Methods of Constructing Index Numbers

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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:

Commodities Prices in 2010 
(in ₹) Base 
year) p0
Prices in 2015
(in ₹) (Current 
year) p1
A 20 30
B 60 80
100 130
D 40 60
Total Σp0 = 220 Σp1 = 300

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
Σq= sum total of the quantities of the base year

Commodities Qty in 2000
(Base year) q0
Qty in 2001
 (Current year) q1
A 30 45
B 55 70
90 105
D 35 60
Total Σq0 = 210 Σq1 = 280

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.

Commodities Base year p0 Base year q0 Base year
p0q0
Current year p1 Current year q1 Current year p1q1
P 5 4 20 20 10 200
Q 10 3 30 30 8 240
R 15 2 30 40 6 240
S 20 1 20 50 4 200
Total Σp0q0 = 100 Σp1q1 = 880

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

Notes

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`

Commodities Base year p0 Base year q0 Current year p1 Current year q1
A 20 4 30 6
B 10 5 20 8
C 40 8 60 5
D 30 4 40 4

 

Commodities Base
year p0
Base
year q0
Current
year p1
Current
year q1
p1q0 p0q0
A 20 4 30 6 120 80
B 10 5 20 8 100 50
C 40 8 60 5 480 320
D 30 4 40 4 160 120
Total         860 570

`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 Σp0q1.
5) Apply the given formula :
`P_(01)=(Σp_1q_1)/(Σp_0q_1) xx 100`

Commodities Base year p0 Base year q0 Current year p1 Current year q1
M 2 10 5 8
N 4 5 8 3
O 1 7 2 10
P 5 8 10 5

 

Commodities Base
year p0
Base
year q0
Current
year p1
Current
year q1
p1q1 p0q1
M 2 10 5 8 40 16
N 4 5 8 3 24 12
O 1 7 2 10 20 10
P 5 8 10 5 50 25
Total         134 63

`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

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