Q.Which of the following price index depends on base period quantity ?

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:

Where:

• $p_t$ = price of a commodity in the current year
• $p_0$ = price of that commodity in the base year
• $q_0$ = quantity of that commodity consumed in the base year
• $\sum$ means "sum over all commodities"

The numerator $\sum (p_t \times q_0)$ is the total cost of buying the base-year basket at current-year prices. The denominator $\sum (p_0 \times q_0)$ 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.

The weight of each commodity is effectively $p_0 q_0$ — 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:

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 = $(20 \times 10) + (5 \times 0.5) = 200 + 2.5 = 202.5$
• Current-year basket cost = $(25 \times 10) + (15 \times 0.5) = 250 + 7.5 = 257.5$
• Index = $(257.5 / 202.5) \times 100 \approx 127.2$

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. …