Laspeyres Index Formula

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Appendix Price Index Formulas
g698002 - index
Fisher Ideal Index Formula
Appendix IV
Price Index Formulas
The following descriptions are simplified to show how the indexes differ
conceptually. Although the basic concepts presented are accurate, the
actual calculations would be substantially more complex.
An index calculated with a Laspeyres index formula measures price
Laspeyres Index
changes in relation to the base period's market basket and thereby "fixes"
the market basket by holding the items in it constant. It calculates what
that market basket would cost in later periods, even if some of the items
were no longer purchased.
For our hypothetical shopper, the Laspeyres index formula uses what she
purchased in the first week as the base of the calculation--the fixed
market basket. All comparisons are made with respect to the quantities of
items she purchased and the prices she paid for them in the first week.
Since she purchased the same items in the second week, a Laspeyres
index would divide her grocery bill for the second week by the first week's
bill and obtain an index value of 101.0, as shown in table IV.2.
Since the shopper bought blueberries instead of bananas in the third week,
the third week's grocery bill cannot be simply divided by the first week's
bill. An adjustment must be made to reconstruct the first week's fixed
market basket by subtracting the cost of the blueberries and adding the
cost of the bananas as if she had purchased bananas in the third week.
This is done to make the third week's market basket identical to the first
week's market basket. A Laspeyres index value of 103.2 is obtained by
dividing the adjusted third week's grocery bill by the first week's bill.
An index calculated with a Paasche index formula measures price changes
Paasche Index
for a market basket containing what consumers are currently purchasing,
rather than what they purchased in a previous period. This index assumes
that consumers' tastes and preferences change to maintain a constant level
of satisfaction and compares the cost of the consumers' current market
basket with what it would have cost to buy this basket of goods and
services in an earlier period.
As shown in table IV.2 for the hypothetical illustration, the Paasche index
value (101.0) is the same as the value obtained with the Laspeyres index
formula (101.0) in the first 2 weeks because our hypothetical shopper
purchased the same items. However, the difference between the Paasche
and the Laspeyres formulas is evident in the third week when the shopper
Page 53
GAO/GGD/OCE-98-2 Market Basket Expenditure Weights

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