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प्रश्न
Using the following data, construct Fisher’s Ideal Index Number and Show that it satisfies Factor Reversal Test and Time Reversal Test?
| Commodities | Price | Quantity | ||
| Base Year | Current Year | Base Year | Current Year | |
| Wheat | 6 | 10 | 50 | 56 |
| Ghee | 2 | 2 | 100 | 120 |
| Firewood | 4 | 6 | 60 | 60 |
| Sugar | 10 | 12 | 30 | 24 |
| Cloth | 8 | 12 | 40 | 36 |
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उत्तर
| Commodities | Base Year | Current Year | p0q0 | p0q1 | p1q0 | p1q1 | ||
| Price (p0) |
Quantity (q0) |
Price (p1) |
Quantity (q1) |
|||||
| Wheat | 6 | 10 | 50 | 56 | 300 | 336 | 500 | 560 |
| Ghee | 2 | 2 | 100 | 120 | 200 | 240 | 200 | 240 |
| Firewood | 4 | 6 | 60 | 60 | 240 | 240 | 360 | 360 |
| Sugar | 10 | 12 | 30 | 24 | 300 | 240 | 360 | 288 |
| Cloth | 8 | 12 | 40 | 36 | 320 | 288 | 480 | 432 |
| Total | 1360 | 1344 | 1900 | 1880 | ||||
Fisher's ideal index number = `sqrt((sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx (sum"p"_1"q"_1)/(sum"p"_0"q"_1)) xx 100`
`"P"_01^"F" = sqrt((1900 xx 1880)/(1360 xx 1344)) xx 100`
= `sqrt((3,572,000)/(1,827,840)) xx 100`
= `sqrt(1.9542) xx 100`
Factor reversal test
Test is satisfied when `"P"_01 xx "Q"_01 = (sum"p"_1"q"_1)/(sum"p"_0"q"_0)`
`"Q"_01 = sqrt((sum"p"_0"q"_1 xx sum"p"_1"q"_1)/(sum"p"_0"q"_0 xx sum"p"_1"q"_0))`
= `sqrt((1344 xx 1880)/(1360 xx 1900))`
`"P"_01 xx "Q"_01 = sqrt((1900 xx 1880)/(1360 xx 1344) xx (1344 xx 1880)/(1360 xx 1900)`
= `sqrt((1880 xx 1880)/(1360 xx 1360))`
= `1880/1360`
= `(sum"p"_1"q"_1)/(sum"p"_0"q"_0)`
Hence Fisher’s Ideal Index satisfies Factor reversal test.
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संबंधित प्रश्न
Statements that are incorrect in relation to index numbers:
- An index number is a geographical tool.
- Index numbers measure changes in air pressure.
- Index numbers measure relative changes in an economic variable.
- Index numbers are specialized averages.
Mention the classification of Index Number
State the test of adequacy of 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 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 |
Choose the correct alternative:
Laspeyre’s index = 110, Paasche’s index = 108, then Fisher’s Ideal index is equal to:
Choose the correct alternative:
Most commonly used index number is:
Assertion and reasoning question:
- Assertion (A): The index number considers all factors.
- Reasoning (R): The index number is based on samples.
Explain the meaning of index number.
The base year's index of a selected variable is assumed as ______.
