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प्रश्न
Calculate Laspeyre’s, Paasche’s, Dorbish-Bowley’s, and MarshallEdgeworth’s Price index numbers.
| 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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उत्तर
| Commodity | Base Year | Current Year | p0q0 | p1q0 | p0q1 | p1q1 | ||
| p0 | q0 | p1 | q1 | |||||
| A | 8 | 20 | 11 | 15 | 160 | 220 | 120 | 165 |
| B | 7 | 10 | 12 | 10 | 70 | 120 | 70 | 120 |
| C | 3 | 30 | 5 | 25 | 90 | 150 | 75 | 125 |
| D | 2 | 50 | 4 | 35 | 100 | 200 | 70 | 140 |
| Total | - | - | - | - | 420 | 690 | 335 | 550 |
From the table,
`sum "p"_0"q"_0 = 420, sum "p"_1"q"_0 = 690`
`sum "p"_0"q"_1 = 335, sum "p"_1"q"_1 = 550`
(i) Laspeyre’s Price Index Number:
`"P"_01 ("L") = (sum "p"_1"q"_0)/(sum "p"_0"q"_0) xx 100 = 690/420 xx 100 = 164.29`
(ii) Paasche’s Price Index Number:
`"P"_01 ("P") = (sum "p"_1"q"_1)/(sum "p"_0"q"_1) xx 100 = 550/335 xx 100 = 164.18`
(iii) Dorbish-Bowley’s Price Index Number:
`"P"_01 ("D - B") = ("P"_01 ("L") + "P"_01 ("P"))/2`
`= (164.29 + 164.18)/2`
= 164.24
(iv) Marshall-Edgeworth’s Price Index Number:
`"P"_01 ("M- E") = (sum "p"_1"q"_0 + sum "p"_1"q"_1)/(sum "p"_0"q"_0 + sum "p"_0"q"_1) xx 100`
`= (690 + 550)/(420 + 335) xx 100`
`= 1240/755 xx 100`
= 164.24
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संबंधित प्रश्न
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 |
If ∑p0q0 = 140, ∑p0q1 = 200, ∑p1q0 = 350, ∑p1q1 = 460, find Laspeyre’s, Paasche’s, Dorbish-Bowley’s and Marshall-Edgeworth’s Price Index Numbers.
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.
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.
Fill in the blank :
Dorbish-Bowley’s Price Index Number is given by _______.
Fill in the blank :
Marshall-Edgeworth’s Price Index Number is given by _______.
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.
`(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 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 :
Find x if Paasche’s Price Index Number is 140 for the following data.
| Commodity | Base Year | Current Year | ||
| Price p0 |
Quantity q0 |
Price p1 |
Quantity q1 |
|
| A | 20 | 8 | 40 | 7 |
| B | 50 | 10 | 60 | 10 |
| C | 40 | 15 | 60 | x |
| D | 12 | 15 | 15 | 15 |
Solve the following problem :
Given that Laspeyre’s and Paasche’s Price Index Numbers are 25 and 16 respectively, find Dorbish-Bowley’s and Fisher’s Price Index Number.
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.
Choose the correct alternative:
Price Index Number by using Weighted Aggregate Method is given by
Fisher's Price Index Number is given by ______.
State whether the following statement is True or False:
`(sum"p"_1"q"_1)/(sum"p"_0"q"_1) xx 100` is Paasche’s Price Index Number
State whether the following statement is True or False:
`[sqrt((sum"p"_1"q"_1)/(sum"p"_0"q"_1)) + (sumsqrt("q"_0"q"_1))/(sum("p"_0 + "p"_1))] xx 100` is Fisher’s Price Index Number.
If Laspeyre’s and Paasche’s Price Index Numbers are 50 and 72 respectively, find Dorbish-Bowley’s and Fisher’s Price Index Numbers
Given P01(M-E) = 120, `sum"p"_1"q"_1` = 300, `sum"p"_0"q"_0` = 120, `sum"p"_0"q"_1` = 320, Find P01(L)
If `sum"p"_0"q"_0` = 150, `sum"p"_0"q"_1` = 250, `sum"p"_1"q"_1` = 375 and P01(L) = 140. Find P01(M-E)
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.
If P01 (L) = 121, P01 (P) = 100, then P01 (F) = ______.
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`
