CMA Foundation · Fundamentals of Business Mathematics and Statistics · Index Numbers and Time Series
The Fisher ideal price index for 2023 with 2022 as base is 125. If the base is shifted to 2023, what is the Fisher price index for 2022 (expressed on a base of 100)?
The Fisher index passes the time reversal test, so the forward and backward indices multiply to one. With a forward index of 1.25, the reversed index is 1 divided by 1.25, which is 0.80, or 80 on a base of 100.
- A75
- B80Correct
- C125
- D120
Explanation
Fisher's index satisfies the time reversal test, so P01 × P10 = 1. With P01 = 1.25, P10 = 1/1.25 = 0.80, which is 80 on a base of 100. Choosing 75 comes from subtracting 125 from 200, which is not how reversal works.
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