The Consumer Price Index (Cost of Living Index) — Meaning and Construction

The Consumer Price Index (CPI), also called the Cost of Living Index Number, measures the average change in the retail prices of a FIXED basket of goods and services actually consumed by a specific class of consumers (industrial workers, agricultural labourers, urban non-manual employees) over time. Unlike a general wholesale price index, a CPI is always defined for a PARTICULAR group of consumers, because different groups spend very differently across categories such as food, clothing, fuel, rent and miscellaneous items.

Steps in constructing a CPI.

1. Conduct a family budget enquiry to find out how a representative family of the target group actually spends its income — this yields the WEIGHT for each broad group (food, clothing, fuel & lighting, house rent, miscellaneous).
2. Collect retail PRICES of representative items within each group, for both the base year and the current year.
3. Compute the price relative of each group (or item), $(p_1/p_0)\times100$.
4. Combine the group-wise price relatives with their weights using one of the two methods below.

1. Aggregate Expenditure Method. Treat the whole family's base-year basket exactly like a Laspeyres price index — price the SAME base-year quantities at both years' prices:

   $CPI = \frac{\sum p_1q_0}{\sum p_0q_0}\times 100$

2. Family Budget Method. Work at the level of broad GROUPS rather than individual items — take each group's price relative $P=(p_1/p_0)\times100$ and its expenditure weight $W$ (the base-year value of that group's consumption, or its percentage share of the family budget), then:

   $CPI = \frac{\sum (P\times W)}{\sum W}$

   A genuinely useful fact, verified numerically in Example 9 below: when the SAME underlying data is used consistently — group weights equal to base-year group EXPENDITURE — the Family Budget Method and the Aggregate Expenditure Method give the IDENTICAL CPI figure, because they are algebraically the same computation done at two different levels of grouping (this is the same identity already noted in Section 4 between the weighted average of price relatives and the Laspeyres index). …