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A price index is any single number calculated from an array of prices and quantities over a period. Since not all prices and quantities of purchases can be recorded, a representative sample is used instead. Inflation and cost indices are calculated as price indices.
Notable price indices are
Calculating price indices
There are two main methods to calculate price indices, the Paasche index (after Hermann Paasche) and the Laspeyre index (after
Etienne Laspeyres.
The Paasche Index is
<math>
\Delta P_P = \frac{\sum p_1 q_1}{\sum p_1 q_0},
<math>
while the Laspeyres index computes as
<math>
\Delta P_L = \frac{\sum p_1 q_0}{\sum p_0 q_0},
<math>
where <math>\Delta P<math> is the change in price level, <math>p_0<math> and <math>q_0<math> are the prices and quantities in the first period, <math>p_1<math> and <math>q_1<math> those in the second.
The Laspeyres index systematically overstates inflation while the Paasche index understates it.
A third index, the Fisher index (after Irving Fisher), tries to get around this problem. It is calculated as the geometric mean of <math>\Delta P_P<math> and <math>\Delta P_L<math>:
<math>
\Delta P_F = \sqrt{\Delta P_P \cdot \Delta P_L}.
<math>
See also
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