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:
Price Relative=P0P1×100
where P1 is the price in the current year and P0 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:
I=∑W∑(W×P0P1×100)
where:
- I = index number for the current year
- W = weight assigned to each commodity
- P1 = current year price
- P0 = base year price
- ∑ = sum over all commodities
I=∑W∑W⋅P0P1×100
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.
| Commodity | Base Price (P0) | Current Price (P1) | Price Relative (P0P1×100) | Weight (W) – base expenditure | W× Price Relative |
|---|
| Wheat | ₹10/kg | ₹15/kg | 150 | ₹200 | 30,000 |
| Oil | ₹100/litre | ₹200/litre | 200 | ₹100 | 20,000 |
| Total | | | | ₹300 | 50,000 |
The weighted price relative index is:
I=30050,000=166.67
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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