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Solve the following problem : Given that ∑p0q0=130,∑p1q1=140,∑p0q1=160,and∑p1q0=200, find Laspeyre’s, Paasche’s, Dorbish-Bowley’s, and Marshall-Edgeworth’s Price Index Numbers. - Mathematics and Statistics

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Question

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.

Sum
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Solution

Given,
`sum"P"_0"q"_0 = 130, sum"p"_0"q"_1 = 160`,
`sum"p"_1"q"_1 = 140, sum"p"_1"q"_0 = 200`

Laspeyre’s Price Index Number:

P01(L) = `(sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100`

= `(200)/(130) xx 100` = 153.85

Laspeyre’s Price Index Number:

P01(P) = `(sum"p"_1"q"_1)/(sum"p"_0"q"_1) xx 100`

= `(140)/(160) xx 100` = 87.5

Dorbish-Bowley’s Price Index Number:

P01(D–B) = `("P"_01("L") + "P"_01("P"))/(2)`

= `(153.85 + 87.5)/(2)` = 120.68

Marshall-Edgeworth’s Price Index Number:

P01(M–E) = `(sum"p"_1"q"_0 + sum"p"_1"q"_1)/(sum"p"_0"q"_0 + sum"p"_0"q"_1) xx 100`

= `(200 + 140)/(130 + 160) xx 100`
= 117.24

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Construction of Index Numbers - Weighted Aggregate Method
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Chapter 5: Index Numbers - Miscellaneous Exercise 5 [Page 93]

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Balbharati Mathematics and Statistics 2 (Commerce) [English] Standard 12 Maharashtra State Board
Chapter 5 Index Numbers
Miscellaneous Exercise 5 | Q 4.16 | Page 93

RELATED QUESTIONS

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 ______.


Paasche’s Price Index Number is given by ______.


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


Choose the correct alternative :

Marshall-Edgeworth’s Price Index Number is given by


Walsh’s Price Index Number is given by _______.


`(sump_1q_0)/(sump_0q_0) xx 100` is Paasche’s Price Index Number.


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 :

`(sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx (sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100` is Dorbish-Bowley’s Price Index Number.


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


State whether the following is True or False :

`sqrt(("p"_1"q"_0)/(sum"p"_0"q"_0)) xx sqrt((sum"p"_1"q"_1)/(sum"p"_0"q"_1)) xx 100` is Fisher’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 :

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

Solve the following problem :

If `sum"p_"0"q"_0 = 120, sum "p"_0"q"_1 = 160, sum "p"_1"q"_1 = 140, and sum "p"_1"q"+0` = 200, find Laspeyre’s, Paasche’s Dorbish-Bowley’s and Marshall Edgeworth’s Price Index Number.


Choose the correct alternative:

Walsh's Price Index Number is given by


Choose the correct alternative:

Fisher’s Price Index Number is


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

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.


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


Laspeyre’s Price Index Number uses current year’s quantities as weights.


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


In the following table, Laspeyre's and Paasche's Price Index Numbers are equal. Complete the following activity to find x :

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

Solution: P01(L) = P01(P)

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

`(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`


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