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Question
Calculate price index number for 2005 by (a) Laspeyre’s (b) Paasche’s method
| Commodity | 1995 | 2005 | ||
| Price | Quantity | Price | Quantity | |
| A | 5 | 60 | 15 | 70 |
| B | 4 | 20 | 8 | 35 |
| C | 3 | 15 | 6 | 20 |
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Solution
| Commodity | 1995 (Base year) |
2005 (Current year) |
p0q0 | p0q1 | p1q0 | p1q1 | ||
| p0 | q0 | p1 | q1 | |||||
| A | 5 | 60 | 15 | 70 | 300 | 350 | 900 | 1050 |
| B | 4 | 20 | 8 | 35 | 80 | 140 | 60 | 280 |
| C | 3 | 15 | 6 | 20 | 45 | 60 | 90 | 120 |
| Total | `sum"p"_0"q"_0` = 425 | `sum"p"_0"q"_0` = 550 | `sum"p"_1"q"_0` = 1150 | `sum"p"_1"q"_1` = 1450 | ||||
(a) Laspeyre’s price index number
`"P"_01^"L" = (sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100`
= `1150/425 xx 100`
= 270.6
(b) Passche's price index
`"P"_01^"P" = (sum"p"_1"q"_1)/(sum"p"_0"q"_1) xx 100`
= `2230/550 xx 100`
= 405.5
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| Commodities | Base Year | Current Year | ||
| Price | Quantity | Price | Quantity | |
| A | 170 | 562 | 72 | 632 |
| B | 192 | 535 | 70 | 756 |
| C | 195 | 639 | 95 | 926 |
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| E | 1985 | 542 | 92 | 632 |
| F | 150 | 217 | 180 | 314 |
| 7 | 12.6 | 12.7 | 12.5 | 12.8 |
| 8 | 12.4 | 12.3 | 12.6 | 12.5 |
| 9 | 12.6 | 12.5 | 12.3 | 12.6 |
| 10 | 12.1 | 12.7 | 12.5 | 12.8 |
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- Assertion (A): The index number considers all factors.
- Reasoning (R): The index number is based on samples.
State with reasons whether you agree or disagree with the following statement:
Index number measures changes in the price level only.
Choose the correct pair :
| Group A | Group B | ||
| 1) | Price Index | a) | `(sump_1q_1)/(sump_0q_0) xx100` |
| 2) | Value Index |
b) |
`(sumq_1)/(sumq_0) xx 100` |
| 3) | Quantity Index | c) | `(sump_1q_1)/(sump_0q_1) xx100` |
| 4) | Paasche's Index | d) | `(sump_1)/(sump_0) xx 100` |
The base year's index of a selected variable is assumed as ______.
