What is the Fisher's Index Number?

Question

Accepted Answer

The correct option is 3:

The Fisher's Ideal Index Number is defined as the Geometric Mean (G. M.) of the Laspeyre's Price Index and the Paasche's Price Index. It is called the "Ideal" index because it satisfies both the Time Reversal Test and the Factor Reversal Test, which are considered essential criteria for a good index number formula. The index is calculated by taking the square root of the product of the Laspeyre's Index (which uses base period quantities as weights) and the Paasche's Index (which uses current period quantities as weights). This method balances the upward bias inherent in the Laspeyre's index and the downward bias inherent in the Paasche's index, thus providing a more accurate measure of price changes.

The incorrect option is 1: The H. M. of Indexes of Laspeyre and Paasche. The Harmonic Mean (H. M.) is not the statistical measure used to calculate the Fisher's Ideal Index; using the H. M. would not satisfy the key tests for index number adequacy.

The incorrect option is 2: The A. M. of Indexes of Laspeyre and Paasche. The Arithmetic Mean (A. M.) is sometimes used in certain contexts but results in an index that does not satisfy the critical reversal tests, making it theoretically inferior to the Fisher's index.

The incorrect option is 4: The multiplier of Indexes of Laspeyre and Paasche. Although the Fisher's index involves multiplication, the final result is the square root of the product of the two indices, which is mathematically defined as the Geometric Mean, not just the multiplier.