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Mathematics and Statistics · Ch 13 — Index Numbers

Simple (Unweighted) Aggregate Method

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Simple (Unweighted) Aggregate Method

The most direct way to build a price index for a group of commodities is the simple aggregate method. We total the current-year prices of all commodities, total their base-year prices, and express the first total as a percentage of the second:

P01=∑p1∑p0×100,P_{01} = \frac{\sum p_1}{\sum p_0} \times 100,

where P01P_{01} is the price index of the current year (11) with respect to the base year (00), ∑p1\sum p_1 is the sum of current-year prices and ∑p0\sum p_0 the sum of base-year prices.

Steps: (i) add up all the base-year prices to get ∑p0\sum p_0; (ii) add up all the current-year prices to get ∑p1\sum p_1; (iii) substitute in the formula.

Watch out

Two serious limitations

The simple aggregate method is easy but crude, because:

  1. It is affected by the units in which prices are quoted — a price 'per quintal' swamps a price 'per kg', so a change in the costly-unit item dominates the index unfairly.
  2. It gives equal importance to every commodity, ignoring how much of each is actually bought. A rise in the price of a rarely-used luxury counts as much as the same rise in a daily staple. …
Definition 1Simple aggregate price index

P01=∑p1∑p0×100P_{01} = \dfrac{\sum p_1}{\sum p_0} \times 100 — the total of current prices expressed as a percentage of the total of base-year prices, giving ev …