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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 |
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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
______ : Base year prices :: P1 : Current year prices.
Explain the features of index numbers.
Define Time Reversal Test
Discuss about Cost of Living Index Number
Define family budget method
Calculate the Laspeyre’s, Paasche’s and Fisher’s price index number for the following data. Interpret on the data.
| Commodities | Base Year | Current Year | ||
| Price | Quantity | Price | Quantity | |
| A | 170 | 562 | 72 | 632 |
| B | 192 | 535 | 70 | 756 |
| C | 195 | 639 | 95 | 926 |
| D | 1987 | 128 | 92 | 255 |
| E | 1985 | 542 | 92 | 632 |
| F | 150 | 217 | 180 | 314 |
| 7 | 12.6 | 12.7 | 12.5 | 12.8 |
| 8 | 12.4 | 12.3 | 12.6 | 12.5 |
| 9 | 12.6 | 12.5 | 12.3 | 12.6 |
| 10 | 12.1 | 12.7 | 12.5 | 12.8 |
Assertion and reasoning question:
- Assertion (A): The index number considers all factors.
- Reasoning (R): The index number is based on samples.
Choose the correct pair :
| Group A | Group B | ||
| 1) | Price Index | a) | `(sump_1q_1)/(sump_0q_0) xx100` |
| 2) | Value Index |
b) |
`(sumq_1)/(sumq_0) xx 100` |
| 3) | Quantity Index | c) | `(sump_1q_1)/(sump_0q_1) xx100` |
| 4) | Paasche's Index | d) | `(sump_1)/(sump_0) xx 100` |
The base year's index of a selected variable is assumed as ______.
Complete the correlation:
P0 : ______ : : P1 : Current year price.
