The 1995/1996 Household Income, Expenditure - (PDF, 101 mb ...

(CPI).2
(1 )
V.S
The current price is multiplied by fixed quantities and divided by the
previous price multiplied by the same fixed quantities.
The Laspeyres price index is only an approximation to the true cost of
living because it assumes that quantities are fixed from time period to time
period. In the real world, consumers respond to changes in relative prices by
substituting away from more expensive goods, depending on the consumer's
opportunity to substitute, the nature of the good whose price has changed,
and other things. Most of the problems of measuring price changes can be
traced to the need to assume that consumer behavior is constant over time
when it really is not. Relative prices change, and a single consumption basket
is a rather restrictive interpretation for a constant living standard. In the
case of the Laspeyres, since base period prices do not change, the same living
standard can be secured along the same proportional budget - the Laspeyres
index is an upward bound on the true cost of living. Another index, the
Paasche, allows quantities to change with prices each period. The Paaschj
estimator produces an index which is a lower bound on the cost of living.
(2 )
There is no such thing as the price index because the true cost of
living depends on reference utilities which are different for different
households and conrtantly changing. Because cost functions vary with utility
in nearly all cases, if expenditure levels are different then price changes will
2 One thing to note from the outset is that in CAP MAS official
publications, the index is somewhat confusing if the full index is being
represented. The numerator should be the sum of all shares times the price
relatives of all shares. The denominator should be the weight of all items in
the fixed basket. Further (see below), instead of averaging the price
relatives, a less biased estimator would be a sum of all prices in the
numerator divided simply by the sum of previous prices in the denominator.
3 It is actually possible for the Paasche Index to exceed the Laspeyres.
See Deaton and Muellbauer (1989), p. 172.
4 The exception occurs under conditions of homothetic preferences
(identical indifference curves) and an invariant utility/consumption
relationship. In this case, there is a true cost of living index, and it lies
between the Paasche and the Laspeyres.