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.

Question

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.

Sum

Solution

Given, P₀₁(L) = 25, P₀₁(P) = 16
Dorbish-Bowley’s Price Index Number:

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

= (25 + 16)/(2)`

= `(41)/(2)`
= 20.5

Fisher’s Price Index Number:

P₀₁(F) = `sqrt("P"_01("L") xx "P"_01("P"))`

= `sqrt(25 xx 16)`

= `sqrt(400)`
= 20

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Construction of Index Numbers - Weighted Aggregate Method

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Q 4.13 Q 4.12 Q 4.14

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 4.13 | Page 93

RELATED QUESTIONS

Calculate Walsh’s Price Index Number.

Commodity	Base Year		Current Year
Commodity	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).

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Given that ∑p₀q₀ = 220, ∑p₀q₁ = 380, ∑p₁q₁ = 350 and Marshall-Edgeworth’s Price Index Number is 150, find Laspeyre’s Price Index Number.

If Dorbish-Bowley's and Fisher's Price Index Numbers are 5 and 4, respectively, then find Laspeyre's and Paasche's Price Index Numbers.

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

Laspeyre’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 _______.

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

Solve the following problem :

Calculate Marshall-Edgeworth’s Price Index Number for the following data.

Commodity	Base Year		Current Year
	Price p₀	Quantity q₀	Price p₁	Quantity q₁
X	12	35	15	25
Y	29	50	30	70

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

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 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 :

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 `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:

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

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

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Calculate Marshall – Edgeworth’s price index number for the following data:

Commodity	Base year		Current year
Commodity	Price	Quantity	Price	Quantity
P	12	20	18	24
Q	14	12	21	16
R	8	10	12	18
S	16	15	20	25

Complete the following activity to calculate, Laspeyre's and Paasche's Price Index Number for the following data :

Commodity	Base Year		Current Year
Commodity	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	p₁q₀	p₀q₀	p₁q₁	p₀q₁
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`

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.

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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.

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