Test Index

Index Numbers and Time series

Question : 38 of 81

Marks: +1, -0

\sum\limits P_1 q_0 = 500, \sum\limits P_0 q_0 = 425

\sum\limits P_1 q_1 = 540, \sum\limits P_0 q_1 = 480

the Fisher's index number is

Solution:

Concept:

Fisher’s index is the geometric mean of Laspeyres and Paasche indices.

Explanation:

Given:

\sum P_1 q_0 = 500

\sum P_0 q_0 = 425

\sum P_1 q_1 = 540

\sum P_0 q_1 = 480

Laspeyres index

L = \frac{\sum P_1 q_0}{\sum P_0 q_0} \times 100 = \frac{500}{425} \times 100 = \frac{100}{85} \times 100 = \frac{2000}{17} \approx 117.65

Paasche index

P = \frac{\sum P_1 q_1}{\sum P_0 q_1} \times 100 = \frac{540}{480} \times 100 = \frac{9}{8} \times 100 = 112.5

Fisher’s index

F = \sqrt{L \times P} = \sqrt{\frac{2000}{17} \times 112.5} = \sqrt{\frac{2000}{17} \times \frac{900}{8}} = \sqrt{\frac{1800000}{136}} = \sqrt{\frac{450000}{34}} \approx \sqrt{13235.29} \approx 115.05

Thus, Fisher’s index is approximately 115.

Answer:

115, which corresponds to option B.

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