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While price index for a single item can be used to identify price changes of a single item, we often are interested in the general price change for a group of items taken as a whole. An unweighted aggregate price index can be developed by simply summing the unit prices in the time of interest and dividing this sum by the sum of the unit prices in the base year. Suppose that we have K number of items. Let
denote the price of the item in base period
denote the price of the item in period t
The unweighted aggregate price index in period t, denoted , is given by
Example:
The following table lists prices of three different types of cars in different years
Year | Car types | ||
A | B | C | |
15.000 16.000 18.000 21.000 23.000 | 32.000 34.000 35.000 37.000 39.000 | 25.000 26.000 31.000 32.000 35.000 |
Use year as a base year, find and interpret unweighted aggregate price index.
Solution:
Year Car types
A | B | C | Sum | ||
15.000 16.000 18.000 21.000 23.000 | 32.000 34.000 35.000 37.000 39.000 | 25.000 26.000 31.000 32.000 35.000 | 72.000 76.000 84.000 90.000 97.000 | 100% 105.56% 116.67 % 125 % 134.47% |
For example, 116.67 % indicates that as a group, prices for the three types of cars in 2002 year have increased by 16.67 % since 2000 year.
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Price index for a single item (Simple index number) | | | A weighted aggregate price index |