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CA Foundation · Quantitative Aptitude · Index Numbers

Which one of the following index number formulae satisfies both the time reversal test and the factor reversal test?

Fisher's ideal index satisfies both tests. As the geometric mean of the Laspeyres and Paasche indices, its price index multiplied by its quantity index equals the value ratio, and swapping base and current periods gives reciprocal results. The other formulae fail at least one of the two tests.

  1. ALaspeyres' index
  2. BPaasche's index
  3. CFisher's ideal indexCorrect
  4. DMarshall-Edgeworth index

Explanation

Fisher's index is the geometric mean of Laspeyres' and Paasche's indices. Because of this construction, P01 × P10 = 1 and the price index multiplied by the quantity index equals the value ratio. Marshall-Edgeworth satisfies time reversal but not factor reversal, and Laspeyres and Paasche satisfy neither.

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