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Unweighted aggregate price index

Читайте также:
  1. A weighted aggregate price index
  2. A weighted aggregate quantity index
  3. Deflating a series by price indexes
  4. Price index for a single item (Simple index number)

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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Читайте в этой же книге: Exercises | Confidence interval for the difference between the population means: unknown population variances that are assumed to be equal | Exercises | Confidence interval for the difference between the | Exercises | Distribution | Exercises | Sample size determination for the estimation of mean | Sample size determination for the estimation of proportion | Exercises |
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Price index for a single item (Simple index number)| A weighted aggregate price index

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