Law of
variable Proportions
The law of variable proportions is
also named as the laws of returns or the laws of returns to a variable factor.
The law states that as the quantity
of a variable impute is increased by equal doses, keeping the quantities of
other inputs constant, total product will increase, but after a point, at
diminishing rate. This principle can also be defined thus, when more units of
variable factors are used having the quantities of fixed factors constant, a
point is reached beyond which the marginal product, then the average and
finally the total product will diminish.'
According
to Prof. Watson, "The law of variable proportions, also known as
the law of diminishing returns, can be stated as follows: when total output or
production of a commodity is increased by adding units of a variable input while
the quantities of other inputs are held constant then increase in total
production becomes, after some point, smaller."
In simple
words, the law of variable proportions (or returns to a variable factor) states
that with the increase in variable factor, keeping other factors constant, the
marginal product after rising to some extent becomes smaller and smaller.
Why is it called the Law of
variable proportions?
It is
because of two reasons:
(i) The
factor: proportion (or factor-ratio) varies as one input varies and others
are held constant. This can be understood with the help of an example. Suppose
in the beginning 10 Ropani of land and 1 unit of labor are taken for
production, hence the land- labor ratio was: 10 1. Now if the land remains the
same but the unit of labor increases to 2, now the land- labor ratio would
become 5: 1. Thus law analyses the effects of change in factor-proportions on
the amount of output and therefore called the law of variable proportions:
(ii) The
return also varies non-proportionally with the change in factor-ratio: It
means when one factor is varied keeping other factors constant, the
input-output ratio also undergoes a change. For example, if 10 Ropani of land
and 1 unit of labor give the output of 20 quintals of wheat then the ratio
between labor (variable factor) and output of what is 1:20? Now if with 2 units
of labor, the output increases to 30 quintals then the labor-output ratio would
become 1: 15. Thus, the ratio between the variable factor and the output change
and that is why it is termed as the law of variable proportions.
Assumptions
(i) One is variable factor and others are the
fixed factors.
(ii) It is possible to make chances in the
factor-proportions.
(iii) No change in technique of production and
organization.
(iv) All units of the variable factors are
homogeneous
Causes
of the Operation of the Law:
(i) In the short period all factors of production
cannot be varied i.e. some are fixed factors in the short-run.
(ii) Factor of productions is not perfect substitutes.
(iii) Factors of production are scarce in relation to
their demand.
Explanation
of Law
This law of variable proportion can
be illustrated with the help of the following example and diagram. In this
example, we have presumed that land is a fixed factor and labor is a variable
factor.
Example
|
Fixed factor
land (Ropani)
|
Variable
Factor
Labor (VF)
(Units)
|
TP
(Qnt.)
|
AP=TP/VF
(Qnt.)
|
MP
(Qnt.)
|
|
1
|
0
|
0
|
0
|
-
|
|
1
|
1
|
4
|
4
|
4
|
|
1
|
2
|
12
|
6
|
8
|
|
1
|
3
|
24
|
8
|
12
|
|
1
|
4
|
32
|
8
|
8
|
|
1
|
5
|
36
|
7.2
|
4
|
|
1
|
6
|
36
|
6
|
0
|
|
1
|
7
|
28
|
4
|
-8
|
In this example we have assumed that
sand is the fixed factor and labor is a variable factor. The table shows the
different amounts of output obtained by applying different units of labor to
one acre of labor to one Ropani of land, which is fixed.
Three
stages of the Law
The relation
between variable factor and physical output has three stages that are shown in
the example as well as in the diagram. These are known as the three stages of
the law
Stage
I.
In this
stage total product increases at an increasing rate and the average product of
labor (AP) also increases. In the beginning of this stage marginal product (MP)
also increased but increases but after a point it starts to decline. Average
product continues to increase till marginal product is greater than the average
product. But when marginal product becomes equal to average product, the
increase in average product is withheld and this is the outer limit of the
first stage. In our example, the first stage, of the law runs up to four units
are labor and this limit is shown by point A in the diagram. Since in this
stage average product increases with the increases in the units the variable
factor, it is called the stage of increasing returns.
Why does
the law of increasing return operate? Following are given its main reasons:
(i) Indivisibility
of Factors. There are some factors that cannot be purchased in parts. For
example, if no generator is available in the market less than the size of
15-horse power then we have to purchase and use this generator. If at present
we are not using this generator to its full capacity then with the increase in
production marginal cost will decline.
(ii) Increase
in Efficiency. If the efficiency of fixed factor increases with the
increase in the quantities of variable factor, the law of increasing returns
will apply.
(iii) Fixed
Factors. The cost of fixed factors is also fixed. Hence, with the increase
in output per unit fixed cost will decline which in turn will lower the over
all average cost also up to a certain limit.
(iv) Division
of Labor. If the increase in the units of labor brings greater division of
labor and specialization in the production, it will also create the conditions
of increasing returns.
(v) Optimum
combination. If to achieve optimum combination of various factors of
production, the increase in the quantities of a particular factor is required
it will also bring increasing returns.
Stage
II.
In this stage also
the total product continues to increase but at a diminishing rate. This stage
goes to the point when total product reaches the maximum and marginal product
becomes zero. In this stage average product goes on diminishing. It means there
is decline in the efficiency of labor. In our example second stages runs
between 5 units and 6 units of labor and in the diagram it is between point A
and point M. In this stage both average product and marginal product decline
but remains positive. This stage is known as the stage of diminishing returns
also. Why does the law of diminishing returns operate? Following are given its
main reasons:
(i) Fixed
Factor. The quantity of the fixed factor-input per unit of the variable
input flls as more and more of the later is put to use successive units of the
variable input, therefore, must add decreasing amounts to the total output as
they have less of the fixed input to work e.g. land is a fixed factor.
(ii) Scarcity
of Factors. Factors of production are scarce and limited in supply. If
factors had not been limited, this law would also not have come into
existence.
(iii) Imperfect
Substitutes. Factors of production cannot be substituted fully. For
example, labor or capital cannot be substituted in place of land.
(iv) Optimum
Combination. These are an optimum combination pf different factors that
gives the maximum output. When we increase a particular factor of production
beyond this optimum combination, marginal product of that variable factor
declines naturally.
Importance
Samuelson has
regarded the law of diminishing returns as a natural Law. Since this law is
applicable in all the fields of production, it is called as the universal law
of production. Many principles of economics such as the Malthusian theory of
population, Ricardian theory of rent, marginal productivity theory of
distribution are based on the assumption of the law of diminishing returns.
Though this law is applicable in all fields yet it is more applicable in the
fields of agriculture. The main reason behind this is that in agriculture
nature plays a greater role than the man. In the words of Wick steed the law of
diminishing returns " is as universal as the law of life itself." The
universal applicability of this law has transcended economics to the realm of
science. Above all, it is of fundamental importance for understanding the
problems of under developed countries.
Stage
III.
In the third stage
total product starts to decline and marginal product becomes negative. That is
why total product curve starts to decline and marginal product curve goes below
the X-axis. In our example this stage comes when 7Th and 8th
units of labor are employed and according to diagram this stage starts when
more than OM units of labor are employed. This stage is called the stage of
negative returns
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