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Question
Calculate Walsh’s Price Index Number.
| 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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Solution
Walsh’s Price Index = `(sum(P_1 xx sqrt(q_0q_1)))/(sum(P_0 xx sqrt(q_0q_1))) xx 100`
For Commodity L:
P0 = 4, q0 = 16, P1 = 3, q1 = 19
`sqrt(16xx19) = sqrt304 = 17.44`
`P_1 xx sqrt(q_0q_1) = 3 xx 17.44 = 52.32`
P0 × `sqrt(q_0q_1)` = 4 × 17.44 = 69.76
For Commodity M:
P0 = 6, q0 = 16, P1 = 8, q1 = 14
`sqrt(16xx14) = sqrt224 = 14.97`
P1 × `sqrt(q_0q_1)` = 8 × 14.97 = 119.76
P0 × `sqrt(q_0q_1)` = 6 × 14.97 = 89.82
For Commodity N:
P0 = 8, q0 = 28, P1 = 7, q1 = 32
`sqrt(28xx32) = sqrt896 = 29.93`
P1 × `sqrtq_0q_1` = 7 × 29.93 = 209.51
P0 × `sqrt(q_0q_1)` = 8 × 29.93 = 239.44
Totals:
`sum P_1sqrt(q_0q_1)` = 52.32 + 119.76 + 209.51 = 381.59
`sum P_0sqrt(q_0q_1)` = 69.76 + 89.82 + 239.44 = 398.99
`= 381.59/398.99 = 100`
= 95.64
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| Commodity | Base Year | Current Year | ||
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