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प्रश्न
Calculate Fisher’s index number to the following data. Also show that it satisfies Time Reversal Test.
| Commodity | 2016 | 2017 | ||
| Price (Rs.) | Quantity (kg) | Price (Rs.) | Quantity (kg) | |
| Food | 40 | 12 | 65 | 14 |
| Fuel | 72 | 14 | 78 | 20 |
| Clothing | 36 | 10 | 36 | 15 |
| Wheat | 20 | 6 | 42 | 4 |
| Others | 46 | 8 | 52 | 6 |
उत्तर
| Commodity | 2016 (Base year) |
2017 (Current year) |
p0q0 | p0q1 | p1q0 | p1q1 | ||
| p0 | q0 | p1 | q1 | |||||
| Food | 40 | 12 | 65 | 14 | 480 | 560 | 780 | 910 |
| Fuel | 72 | 14 | 78 | 20 | 1008 | 1440 | 1092 | 1560 |
| Clothing | 36 | 10 | 36 | 15 | 360 | 540 | 60 | 540 |
| Wheat | 20 | 6 | 42 | 4 | 120 | 80 | 252 | 168 |
| Others | 46 | 8 | 52 | 6 | 68 | 276 | 416 | 312 |
| Total | `sum"p"_0"q"_0` = 2336 | `sum"p"_0"q"_1` =2896 | `sum"p"_1"q"_0` = 2900 | `sum"p"_1"q"_1` = 3490 | ||||
Fisher’s Price 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`
= `sqrt((2900 xx 3490)/(2336 xx 2896)) xx 100`
= `sqrt((10121000)/(6765056)) xx 100`
= `sqrt(1.4961) xx 100`
= `1.2232 xx 100`
= 122.32
Time Reserved Test: P01 × P10 = 1
= `sqrt((sum"p"_1"q"_0 xx sum"p"_1"q"_1 xx sum"q"_1"p"_0 xx sum"q"_0"p"_0)/(sum"p"_0"q"_0 xx sum"p"_0"q"_1 xx sum"p"_1"q"_1 xx sum"p"_0"p"_1))`
= `sqrt((2900 xx 3490 xx 2896 xx 2336)/(2336 xx 2896 xx 3490 xx 2900)`
= 1
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संबंधित प्रश्न
Device that measures changes in an economic variable or a group of variables over a period of time –
Index number was originally developed to measure ______.
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State the uses of Index Number
Define Laspeyre’s price index number
Discuss about Cost of Living Index Number
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 |
Using Fisher’s Ideal Formula, compute price index number for 1999 with 1996 as base year, given the following:
| Year | Commodity: A | Commodity: B | Commodity: C | |||
| Price (Rs.) | Quantity (kg) | Price (Rs.) | Quantity (kg) | Price (Rs.) | Quantity (kg) | |
| 1996 | 5 | 10 | 8 | 6 | 6 | 3 |
| 1999 | 4 | 12 | 7 | 7 | 5 | 4 |
Choose the correct alternative:
Laspeyre’s index = 110, Paasche’s index = 108, then Fisher’s Ideal index is equal to:
State with reasons whether you agree or disagree with the following statement:
Index number measures changes in the price level only.
