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Question
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 |
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Solution
Construct the following table:
| Commodity | Base Year |
Current Year |
`sqrt("q"_1"q"_1)` | `"p"_0sqrt("q"_0"q"_1)` | `"p"_1 sqrt("q"_0"q"_1)` | ||
| p0 | q0 | p1 | q1 | ||||
| I | 10 | 12 | 40 | 3 | 6 | 60 | 240 |
| II | 20 | 2 | 25 | 8 | 4 | 80 | 100 |
| III | 30 | 3 | 50 | 27 | 9 | 270 | 450 |
| IV | 60 | 9 | 90 | 36 | 18 | 1080 | 1620 |
| Total | – | – | – | – | – | 1490 | 2410 |
From the table, `sum"p"_0 sqrt("q"_0"q"_1)` = 1490, `sum"p"_1sqrt("q"_0"q"_1)` = 2410
Walsh’s Price Index Number:
P01(W) = `(sum"p"_1sqrt("q"_0"q"_1))/(sum"p"_0sqrt("q"_0"q"_1)) xx 100`
= `2410/1490 xx 100`
= 161.74
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