A weighted price index number measures the change in the prices of a group of commodities when we also take the relative importance of the commodities ( weight) into account. We generally divide weighted indices into two categories;

1) weighted aggregative indices, and
2) weighted average of relatives indices.

1. Weighted Aggregation Price Index Numbers

We construct a weighted aggregative index for an aggregate of items (prices) that have been weighted in some way (by corresponding quantities produced, consumed, or sold) to reflect their importance. There are various kinds of weighted aggregative index numbers. We have discussed some of them 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 we only need to update the information on the latest prices.

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:

We calculate Marshall-Edgeworth by taking an average of the respective quantities in the base period and the given period. Consequently, we get a compromise solution, although it is the index that 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

We computer this index 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.

Below we discuss some important types of the weighted average of relative price indices:

a) Laspeyres:

Here the price relatives are weighted by the total value of commodities in the base year. Laspeyres is equivalent to the Laspeyres weighted aggregative price index. In other words, these methods are alternative ways of getting the same result.

b) Paasche:

Here the price relatives are weighted by the total value of commodities in the given year at base-year prices. Paasche is also identical to Passche’s weighted aggregative price index.

c) Palgrave:

In Palgrave, the price relatives are weighted by the total value of commodities in the given year.

In all these index numbers, we get the computational labor reduced if the weights are equal to total unity. The advantage of the weighted price index is that it indicates how many points a commodity is contributing to the index each year.