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Question
Given that ∑p0q0 = 220, ∑p0q1 = 380, ∑p1q1 = 350 and Marshall-Edgeworth’s Price Index Number is 150, find Laspeyre’s Price Index Number.
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Solution
Given:
∑p0q0 = 220,
∑p0q1 = 380,
∑p1q1 = 350 and
P01 (M − E) = 150
To find:
P01(L) = ?
We have
`P_01(M - E) = (sum p_1q_0 + sum p_1q_1)/(sum p_0q_0 + sum p_0q_1) xx 100`
∴ `150 = (sum p_1q_0 + 350)/(220 + 380) xx 100`
∴ `150 = (sum p_1q_0 + 350)/600 xx 100`
∴ `(150 xx 600)/100 = sum p_1q_0 + 350`
∴ 150 × 6 = ∑p1q0 + 350
∴ 900 = ∑p1q0 + 350
∴ ∑p1q0 = 900 − 350
∴ ∑p1q0 = 550
`P_01(L) = (sum p_1q_0)/(sum p_0q_0) xx 100`
= `550/220 xx 100`
= 2.5 × 100
= 250
Hence, Laspeyre’s Price Index Number is 250.
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| I | 10 | 9 | 20 | 8 |
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| Commodity | Base year | Current year | ||
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If find x is Walsh’s Price Index Number is 150 for the following data
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| A | 5 | 3 | 10 | 3 |
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| Commodity | Base Year | Current Year | ||
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| A | 20 | 8 | 40 | 7 |
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Given that `sum "p"_1"q"_1 = 300, sum "p"_0"q"_1 = 320, sum "p"_0"q"_0` = 120, and Marshall- Edgeworth’s Price Index Number is 120, find `sum"p"_1"q"_0` and Paasche’s Price Index Number.
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| I | 20 | 9 | 30 | 4 | 36 | `square` | `square` | 180 |
| II | 10 | 5 | 50 | 5 | `square` | 5 | 50 | `square` |
| III | 40 | 8 | 10 | 2 | 16 | `square` | 160 | `square` |
| IV | 30 | 4 | 20 | 1 | `square` | 2 | `square` | 40 |
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| Commodity | Base year | Current year | ||
| Price | Quantity | Price | Quantity | |
| 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 | Quantity | Price | Quantity | |
| A | 2 | 10 | 2 | 5 |
| B | 2 | 5 | x | 2 |
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`(20 + 5x)/square xx 100 = square/14 xx 100`
∴ 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`
