1. Definition:
The law ofvariable proportion can be started as,
“In a given state of technology, when the units of variable factors of production (labor) are
increased with the units of other fixed factors, the marginal productivity increases at increasing
rate up to a point after that point it will become less and less”.
Assumptions of Law:
1. This law assumes that technology does not change throughout the operation of the law.
2. One factor of production has to be fixed for this law.
3. The law is based on the possibility of varying the proportions in which the various factors can
be combined to produce a product. This law is not applicable where the factors must be used in
fixed proportion to yield a product.
Explanation of the law:
The law of variable proportion can be explained with the help of table and graph.
Schedule:
Explanation:
In the above schedule units of variable factors (workers) are employed with the other fixed
factors of production. The marginal productivity of labor goes on increase up to 3rd worker.
After the 3rd worker the marginal productivity goes on falling on wards till it drops down to zero
at the 6th unit of labor.
The 7th worker is responsible in making the making the marginal productivity negative. The
marginal productivity (MPW) and average productivity (APW) equalize at the 4th worker then
MPWfalls more sharply.
Land Workers (w) TPW MPW APW Stage of Production
1 1 10 10 10 I.Increasing returns
1 2 30 20 15
1 3 60 30 20
1 4 80 20 20
1 5 90 10 18 II. Diminishing
Returns1 6 90 0 15
1 7 80 (10) 11.5 III. Negative returns
1 8 64 (16) 8

2. Graph:
Explanation:
Stage-I (Increasing Return)
First stage begins from the originand ends where MP curve cuts AP curve at point E from
above.Here, TP increases at an increasing rate to the point A (point of inflection) and then
increases at a decreasing rate. Corresponding to the point A,MP increases up to the point D and
then starts falling -but is still higher than average production and the AP continues to rise.
Stage-II (Diminishing Return)
The second stage begins from the point E and ends at that point F where MP is zero. At this stage
both MP and AP go on falling and both of them are positive. The total production TP goes on
rising at a diminishing rate. This is stage where a firm wishes to operate.
Stage-III (Negative Return)
The third stage begins whereMP curve cuts the OW-axis at point F and goes downward.Here MP
is negative, TP starts diminishing and AP continues to diminish but must always be greater than
zero.