Price Index Weighting: Why Not All Price Changes Are Equal
Imagine you're tracking your monthly spending. The price of salt doubles one month — you barely notice, because salt is cheap and you buy very little. But the price of petrol goes up by just 10% — and suddenly your whole budget feels tight. That difference is the entire point of weighting in a price index.
A price index is not a simple average of all price changes. If it were, a 50% rise in the price of matchboxes would matter as much as a 50% rise in the price of rice. That would be absurd, because households spend far more on rice than on matchboxes. Weighting fixes this: it gives each item a relative importance that reflects its share in total expenditure.
The Precise Meaning
A price index measures the average change in prices over time. But "average" here is a weighted average, not a simple one. The weight of each commodity is its share in total consumption expenditure in a chosen base year.
The most common formula is the Laspeyres Price Index, which uses base-year quantities as weights:
PL=∑(p0×q0)∑(pt×q0)×100
Where:
- pt = price of a commodity in the current year
- p0 = price of that commodity in the base year
- q0 = quantity of that commodity consumed in the base year
- ∑ means "sum over all commodities"
The numerator ∑(pt×q0) is the total cost of buying the base-year basket at current-year prices. The denominator ∑(p0×q0) is the cost of that same basket in the base year. The ratio, multiplied by 100, tells you by what percentage the cost of living has changed — assuming you keep buying exactly what you bought in the base year.
Price Index=Cost of base-year basket at base pricesCost of base-year basket at current prices×100
The weight of each commodity is effectively p0q0 — its expenditure share in the base year. A commodity on which people spend a larger share of their income gets a larger weight.
Why Weighting Matters
Without weighting, a price index would be misleading. Consider a simple example with two goods:
| Good | Base Price | Current Price | Base Quantity |
|---|
| Rice | ₹20/kg | ₹25/kg | 10 kg |
| Salt | ₹5/kg | ₹15/kg | 0.5 kg |
The simple (unweighted) average of price changes: rice rose 25%, salt rose 200%. Average = 112.5% — implying prices rose 12.5%. But that's nonsense, because you spend ₹200 on rice and only ₹2.50 on salt.
The weighted index:
- Base-year basket cost = (20×10)+(5×0.5)=200+2.5=202.5
- Current-year basket cost = (25×10)+(15×0.5)=250+7.5=257.5
- Index = (257.5/202.5)×100≈127.2
This tells you the cost of living has risen by about 27% — far more than the unweighted average suggested. The salt price spike barely registers because its weight is tiny. …