Essential definitions

Price relative

A current price divided by its base-period price, multiplied by 100.

Expenditure weight

A product category’s share of total spending in the basket.

Weighted price index

An average of price relatives weighted by expenditure shares.

Give important purchases more weight

A 10% rent increase usually matters more to a household than a 10% pencil-price increase because rent takes more of its budget. An expenditure weight records that spending share. Weights must cover the basket and add to 1 as decimals, or 100 as percentages.

A price relative compares one item's current price with its base price: current price ÷ base price × 100. It has no currency unit. A relative of 120 means the item costs 20% more than in the base. Calculate each relative before combining categories with different prices or units.

Build the index step by step

For decimal weights, weighted CPI = sum of each weight multiplied by its price relative. The symbol Σ, if used, means add the terms. With food weight 0.40 and relative 120, food contributes 48 index points. The worked example adds this to the other categories' contributions.

With percentage weights, divide the sum by 100. With expenditure amounts as weights, divide by total expenditure. Physical quantities alone cannot directly weight price relatives: multiply each period's prices by the fixed quantities to find basket costs instead. Check the form of the supplied data before choosing a method.

Turn the index into an inflation rate

An index of 111.8 means prices are 11.8% above the base. If the previous year's index were 108, annual inflation would be (111.8 − 108) ÷ 108 × 100, about 3.52%. It would not be 11.8%. Index level and rate of change answer different questions.

A large price rise in a low-weight item may contribute little overall, while a modest rise in a high-weight item matters greatly. Fixed weights simplify comparison but may miss substitution and changing spending patterns. Explain whose basket the index represents and how quality changes or new products could affect the estimate.

Apply and evaluate

• Representative weights improve aggregate measurement but do not eliminate differences across households.
• Substitution and quality adjustments complicate a literal fixed-basket interpretation.

Real-world application