Cost of Living Index (Family Budget Method)

While the Weighted Aggregate Method weights the AGGREGATE prices, the Cost of Living Index — also called the Family Budget Method — takes a slightly different route: it first converts each commodity's own price change into a percentage (its price relative), and only then combines these percentages using weights.

For a single commodity, the price relative $I$ measures how much its OWN price has moved, expressed as a percentage of its own base-year price:

The weight $W$ used here is the proportion of the household's total budget that was spent on that commodity in the base year — a large weight for necessities like food and housing that take up a big share of family spending, and a small weight for items on which little is spent. The Cost of Living Index then combines every commodity's price relative $I$ with its own budget weight $W$: