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Economics · Ch 7 — Index Numbers

The Aggregative Method

7.3.1

The Aggregative Method

Simple (unweighted) aggregative index. Add up the current-period prices, divide by the sum of base-period prices, and multiply by 100:

P01=ΣP1ΣP0×100P_{01} = \frac{\Sigma P_1}{\Sigma P_0} \times 100

where P1P_1 and P0P_0 are current- and base-period prices. For the four commodities:

P01=4+6+5+32+5+4+2×100=1813×100=138.5P_{01} = \frac{4+6+5+3}{2+5+4+2} \times 100 = \frac{18}{13} \times 100 = 138.5

so prices have risen by 38.5 per cent. This index is of limited use: the price units of different commodities are not the same, and being unweighted it treats all items as equally important. In reality items differ in importance — food takes a large share of spending — so an equal price rise in a heavily-consumed item and a minor one affect the overall index very differently.

Weighted aggregative index. Weights (here quantity weights) fix a well-specified basket of goods and value it each year; because the basket is fixed, any change in total value is due to price:

P01=ΣP1q0ΣP0q0×100P_{01} = \frac{\Sigma P_1 q_0}{\Sigma P_0 q_0} \times 100

Money is same but basket is getting smaller!!! A person points at a rising price graph beside a row of shopping baskets drawn progressively smaller left to right — illustrating why a fixed-basket weighted price index matters: as prices rise, the same money buys less and less of the same basket of goods.
Money is same but basket is getting smaller!!! A person points at a rising price graph beside a row of shopping baskets drawn progressively smaller left to right — illustrating why a fixed-basket weighted price index matters: as prices rise, the same money buys less and less of the same basket of goods.

Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your textbook's own diagram.

Our own line-art recreation of the NCERT cartoon printed on page 110, right where the weighted aggregative index (Laspeyre's and Paasche's methods) is introduced. It illustrates the real-world effect a weighted aggregative price index is meant to capture — the same money buying a shrinking basket as prices rise. The scene and caption are taken from the textbook as facts; …

  • Laspeyre's index uses base-period quantities q0q_0 as weights. With the sample data 257190×100=135.3\frac{257}{190}\times100 = 135.3 — a 35.3 per cent rise. It answers: if base-period spending on the basket was Rs 100, what would the same basket cost now?

P01=ΣP1q0ΣP0q0×100=257190×100=135.3P_{01} = \frac{\Sigma P_1 q_0}{\Sigma P_0 q_0}\times100 = \frac{257}{190}\times100 = 135.3

  • Paasche's index uses current-period quantities q1q_1 as weights: …
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