7.6 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICSIndex Numbers
Table : Construction of Price Index
Commodities P 0 P 1
Potato (per Kg) 12 20
Wheat (per Kg) 20 25
Bread 10 13
Cheese (per Kg) 80 100
Σp 0 = 122 Σp 1 = 158= Σ ×
Σ
= ×
=01 1
001P 100
(^158100)
122
P 129
p
p
The net increase in price now is only 29%.
(2) The relative importance of various commodities is not taken into account in as it is unweighted. Thus
according to this method equal weights (importance) would be attached to wheat and salt in
computing a cost of living index.
(3) This method is influenced by the magnitude of prices i.e. the higher the price of the commodity, the
greater is the influence on the Index number. Such price quotations become the concealed weights
which have no logical significance.
7.3.2 Weighted Aggregate Method
In this method, appropriate weights are assigned to various commodities to reflect their relative importance
in group. For the construction of price index number, quantity, weights are used i.e. amount of quantity
consumed, purchased or marketed.
By using different systems of weighting we get a number of formulae which are as follows—
Laspeyres’ Price Index
In this method the base year quantities are taken as weights. Symbolically—
= Σ ×
Σ
01 1 0
0 0
P pqp q 100
The main advantage of this method is that it uses only base year quantity; therefore there is no need to
keep record of quantity consumed in each year.
Disadvantage
It is a common knowledge that the consumption of commodity decreases with relative large increase in
price and vice versa. Since in this method base year quantity is taken as weights, it does not take into
account the change in consumption due to increase or decrease in prices and hence may give a biased
result.
Paasche’s Method
In this method current year quantities are taken as weights. Symbolically—