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Question
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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Solution
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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RELATED QUESTIONS
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 |
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 |
Paasche’s Price Index Number is given by ______.
Choose the correct alternative :
Fisher’s Price 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.
State whether the following is True or False :
`(1)/(2)[sqrt((sum"p"_1"q"_0)/(sum"p"_0"q"_0)) + sqrt("p"_1"q"_1)/(sqrt("p"_0"q"_1))] xx 100` is Fisher’s Price Index Number.
`(sump_0(q_0 + q_1))/(sump_1(q_0 + q_1)) xx 100` is Marshall-Edgeworth’s price index number.
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 |
Calculate Walsh’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 |
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
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:
`[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.
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).
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)
Find the missing price if Laspeyre’s and Paasche’s Price Index Numbers are equal for following data.
| Commodity | Base Year | Current Year | ||
| Price | Quantity | Price | Quantity | |
| A | 1 | 10 | 2 | 5 |
| B | 1 | 5 | – | 12 |
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`
If ∑ p0q0 = 120, ∑ p0q1 = 160, ∑ p1q1 = 140, ∑ p1qo = 200, find Laspeyre’s, Paasche’s, Dorbish-Bowley’s and Marshall-Edgeworth’s Price Index Numbers.
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`
