Consider the following price relatives and quantity...

Consider the following price relatives and quantity information for grain production in Iowa (Census Bureau website, March 19,2009 ). $$\begin{array}{lccc} & \text { 1991 Quantities } & \text { Base Price } & \text { 1991-2007 } \\ \text { Product } & \text { (millions of bushels) } & \text { per Bushel (\$) } & \text { Price Relatives } \\ \text { Corn } & 1427 & 2.30 & 173.9 \\ \text { Soybeans } & 350 & 5.51 & 197.8 \end{array}$$ What is the 2007 weighted aggregate price index for the Iowa grains?

Consider the following price relatives and quantity information for grain production in Iowa (Census Bureau website, March 19,2009 ). $$\begin{array}{lccc}
& \text { 1991 Quantities } & \text { Base Price } & \text { 1991-2007 } \\
\text { Product } & \text { (millions of bushels) } & \text { per Bushel (\$) } & \text { Price Relatives } \\
\text { Corn } & 1427 & 2.30 & 173.9 \\
\text { Soybeans } & 350 & 5.51 & 197.8
\end{array}$$
What is the 2007 weighted aggregate price index for the Iowa grains?

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Key Concepts

Price Relative

A price relative is the ratio of the price of an item in a later period to its price in the base period. It is used to quantify how much the price of each good has changed over time, serving as a building block for constructing various price indices.

Weighting Scheme

The weighting scheme in the context of price indices assigns importance to different goods based on quantities or expenditure data from a base period. This approach ensures that the aggregate measure accurately reflects the relative significance of each item in the overall consumption mix.

Price Index

A price index is a statistical measure that tracks the change in the overall price level of a basket of goods or services over time relative to a base period. It is used to gauge inflation or deflation and to understand cost-of-living adjustments.

Weighted Aggregate Price Index

A weighted aggregate price index combines the price changes of individual items, each multiplied by its relative importance or weight in a fixed basket, to produce an overall measure of price change. This method ensures that items with higher consumption or expenditure shares have a proportionately larger impact on the aggregated index.

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