Index Numbers
This domain tests weighted price and quantity indices, the choice of weights, and the use of index numbers to deflate nominal values. You should know why Laspeyres and Paasche give different answers and how to link or rebase a series.
Core rules
- Simple price relative = (p1/p0) × 100.
- Laspeyres price index = Σp1q0/Σp0q0 × 100; it uses base-year quantities.
- Paasche price index = Σp1q1/Σp0q1 × 100; it uses current-year quantities.
- Fisher ideal index = √(Laspeyres × Paasche); it is a geometric mean and satisfies reversal tests.
- A price deflator converts nominal to real: real = nominal/(price index/100).
- To rebase, divide each old index by the old base value and multiply by 100.
- To splice, scale the new series so that it matches the old series at the overlap.
Worked example
Base: A p0 = 10, q0 = 20; B p0 = 20, q0 = 10. Current: A p1 = 14, q1 = 25; B p1 = 24, q1 = 8. Laspeyres = (14×20 + 24×10)/(10×20 + 20×10) × 100 = 520/400 × 100 = 130. Paasche = (14×25 + 24×8)/(10×25 + 20×8) × 100 = 542/410 × 100 = 132.2. Fisher = √(130 × 132.2) = 131.1. Laspeyres is higher here because it weights the item whose relative price rose more heavily by base quantities; changing weights changes the index.
Traps
- Mixing base and current quantities in the same formula.
- Treating a 30% index rise as a 30% rise in real income without deflating.
- Rebasing by subtracting the new base instead of dividing.
- Assuming Fisher always lies between the other two in every data set.