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Question
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 |
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Solution
| Commodity | Base Year | Current Year | p0q0 | p1q0 | p0q1 | p1q1 | ||
| p0 | q0 | p1 | q1 | |||||
| A | 20 | 18 | 30 | 15 | 360 | 540 | 300 | 450 |
| B | 25 | 8 | 28 | 5 | 200 | 224 | 125 | 140 |
| C | 32 | 5 | 40 | 7 | 160 | 200 | 224 | 280 |
| D | 12 | 10 | 18 | 10 | 120 | 180 | 120 | 180 |
| Total | – | – | – | – | 840 | 1144 | 769 | 1050 |
From the table,
`sum"p"_0"q"_0 = 840, sum"p"_1"q"_0 = 1144`,
`sum"p"_0"q"_1 = 769, sum"p"_1"q"_1 = 1050`
Laspeyre's Price Index Number:
P01(L) = `(sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100`
= `(1144)/(840) xx 100`
= 136.19
Paasche's Price Index Number:
P01(P) = `(sum"p"_1"q"_1)/(sum"p"_0"q"_1) xx 100`
= `(1050)/(769) xx 100`
= 136.54
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| Commodity | Base Year | Current Year | ||
| Price p0 |
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| Price | Quantity | Price | Quantity | |
| A | 8 | 20 | 11 | 15 |
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| I | 10 | 12 | 40 | 3 |
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