Laspeyres, Paasche and Fisher Price Index Calculator (Cost of Living Basket)
Price index of a small basket of goods from base-period and current prices and quantities, by the Laspeyres, Paasche and Fisher methods.
Results
What this tool does
A price index asks what a basket of goods costs now compared with the base period. Laspeyres keeps the base-period quantities fixed, so it ignores people switching to cheaper goods and tends to overstate inflation; Paasche uses today's quantities and tends to understate it. Fisher's ideal index is their geometric mean and sits between the two, which is why it is used as a benchmark by statisticians. Official consumer price indices are chained or weighted variants of these ideas, with far more goods than the three here.
Formula
Laspeyres = Σ p₁q₀ ÷ Σ p₀q₀ × 100 · Paasche = Σ p₁q₁ ÷ Σ p₀q₁ × 100 · Fisher = √(L × P)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
a1 | Good 1 — price in the base period | — |
b1 | Good 1 — price now | — |
q1 | Good 1 — quantity in the base period | — |
r1 | Good 1 — quantity now | — |
a2 | Good 2 — price in the base period | — |
b2 | Good 2 — price now | — |
q2 | Good 2 — quantity in the base period | — |
r2 | Good 2 — quantity now | — |
a3 | Good 3 — price in the base period | — |
b3 | Good 3 — price now | — |
q3 | Good 3 — quantity in the base period | — |
r3 | Good 3 — quantity now | — |
L | Laspeyres price index (base = 100) | — |
P | Paasche price index (base = 100) | — |
F | Fisher ideal price index (base = 100) | — |
FI | Average price change by the Fisher index | % |
Worked example
- Good 1 — price in the base period1
- Good 1 — price now1.1
- Good 1 — quantity in the base period100
- Good 1 — quantity now90
- Good 2 — price in the base period2.5
- Good 2 — price now2.6
- Good 2 — quantity in the base period50
- Good 2 — quantity now55
- Good 3 — price in the base period0.8
- Good 3 — price now0.95
- Good 3 — quantity in the base period200
- Good 3 — quantity now180
- Laspeyres price index (base = 100)111.69
- Paasche price index (base = 100)111.17
- Fisher ideal price index (base = 100)111.43
- Average price change by the Fisher index11.43 %
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- The tool works with whatever currency you use for the inputs; it does not convert between currencies.