A weighted aggregate price index

The philosophy behind the weighted aggregate index is that each item in the group should be weighted according to its importance. In most cases the quantity of usage provides the best measure of importance.

Suppose that we have a group of K items. Let

be the quantity of item in the base period;

be the price of item in the base period;

be the price of item in the period of t

The Laspeyres price index for the period t is given by

Example:

The company sells beer, wine, and soft drinks. Prices and quantity are shown below

Quantity Unit price ($)

Item (bottles) 2000 2004

Beer 35 000 5.1 5.7

Wine 5 000 35.0 37.0

Soft drink 50 000 2.80 3.5

Compute a weighted aggregate price index for the company sales in 2004, with 2000 as the base period.

Solution:

From the information

; ;

; ;

; ;

It means in year 2004, at the prices prevailing, the total income of company from sales in the base period would have been increased by 13.37%.

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