Production Function
5.3. LAW OF VARIABLE PROPORTION
Production is the back bone of all economic activity. The main objective of every producer is to maximize his profits with the given input. In the process the producer combines various inputs to get a suitable output, thus varying certain inputs and keeping the other factors of input constant. The level of output of a firm depends on the combination of different factors of production viz., land, labour, capital and organization. An increase in production would be possible when either the quantity of all the factors is increased simultaneously or when the quantity of some of the factors is increased. Thus the law of variable proportion states that, 'As the proportion of one factor in a combination of factors is increased after a point, the average and marginal production of factor will diminish'. Professor Stigler defines it 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 product will diminish”.
Thus in the short run, as the amount of variable factor increases, other things remaining equal, the output will increase more than proportionately to the amount of variable inputs in the beginning, that it may increase in the same proportion and ultimately it will increase less proportionately.
Certain concepts have to be known to understand the law of variable proportion:
● Total Product (TP): It refers to the total units of out put produced per unit of time by combining the inputs. In the short run however, the total product increases with an increase in the variable factor.
Thus TP = f(QVF), where TP denotes total produce
QVF denotes the quantity of the variable factor Example: 30 workers produce 40 shirts in a day. Here the total product is 40 units.
● Average Product: Refers to the product per unit of product. In other words it is obtained by dividing the total product by the quantity of the product produced.
AP TP
=QVF
Suppose, 5 units of the labour gives out 100 units of the product.
Here the average product is 100 / 5 = 20 units. Hence 20 units is the average product.
● Marginal Product: The additional product obtained due to the additional input induced into the production system is known is marginal product. The marginal concept plays an important in the production system, as the producer is keen to known the additional product produced and the additional profit obtained thereon. Algebraically, it may written as MPn = TPn – TPn–1. Suppose, 20 workers produce 100 units of the commodity in a day. And the next day an additional 2 workers are employed and the production is 120 units. The marginal product is 20 units.
ASSUMPTIONS
● The state of technology remains constant and unchanged, if for instance the technology changes the average and marginal output will increase and not decrease.
● The fixed factors are kept constant and the variable factors are changed due to increase in the level of output.
● All units of variable factors are homogenous.
● The entire operation is only for the short run and not for the long run period.
The law of variable proportion can be explained through the table below:
Variable Total Average Marginal
Factor Product Product(TP/N) Product (MP)
(TPn – TPn–1)
1 10 10 10
2 25 12.5 15 Stage I
3 45 15 20
4 70 17.5 25
5 88 17.6 18 Stage II
6 100 16.7 12
7 107 15.3 7
8 107 13.4 0
9 106 11.8 – 1 Stage III
10 102 10.2 – 4
In the schedule it is seen that as the doses of the variable factor is induced into the production system, the total product, the average product, and the marginal product keep increasing in the first stage.
As the doses of the variable factor is further induced into the production system, it is seen that the total product increases, but at a diminishing rate, the average product also decreases, but the rapid changes are noticed in the marginal product, where its value diminishes more than the decrease in the average product. This stage is also known as stage of decreasing returns. When the doses of variable factor are further added to the production system, the total product and average product diminish further. The marginal product diminishes reaches a zero level and then a negative level.
It can also be seen that the when the marginal is zero, the total product is maximum. Even after this point, if the variable factor
is added, the total product only shows a decline in production.
The law of variable proportion can also be explained through a figure.
In the figure x axis measures the units of variable factor. And y axis measures the output. In the first stage, the total product, the average product and the marginal product curve increase, with an increase in every additional input. This stage is known as stage of increasing returns. When the short run production function is adjusted to obtain the maximum output, the resulting output tends to be in a greater proportionate to the increase in the variable factor units. The services of certain factors like that of the machines will be used more efficiently when greater input of variable factors like labour and raw material are applied.
In the second stage, the increasing dosage of input results in diminishing returns to scale. In the short period, since the fixed factors cannot be changed, the firm seeks to increase output by employing more and more units of variable factors, thus the imperfect substitution of factors leads to internal diseconomies and thereby diminishing returns to scale.
In the third stage, there is negative returns to scale, where the
input of the variable factor is much in excess in relation to the fixed factor. Thus with every increase in the variable factor, the total product and the average product falls. The marginal product also diminishes reaches a zero level and then a negative level.
When the marginal curve intercepts at point n on the x axis, it corresponds to point b on the total product curve, which indicates that when MP = 0, TP is maximum. Hence the declining part of the total product curve is in proportion to the negative part of the marginal product curve.
Under the given technology, the producer being rational will not reach the third stage, where the marginal returns are negative, he will not produce at a point, where he faces loss. The producer will not choose to either produce much in stage I, as the fixed factor will not be utilized to the optimum extent possible. The second stage is one in which the producer would tend to use both the factors in order to maximize his profits.
SIGNIFICANCE OF THE LAW
The economic significance of the law is that it is useful to producers in taking appropriate decisions with regard to the type of commodity to be produced and if needed to take adhoc decision to diversify into a new product region, or to produce an entirely new product. Given the variation in the total output and marginal out put, it helps the producer to find the appropriate region which would enable him to produce to the optimum and thereby earn profits.