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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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Question

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
Sum
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Solution

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
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Chapter 5: Index Numbers - Exercise 5.2 [Page 82]

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RELATED QUESTIONS

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 ______.


Paasche’s Price Index Number is given by ______.


Choose the correct alternative :

Fisher’s Price Number is given by


Choose the correct alternative :

Marshall-Edgeworth’s Price Index Number is given by


Fill in the blank :

Marshall-Edgeworth’s Price Index Number is given by _______.


Walsh’s Price Index Number is given by _______.


State whether the following is True or False :

`sum("p"_1"q"_1)/("p"_0"q"_1)` is Laspeyre’s Price Index Number.


State whether the following is True or False :

`(1)/(2)[sqrt((sum"p"_1"q"_0)/(sum"p"_0"q"_0)) + sqrt("p"_1"q"_1)/(sqrt("p"_0"q"_1))] xx 100` is Fisher’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 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
A 20 18 30 15
B 25 8 28 5
C 32 5 40 7
D 12 10 18 10

Solve the following problem:

If find x is Walsh’s Price Index Number is 150 for the following data

Commodity Base Year Current Year
  Price
p0
Quantity
q0
Price
p1
Quantity
q1
A 5 3 10 3
B x 4 16 9
C 15 5 23 5
D 10 2 26 8

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:

Price Index Number by using Weighted Aggregate Method is given by


Choose the correct alternative:

Fisher’s Price Index Number is


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


The average of Laspeyre’s and Paasche’s Price Index Numbers is called ______ Price Index Number


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.


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)


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

If `sum"p"_0"q"_0` = 150, `sum"p"_0"q"_1` = 250, `sum"p"_1"q"_1` = 375 and P01(L) = 140. Find P01(M-E)


State whether the following statement is true or false:

Dorbish-Bowley's Price Index Number is the square root of the product of Laspeyre's and Paasche's Index Numbers.


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


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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