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प्रश्न
Solve the following problem:
If find x is Walsh’s Price Index Number is 150 for the following data
| Commodity | Base Year | Current Year | ||
| Price p0 |
Quantity q0 |
Price p1 |
Quantity q1 |
|
| A | 5 | 3 | 10 | 3 |
| B | x | 4 | 16 | 9 |
| C | 15 | 5 | 23 | 5 |
| D | 10 | 2 | 26 | 8 |
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उत्तर
| Commodity | Base Year | Current Year | ||||||
| p0 | q0 | p1 | q1 | q0q1 | `bb(sqrt("q"_0"q"_1))` | `bb("p"_1sqrt("q"_0"q"_1))` | `bb("p"_0sqrt("q"_0"q"_1))` | |
| A | 5 | 3 | 10 | 3 | 9 | 3 | 30 | 15 |
| B | x | 4 | 16 | 9 | 36 | 6 | 96 | 6x |
| C | 15 | 5 | 23 | 5 | 25 | 5 | 115 | 75 |
| D | 10 | 2 | 26 | 8 | 16 | 4 | 104 | 40 |
| Total | – | – | – | – | – | – | 345 | 6x + 130 |
From the table,
`sum"p"_1sqrt("q"_0"q"_1) = 345, sum"p"_0sqrt("q"_0"q"_1) = 6x + 130`
Walsh’s Price Index Number:
P01(W) = `(sum"p"_1sqrt("q"_0"q"_1))/(sum"p"_0sqrt("q"_0"q"_1)) xx 100`
∴ 150 = `(345)/(6x + 130) xx 100` ...[∵ P01(W) = 150]
∴ 6x + 130 = `(345 xx 100)/(150)`
∴ 6x + 130 = 230
∴ 6x = 230 – 130
∴ 6x = 100
∴ x = `(100)/(6)`
∴ x = 16.67
संबंधित प्रश्न
Calculate Laspeyre’s, Paasche’s, Dorbish-Bowley’s, and Marshall - Edgeworth’s Price index numbers.
| Commodity | Base Year | Current Year | ||
| Price | Quantity | Price | Quantity | |
| I | 10 | 9 | 20 | 8 |
| II | 20 | 5 | 30 | 4 |
| III | 30 | 7 | 50 | 5 |
| IV | 40 | 8 | 60 | 6 |
Calculate Walsh’s Price Index Number.
| Commodity | Base Year | Current Year | ||
| Price | Quantity | Price | Quantity | |
| I | 10 | 12 | 20 | 9 |
| II | 20 | 4 | 25 | 8 |
| III | 30 | 13 | 40 | 27 |
| IV | 60 | 29 | 75 | 36 |
Given that Laspeyre’s and Dorbish-Bowley’s Price Index Numbers are 160.32 and 164.18 respectively, find Paasche’s Price Index Number.
Given that ∑p0q0 = 220, ∑p0q1 = 380, ∑p1q1 = 350 and Marshall-Edgeworth’s Price Index Number is 150, find Laspeyre’s Price Index Number.
If Laspeyre's Price Index Number is four times Paasche's Price Index Number, then find the relation between Dorbish-Bowley's and Fisher's Price Index Numbers.
Choose the correct alternative :
The price Index Number by Weighted Aggregate Method is given by ______.
Paasche’s Price Index Number is given by ______.
Dorbish-Bowley’s Price Index Number is given by ______.
Choose the correct alternative :
Walsh’s Price Index Number is given by
Fill in the blank :
Paasche’s Price Index Number is given by _______.
State whether the following is True or False :
`(1)/(2)[sqrt((sum"p"_1"q"_0)/(sum"p"_0"q"_0)) + sqrt("p"_1"q"_1)/(sqrt("p"_0"q"_1))] xx 100` is Fisher’s Price Index Number.
`(sum"p"_0sqrt("q"_0"q"_1))/(sum"p"_1sqrt("q"_0"q"_1)) xx 100` is Walsh’s Price Index Number.
State whether the following is True or False :
`sqrt(("p"_1"q"_0)/(sum"p"_0"q"_0)) xx sqrt((sum"p"_1"q"_1)/(sum"p"_0"q"_1)) xx 100` is Fisher’s Price Index Number.
Solve the following problem :
Calculate Laspeyre’s and Paasche’s Price Index Number for the following data.
| Commodity | Base year | Current year | ||
| Price p0 |
Quantity q0 |
price p1 |
Quantity q1 |
|
| A | 20 | 18 | 30 | 15 |
| B | 25 | 8 | 28 | 5 |
| C | 32 | 5 | 40 | 7 |
| D | 12 | 10 | 18 | 10 |
Solve the following problem :
Calculate Marshall-Edgeworth’s Price Index Number for the following data.
| Commodity | Base Year | Current Year | ||
| Price p0 |
Quantity q0 |
Price p1 |
Quantity q1 |
|
| X | 12 | 35 | 15 | 25 |
| Y | 29 | 50 | 30 | 70 |
Solve the following problem :
Calculate Laspeyre’s and Paasche’s Price Index Number for the following data.
| Commodity | Base Year | Current Year | ||
| Price P0 |
Quantity q0 |
Price p1 |
Quantity q1 |
|
| I | 8 | 30 | 12 | 25 |
| II | 10 | 42 | 20 | 16 |
Solve the following problem :
Given that `sum "p"_1"q"_1 = 300, sum "p"_0"q"_1 = 320, sum "p"_0"q"_0` = 120, and Marshall- Edgeworth’s Price Index Number is 120, find `sum"p"_1"q"_0` and Paasche’s Price Index Number.
Choose the correct alternative:
Price Index Number by using Weighted Aggregate Method is given by
Choose the correct alternative:
The formula P01 = `(sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100` is for
The average of Laspeyre’s and Paasche’s Price Index Numbers is called ______ Price Index Number
State whether the following statement is True or False:
`(sum"p"_0sqrt("q"_0 + "q"_1))/(sum"p"_1sqrt("q"_0 + "q"_1)) xx 100` is Marshall-Edgeworth Price Index Number
Calculate
a) Laspeyre’s
b) Passche’s
c) Dorbish-Bowley’s Price Index Numbers for following data.
| 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 |
If P01(L) = 40 and P01(P) = 90, find P01(D-B) and P01(F).
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 |
Laspeyre’s Price Index Number uses current year’s quantities as weights.
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`
