# Weighted Index Numbers

When all commodities are not of equal importance, we assign weight to each commodity relative to its importance and the index number computed from these weights is called a weighted index number.

Laspeyre’s Index Number

In this index number the base year quantities are used as weights, so it also called the base year weighted index.

Paasche’s Index Number

In this index number the current (given) year quantities are used as weights, so it is also called the current year weighted index.

Fisher’s Ideal Index Number

The geometric mean of Laspeyre’s and Paasche’s index numbers is known as Fisher’s ideal index number. It is called ideal because it satisfies the time reversal and factor reversal test.

Marshal-Edgeworth Index Number

In this index number the average of the base year and current year quantities are used as weights. This index number was proposed by two English economists, Marshal and Edgeworth.

Example:

Compute the weighted aggregative price index numbers for $1981$ with $1980$ as the base year using (1) Laspeyre’s Index Number (2) Paashe’s Index Number (3) Fisher’s Ideal Index Number (4) Marshal-Edgeworth Index Number.

 Commodity Prices Quantities $1980$ $1981$ $1980$ $1981$ $A$ $10$ $12$ $20$ $22$ $B$ $8$ $8$ $16$ $18$ $C$ $5$ $6$ $10$ $11$ $D$ $4$ $4$ $7$ $8$

Solution:

 Commodity Prices Quantity ${P_1}{q_o}$ ${P_o}{q_o}$ ${P_1}{q_1}$ ${P_o}{q_1}$ $1980$ $1981$ $1980$ $1981$ ${P_o}$ ${P_1}$ ${q_o}$ ${q_1}$ $A$ $10$ $12$ $20$ $22$ $240$ $200$ $264$ $220$ $B$ $8$ $8$ $16$ $18$ $128$ $128$ $144$ $144$ $C$ $5$ $6$ $10$ $11$ $60$ $50$ $66$ $55$ $D$ $4$ $4$ $7$ $8$ $28$ $28$ $32$ $32$ $\begin{gathered} \sum {P_1}{q_o} \\ = 456 \\ \end{gathered}$ $\begin{gathered} \sum {P_o}{q_o} \\ = 406 \\ \end{gathered}$ $\begin{gathered} \sum {P_1}{q_1} \\ = 506 \\ \end{gathered}$ $\begin{gathered} \sum {P_o}{q_1} \\ = 451 \\ \end{gathered}$

Laspeyre’s Index Number

Paashe’s Index Number

Fisher’s Ideal Index Number

Marshal-Edgeworth Index Number