Page 220 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 10: Index Number

Further, it can be shown that an arithmetic average type of index number can be converted into Notes
an aggregative type by a suitable selection of weights.

p
w
1
p
Consider P 0 100
01
w
Let w = p q , then the above equation can be written as
0 1
p
1
p q
p 0 1 p q Pa
1 1
P 0 100 100 P
01 01
p q p q
0 1 0 1
From the practical point of view, the weighted aggregative methods are preferred to weighted
average of price relatives because the former are easy to compute and have simple interpretation.
However, the weighted average of price relatives may be useful when we are interested in
knowing the extent of homogeneity in price movements of a certain sub-group or the whole
group of commodities. Further, to determine the relative importance of an item, it is necessary
to write the index number formula in weighted average of price relative form.

p p q
La
P 1 0 0 100
From equation (1), we can write 01
p p q
0 0 0
p q p q
w 0 0 0 0
Let then Sw = 1. Thus, for an item gives its relative importance (or
p q p q
0 0 0 0
weight) in the group.
10.9.1 Change in the Cost of Living due to Change in Price of an Item

Let q , q , ...... q be the fixed quantities of the n commodities consumed by a group of consumers
1 2 n
irrespective of price changes; and p , p , ...... p and p , p , ...... p be their prices in base and
01 02 0n 11 12 1n
current years respectively. Their cost of living index, measured by the change in expenditure of
p q
1i i
P 100
purchasing a given bundle of commodities, can be written as 01
p q
0i i
th
Let the price of i commodity changes by 100a%. Thus, the new price, denoted as p' , can be
01
written as (1 + a)p and the changed index number would be
1i
p q p q p q
1i i
1i i
' P 01 100 P 01 1i i 100
p q p q
0i i
0i i
Hence, the absolute change in the cost of living is given by
p q
' P P 1i i 100
01 01 and the proportionate change is given by
p q
0i i
' P P p q p q 1 p q
0i i
01 01 1i i 100 1i i
P 01 p q p q 100 p q
1i i
0i i
1i i
LOVELY PROFESSIONAL UNIVERSITY 215