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Question
Find x in the following table if Laspeyre’s and Paasche’s Price Index Numbers are equal.
| Commodity | Base Year | Current year | ||
| Price | Quantity | Price | Quantity | |
| A | 2 | 10 | 2 | 5 |
| B | 2 | 5 | x | 2 |
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Solution
| Commodity | Base Year | Current year | p0q0 | p1q0 | p0q1 | p1q1 | ||
| p0 | q0 | p1 | q1 | |||||
| A | 2 | 10 | 2 | 5 | 20 | 20 | 10 | 10 |
| B | 2 | 5 | x | 2 | 10 | 5x | 4 | 2x |
| Total | - | - | - | - | 30 | 20+5x | 14 | 10+2x |
From the table,
∑ p0q0 = 30, ∑ p1q0 = 20 + 5x
∑ p0q1 = 14, ∑ p1q1 = 10 + 2x
`"P"_01("L") = (sum "p"_1"q"_0)/(sum "p"_0"q"_0) xx 100`
∴ `"P"_01("L") = (20 + 5 x)/30 xx 100` ...(i)
`"P"_01("P") = (sum "p"_1"q"_1)/(sum "p"_0"q"_1) xx 100`
∴ `"P"_01("P") = (10 + 2x)/14 xx 100` ....(ii)
Since P01(L) = P01(P),
`(20 + 5x)/30 xx 100 = (10 + 2x)/14 xx 100` ....[From (i) and (ii)]
∴ 14(20 + 5x) = 30(10 + 2x)
∴ 280 + 70x = 300 + 60x
∴ 70x - 60x = 300 - 280
∴ 10x = 20
∴ x = `20/10 = 2`
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RELATED QUESTIONS
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| Commodity | Base Year | Current Year | ||
| Price | Quantity | Price | Quantity | |
| A | 8 | 20 | 11 | 15 |
| B | 7 | 10 | 12 | 10 |
| C | 3 | 30 | 5 | 25 |
| D | 2 | 50 | 4 | 35 |
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| Commodity | Base Year | Current Year | ||
| Price p0 |
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| I | 8 | 30 | 11 | 28 |
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If find x is Walsh’s Price Index Number is 150 for the following data
| Commodity | Base Year | Current Year | ||
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Find x if Paasche’s Price Index Number is 140 for the following data.
| Commodity | Base Year | Current Year | ||
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| A | 20 | 8 | 40 | 7 |
| B | 50 | 10 | 60 | 10 |
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If `sum"p_"0"q"_0 = 120, sum "p"_0"q"_1 = 160, sum "p"_1"q"_1 = 140, and sum "p"_1"q"+0` = 200, find Laspeyre’s, Paasche’s Dorbish-Bowley’s and Marshall Edgeworth’s Price Index Number.
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| Commodity | Base Year | Current Year | ||
| Price | Quantity | Price | Quantity | |
| A | 10 | 9 | 50 | 8 |
| B | 20 | 5 | 60 | 4 |
| C | 30 | 7 | 70 | 3 |
| D | 40 | 8 | 80 | 2 |
Calculate Marshall-Edgeworth Price Index Number for following.
| Commodity | Base Year | Current Year | ||
| Price | Quantity | Price | Quantity | |
| A | 8 | 20 | 11 | 15 |
| B | 7 | 10 | 12 | 10 |
| C | 3 | 30 | 5 | 25 |
| D | 2 | 50 | 4 | 35 |
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| Commodity | Base Year | Current Year | ||
| Price | Quantity | Price | Quantity | |
| I | 10 | 12 | 40 | 3 |
| II | 20 | 2 | 25 | 8 |
| III | 30 | 3 | 50 | 27 |
| IV | 60 | 9 | 90 | 36 |
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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 |
Given the following table, find Walsh’s Price Index Number by completing the activity.
| Commodity | p0 | q0 | p1 | q1 | q0q1 | `sqrt("q"_0"q"_1)` | p0`sqrt("q"_0"q"_1)` | p1`sqrt("q"_0"q"_1)` |
| I | 20 | 9 | 30 | 4 | 36 | `square` | `square` | 180 |
| II | 10 | 5 | 50 | 5 | `square` | 5 | 50 | `square` |
| III | 40 | 8 | 10 | 2 | 16 | `square` | 160 | `square` |
| IV | 30 | 4 | 20 | 1 | `square` | 2 | `square` | 40 |
| Total | – | – | – | – | 390 | `square` |
Walsh’s price Index Number is
P01(W) = `square/(sum"p"_0sqrt("q"_0"q"_1)) xx 100`
= `510/square xx 100`
= `square`
In the following table, Laspeyre's and Paasche's Price Index Numbers are equal. Complete the following activity to find x :
| Commodity | Base Year | Current year | ||
| Price | Quantity | Price | Quantity | |
| A | 2 | 10 | 2 | 5 |
| B | 2 | 5 | x | 2 |
Solution: P01(L) = P01(P)
`(sum "p"_1"q"_0)/(sum "p"_0"q"_0) xx 100 = square/(sum "p"_0"q"_1) xx 100`
`(20 + 5x)/square xx 100 = square/14 xx 100`
∴ x = `square`
