# Weighted Index Numbers

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

Laspeyre’s Index Number:

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

Fisher’s Ideal Index Number:

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 is proposed by two English economists Marshal and Edgeworth.

Example:

Compute the weighted aggregative price index numbers for $1981$ with $1980$as 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