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CA Foundation · Quantitative Aptitude · Index Numbers

The Laspeyres price index for a set of goods is 120 and the Paasche price index is 96. Since Laspeyres exceeds Paasche, which statement correctly explains this, together with the Fisher index?

Fisher's index is the geometric mean √(120×96) ≈ 107.3. The gap arises because Laspeyres, using base year quantities, overstates price rise, while Paasche, using current quantities, understates it, as consumers substitute away from goods whose prices have risen.

  1. AFisher's index is 108, the arithmetic mean of the two, and the gap shows no bias
  2. BFisher's index is about 107.3, the geometric mean, and the gap reflects Laspeyres overstating and Paasche understating due to consumers shifting away from goods whose prices roseCorrect
  3. CFisher's index is 115.2, the product divided by 100, and the gap is caused by sampling error
  4. DFisher's index is about 107.3, and the gap arises because Paasche uses base year prices as weights

Explanation

Fisher = √(120 × 96) = √11520 ≈ 107.3. Laspeyres uses base year quantities and tends to overstate, because buyers substitute away from goods that became dearer; Paasche uses current quantities and tends to understate. The arithmetic mean 108 is wrong because Fisher uses the geometric mean, and Paasche uses current year quantities, not base prices.

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