Page 268 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes consumed in the base year and the aggregate expenditure incurred in buying those commodities
is obtained. In a similar manner the prices of the base year are multiplied by the quantities of
the base year and aggregate expenditure for the base period is obtained. The aggregate
expenditure of the current year is divided by the aggregate expenditure of the base year and
the quotient is multiplied by 100. Symbolically,
∑ pq
10
Consumer Price Index = ∑ pq × 100
00
There is in fact the Laspeyre’s method discussed earlier. This method is the most popular method
for consumer price index.
2. Family Budget Method: When this method is applied the family budgets of a large number of
people for whom the index is meant are carefully studied and the aggregate expenditure of an
average family on various items is estimated. These constitute the weights. The weights are
thus the value weights obtained by multiplying the prices by quantities consumed (i.e., p q ).
0 0
The price relatives for each commodity are obtained and these price relatives are multiplied by
the value weight for each item and the product is divided by the sum of the weight. Symbolically,
∑ PV
Consumer Price Index =
∑ V
p 1
where, P = × 100 for each item
p 0
V = Value weights, i.e., p q .
0 0
This method is the same as the weighted average of price relative method discussed earlier.
It should be noted that the answer obtained by applying the aggregate expenditure method
and the family budget method shall be the same.
Example 1: Construct the consumer price index number of 2005 on the basis from the following
data using (i) the average expenditure method, and (ii) the family budget method:

Commodity Quantity Unit Price in 2004 Price in 2005
consumed Rs. Paise Rs. Paise
in 2004

A 6 Quintal Quintal 5 75 6 0
B 6 " " 5 0 8 0
C 1 " " 6 0 9 0
D 6 " " 8 0 10 0
E 4 Kg. Kg. 2 0 1 50
F 1 Quintal Quintal 20 0 15 0

Solution:
Computation of Consumer Price Index Number for 2005
(Base 2004 = 100) By the Aggregate Expenditure Method

Commodities Quantities Unit Price in Price in p q p q
1 0 0 0
consumed 2004 2005
q p p
0 0 1
A 6 Qtl. Qtl. 5.75 6.00 36.00 34.50
B 6 " " 5.00 8.00 48.00 30.00

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