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प्रश्न
Find the missing price if Laspeyre’s and Paasche’s Price Index Numbers are equal for following data.
| Commodity | Base Year | Current Year | ||
| Price | Quantity | Price | Quantity | |
| A | 1 | 10 | 2 | 5 |
| B | 1 | 5 | – | 12 |
उत्तर
Let us denote the missing value by x and reconstruct the table as follows.
| Commodity | Base Year | Current Year | p0q0 | p1q0 | p1q1 | p0q1 | ||
| p0 | q0 | p1 | q1 | |||||
| A | 1 | 10 | 2 | 5 | 10 | 20 | 10 | 5 |
| B | 1 | 5 | x | 12 | 5 | 5x | 1 | 12 |
| Total | 15 | 20 + 5x | 10 + 12x | 17 | ||||
The above table gives
`sum"p"0"q"_0` = 15, `sum"p"_1"q"_0` = 20 5x, `sum"p"_1"q"_1` = 10 + 12x, `sum"p"_0"q"_1` = 17
It is given that
P01(L) = P01(P)
`(sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100`
`(sum"p"_1"q"_1)/(sum"p"_0"q"_1) xx 100`
∴ `(5x + 20)/15 = (12x + 10)/17`
∴ `(5(x + 4))/15 = (12x + 10)/17`
∴ 17(x + 4) = 3(12x + 10)
∴ 17x + 68 = 36x + 30
∴ x = 2
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| Price | Quantity | Price | Quantity | |
| I | 10 | 12 | 20 | 9 |
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| III | 30 | 13 | 40 | 27 |
| IV | 60 | 29 | 75 | 36 |
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| Commodity | Base year | Current year | ||
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price p1 |
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| A | 20 | 18 | 30 | 15 |
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| Commodity | Base Year | Current Year | ||
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| Commodity | Base Year | Current Year | ||
| Price p0 |
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| Commodity | Base Year | Current Year | ||
| Price P0 |
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Price p1 |
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| Commodity | Base Year | Current Year | ||
| Price p0 |
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|
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