Q.State the steps involved in constructing a Consumer Price Index, and explain briefly how the Aggregate Expenditure Method differs from the Family Budget Method.

Building a CPI needs a family budget enquiry for weights and price data for relatives; the two construction methods differ in whether they work at the level of individual items or broad groups.

Steps in constructing a CPI:

1. Conduct a family budget enquiry on the target class of consumers to determine how much they spend on each group of items — this fixes the WEIGHTS.
2. Collect retail prices of representative items in each group, for both the base year and the current year.
3. Compute the price relative for each item or group, $(p_1/p_0)\times100$.
4. Combine the relatives and weights using one of the two methods below.

Aggregate Expenditure Method vs Family Budget Method. The Aggregate Expenditure Method works at the level of individual ITEMS, pricing the exact base-year quantity basket at both years' prices — the same structure as the Laspeyres price index: $CPI=(\sum p_1q_0/\sum p_0q_0)\times100$. The Family Budget Method instead works at the level of broad expenditure GROUPS (food, clothing, fuel, rent, miscellaneous), combining each group's own price relative with its expenditure weight: $CPI=\sum(P\times W)/\sum W$. When the weight $W$ used in the Family Budget Method is defined consistently as the base-year expenditure on that group, the two methods give the SAME final CPI figure — they are the identical underlying calculation, only grouped differently (Example 8's identity between the weighted average of price relatives and Laspeyres is the same principle applied here).

Treating the Aggregate Expenditure and Family Budget Methods as giving genuinely DIFFERENT answers on the same data — they differ only in the LEVEL at which the calculation is organised (item-by-item vs group-by-group), not in the underlying formula's logic, so a large discrepancy between the two on the same consistent data signals an arithmetic error, not a real methodological difference.