Index Numbers
What the domain covers
Index numbers measure relative change over time in prices, quantities or values. The exam tests simple aggregative and average-of-relatives indices, Laspeyres, Paasche and Fisher ideal indices, base-year choice and interpretation.
Core rules
- Simple aggregative price index: P01 = (Σp1/Σp0) × 100.
- Simple average of price relatives: average of (p1/p0) × 100.
- Laspeyres price index: L = (Σp1q0/Σp0q0) × 100; base-year quantities are weights.
- Paasche price index: P = (Σp1q1/Σp0q1) × 100; current-year quantities are weights.
- Fisher's ideal index: F = √(L × P). It is a geometric mean and satisfies the time-reversal and factor-reversal tests.
- Index numbers are unit-free percentages relative to the base year.
Worked example
Base prices are 10 and 20 with quantities 5 and 2; current prices are 12 and 25. Σp1q0 = 12×5 + 25×2 = 110; Σp0q0 = 10×5 + 20×2 = 90. Laspeyres index = (110/90) × 100 = 122.22. Prices rose about 22.22% on the base-weighted basket. A Paasche calculation would use current quantities and can give a different figure.
Traps
Do not mix base and current quantities in one weighted index. Fisher is not the arithmetic mean of Laspeyres and Paasche; it is their geometric mean. A change of base year changes the index series but not the underlying price relatives. Do not interpret an index of 122.22 as '122.22% inflation' without the base period.