How is a Fisher ideal price index calculated?
Correct Answer
A) As the geometric average of the Laspeyres and Paasche indexes
The Fisher ideal price index is the geometric average of the Laspeyres and Paasche price indexes for the same period. A fixed base-period basket describes the Laspeyres index.
Why This Is the Correct Answer
Option A is correct because the Fisher ideal price index is the geometric average of the Laspeyres and Paasche price indexes for the same period. That is, the square root of their product.
Why the Other Options Are Wrong
Option B: As the arithmetic mean of the Laspeyres and Paasche indexes
Option B, the arithmetic mean of the Laspeyres and Paasche indexes, is wrong because the Fisher index uses the geometric average, not the simple arithmetic average of the two.
Option C: As a fixed base-period basket priced in the current period
Option C, a fixed base-period basket priced in the current period, describes the Laspeyres index, not the Fisher index. The Fisher index combines Laspeyres with Paasche.
Option D: As the median price of all houses sold in the period
Option D, the median price of all houses sold in the period, is a simple summary statistic, not an index formula. It does not combine the Laspeyres and Paasche indexes.
Fisher multiplies, then roots
Fisher equals the square root of Laspeyres times Paasche, which is the geometric average.
How to use: Use this to separate the Fisher index from an arithmetic average or from the Laspeyres index.
Exam Tip
Watch for the arithmetic versus geometric average swap; Fisher uses geometric.
Common Mistakes to Avoid
- -Using the arithmetic mean of the two indexes
- -Confusing the Fisher index with the Laspeyres index
- -Treating a median price as a price index
Concept Deep Dive
Analysis
This question tests the definition of the Fisher ideal price index. It combines the Laspeyres and Paasche indexes by taking their geometric average. Distractors substitute an arithmetic mean, describe the Laspeyres index itself, or describe a simple median price.
Background Knowledge
A Laspeyres index uses base-period quantities, while a Paasche index uses current-period quantities. The Fisher ideal index takes their geometric mean, balancing the two weighting approaches. Housing agencies use such indexes to track constant-quality price changes.
Real-World Application
An appraiser reviewing a government new-home price report sees it cites a Fisher ideal index. Knowing it is the geometric average of the Laspeyres and Paasche indexes, the appraiser reads the published definitions to see what the series measures and treats it as broad market background. Local paired sales still provide the support for any adjustment.
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