A weighted price index number is an index number that measures the change in the prices of a group of commodities when the relative importance of the commodities (i.e. weight) has been taken into account.
Weighted indices are generally divided into 1) Weighted Aggregative Indices and 2) Weighted Average of relatives indices.
1. Weighted Aggregation Price Index Numbers
An index is called a weighted aggregative index when it is constructed for an aggregate of items (prices) that have been weighted in some way (by corresponding quantities produced, consumed or sold) so as to reflect their importance. There are various kinds of weighted aggregative index numbers, some of them are discussed below:
a) Laspeyres Price Index:
The percentage ratio of the aggregate of the given period prices weighted by the quantities produced, consumed or sold in the base period to the aggregate of base period prices weighted by the base period quantities. The index represents the relative cost in different years of purchasing the base year quantities of various commodities at the given year price. The advantage of Laspeyres formula is that the quantity weights remain unchanged for the subsequent periods and only information on latest prices need be obtained.
b) Paasche’s Price Index:
The percentage ratio of the aggregate of given period prices weighed by the quantities produced, consumed or sold in the given period to the aggregate of base period prices weighted by the given period quantities. It represents the relative cost in different years of purchasing the given year quantities of various commodities at the given year price.
c) Marshall-Edgeworth Price Index:
The weights are taken as an average of the respective quantities in the base period and in the given period. This is, so to say, a compromise solution, although it is the index which has no general bias in either direction.
d) Fisher’s “Ideal” Index:
Fisher called it “ideal” index because it meets certain theoretical tests of quality which he considered appropriate for a good index number. It is sometimes known as crossed-weight formula because it is the result of geometrically crossing (averaging) two index numbers with different systems of weighting.
2. Weighted Average of Relatives Price Index Number
It is computed by multiplying each price relative by its weight, summing these products and dividing by the sum of the weights. The weights are always the total values of the commodities. The important types of the weighted average of relative price indices are given below:
Here the price relatives are weighted by the total value of commodities in the base year. This is equivalent to Laspeyres weighted aggregative price index. In other words, these methods are alternative ways of getting the same result.
Here the price relatives are weighted by the total value of commodities in the given year at base year prices. This is also identical with Passche’s weighted aggregative price index.
Here the price relatives are weighted by the total value of commodities in the given year. In all these index numbers, the computational labour is reduced if the weights are made to total unity. The advantages of this procedure is that it indicates how many points each commodity contributed to the index number each year.