Methods of Constructing Index Numbers

Methods of Constructing Index Numbers :
a) Simple Index Number
b) Weighted Index Number
The following chart explains the methods of constructing index numbers :

A) Simple Index Number :
In this method, every commodity is given equal importance. It is the easiest method of constructing index numbers. This method can be applied to determine.
1) Price Index Number
2) Quantity Index Number
3) Value Index Number

`P_(01)=(∑p_1)/(∑p_0)xx100`
where,
Σp₁ = sum total of the prices of the current year
 Σp₀  = sum total of the prices of the base year
Steps :
1) Add the prices of the different commodities of the base year to derive Σp₀
2) Add the prices of the different commodities of the current year to derive Σp₁
3) Apply the formula :
Price Index Number `P_(01)=(∑p_1)/(∑p_0)xx100`
Example:

Price Index Number `P_(01)=(∑p_1)/(∑p_0)xx100`

`P_(01)= 300/220 xx 100 = 136.36`
_P01 = 136.36

2) Quantity index number : 
Steps :
1) Add the quantities of the different commodities of the base year to derive Σq₀
2) Add the quantities of the different commodities of the current year to derive Σq₁
3) Apply the formula :

Quantity Index Number `Q_(01)=(∑q_1)/(∑q_0)xx100`
where,
Σq₁ = sum total of the quantities of the current year
Σq₀ = sum total of the quantities of the base year

Quantity Index Number `Q_(01)=(∑q_1)/(∑q_0)xx100`
`Q_(01)= 280/210 xx 100 = 133.33`
Q₀₁ = 133.33

3) Value Index Number :
Steps :
1) Find the product of prices and their respective quantities of the different commodities for the base year to derive p0 q0. Take the sum total of the products to derive Σp₀q₀.
2) Find the product of prices and their respective quantities of the different commodities for the current year to derive p1q1. Take sum total of the products to derive Σp₁q₁.
3) Apply the formula :
Value Index Number `V_(01)= (∑p_1q_1)/(∑p_0q_0)xx 100`
where,
Σp₁q₁ = sum total of the product of the prices and quantities of the current year.
Σp₀q₀ = sum total of the product of the prices and quantities of the base year.

Value Index Number `V_(01)= (∑p_1q_1)/(∑p_0q_0)xx 100`
`V_(01)= 880/100 xx 100 = 880`
V₀₁=  880

B) Weighted Index Number :
In this method, suitable weights are assigned to various commodities. It gives relative importance to the commodity in the group. In most of the cases ‘quantities’ are used as weights. There are various methods of constructing weighted index number such as Laaspeyre’s Price Index, Paasche’s Price Index etc.
1) Laaspeyre’s Price Index Number:
In his technique, ‘base year’ quantities are considered as weights. 
Steps :
1) Find out the product p₁q₀ of the different commodities.
2) Find out the product p₀q₀ of the different commodities. 
3) Add all the products p₁q₀  obtained to derive Σp₁q₀. 
4) Add all the products p₀q₀ obtained to derive Σp₀q₀. 
5) Apply the given formula :
`P_(01)=(Σp_1q_0)/(Σp_0q_0) xx 100`

`P_(01)=(Σp_1q_0)/(Σp_0q_0) xx 100`
`P_(01)= 860/570 xx 100 = 150.87`
Thus, Laaspeyre’s index P₀₁ = 150.87

2) Paasche’s Price Index Number :
In this technique, quantities of the ‘current year’ are considered as weights.
Steps :
1) Find out the product p₁q₁ of the different commodities.
2) Find out the product p₀q₁ of the different commodities. 
3) Add all the products p1q1 obtained to derive Σp₁q₁. 
4) Add all the products p0q1 obtained to derive Σp₀q_1.
5) Apply the given formula :
`P_(01)=(Σp_1q_1)/(Σp_0q_1) xx 100`

`P_(01)=(Σp_1q_1)/(Σp_0q_1) xx 100`

`P_(01)= 134/63 xx 100 = 212.69`
Thus, Paasche’s index P₀₁ = 212.69