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Question
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 |
Solution
| Commodity | Base Year | Current Year | p0q1 | p1q1 | ||
| p0 | q0 | p1 | q1 | |||
| A | 20 | 8 | 40 | 7 | 140 | 280 |
| B | 50 | 10 | 60 | 10 | 500 | 600 |
| C | 40 | 15 | 60 | x | 40x | 60x |
| D | 12 | 15 | 15 | 15 | 180 | 225 |
| Total | – | – | – | – | 40x + 820 | 60x + 1105 |
From the table,
`sum"p"_0"q"_1 = 40x + 820, sum"p"_1"q"_1 = 60x + 1,105`
Paasche’s Price Index Number:
P01(P) = `(sum"p"_1"q"_1)/(sum"p"_0"q"_1) xx 100`
∴ 140 = `(60x + 1105)/(40x + 820) xx 100` ...[P01(P) = 140]
∴ `(140)/(100) = (60x + 1,105)/(40x + 820)`
∴ `(7)/(5) = (60x + 1,105)/(40x + 820)`
∴ 280x + 5,740 = 300x + 5,525
∴ 300x – 280x = 5,740 – 5,525
∴ 20x = 215
∴ x = 10.75
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RELATED QUESTIONS
Given that Laspeyre’s and Dorbish-Bowley’s Price Index Numbers are 160.32 and 164.18 respectively, find Paasche’s Price Index Number.
Choose the correct alternative :
The price Index Number by Weighted Aggregate Method is given by ______.
Dorbish-Bowley’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 :
Dorbish-Bowley’s Price Index Number is given by _______.
Solve the following problem :
Calculate Dorbish-Bowley’s Price Index Number for the following data.
| Commodity | Base Year | Current Year | ||
| Price p0 |
Quantity q0 |
Price p1 |
Quantity q1 |
|
| I | 8 | 30 | 11 | 28 |
| II | 9 | 25 | 12 | 22 |
| III | 10 | 15 | 13 | 11 |
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 `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:
The formula P01 = `(sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100` is for
Choose the correct alternative:
Walsh's Price Index Number is given by
Fisher's Price Index Number is given by ______.
Marshall-Edgeworth's Price Index Number is given by ______
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 |
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`
If P01 (L) = 121, P01 (P) = 100, then P01 (F) = ______.
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 |
