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Question
Calculate Walsh’s Price Index Number.
| Commodity | Base Year | Current Year | ||
| Price | Quantity | Price | Quantity | |
| I | 10 | 12 | 20 | 9 |
| II | 20 | 4 | 25 | 8 |
| III | 30 | 13 | 40 | 27 |
| IV | 60 | 29 | 75 | 36 |
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Solution
| Commodity | Base Year | Current Year | q0q1 | `sqrt("q"_0"q"_1)` | `"p"_0 sqrt("q"_0"q"_1)` | `"p"_1 sqrt("q"_0"q"_1)` | ||
| p0 | q0 | p1 | q1 | |||||
| I | 10 | 12 | 20 | 9 | 108 | 10.39 | 103.9 | 207.8 |
| II | 20 | 4 | 25 | 8 | 32 | 5.66 | 113.2 | 141.5 |
| III | 30 | 13 | 40 | 27 | 351 | 18.73 | 561.9 | 749.2 |
| IV | 60 | 29 | 75 | 36 | 1044 | 32.31 | 1938.6 | 2423.25 |
| Total | - | - | - | - | - | 2717.6 | 3521.75 | |
From the table,
`sum "p"_0 sqrt("q"_0"q"_1) = 2717.6, sum "p"_1 sqrt("q"_0"q"_1) = 3521.75`
Walsh’s Price Index Number:
`"P"_01 ("W") = (sum "p"_1 sqrt("q"_0"q"_1))/(sum "p"_0 sqrt ("q"_0"q"_1)) xx 100`
`= 3521.75/2717.6 xx 100`
= 129.59
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| Commodity | Base year | Current year | ||
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Find x if Paasche’s Price Index Number is 140 for the following data.
| Commodity | Base Year | Current Year | ||
| Price p0 |
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| A | 20 | 8 | 40 | 7 |
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∴ x = `square`
Complete the following activity to calculate, Laspeyre's and Paasche's Price Index Number for the following data :
| Commodity | Base Year | Current Year | ||
| Price p0 |
Quantity q0 |
Price p1 |
Quantity q1 |
|
| 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`
