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Question
Calculate by a suitable method, the index number of price from the following data:
| Commodity | 2002 | 2012 | ||
| Price | Quantity | Price | Quantity | |
| A | 10 | 20 | 16 | 10 |
| B | 12 | 34 | 18 | 42 |
| C | 15 | 30 | 20 | 26 |
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Solution
| Commodity | 2002 (Base year) |
2012 (Current year) |
p0q0 |
p0q1 |
p1q0 |
p1q1 |
||
| p0 | q0 | p1 | q1 | |||||
| A | 10 | 20 | 16 | 10 | 200 | 100 | 320 | 160 |
| B | 12 | 34 | 18 | 42 | 408 | 504 | 612 | 756 |
| C | 15 | 30 | 20 | 26 | 450 | 390 | 600 | 520 |
| Total | `sum"p"_0"q"_0` = 1058 | `sum"p"_0"q"_1` = 1054 | `sum"p"_1"q"_0` = 1532 | `sum"p"_1"q"_0` = 1436 | ||||
Laspeyres price index number
`"P"_01^"L" = (sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100`
= `1532/1058 xx 100`
= 144.8
Peasche's price index number
`"P"_01^"P" = (sum"p"_1"q"_1)/(sum"p"_0"q"_1) xx 100`
= `1436/1054 xx 100`
= 136.24
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| Commodity | Price | Weights | |
| 2012 | 2015 | ||
| Rice | 250 | 280 | 10 |
| Wheat | 70 | 85 | 5 |
| Corn | 150 | 170 | 6 |
| Oil | 25 | 35 | 4 |
| Dhal | 85 | 90 | 3 |
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Calculate the Laspeyre’s, Paasche’s and Fisher’s price index number for the following data. Interpret on the data.
| Commodities | Base Year | Current Year | ||
| Price | Quantity | Price | Quantity | |
| A | 170 | 562 | 72 | 632 |
| B | 192 | 535 | 70 | 756 |
| C | 195 | 639 | 95 | 926 |
| D | 1987 | 128 | 92 | 255 |
| 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 |
Using the following data, construct Fisher’s Ideal Index Number and Show that it satisfies Factor Reversal Test and Time Reversal Test?
| Commodities | Price | Quantity | ||
| Base Year | Current Year | Base Year | Current Year | |
| Wheat | 6 | 10 | 50 | 56 |
| Ghee | 2 | 2 | 100 | 120 |
| Firewood | 4 | 6 | 60 | 60 |
| Sugar | 10 | 12 | 30 | 24 |
| Cloth | 8 | 12 | 40 | 36 |
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)xx100` |
| 3) Quantity Index | c) `(sump_1q_1)/(sump_0q_1)xx100` |
| 4) Paasche's Index | d) `(sump_1)/(sump_0)xx100` |
