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प्रश्न
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.
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उत्तर
Laspeyre’s Price Index Number:
`"P"_01("L") = (sum "p"_1"q"_0)/(sum "p"_0"q"_0) xx 100`
Paasche’s Price Index Number:
`"P"_01("P") = (sum "p"_1"q"_1)/(sum "p"_0"q"_1) xx 100`
It is given that
P01(L) = 4 × P01(P)
∴ `(sum "p"_1"q"_0)/(sum "p"_0"q"_0) xx 100 = 4 xx (sum "p"_1"q"_1)/(sum "p"_0"q"_1) xx 100`
∴ `(sum "p"_1"q"_0)/(sum "p"_0"q"_0) = 4 xx (sum "p"_1"q"_1)/(sum "p"_0"q"_1)`
If we denote `(sum "p"_1"q"_0)/(sum "p"_0"q"_0) = "A", (sum "p"_1"q"_1)/(sum "p"_0"q"_1) = "B"`,
then A = 4B
Dorbish-Bowley’s Price Index Number:
`"P"_01("D - B") = ("P"_01("L") + "P"_01("P"))/2`
`"P"_01("D - B") = ((sum "p"_1"q"_0)/(sum "p"_0"q"_0) + (sum "p"_1"q"_1)/(sum "p"_0"q"_1))/2 xx 100`
`= ("A + B")/2 xx 100`
`= (4"B" + "B")/2 xx 100` ....[∵ A = 4B]
`= "5B"/2 xx 100`
= 250 B
∴ P01(D-B) = 250 B ....(i)
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("A" xx "B") xx 100`
`= sqrt("4B" xx "B") xx 100`
`= sqrt("4B"^2) xx 100`
= 2B × 100
∴ P01 (F) = 200 B ...(ii)
Dividing (i) by (ii), we get
`("P"_01 ("D - B"))/("P"_01 ("F")) = (250"B")/(200 "B")`
∴ `("P"_01 ("D - B"))/("P"_01 ("F")) = 5/4`
∴ `"P"_01 ("D - B") = 5/4 xx "P"_01 ("F")`
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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 | |
| L | 4 | 16 | 3 | 19 |
| M | 6 | 16 | 8 | 14 |
| N | 8 | 28 | 7 | 32 |
If ∑p0q0 = 140, ∑p0q1 = 200, ∑p1q0 = 350, ∑p1q1 = 460, find Laspeyre’s, Paasche’s, Dorbish-Bowley’s and Marshall-Edgeworth’s Price Index Numbers.
Given that ∑p0q0 = 220, ∑p0q1 = 380, ∑p1q1 = 350 and Marshall-Edgeworth’s Price Index Number is 150, find Laspeyre’s Price Index Number.
If Dorbish-Bowley's and Fisher's Price Index Numbers are 5 and 4, respectively, then find Laspeyre's and Paasche's Price Index Numbers.
Choose the correct alternative :
Walsh’s Price Index Number is given by
Laspeyre’s Price Index Number is given by _______.
Fill in the blank :
Paasche’s Price Index Number is given by _______.
Fill in the blank :
Marshall-Edgeworth’s Price Index Number is given by _______.
`(sump_1q_0)/(sump_0q_0) xx 100` is Paasche’s Price Index Number.
State whether the following is True or False :
`sum("p"_1"q"_1)/("p"_0"q"_1)` is Laspeyre’s Price Index Number.
State whether the following is True or False :
`(sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx (sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100` is Dorbish-Bowley’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 :
Given that `sum "p"_0"q"_0 = 130, sum "p"_1"q"_1 = 140, sum "p"_0"q"_1 = 160, and sum "p"_1"q"_0 = 200`, find Laspeyre’s, Paasche’s, Dorbish-Bowley’s, and Marshall-Edgeworth’s Price Index Numbers.
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.
Fisher's Price Index Number is given by ______.
The average of Laspeyre’s and Paasche’s Price Index Numbers is called ______ 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 |
Calculate Walsh’s price Index Number for the following data.
| 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 |
If P01(L) = 40 and P01(P) = 90, find P01(D-B) and P01(F).
State whether the following statement is true or false:
Dorbish-Bowley's Price Index Number is the square root of the product of Laspeyre's and Paasche's Index Numbers.
`sqrt((sump_1q_0)/(sump_0q_0)) xx sqrt((sump_1q_1)/(sump_0q_1)) xx 100`
Calculate Marshall – Edgeworth’s price index number for the following data:
| Commodity | Base year | Current year | ||
| Price | Quantity | Price | Quantity | |
| P | 12 | 20 | 18 | 24 |
| Q | 14 | 12 | 21 | 16 |
| R | 8 | 10 | 12 | 18 |
| S | 16 | 15 | 20 | 25 |
If ∑ p0q0 = 120, ∑ p0q1 = 160, ∑ p1q1 = 140, ∑ p1qo = 200, find Laspeyre’s, Paasche’s, Dorbish-Bowley’s and Marshall-Edgeworth’s Price Index Numbers.
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`
