Q.The impact of change in the price of a commodity with little weight in the index will be

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.

The Intuition in One Sentence

Weighting ensures that a price index reflects what actually matters to consumers: a big price rise in a heavily consumed good hurts more than a huge price rise in a trivial one.

A Note on the Diagram

If you draw a bar chart of expenditure shares in the base year — rice taking up a tall bar, salt a tiny one — you can visualise weighting. When prices change, each bar grows or shrinks proportionally to its price change, but the height of the bar (the weight) determines how much that change affects the total. A tall bar growing a little changes the total more than a short bar doubling.

Why This Matters for Exams

In Class 12 Economics, you are expected to:

• Define a price index and explain the need for weighting
• Write the Laspeyres formula and identify each symbol
• Compute a simple weighted price index from given data
• Explain why the Consumer Price Index (CPI) and Wholesale Price Index (WPI) use different baskets and weights — CPI weights household consumption, WPI weights wholesale transactions

The concept of weighting is not just a mathematical trick. It is the bridge between raw price data and a meaningful measure of inflation — one that tells you how much your rupee has actually lost its purchasing power.