Explain the various methods of constructing Index Numbers?
Ans.: Various methods of calculating index numbers can be shown by the following chart –
|
Index Numbers (P01) |
|||||
|
Unweighted |
|
|
Weighted |
||
|
Simple Aggregative |
Simple Average of Relatives |
|
Weighted Aggregative |
Weighted Average of Relatives |
|
|
Laspeyse’s Method |
Paasche’s Method |
Dorbish & Bowley’s Method |
Fishers Ideal Method |
Marshall Edgeworth Method |
Kelly’s Method |
(I) Unweighted Index Numbers :
- Simple Aggregative Method :
P01 = ∑P1 X 100
∑P0
Where –
|
P01 |
= |
∑R |
and |
R |
= |
P1 |
X 100 |
|
|
|
N |
|
|
|
P0 |
|
|
|
∑P0 q0 |
||
|
|
Where – |
|
|
|
|
P1 |
à |
Price of current year. |
|
|
P0 |
à |
Price of base year. |
|
(ii) |
q0 Paasche’s |
à Method : |
Quantity of base year |
|
|
P01 |
= |
∑P1 q1 X 100 |
|
|
|
|
∑P0 q1 |
Where –
q1 à Quantity of current year.
(i) Dorbish & Bowley’s Method :
P01 = Laspeyre‘s Index + Paasche‘s Index
2
or P01 = ∑P1 q0 + ∑P1 q1
∑P0 q0 ∑P0 q1 X 100
2
(ii) Marshall - Edgeworth’s Method :
P01 = ∑P1 q0 + ∑P1 q1
∑P0 q0 + ∑P0 q1 X 100 2
(iii) Fisher’s Ideal Method :
P01 = ∑P1 q0 X ∑P1 q1 X 100 or L X P
∑P0 q0 ∑P0 q1
(iv) Kelly’s Method :
P01 = ∑P1 q X 100
∑P0 q
Where – q = q0 + q1
2
- Weighted Average of Relatives : In this method, the price relatives for each commodity are obtained and these price relatives are multiplied by the value weights for each item and the product is divided by the total of
Consumer price index = ΣRW
ΣW
Where R = P1 X 100 and W = P0 q0
P0
Q.2 Fisher’s Formula is called the Ideal Formula. Why?
Ans.: Fisher‘s formula is called the ideal because of the following reasons:
- It is based on geometric mean which is considered best for constructing index
- It fulfills both the time reversal and factor reversal
- It takes into account both current year as well as base year prices and
- It is free from bias.
