Law of Variable Proportions/Law
of Non Proportional Returns/Law of Diminishing Returns:
(Short Run Analysis of Production):
There were three laws of returns
mentioned in the history of economic thought up till Alfred
Marshall's time. These laws were the laws of increasing returns,
diminishing returns and constant returns. Dr. Marshall was of
the view that the law of diminishing returns applies to
agriculture and the law of increasing returns to industry. Much
time was wasted in discussion of this issue. However, it was
later on recognized that there are not three laws of production.
It is only one law of production which has three phases,
increasing, diminishing and negative production. This general
law of production was named as the Law of Variable
Proportions or the Law of Non-Proportional Returns.
The Law of Variable Proportions
which is the new name of the famous law of Diminishing Returns
has been defined by Stigler in the following words:
increments of one input are added, the inputs of other
productive services being held constant, beyond a certain point,
the resulting increments of produce will decrease i.e., the
marginal product will diminish".
According to Samuelson:
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 addition of
extra inputs will become less".
The law of variable proportions also
called the law of diminishing returns holds good under the
(i) Short run. The law
assumes short run situation. The time is too short for a firm to
change the quantity of fixed factors. All the, resources apart
from this one variable, are held unchanged in quantity and
(ii) Constant technology. The
law assumes that the technique of production remains unchanged
(iii) Homogeneous factors.
Each factor unit in assumed to he identical in amount and
The law of variable proportions is,
now explained with the help of table and graph.
Fixed Inputs (Land Capital)
Variable Resource (labor)
Total Produce (TP
Marginal Product (MP
Average Product (AP Quintals)
Diminishing marginal returns
Negative marginal returns
In the table above, it is assumed
that a farmer has only 30 acres of land for cultivation. The
investment on it in the form of tubewells, machinery etc.,
(capital) is also fixed. Thus land and capital with the farmer
is fixed and labor is the variable resource.
As the farmer increases units of
labor from one to two to the amount of other fixed resources
(land and capital), the marginal as well as average product
increases. The total product also increase at an increasing rate
from 10 to 25 quintals. It is the stage of increasing returns.
The stage of increasing returns with
the employment of more labor does not last long. It is shown in
the table that with the employment of 3rd labor at the farm, the
marginal product and the average product (AP) both fall but
marginal product (MP) falls more speedily than the average
product AP). The fall in MP and AP continues as more men are put
on the farm.
The decrease, however, remains positive up to the
7th labor employed. On the employment of 7th worker, the total
production remains constant at 63 quintals. The marginal product
is zero. if more men are employed the marginal product becomes
negative. It is the stage of negative returns. We here find the
behavior of marginal product (MP). it shows three stages. In the
first stage, it increases, in the 2nd it continues to fall and
in the 3rd stage it becomes negative.
Three Stages of the Law:
There are three phases or stages of
production, as determined by the law of variable proportions:
(ii) Diminishing returns.
(iii) Negative returns.
These stages can be explained with
the help of graph below:
(i) Stage of Increasing Returns.
The first stage of the law of variable proportions is generally
called the stage of increasing returns. In this stage as a
variable resource (labor) is added to fixed inputs of other
resources, the total product increases up to a point at an
increasing rate as is shown in figure 11.1.
The total product from the origin to
the point K on the slope of the total product curve increases at
an increasing rate. From point K onward, during the stage II,
the total product no doubt goes on rising but its slope is declining. This means that from
point K onward, the total product increases at a diminishing
rate. In the first stage, marginal product curve of a variable
factor rises in a part and then falls. The average product curve
rises throughout .and remains below the MP curve.
Causes of Initial Increasing
The phase of increasing returns
starts when the quantity of a fixed factor is abundant relative
to the quantity of the variable factor. As more and more units
of the variable factor are added to the constant quantity of the
fixed factor, it is more intensively and effectively used. This
causes the production to increase at a rapid rate. Another
reason of increasing returns is that the fixed factor initially
taken is indivisible. As more units of the variable factor are
employed to work on it, output increases greatly due to fuller
and effective utilization of the variable factor.
(ii) Stage of Diminishing
Returns. This is the most important stage in the production
function. In stage 2, the total production continues to increase
at a diminishing rate until it reaches its maximum point (H)
where the 2nd stage ends. In this stage both the
marginal product (MP) and average
product of the variable factor are diminishing but are
Causes of Diminishing Returns:
The 2nd phase of the law occurs when
the fixed factor becomes inadequate relative to the quantity of
the variable factor. As more and more units of a variable factor
are employed, the marginal and average product decline. Another
reason of diminishing returns in the production function is that
the fixed indivisible factor is being worked too hard. It is
being used in non-optima! proportion with the variable factor,
Mrs. J. Robinson still goes deeper and says that the diminishing
returns occur because the factors of production are imperfect
substitutes of one another.
In the 3rd stage, the total production declines. The TP,
curve slopes downward (From point H onward). The MP curve falls
to zero at point L2 and then is negative. It goes
below the X axis with the increase in the use of variable factor (labor).
Causes of Negative Returns:
The 3rd phases of the law starts
when the number of a variable, factor becomes, too excessive
relative, to the fixed factors, A producer cannot operate in
this stage because total production declines with the employment
of additional labor.
rational producer will always seek to
produce in stage 2 where MP
and AP of the variable factor are diminishing. At which
particular point, the producer will decide to produce depends
upon the price of the factor he has to pay. The producer will
employ the variable factor (say labor) up to the point where the
marginal product of the labor equals the given wage rate in the
The law of variable proportions has
vast general applicability. Briefly:
(i) It is helpful in understanding
clearly the process of production. It explains the input output
relations. We can find out by-how much the total product will
increase as a result of an increase in the inputs.
(ii) The law tells us that the
tendency of diminishing returns is found in all sectors of the
economy which may be agriculture or industry.
(iii) The law tells us that any
increase in the units of variable factor will lead to increase
in the total product at a diminishing rate. The elasticity of
the substitution of the variable factor for the fixed factor is
From the law of variable
proportions, it may not be understood that there is no hope for
raising the standard of living of mankind. The fact, however, is
that we can suspend the operation of diminishing returns by
continually improving the technique of production through the
progress in science and technology.