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.

**Law of
Variable Proportions**

The law
states that if all other factors are fixed and one input is varied in the short
run, the total output will increase at an increasing rate at first instance, be
constant at a point and then eventually decrease. Marginal product will become
negative at last.

According
to G.Stigler, *“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”.*

The Law
of Variable Proportions is based on the following assumptions.

·
Only one factor is variable while others are held
constant.

·
All units of the variable factor are homogeneous.

·
The product is measured in physical units.

·
There is no change in the state of technology.

·
There is no change in the price of the product.

It refers
to the total amount of commodity produced by the combination of all inputs in a
given period of time.

**„**Summation
of marginal products, i.e.

**TP = ∑MP**

where,
TP= Total Product, MP= Marginal Product

It is the
result of the total product divided by the total units of the input employed.
In other words, it refers to the output per unit of the input.

Mathematically,
*AP
= TP/N*

Where,

AP=
Average Product

TP= Total
Product

N= Total
units of inputs employed

It is the
addition or the increment made to the total product when one more unit of the
variable input is employed. In other words, it is the ratio of the change in
the total product to the change in the units of the input. It is expressed as

*MP= **∆**TP/**∆** N*

where,

MP =
Marginal Product

ΔTP =
Change in total product

ΔN =
Change in units of input It

is also
expressed as

*MP = TP
(n) – TP (n-1)*

Where,

MP =
Marginal Product

TP(n) =
Total product of employing nth unit of a factor

TP(n-1) =
Total product of employing the previous unit of a factor, that is, (n-1)th unit
of a factor.

The Law
of Variable Proportions is explained with the help of the following schedule
and diagram:

In table
3.1, units of variable factor (labour) are employed along with other fixed
factors of production.

The table illustrates that there are three
stages of production. Though total product increases steadily at first instant,
constant at the maximum point and then diminishes, it is always positive for
ever. While total product increases, marginal product increases up to a point
and then decreases. Total product increases up to the point where the marginal
product is zero. When total product tends to diminish marginal product becomes
negative.

In
diagram 3.1, the number of workers is measured on X axis while TP_{L},
AP_{L} and MPL are denoted on Y axis. The diagram explains the three
stages of production as given in the above table.

In the
first stage MPL increases up to third labourer and it is higher than the
average product, so that total product is increasing at an increasing rate. The
tendency of total product to increase at an increasing rate stops at the point
A and it begins to increase at a decreasing rate. This point is known as ** ‘Point
of Inflexion’**.

In the
second stage, MPL decreases up to sixth unit of labour where MPL curve
intersects the X-axis. At fourth unit of labor MP_{L} = AP_{L}.
After this, MP_{L} curve is lower than the AP_{L}. TP_{L}
increases at a decreasing rate.

Third
stage of production shows that the sixth unit of labour is marked by negative
MP_{L}, the AP_{L} continues to fall but remains positive.
After the sixth unit, TP_{L} declines with the employment of more units
of variable factor, labour.

Tags : Production Analysis | Economics , 11th Economics : Chapter 3 : Production Analysis

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11th Economics : Chapter 3 : Production Analysis : Law of Variable Proportions | Production Analysis | Economics

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