Weighted index of price relatives

Indian Economy glossary

Topic: Inflation and Index Numbers: CPI, WPI, IIP and the Deflator · NCERT: Class 11, Ch 7 "Index Numbers"

Meaning

A weighted index of price relatives is a weighted average of the price relatives of all goods. Each good's relative (R = p₁/p₀ × 100) is multiplied by its weight (W), usually its share of spending in the base period.

Formula: Index = ΣWR / ΣW

Base-period weights are preferred for two reasons. Recalculating weights every year is inconvenient. And indices with changing weights value different baskets, so they cannot be strictly compared. This is how the CPI is built.

Example

In the NCERT CPI example, food (weight 35) has R = 96.67, fuel (10) 92, cloth (20) 86.67, rent (15) 100 and miscellaneous (20) 112.5. ΣWR = 9,786.85 and ΣW = 100, so CPI = 97.86. The cost of living fell 2.14%.

Don't confuse with

  • Method of averaging relatives: it takes a simple average of the same relatives with no weights. Where heavy items rise fast, the two can differ widely (149 unweighted vs 156 weighted in the NCERT example).

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