Q.In most of the weighted index numbers the weight pertains to

Weighted Price Relative Index – A First Look

Imagine you're tracking how the cost of your monthly shopping basket changes. You buy 10 eggs, 2 litres of milk, and 1 packet of biscuits. If the price of eggs doubles, your total bill goes up a lot. If the price of biscuits doubles, the effect is smaller — because you buy fewer biscuits. A simple average of price changes would treat both items equally, which is misleading. That's where the weighted price relative index comes in.

The Core Idea

A price relative is simply the ratio of the current price of a commodity to its base-year price, usually expressed as a percentage:

where $P_1$ is the price in the current year and $P_0$ is the price in the base year.

Now, to combine price relatives for multiple commodities, we need to give each commodity its proper importance — its weight. The weight reflects how much of that commodity is consumed or how significant it is in the total expenditure.

The weighted price relative index is then:

where:

• $I$ = index number for the current year
• $W$ = weight assigned to each commodity
• $P_1$ = current year price
• $P_0$ = base year price
• $\sum$ = sum over all commodities

This is the weighted arithmetic mean of price relatives.

Why the Weighting Matters

Without weights, a 50% rise in the price of salt (which you buy in tiny quantities) would count the same as a 50% rise in the price of rice (which you buy in bulk). That would give a distorted picture of inflation. Weighting corrects this by ensuring that items with greater economic importance have a proportionally larger influence on the index.

The weights are usually based on expenditure patterns from a base-period survey. For example, in a consumer price index, food might get a weight of 50%, housing 20%, transport 10%, and so on. These weights sum to 100 (or 1, depending on how you set them).

A Concrete Example

Suppose in the base year, a family spends ₹200 on wheat and ₹100 on oil. In the current year, wheat costs 1.5 times its base price, and oil costs 2 times its base price.

The weighted price relative index is:

This means the overall price level has risen by about 66.67% from the base year. Notice that if you had taken a simple average of the price relatives (150 and 200), you'd get 175 — an overestimate, because the simple average ignores that wheat (with a smaller price rise) had twice the weight of oil.

Where You'll See This

This method is the foundation of most official price indices, including the Consumer Price Index (CPI) and the Wholesale Price Index (WPI) in India. The weights are fixed for a period (say, 5–10 years) based on a comprehensive survey of household consumption or wholesale trade. The index then tracks how the cost of a fixed basket changes over time.

A Common Mistake to Avoid

Students often confuse the weight with the price relative. The weight is not the price — it's the importance attached to the commodity, usually based on quantity consumed or expenditure share. The price relative is the pure price change. You multiply them, not add them.

The Big Picture

The weighted price relative index is a tool for measuring the average change in prices while respecting the fact that not all price changes affect us equally. It turns a messy reality — thousands of goods, each with its own price movement — into a single, meaningful number. That number tells you, at a glance, whether your rupee is buying more or less than it used to.