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Question
Find x if Laspeyre’s Price Index Number is same as Paasche’s Price Index Number for the following data
| Commodity | Base Year | Current Year | ||
| Price p0 |
Quantity q0 |
Price p1 |
Quantity q1 |
|
| A | 3 | x | 2 | 5 |
| B | 4 | 6 | 3 | 5 |
Solution
| Commodity | Base Year | Current Year | p0q0 | p0q1 | p1q0 | p1q1 | ||
| p0 | q0 | p1 | q1 | |||||
| A | 3 | x | 2 | 5 | 3x | 15 | 2x | 10 |
| B | 4 | 6 | 3 | 5 | 24 | 20 | 18 | 15 |
| Total | – | – | – | – | = 24 + 3x | = 35 | = 18 + 2x | = 25 |
From the table,
`sump_0q_0` = 3x + 24,
`sump_0q_1` = 35
`sump_1q_0` = 2x + 18,
`sump_1q_1` = 25
Laspeyre’s Price Index Number:
P01(L) = `(sump_1q_0)/(sump_0q_0) xx 100`
= `(2x + 18)/(3x + 24) xx 100` ...(i)
Paasche’s Price Index Number:
P01(P) = `(sump_1q_1)/(sump_0q_1) xx 100`
= `(25)/(35) xx 100`
= `(5)/(7) xx 100` ...(ii)
Since P01(L) = P01(P),
`(2x + 18)/(3x + 24) xx 100 = (5)/(7) xx 100` ...[From (i) and (ii)]
∴ `(2x + 18)/(3x + 24) = (5)/(7)`
∴ 14x + 126 = 15x + 120
∴ 126 – 120 = 15x – 14x
∴ x = 6.
RELATED QUESTIONS
If ∑ p0q0 = 140, ∑ p0q1 = 200, ∑ p1q0 = 350, ∑ p1q1 = 460, find Laspeyre’s, Paasche’s, Dorbish-Bowley’s and Marshall-Edgeworth’s Price Index Numbers.
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 |
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.
Laspeyre’s Price Index Number is given by ______.
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Choose the correct alternative :
Fisher’s Price Number is given by
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Marshall-Edgeworth’s Price Index Number is given by
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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 |
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"_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:
The formula P01 = `(sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100` is for
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Fisher’s Price Index Number is
Fisher's Price Index Number is given by ______.
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"_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:
`(sum"p"_0sqrt("q"_0 + "q"_1))/(sum"p"_1sqrt("q"_0 + "q"_1)) xx 100` is Marshall-Edgeworth Price Index Number
State whether the following statement is True or False:
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If P01(L) = 40 and P01(P) = 90, find P01(D-B) and P01(F).
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`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 |
