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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
State with reason whether you agree or disagree with the following statement:
Index numbers measure changes in the price level only.
Index numbers that measure changes in the level of output or physical volume of production in the economy −
Find the odd word
Types of index numbers -
Define Laspeyre’s price index number
Write note on Fisher’s price index number
Calculate by a suitable method, the index number of price from the following data:
| Commodity | 2002 | 2012 | ||
| Price | Quantity | Price | Quantity | |
| A | 10 | 20 | 16 | 10 |
| B | 12 | 34 | 18 | 42 |
| C | 15 | 30 | 20 | 26 |
Calculate price index number for 2005 by (a) Laspeyre’s (b) Paasche’s method
| Commodity | 1995 | 2005 | ||
| Price | Quantity | Price | Quantity | |
| A | 5 | 60 | 15 | 70 |
| B | 4 | 20 | 8 | 35 |
| C | 3 | 15 | 6 | 20 |
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 |
Construct the cost of living Index number for 2015 on the basis of 2012 from the following data using family budget method.
| Commodity | Price | Weights | |
| 2012 | 2015 | ||
| Rice | 250 | 280 | 10 |
| Wheat | 70 | 85 | 5 |
| Corn | 150 | 170 | 6 |
| Oil | 25 | 35 | 4 |
| Dhal | 85 | 90 | 3 |
Choose the correct alternative:
Cost of living at two different cities can be compared with the help of
