CA Foundation · Quantitative Aptitude · Index Numbers

For a group of commodities, Σp0q0 = 100, Σp1q0 = 180, Σp0q1 = 200 and Σp1q1 = 250. What is Fisher's ideal price index number?

Fisher's ideal price index is 150. Laspeyres' index is 180 and Paasche's index is 125, and Fisher's index is their geometric mean, the square root of 22,500. Using the arithmetic mean would give 152.5, which is the common mistake.

A152.5
B143.3
C180.0
D150.0Correct

Explanation

Laspeyres = 180/100 × 100 = 180. Paasche = 250/200 × 100 = 125. Fisher = √(180 × 125) = √22,500 = 150. The arithmetic mean of 180 and 125 gives 152.5, and Marshall-Edgeworth, (180+250)/(100+200) × 100, gives 143.3; neither is Fisher's index.

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For a group of commodities, Σp0q0 = 100, Σp1q0 = 180, Σp0q1 = 200 and Σp1q1 = 250. What is Fisher's ideal price index number?

Explanation

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