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Quantitative Techniques – I
Notes p q
1i i
th
We note that p q is the proportion of expenditure on the i commodity before the change
1i i
of price.
Alternatively, the above equation can be written as:
Proportionate Change in Proportion of expenditure Proportionate Change in
price of the commodity on the commodity the cost of living
It may be pointed out here that the above result assumes that the consumption of the commodity
remains unchanged as a result of change in its price.
Consumer price index number was formerly known as cost of living index.
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Self Assessment
Fill in the blanks:
15. Weighted aggregative and weighted arithmetic average of price relatives, are ...................
16. One type of index number can be obtained from the other by .......................... of weights.
17. The weighted aggregative index numbers are ....................... to calculate and have
.............................. interpretation.
10.10 Chain Base Index Numbers
So far, we have considered index numbers where comparisons of various periods were done
with reference to a particular period, termed as base period. Such type of index number series is
known as fixed base series. There are several examples of fixed base series like the series of
index numbers of industrial production, of agricultural production, of wholesale prices, etc. The
main problem with a fixed base series arises when the base year becomes too distant from the
current year. In such a situation, it may happen that commodities which used to be very important
in the base year are no longer so in current year. Furthermore, certain new commodities might
be in use while some old commodities are dropped in current year. In short, this implies that the
relative importance of various items is likely to change and, therefore, the comparison of a
particular year with a remote base year may appear to be meaningless. A way out to this
problem is to construct Chain Base Index Numbers, where current year is compared with its
preceding year.
Similar to price relatives, here we define link relatives. A link relative of a commodity in a
particular year is equal to the ratio of this year’s price to last year’s price multiplied by hundred.
p
Using symbols, the link relative of i th commodity in period t is written as L ti 100 .
ti
p
t 1i
When there are n commodities, the chain base index for period t is given by a suitable average
of their link relatives. For example, taking simple arithmetic mean of link relatives we can write
p t
L t 100
the chain base index as P CB 100 p t 1 .... (1)
t
n n
We may note here that a chain base index is equal to link relative of a commodity when there is
only one commodity.
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