CA Foundation · Quantitative Aptitude · Index Numbers
For a firm's products, Σp0q0 = ₹400, Σp1q0 = ₹500, Σp0q1 = ₹500 and Σp1q1 = ₹900 (thousand). What is Fisher's ideal quantity index for the current year (base year = 100)?
Fisher's quantity index is 150. The Laspeyres quantity index is 500/400 × 100 = 125 and the Paasche quantity index is 900/500 × 100 = 180. Their geometric mean is the square root of 22500, which is 150. The arithmetic mean of 152.5 is incorrect.
- A125
- B180
- C152.5
- D150Correct
Explanation
The Laspeyres quantity index is Σp0q1/Σp0q0 × 100 = 125. The Paasche quantity index is Σp1q1/Σp1q0 × 100 = 180. Fisher = √(125 × 180) = √22500 = 150. Check: the Fisher price index is √(125 × 180) = 150 and 150 × 150/100 = 225, which equals the value ratio 900/400 × 100. The value 152.5 is the arithmetic mean, not Fisher's geometric mean.
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