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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
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- Index numbers measure relative changes in an economic variable.
- Index numbers are specialized averages.
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Index numbers that measure changes in the level of output or physical volume of production in the economy −
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Index number was originally developed to measure ______.
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Choose the correct alternative:
Most commonly used index number is:
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 |
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)xx100` |
| 3) Quantity Index | c) `(sump_1q_1)/(sump_0q_1)xx100` |
| 4) Paasche's Index | d) `(sump_1)/(sump_0)xx100` |
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` |
