by Simple Aggregative Method is the most basic way to construct an index number. It is calculated by taking the total of current year prices of selected commodities and dividing it by the total of base year prices, then multiplying by 100.
Formula:
Index Number (P) = (∑P1 / ∑P0) × 100
Where:
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P1 = Price of the commodity in the current year
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P0 = Price of the commodity in the base year
Features:
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No weights are assigned to commodities.
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Assumes equal importance for all items.
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Easy to calculate.
Limitations:
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It does not consider the relative importance of different commodities.
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Heavily priced items can dominate the index and distort the results.
Weighted Index Number Method
Weighted Index Number Method overcomes the limitations of the simple method by assigning weights to each commodity according to its importance (e.g., consumption level or expenditure share).
Types:
(a) Weighted Aggregative Method
This method uses weights to multiply the price of each item. Common formulas include:
i. Laspeyres’ Price Index
Uses base year quantities as weights.
Formula:
PL = (∑(P1×Q0) / ∑(P0×Q0)) × 100
ii. Paasche’s Price Index
Uses current year quantities as weights.
Formula:
Pp = (∑(P1×Q1) / ∑(P0×Q1)) × 100
iii. Fisher’s Ideal Index
Geometric mean of Laspeyres and Paasche indices.
Formula:
PF = √(PL × PP)
(b) Weighted Average of Price Relatives Method
In this method, we first compute the price relatives and then find their weighted average.
Formula:
Price Relative (R) = (P1 / P0 × 100)
Then,
Index = ∑(R×W) / ∑W
Where:
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R = Price relative
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W = Weight assigned to each commodity
Advantages of Weighted Method:
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More accurate and realistic.
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Reflects the actual importance of each commodity.
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Suitable for both price and quantity index numbers.
