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Question
If Laspeyre’s and Dorbish’s Price Index Numbers are 150.2 and 152.8 respectively, find Paasche’s Price Index Number.
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Solution
Given, P01(L) = 150.2, P01(D-B) = 152.8
Dorbish-Bowley’s Price Index Number:
P01(D-B) = `("P"_01("L") + "P"_01("P"))/(2)`
∴ 152.8 = `(150.2 + "P"_01("P"))/(2)`
∴ 305.6 = 150.2 6 + P01(P)
∴ P01(P) = 305.6 – 150.2 = 155.4
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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`
