Definition:Paasche Index

Definition

Let the prices of a set of $k$ commodities in the base year be $p_{0 1}, p_{0 2}, \ldots, p_{0 k}$.

Let the quantities sold of each of those $k$ commodities in the base year be $q_{0 1}, q_{0 2}, \ldots, q_{0 k}$.

Let the corresponding prices and quantities of those $k$ commodities in the $n$th year after the base year be $p_{n 1}, p_{n 2}, \ldots, p_{n k}$ and $q_{n 1}, q_{n 2}, \ldots, q_{n k}$.

The Paasche index is the index number calculated as:

$L_{0 n} = \dfrac {\ds \sum_j p_{n j} \, q_{n j} } {\ds \sum_j p_{0 j} \, q_{n j} }$

Also see

• Definition:Laspeyres Index, in which the weights are the base year quantities

• Results about the Paasche index can be found here.

Source of Name

This entry was named for Hermann Paasche‎.

Historical Note

The Paasche index was devised by Hermann Paasche in $1874$.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): index (plural indices)${}$: 1. (index number)
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Paasche index
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): index (plural indices)${}$: 1. (index number)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Paasche index