Cost of Living Index Number

A cost of living index number (CLI), also called a consumer price index, measures the change in the general level of prices of the goods and services a particular class of people (e.g. industrial workers, middle-class families) buy, between the base year and the current year. It shows how much more (or less) a family must spend to keep the same standard of living. Commodities are grouped into heads such as food, clothing, fuel and lighting, house rent, and miscellaneous. There are two standard methods, and they always give the same answer.

Method 1 — Aggregate Expenditure Method. Weight each price by the base-year quantity $q_0$ (i.e. value the base-year basket at both years' prices):

This is algebraically identical to Laspeyre's index — the cost of the base-year basket now, as a percentage of its cost then.

Method 2 — Family Budget Method (weighted price-relatives). For each commodity compute its price relative $I = \dfrac{p_1}{p_0} \times 100$, take the value weight $W = p_0 q_0$ (base-year expenditure on that item), and form the weighted average of the price relatives:

Uses of the cost of living index. …