Law of Diminishing Returns
Introduction
The law of diminishing returns is one of the most eminent concepts in the theory of production function. The modern version of the law of diminishing returns is known as law of variable proportions. Production function basically shows the physical relationship between the inputs or resources and the outputs. Here the inputs can be either fixed or variable. Suppose a firm uses both fixed and variable inputs to produce certain amount of output. The law of diminishing returns studies the relationship between these fixed and variable inputs in the shortrun. However, here it is assumed that only one factor of production is variable and all other factors of production are fixed. The law of diminishing returns examines how an increase in the variable factor of production, while keeping other factors of production constant, affects the output level. The study attributes that in the initial stage of production, an increase in the variable factor of production increases the output level proportionately. However, eventually the output level will not increase even proportionately. That is why Prof. Ryan calls this law as the law of nonproportional returns.
The 19^{th} century classical economists like Tugot, Ricardo, West and Malthus visualized the operation of this law in agriculture. Alfred Marshall, a neoclassical economist too considered the law of diminishing returns in relation to agriculture only. He thought that in industry increasing returns would prevail.
The law of diminishing returns has been defined by economists in the following way: “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.”
Assumptions of the Law
The law of diminishing returns is valid when the following conditions are fulfilled.
 The state of technology is given.
 Only one factor is varied and all other factors remain fixed
 The fixed factor and the variable factor are combined together in variable proportions in the process of production.
 The units of the variable factor are homogeneous.
 The law operates in the short run.
Illustration of the law
Let us take the case of a farmer who is cultivating one acre of land; land is fixed factor. The farmer tries to increase output by varying the variable factor, i.e., labor. The change in total product, average product and marginal product of the variable factor (labor in our case) are depicted in the following table:
Table 1
Units of Input (L)
 Total Product (TP)
 Marginal Product (MP)
 Average Product (AP)
 Stage


1
 100
 100
 100
 I

2
 220
 120
 110
 I

3
 360
 140
 120
 I

4
 460
 100
 115
 II

5
 530
 70
 106
 II

6
 570
 40
 95
 II

7
 595
 25
 85
 II

8
 600
 5
 75
 II

9
 594
 6
 66
 III

10
 560
 34
 56
 III

Total product (TP)
Total product is the amount of output produced from land with given number of laborers employed.
Average Product (AP_{L})
The average product of labor (AP_{L}) is total product (TP) divided by the number of laborers employed AP_{L} = TP_{L}/L
Marginal product (MP_{L})
The marginal product of labor (MP_{L}) is the change in the total product due to a change in labor. MP_{L} = ΔTP/ΔL
In our example in table 1, there are increasing returns to labor for the first three units of labor employed. The law of diminishing returns sets in with addition of the fourth worker. Both the average and the marginal products increase at first and then decline. The marginal product declines faster than the average product. When 8 men are employed, total product is at a maximum. The marginal product of the 9^{th} laborer is negative.
Thus,
 If MP > 0, TP will be increasing as L increases
 If MP = 0, TP will be constant as L increases
 IF MP < 0, TP will be falling as L increases.
Graphical presentation of the law of diminishing returns
Table 2: Properties of total product, marginal product and average product curves during the three stages of production
Total Product
 Marginal Product
 Average Product


Stage I (Increases at an increasing rate)
 Increases
 Increases

Stage I (Increases at a diminishing rate)
 Reaches a maximum and begins to diminish
 Continues to increase

Stage II (Continues to increase at a diminishing rate)
 Continues to diminish
 Reches maximum and begins to diminish

Stage II (Reaches maximum)
 Becomes zero
 Continues to diminish

Stage III (Diminishes)
 Becomes negative
 Continues to diminish but must always be greater than zero

The implications of the law of eventually diminishing returns are shown in figure 1. OXaxis measures the variable input, labor. Average product, marginal product and total product is shown along the vertical axis.
The total product has increased up to the point B. In other words the total product curve reaches a maximum when MP = 0 and then starts declining when MP < 0.
The total product curve exhibits the following characteristics:
 MP > 0 and increasing (from 0 to A)
 MP > 0 but decreasing (from A to B)
 MP = 0 at the point B
 MP < 0 after the point B
The point A where the total product stops increasing at an increasing rate and starts increasing at a diminishing rate is called the point of inflexion. This is the point at which the curvature of the TP curve changes. It is here that diminishing returns set in. Average and marginal product curves also rise initially. However, they start declining much earlier than the TP curve. The MP curve starts declining earlier than the average product curve. The MP curve starts declining earlier, cuts the AP curve at its maximum point (P) and then falls at a steeper rate than the AP curve.
Three stage of production in the shortrun
Production in the shortrun can be divided into three stages:
Stage I – from the origin to N_{1}
Stage II – from N_{1} to N_{2}
Stage III – to the right of N_{1}
These three stages are illustrated in figure 1. No profit maximizing production would take place in stage I or III. In stage I, the proportion of variable factor to fixed factor is low. Therefore, by adding one more unit of labor, the producer can increase the average productivity for all the units. A restaurant with 100 tables and only tow waiter would be operating in a stage I of the shortrun production function. By increasing the amount of labor in stage I and the average product of labor increases. As for stage III, it does not pay the producer to be in this region because by reducing the labor input he can increase total output and save in the cost of a unit of labor. In this stage, there is too much of the variable factor relation to the fixed factor. A restaurant with too many waiters in relation to the number of tables is an example of stage III. Therefore, stage III is considered as an irrational phase of production. Nevertheless, it is quite likely that a firm lacking perfect knowledge may be operating in this stage. In agriculture, this may be found to be very common. For instance, some economists have explained evidence of overcrowding of broilers and layers in poultry houses.
Stage II is the only stage in which there is neither a redundancy of the variable factor nor a redundancy of the fixed factor. Throughout this range the average product of labor declines, but he marginal product is positive. Thus, the economically meaningful range is the II stage.
Diminishing and increasing returns
The classical economists confined their discussion of the law of diminishing returns to that of agriculture only. Marshall held the view that if the role of nature is more predominant than man, diminishing returns occur and where man occupies a primary role compared to nature increasing returns may occur. In short, he visualized diminishing returns in agriculture and increasing returns in industry.
The operation of the law of diminishing returns is quicker in agriculture than in industry. The simple reason is that in agriculture, nature does the business and man is merely a manager. There is little scope for the application of division of labor. In addition, agriculture is seasonal in character. Further, the overall supply of land is inelastic. Therefore, the alternative to increase output is to apply more of labor and capital. However, after a point, the increase in the variable factor results in diseconomies of scale. The next option left is to increase output by the extension of plough in less fertile lands also. Since output and fertility are correlated, less fertile lands will yield only lesser returns. This, the law operates both under intensive and under extensive cultivation.
Increasing returns is a major possibility in industry. In industry, the role of man is supreme and nature plays a negligible role. A manufacturing firm benefits from division of labor and specialization. The emergence of various forms of economies will tend to raise the output more than proportionately. However, in industry also diminishing returns will occur beyond a limit.