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

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Question

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

Commodity Base Year Current Year
Price Quantity Price Quantity
A 8 20 11 15
B 7 10 12 10
C 3 30 5 25
D 2 50 4 35
Sum
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Solution

Commodity Base Year Current Year p0q0 p1q0 p0q1 p1q1
p0 q0 p1 q1
A 8 20 11 15 160 220 120 165
B 7 10 12 10 70 120 70 120
C 3 30 5 25 90 150 75 125
D 2 50 4 35 100 200 70 140
Total - - - - 420 690 335 550

From the table,

`sum "p"_0"q"_0 = 420, sum "p"_1"q"_0 = 690`

`sum "p"_0"q"_1 = 335, sum "p"_1"q"_1 = 550`

(i) Laspeyre’s Price Index Number:

`"P"_01 ("L") = (sum "p"_1"q"_0)/(sum "p"_0"q"_0) xx 100 = 690/420 xx 100 = 164.29`

(ii) Paasche’s Price Index Number:

`"P"_01 ("P") = (sum "p"_1"q"_1)/(sum "p"_0"q"_1) xx 100 = 550/335 xx 100 = 164.18`

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

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

`= (164.29  +  164.18)/2`

= 164.24

(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`

`= (690 + 550)/(420 + 335) xx 100`

`= 1240/755 xx 100`

= 164.24

shaalaa.com
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

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

Calculate Walsh’s Price Index Number.

Commodity Base Year Current Year
Price Quantity Price Quantity
L 4 16 3 19
M 6 16 8 14
N 8 28 7 32

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 ______.


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 :

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


Fill in the blank :

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


`(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 :

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 :

Find x if Paasche’s Price Index Number is 140 for the following data.

Commodity Base Year Current Year
  Price
p0
Quantity
q0
Price
p1
Quantity
q1
A 20 8 40 7
B 50 10 60 10
C 40 15 60 x
D 12 15 15 15

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.


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


State whether the following statement is True or False:

`(sum"p"_1"q"_1)/(sum"p"_0"q"_1) xx 100` is Paasche’s Price Index Number


Calculate
a) Laspeyre’s
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
C 30 7 70 3
D 40 8 80 2

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


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)


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 P01 (L) = 121, P01 (P) = 100, then P01 (F) = ______.


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


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`


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