Solve the following problem : If ∑p_0q0=120,∑p0q1=160,∑p1q1=140,and∑p1q+0 = 200, find Laspeyre’s, Paasche’s Dorbish-Bowley’s and Marshall Edgeworth’s Price Index Number.

प्रश्न

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.

योग

उत्तर

Given,
`sum"p"_0"q"_0 = 120, 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)/(120) xx 100` = 166.67

Paasche’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)`

= `(166.67 + 87.5)/(2)`

= `(254.17)/(2)`
= 127.085

Marshall-Edgeworth’s Price Index Number:

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

= `(200 + 140)/(120 + 160) xx 100`

= `(340)/(280) xx 100`
= 121.43

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Construction of Index Numbers - Weighted Aggregate Method

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Q 4.15 Q 4.14 Q 4.16

अध्याय 5: Index Numbers - Miscellaneous Exercise 5 [पृष्ठ ९३]

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बालभारती Mathematics and Statistics 2 (Commerce) [English] Standard 12 Maharashtra State Board

अध्याय 5 Index Numbers
Miscellaneous Exercise 5 | Q 4.15 | पृष्ठ ९३

संबंधित प्रश्न

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

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

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

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.

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 :

Fisher’s Price 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.

`(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

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

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:

Dorbish–Bowley’s Price Index Number is

Choose the correct alternative:

Fisher’s Price Index Number is

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

Calculate
a) Laspeyre’s
b) Passche’s
c) Dorbish-Bowley’s Price Index Numbers for following data.

Commodity	Base Year		Current Year
Commodity	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 Laspeyre’s and Paasche’s Price Index Numbers are 50 and 72 respectively, find Dorbish-Bowley’s and Fisher’s Price Index Numbers

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.

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

If ∑ p₀q₀ = 120, ∑ p₀q₁ = 160, ∑ p₁q₁= 140, ∑ p₁q_o= 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
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 : If ∑p_0q0=120,∑p0q1=160,∑p1q1=140,and∑p1q+0 = 200, find Laspeyre’s, Paasche’s Dorbish-Bowley’s and Marshall Edgeworth’s Price Index Number.

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Solve the following problem : If ∑p_0q0=120,∑p0q1=160,∑p1q1=140,and∑p1q+0 = 200, find Laspeyre’s, Paasche’s Dorbish-Bowley’s and Marshall Edgeworth’s Price Index Number.

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