The following table reports prices and usage quantities for...

The following table reports prices and usage quantities for two items in 2007 and 2009$$\begin{array}{ccccc} & {\text { Quantity }} & & \ \ \ {\text { Unit Price (\$) }} \\ \text { Item } & \mathbf{2 0 0 7} & \mathbf{2 0 0 9} & \mathbf{2 0 0 7} & \mathbf{2 0 0 9} \\ \text { A } & 1500 & 1800 & 7.50 & 7.75 \\ \text { B } & 2 & 1 & 630.00 & 1500.00 \end{array}$$ a. Compute price relatives for each item in 2009 using 2007 as the base period. b. Compute an unweighted aggregate price index for the two items in 2009 using 2007 as the base period. c. Compute a weighted aggregate price index for the two items using the Laspeyres method. d. Compute a weighted aggregate price index for the two items using the Paasche method.

The following table reports prices and usage quantities for two items in 2007 and 2009$$\begin{array}{ccccc}
& {\text { Quantity }} & & \ \ \ {\text { Unit Price (\$) }} \\
\text { Item } & \mathbf{2 0 0 7} & \mathbf{2 0 0 9} & \mathbf{2 0 0 7} & \mathbf{2 0 0 9} \\
\text { A } & 1500 & 1800 & 7.50 & 7.75 \\
\text { B } & 2 & 1 & 630.00 & 1500.00
\end{array}$$
a. Compute price relatives for each item in 2009 using 2007 as the base period.
b. Compute an unweighted aggregate price index for the two items in 2009 using 2007 as the base period.
c. Compute a weighted aggregate price index for the two items using the Laspeyres method.
d. Compute a weighted aggregate price index for the two items using the Paasche method.

Key Concepts

Paasche Price Index

The Paasche price index is a weighted aggregate price index that employs current period quantities as weights. Unlike the Laspeyres index, it reflects the cost of purchasing the current basket of goods and services, thereby capturing consumers' adjustments to changes in relative prices over time.

Laspeyres Price Index

The Laspeyres price index is a weighted aggregate price index that uses the quantities from the base period as weights. It measures the change in the cost of purchasing the fixed base period basket of goods and services, making it a common method for calculating inflation since it reflects how costs change over time with the quantities held constant.

Price Relative

A price relative is a measure that expresses the price of an item in a current period relative to its price in a base period, usually presented as a ratio or percentage. It allows economists and analysts to compare changes in price levels over time for individual items or groups of items.

Base Period

The base period is the reference point against which changes in prices (or quantities) are measured over time. It provides a foundation for comparison, meaning that values in subsequent periods are expressed relative to the values in the base period. This concept is central in index number calculations and economic analyses to gauge inflation or growth.

Unweighted Aggregate Price Index

The unweighted aggregate price index is an average of price relatives for several items without taking into account the different weights that reflect the significance of each item's consumption or usage. This type of index treats all items equally regardless of their relative importance in the overall consumption basket.

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