CA Foundation · Quantitative Aptitude · Index Numbers
For a basket of goods, Σp0q0 = 400, Σp1q0 = 600, Σp0q1 = 500 and Σp1q1 = 720. Using Fisher's ideal formula, the product of the Fisher price index and the Fisher quantity index (both as ratios) is closest to which value?
The product is 1.80. Fisher's index satisfies the factor reversal test, so the price index times the quantity index equals the value ratio Σp1q1/Σp0q0 = 720/400 = 1.80. Direct computation of both Fisher indices also gives √3.24 = 1.80.
- A1.50
- B1.80Correct
- C1.20
- D1.44
Explanation
Fisher satisfies the factor reversal test, so P × Q = Σp1q1/Σp0q0 = 720/400 = 1.80. Check: P = √((600/400)(720/500)) = √(1.5×1.44) = √2.16; Q = √((500/400)(720/600)) = √(1.25×1.2) = √1.5; product = √(2.16×1.5) = √3.24 = 1.80. The value 1.44 is only the Paasche price relative.
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