Value Index Number

The value of a single commodity is the product of its price and quantity. Thus a value index V is the sum of the value of a given year dividend by the sum of the values of the base year. The formula, therefore, is


Where ∑p₁q₁ = Total value of all commodities in the given period and ∑p₀q₀ = Total value of all commodities in the base period.

Since in most cases the value figures are given, the formula can be stated more simply


In which V stands for value.

In this type of index both price and quantity are variables in the numerator. Weights do not have to be applied, since they are inherent in the value figures. A value index, therefore, is an aggregate of values. It measures the changes in actual values between the base and the given period.

The value index is not in wide use, although, because of the unsatisfactory nature of price and quantity indices, it has been occasionally suggested that they be replaced by the value index. The temptation, however, must be resisted, since the concepts of price level and quantity level answer questions that cannot be answered by the value level. Furthermore, an aggregate of values may be viewed as the product of a price level and a quantity level. The division of an aggregate of value into its price and quantity factors may be arbitrary, but this arbitrariness need not create any confusion of thought as long as our concepts of the two factors are consistent.

The test of consistency is that the product of the price and quantity indices must produce the value index.

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