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Question
Write note on Fisher’s price index number
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Solution
Fisher defined a weighted index number as the geometric mean of Laspeyre’s index number and Paasche’s Index number
`"P"_01^"F" = sqrt((sum"p"_1"q"_0 xx sum"p"_1"q"_1)/(sum"p"_0"q"_0 xx sum"p"_0"q"_1)) xx 100`
The Fisher-price index number is also known as the “ideal” price index number.
This requires more data than the other two index numbers and as a result, may often be impracticable.
But this is a good index number because it satisfies both the time-reversal test and factor reversal test.
i.e `"P"_01^"F" xx "P"_10^"F"` = 1
And
`"P"_01^"F" xx "Q"_01^"F" = (sum "p"_1"q"_1)/(sum"p"_0"q"_0)`
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Compute (i) Laspeyre’s (ii) Paasche’s (iii) Fisher’s Index numbers for the 2010 from the following data.
| Commodity | Price | Quantity | ||
| 2000 | 2010 | 2000 | 2010 | |
| A | 12 | 14 | 18 | 16 |
| B | 15 | 16 | 20 | 15 |
| C | 14 | 15 | 24 | 20 |
| D | 12 | 12 | 29 | 23 |
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Laspeyre’s index = 110, Paasche’s index = 108, then Fisher’s Ideal index is equal to:
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