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.

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