity due to lack of experience and adaptability with the fixed factor. As a result, the marginal and the average products both decline with the rising levels of their employment.
Finally, the reason for the negative returns to the variable proportions is partly the overcrowding of the fixed factors by the variable factors and partly, the depreciation of the fixed factor which leads to its frequent breakdowns.
As a result, the marginal product of the variable factor becomes negative and the total and the average products both register steep fall. From the analysis above, it is clear that no producer would like to produce in the third stage of production. Each additional unit of the variable factor employed has a negative marginal product with the total product rapidly falling.
Likewise, no producer would like to remain in the first stage of production when rising average product encourages him to employ additional units of the variable factor. Producers, therefore, like to be in the second stage, preferably at the point where the marginal product of the variable factor is zero.
This is so due to their twin objectives of higher competitiveness and higher market share. Their competitiveness is high when the quantity produced is as large as possible so that the costs get spread over larger quantity and the production cost per unit of the output works out lowest.
This facilitates fixing the lowest selling price for the product without adversely affecting their profit-margins. Likewise, for a higher share in the market demand, the producers need to produce as much as is possible for them so that they may not loose their customers to their competitors.