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प्रश्न
Using the following data, construct Fisher’s Ideal index and show how it satisfies Factor Reversal Test and Time Reversal Test?
| Commodity | Price in Rupees per unit | Number of units | ||
| Basic year | Current year | Base year | Current year | |
| A | 6 | 10 | 50 | 56 |
| B | 2 | 2 | 100 | 120 |
| C | 4 | 6 | 60 | 60 |
| D | 10 | 12 | 50 | 24 |
| E | 8 | 12 | 40 | 36 |
उत्तर
| Commodity | Base year | Current year | p0q0 | p0q1 | p1q0 | p1q1 | ||
| p0 | q0 | p1 | q1 | |||||
| A | 6 | 10 | 50 | 56 | 300 | 336 | 500 | 560 |
| B | 2 | 2 | 100 | 120 | 200 | 240 | 200 | 240 |
| C | 4 | 6 | 60 | 60 | 240 | 240 | 360 | 360 |
| D | 10 | 12 | 50 | 24 | 500 | 240 | 600 | 288 |
| E | 8 | 12 | 40 | 36 | 320 | 288 | 480 | 432 |
| Total | `sum"p"_0"q"_0` = 1560 | `sum"p"_0"q"_1` = 1344 | `sum"p"_1"q"_0` = 2140 | `sum"p"_1"q"_1` = 1880 | ||||
Fisher’s Price Index Number
`"P"_01^"F" = sqrt((sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx (sum"p"_1"q"_1)/(sum"p"_0"q"_1)) xx 100`
= `sqrt(2140/1560 xx 1880/1344) xx 100`
= `sqrt((40,23,200)/(20,96,640)) xx 100`
= `sqrt(1.92) xx 100`
= `1.385 xx 100`
= 138.5
Time Reversal Test: To prove P01 × P10 = 1
P01 × P10 = `sqrt((sum"p"_1"q"_0 xx sum"p"_1"q"_1)/(sum"p"_0"q"_0 xx sum"p"_0"q"_1)) xx sqrt((sum"p"_0"q"_1 xx sum"p"_0"q"_0)/(sum"p"_1"q"_1 xx sum"p"_1"q"_0))`
= `sqrt(2140/1560 xx 1880/1344 xx 1344/1880 xx 1560/2140)`
P01 × P10 = 1
Time reversal test is satisfied.
Factor Reversal Test: To prove P01 × Q01 = `(sum"p"_1"q"_1)/(sum"p"_0"q"_0)`
= `sqrt((sum"p"_1"q"_0 xx sum"p"_1"q"_1)/(sum"p"_0"q"_0 xx sum"p"_0"q"_1)) xx sqrt((sum"q"_1"P"_0 xx sum"q"_1"P"_1)/(sum"q"_0"p"_0 xx sum"q"_0"p"_1))`
= `sqrt(2140 /1560 xx 1880/1344 xx 1344/1560 xx 188/2140)`
= `sqrt((1880 xx 1880)/(1560 xx 1560)`
= `1880/1560`
⇒ `"P"_01 xx "Q"_01 = (sum"p"_1"q"_1)/(sum"p"_0"q"_0)`
Factor reversal test is satisfied.
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संबंधित प्रश्न
Index number which is computed from a single variable called is a ______.
Define Index Number
State the test of adequacy of index number
Explain factor reversal test
Discuss about Cost of Living Index Number
The following are the group index numbers and the group weights of an average working class family’s budget. Construct the cost of living index number:
| Groups | Food | Fuel and Lighting |
Clothing | Rent | Miscellaneous |
| Index Number | 2450 | 1240 | 3250 | 3750 | 4190 |
| Weight | 48 | 20 | 12 | 15 | 10 |
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 |
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 |
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` |
