Advertisements
Advertisements
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 |
Advertisements
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 1880/2140)`
= `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.
APPEARS IN
संबंधित प्रश्न
State with reason whether you agree or disagree with the following statement:
Index numbers measure changes in the price level only.
Define Laspeyre’s price index number
Explain Paasche’s price index number
Write note on Fisher’s price index number
State the test of adequacy of index number
Choose the correct alternative:
Laspeyre’s index = 110, Paasche’s index = 108, then Fisher’s Ideal index is equal to:
Choose the correct alternative:
While computing a weighted index, the current period quantities are used in the:
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` |
