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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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| I | 20 | 9 | 30 | 4 | 36 | `square` | `square` | 180 |
| II | 10 | 5 | 50 | 5 | `square` | 5 | 50 | `square` |
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| Total | – | – | – | – | 390 | `square` |
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= `510/square xx 100`
= `square`
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| P | 12 | 20 | 18 | 24 |
| Q | 14 | 12 | 21 | 16 |
| R | 8 | 10 | 12 | 18 |
| S | 16 | 15 | 20 | 25 |
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| Commodity | Base Year | Current Year | ||
| Price p0 |
Quantity q0 |
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| I | 8 | 30 | 12 | 25 |
| II | 10 | 42 | 20 | 16 |
Solution:
| Commodity | Base Year | Current Year | p1q0 | p0q0 | p1q1 | p0q1 | ||
| p0 | q0 | p1 | q1 | |||||
| I | 8 | 30 | 12 | 25 | 360 | 240 | 300 | 200 |
| II | 10 | 42 | 20 | 16 | 840 | 420 | 320 | 160 |
| Total | `bb(sump_1q_0=1200)` | `bb(sump_0q_0=660)` | `bb(sump_1q_1=620)` | `bb(sump_0q_1=360)` | ||||
Laspeyre's Price Index Number:
P01(L) = `(sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100 = square/660xx100`
∴ P01(L) = `square`
Paasche 's Price Index Number:
P01(P) = `(sum"p"_1"q"_1)/(sum"p"_0"q"_1) xx 100=(620)/(square) xx 100`
∴ P01(P) = `square`
