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”.**

**Assumptions:**

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.

**Total Product (TP)**

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

**Average Product (AP)**

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

**Marginal Product (MP)**

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=ΔTP/ΔN

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

TPL, APL and MPL are denoted on

Y axis. The diagram explains the three

stages of production as given in the above

table.

**Stage I**

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’.

**Stage II**

In the second stage, MPL decreases up

to sixth unit of labour where MPL curve

intersects the X-axis. At fourth unit of

labor MPL = APL. After this, MPL curve

is lower than the APL. TPL increases at a

decreasing rate.

**Stage III**

Third stage of production shows that the sixth unit of labour is marked by negative

MPL, the APL continues to fall but remains

positive. After the sixth unit, TPL declines

with the employment of more units of

variable factor, labour.