Aggregative price indices

The aggregative method adds up the prices of the items.

The simple aggregative price index: ΣP1 ÷ ΣP0 × 100, where P0 are the prices in the base period and P1 in the current period. It is easy, but it has two problems: the items are priced in different units (per kg, per litre, per piece), and every item gets equal importance, though people spend far more on some things than others.

Weighted aggregative indices solve this by pricing a fixed basket of goods (with quantities as weights) at the two sets of prices:

• Laspeyre's index uses the base period quantities (q0): ΣP1q0 ÷ ΣP0q0 × 100.
• Paasche's index uses the current period quantities (q1): ΣP1q1 ÷ ΣP0q1 × 100.

An example with two items:

• Simple aggregative: (50 + 110) ÷ (40 + 100) × 100 = 160 ÷ 140 × 100 = 114.3.
• Laspeyre's: ΣP1q0 = 500 + 220 = 720; ΣP0q0 = 400 + 200 = 600; index = 720 ÷ 600 × 100 = 120.0.
• Paasche's: ΣP1q1 = 400 + 330 = 730; ΣP0q1 = 320 + 300 = 620; index = 730 ÷ 620 × 100 = 117.7.

Laspeyre's and Paasche's indices differ only in the weights they use, so they usually give slightly different values.