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Question
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 |
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Solution
Construct the following table:
| Commodity | Base Year |
Current Year |
p0q0 | p1q0 | p0q1 | p1q1 | ||
| p0 | q0 | p1 | q1 | |||||
| I | 10 | 9 | 50 | 8 | 90 | 450 | 80 | 400 |
| II | 20 | 5 | 60 | 4 | 100 | 300 | 80 | 240 |
| III | 30 | 7 | 70 | 3 | 210 | 490 | 90 | 210 |
| IV | 40 | 8 | 80 | 2 | 320 | 640 | 80 | 160 |
| Total | – | – | – | – | 720 | 1880 | 330 | 1010 |
From the table, `sum"p"_0"q"_0` = 720, `sum"p"_1"q"_0` = 1880, `sum"p"_0"q"_1` = 330, `sum"p"_1"q"_1` = 1010
a) Laspeyre’s Price Index Number:
P01(L) = `(sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100`
= `1880/720 xx 100`
= 261.11
b) Paasche’s Price Index Number:
P01(P) = `(sum"p"_1"q"_1)/(sum"p"_0"q"_1) xx 100`
= `1010/330 xx 100`
= 306.06
c) Drobish-Bowley’s Price Index Number:
P01(D-B) = `("P"_01("L") + "P"_01("P"))/2`
= `(261.11 + 306.06)/2`
= `567.17/2`
= 283.59
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 | |
| 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.
Given that Laspeyre’s and Dorbish-Bowley’s Price Index Numbers are 160.32 and 164.18 respectively, find Paasche’s Price Index Number.
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 |
Choose the correct alternative :
Marshall-Edgeworth’s Price Index Number is given by
Fill in the blank :
Paasche’s Price Index Number is given by _______.
Fill in the blank :
Marshall-Edgeworth’s Price Index Number is given by _______.
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 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 :
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 |
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 |
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 |
If Laspeyre’s and Dorbish’s Price Index Numbers are 150.2 and 152.8 respectively, find 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
Choose the correct alternative:
Dorbish–Bowley’s Price Index Number is
Choose the correct alternative:
Walsh's Price Index Number is given by
State whether the following statement is True or False:
Walsh’s Price Index Number is given by `(sum"p"_1sqrt("q"_0"q"_1))/(sum"p"_0sqrt("q"_0"q"_1)) xx 100`
Calculate Marshall-Edgeworth Price Index Number for following.
| 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 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).
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`
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`
