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Question
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 |
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Solution
| Commodity | Base Year | Current Year | p0q0 | p1q0 | p0q1 | p1q1 | ||
| p0 | q0 | p1 | q1 | |||||
| I | 10 | 9 | 20 | 8 | 90 | 180 | 80 | 160 |
| II | 20 | 5 | 30 | 4 | 100 | 150 | 80 | 120 |
| III | 30 | 7 | 50 | 5 | 210 | 350 | 150 | 250 |
| IV | 40 | 8 | 60 | 6 | 320 | 480 | 240 | 360 |
| Total | - | - | - | - | 720 | 1160 | 550 | 890 |
From the table,
`sum "p"_0"q"_0 = 720, sum "p"_1"q"_0 = 1160`
`sum "p"_0"q"_1 = 550, sum "p"_1"q"_1 = 890`
(i) Laspeyre’s Price Index Number:
`"P"_01 ("L") = (sum "p"_1"q"_0)/(sum "p"_0"q"_0) xx 100`
`= 1160/720 xx 100`
= 161.11
(ii) Paasche’s Price Index Number:
`"P"_01 ("P") = (sum "p"_1"q"_1)/(sum "p"_0"q"_1) xx 100`
`= 890/550 xx 100`
= 161.82
(iii) Dorbish-Bowley’s Price Index Number:
`"P"_01 ("D - B") = ("P"_01 ("L") + "P"_01 ("P"))/2`
`= (161.11 + 161.82)/2`
= 161.46
(iv) Marshall-Edgeworth’s Price Index Number:
`"P"_01 ("M- E") = (sum "p"_1"q"_0 + sum "p"_1"q"_1)/(sum "p"_0"q"_0 + sum "p"_0"q"_1) xx 100`
`= (1160 + 890)/(720 + 550) xx 100`
= 161.42
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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 |
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| Commodity | Base Year | Current Year | ||
| Price | Quantity | Price | Quantity | |
| L | 4 | 16 | 3 | 19 |
| M | 6 | 16 | 8 | 14 |
| N | 8 | 28 | 7 | 32 |
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State whether the following is True or False :
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| 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 |
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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.
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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:
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| 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 |
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`(20 + 5x)/square xx 100 = square/14 xx 100`
∴ x = `square`
