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Calculate Laspeyre’s, Paasche’s, Dorbish-Bowley’s, and Marshall - Edgeworth’s Price index numbers. - Mathematics and Statistics

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प्रश्न

Calculate Laspeyre’s, Paasche’s, Dorbish-Bowley’s, and Marshall - Edgeworth’s Price index numbers.

Commodity Base Year Current Year
Price Quantity Price Quantity
I 10 9 20 8
II 20 5 30 4
III 30 7 50 5
IV 40 8 60 6
योग
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उत्तर

Commodity Base Year Current Year p0q0 p1q0 p0q1 p1q1
p0 q0 p1 q1
I 10 9 20 8 90 180 80 160
II 20 5 30 4 100 150 80 120
III 30 7 50 5 210 350 150 250
IV 40 8 60 6 320 480 240 360
Total - - - - 720 1160 550 890

From the table,

`sum "p"_0"q"_0 = 720, sum "p"_1"q"_0 = 1160`

`sum "p"_0"q"_1 = 550, sum "p"_1"q"_1 = 890`

(i) Laspeyre’s Price Index Number:

`"P"_01 ("L") = (sum "p"_1"q"_0)/(sum "p"_0"q"_0) xx 100`

`= 1160/720 xx 100`

= 161.11

(ii) Paasche’s Price Index Number:

`"P"_01 ("P") = (sum "p"_1"q"_1)/(sum "p"_0"q"_1) xx 100`

`= 890/550 xx 100`

= 161.82

(iii) Dorbish-Bowley’s Price Index Number:

`"P"_01 ("D - B") = ("P"_01 ("L") + "P"_01 ("P"))/2`

`= (161.11  +  161.82)/2`

= 161.46

(iv) Marshall-Edgeworth’s Price Index Number:

`"P"_01 ("M- E") = (sum "p"_1"q"_0  +  sum "p"_1"q"_1)/(sum "p"_0"q"_0  +  sum "p"_0"q"_1) xx 100`

`= (1160 + 890)/(720 + 550) xx 100`

= 161.42

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Construction of Index Numbers - Weighted Aggregate Method
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 5: Index Numbers - Exercise 5.2 [पृष्ठ ८२]

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बालभारती Mathematics and Statistics 2 (Commerce) [English] Standard 12 Maharashtra State Board
अध्याय 5 Index Numbers
Exercise 5.2 | Q 1.02 | पृष्ठ ८२

संबंधित प्रश्न

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

If P01(L) = 90 and P01(P) = 40, find P01(D – B) and P01(F).


If ∑p0q0 = 140, ∑p0q1 = 200, ∑p1q0 = 350, ∑p1q1 = 460, find Laspeyre’s, Paasche’s, Dorbish-Bowley’s and Marshall-Edgeworth’s Price Index Numbers.


Given that Laspeyre’s and Dorbish-Bowley’s Price Index Numbers are 160.32 and 164.18 respectively, find Paasche’s Price Index Number.


Find x in the following table if Laspeyre’s and Paasche’s Price Index Numbers are equal.

Commodity Base Year Current year
Price Quantity Price Quantity
A 2 10 2 5
B 2 5 x 2

If Laspeyre's Price Index Number is four times Paasche's Price Index Number, then find the relation between Dorbish-Bowley's and Fisher's Price Index Numbers.


Choose the correct alternative :

The price Index Number by Weighted Aggregate Method is given by ______.


Laspeyre’s Price Index Number is given by ______.


Dorbish-Bowley’s Price Index Number is given by ______.


Fill in the blank :

Paasche’s Price Index Number is given by _______.


`(sump_0(q_0 + q_1))/(sump_1(q_0 + q_1)) xx 100` is Marshall-Edgeworth’s price index number.


`(sum"p"_0sqrt("q"_0"q"_1))/(sum"p"_1sqrt("q"_0"q"_1)) xx 100` is Walsh’s Price Index Number.


Solve the following problem :

Calculate Dorbish-Bowley’s Price Index Number for the following data.

Commodity Base Year Current Year
  Price
p0
Quantity
q0
Price
p1
Quantity
q1
I 8 30 11 28
II 9 25 12 22
III 10 15 13 11

Calculate Walsh’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

Find x if Laspeyre’s Price Index Number is same as Paasche’s Price Index Number for the following data

Commodity Base Year Current Year
  Price
p0
Quantity
q0
Price
p1
Quantity
q1
A 3 x 2 5
B 4 6 3 5

If Laspeyre’s and Dorbish’s Price Index Numbers are 150.2 and 152.8 respectively, find Paasche’s Price Index Number.


Solve the following problem :

Given that `sum "p"_0"q"_0 = 130, sum "p"_1"q"_1 = 140, sum "p"_0"q"_1 = 160, and sum "p"_1"q"_0 = 200`, find Laspeyre’s, Paasche’s, Dorbish-Bowley’s, and Marshall-Edgeworth’s Price Index Numbers.


Choose the correct alternative:

Price Index Number by using Weighted Aggregate Method is given by


Choose the correct alternative:

Walsh's Price Index Number is given by


Marshall-Edgeworth's Price Index Number is given by ______


State whether the following statement is True or False:

Walsh’s Price Index Number is given by `(sum"p"_1sqrt("q"_0"q"_1))/(sum"p"_0sqrt("q"_0"q"_1)) xx 100`


State whether the following statement is True or False:

`(sum"p"_0sqrt("q"_0 + "q"_1))/(sum"p"_1sqrt("q"_0 + "q"_1)) xx 100` is Marshall-Edgeworth Price Index Number


State whether the following statement is True or False:

`[sqrt((sum"p"_1"q"_1)/(sum"p"_0"q"_1)) + (sumsqrt("q"_0"q"_1))/(sum("p"_0 + "p"_1))] xx 100` is Fisher’s Price Index Number.


Calculate Walsh’s price Index Number for the following data.

Commodity Base Year Current Year
Price Quantity Price Quantity
I 10 12 40 3
II 20 2 25 8
III 30 3 50 27
IV 60 9 90 36

If Laspeyre’s and Paasche’s Price Index Numbers are 50 and 72 respectively, find Dorbish-Bowley’s and Fisher’s Price Index Numbers


Given P01(M-E) = 120, `sum"p"_1"q"_1` = 300, `sum"p"_0"q"_0` = 120, `sum"p"_0"q"_1` = 320, Find P01(L)


Given the following table, find Walsh’s Price Index Number by completing the activity.

Commodity p0 q0 p1 q1 q0q1 `sqrt("q"_0"q"_1)` p0`sqrt("q"_0"q"_1)` p1`sqrt("q"_0"q"_1)`
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
Total     390 `square`

Walsh’s price Index Number is

P01(W) = `square/(sum"p"_0sqrt("q"_0"q"_1)) xx 100`

= `510/square xx 100`

= `square`


`sqrt((sump_1q_0)/(sump_0q_0)) xx sqrt((sump_1q_1)/(sump_0q_1)) xx 100`


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`


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