Find the missing price if Laspeyre’s and Paasche’s Price Index Numbers are equal for following data. Commodity Base Year Current Year Price Quantity Price Quantity A 1 10 2 5 B 1 5 – 12 - Mathematics and Statistics

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Find the missing price if Laspeyre’s and Paasche’s Price Index Numbers are equal for following data.

Commodity Base Year Current Year
Price Quantity Price Quantity
A 1 10 2 5
B 1 12
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Solution

Let us denote the missing value by x and reconstruct the table as follows.

Commodity Base Year Current Year p0q0 p1q0 p1q1 p0q1
p0 q0 p1 q1
A 1 10 2 5 10 20 10 5
B 1 5 x 12 5 5x 1 12
Total         15 20 + 5x 10 + 12x 17

The above table gives

`sum"p"0"q"_0` = 15, `sum"p"_1"q"_0` = 20  5x, `sum"p"_1"q"_1` = 10 + 12x, `sum"p"_0"q"_1` = 17

It is given that

P01(L) = P01(P)

`(sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100`

`(sum"p"_1"q"_1)/(sum"p"_0"q"_1) xx 100`

∴ `(5x + 20)/15 = (12x + 10)/17`

∴ `(5(x + 4))/15 = (12x + 10)/17`

∴ 17(x + 4) = 3(12x + 10)

∴ 17x + 68 = 36x + 30

∴ x = 2

Concept: Construction of Index Numbers - Weighted Aggregate Method
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Chapter 2.5: Index Numbers - Q.4

RELATED QUESTIONS

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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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A 2 10 2 5
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X 12 35 15 25
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Solve the following problem :

Calculate Laspeyre’s and Paasche’s Price Index Number for the following data.

Commodity Base Year Current Year
  Price
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I 8 30 12 25
II 10 42 20 16

Solve the following problem :

Given that Laspeyre’s and Paasche’s Price Index Numbers are 25 and 16 respectively, find Dorbish-Bowley’s and Fisher’s Price Index Number.


Choose the correct alternative:

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b) Passche’s
c) Dorbish-Bowley’s Price Index Numbers for following data.

Commodity Base Year Current Year
Price Quantity Price Quantity
A 10 9 50 8
B 20 5 60 4
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I 10 12 40 3
II 20 2 25 8
III 30 3 50 27
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If P01(L) = 40 and P01(P) = 90, find P01(D-B) and P01(F).


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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`
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Total     390 `square`

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P 12 20 18 24
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R 8 10 12 18
S 16 15 20 25

If ∑ p0q0 = 120, ∑ p0q1 = 160, ∑ p1q1 = 140, ∑ p1qo = 200, find Laspeyre’s, Paasche’s, Dorbish-Bowley’s and Marshall-Edgeworth’s Price Index Numbers.


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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:

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∴ 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`


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