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Question
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.
Options
True
False
Solution
This statement is False.
Explanation:
P01 (F) = `sqrt(P_(01) (L) xx P_(01) (P))`
Fisher's Ideal Price. The index Number is the square root of the product of Lospeyre's Price. Index number and Paasche's Price Index Number.
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RELATED QUESTIONS
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 |
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 P01(L) = 90 and P01(P) = 40, find P01(D – B) and P01(F).
Given that ∑ p0q0 = 220, ∑ p0q1 = 380, ∑ p1q1 = 350 and MarshallEdgeworth’s Price Index Number is 150, find Laspeyre’s Price Index Number.
Laspeyre’s Price Index Number is given by ______.
State whether the following is True or False :
`sum("p"_1"q"_1)/("p"_0"q"_1)` is Laspeyre’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 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:
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 :
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 `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
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:
Dorbish–Bowley’s Price Index Number is
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
If P01(L) = 40 and P01(P) = 90, find P01(D-B) and P01(F).
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)
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) = ______.
`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 |
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`
Complete the following activity to 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 |
Solution:
| Commodity | Base Year | Current Year | p1q0 | p0q0 | p1q1 | p0q1 | ||
| p0 | q0 | p1 | q1 | |||||
| I | 8 | 30 | 12 | 25 | 360 | 240 | 300 | 200 |
| II | 10 | 42 | 20 | 16 | 840 | 420 | 320 | 160 |
| Total | `bb(sump_1q_0=1200)` | `bb(sump_0q_0=660)` | `bb(sump_1q_1=620)` | `bb(sump_0q_1=360)` | ||||
Laspeyre's Price Index Number:
P01(L) = `(sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100 = square/660xx100`
∴ P01(L) = `square`
Paasche 's Price Index Number:
P01(P) = `(sum"p"_1"q"_1)/(sum"p"_0"q"_1) xx 100=(620)/(square) xx 100`
∴ P01(P) = `square`
