If ∑ p0q0 = 140, ∑ p0q1 = 200, ∑ p1q0 = 350, ∑ p1q1 = 460, find Laspeyre’s, Paasche’s, Dorbish-Bowley’s and Marshall-Edgeworth’s Price Index Numbers. - Mathematics and Statistics

Question

If ∑ p₀q₀ = 140, ∑ p₀q₁ = 200, ∑ p₁q₀ = 350, ∑ p₁q₁ = 460, find Laspeyre’s, Paasche’s, Dorbish-Bowley’s and Marshall-Edgeworth’s Price Index Numbers.

Sum

Solution

Given, ∑ p₀q₀ = 140, ∑ p₀q₁ = 200,
∑ p₁q₀ = 350, ∑ p₁q₁ = 460

Laspeyre’s Price Index Number:

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

`= 350/140 xx 100 = 250`

Paasche’s Price Index Number:

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

`= 460/200 xx 100 = 230`

Dorbish-Bowley’s Price Index Number:

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

`= (250 + 230)/2 = 480/2 = 240`

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`

`= (350 + 460)/(140 + 200) xx 100`

`= 810/340 xx 100 = 238.24`

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Construction of Index Numbers - Weighted Aggregate Method

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Q 1.06 Q 1.05 Q 1.07

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

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

Chapter 5 Index Numbers
Exercise 5.2 | Q 1.06 | Page 82

RELATED QUESTIONS

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

Commodity	Base Year		Current Year
Commodity	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
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

Paasche’s Price Index Number is given by ______

Choose the correct alternative :

Walsh’s Price Index Number is given by

Laspeyre’s Price Index Number is given by _______.

Walsh’s Price Index Number is given by _______.

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.

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 `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:

Dorbish–Bowley’s Price Index Number is

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)

Given the following table, find Walsh’s Price Index Number by completing the activity.

Commodity	p₀	q₀	p₁	q₁	q₀q₁	`sqrt("q"_0"q"_1)`	p₀`sqrt("q"_0"q"_1)`	p₁`sqrt("q"_0"q"_1)`
I	20	9	30	4	36	`square`	`square`	180
II	10	5	50	5	`square`	5	50	`square`
III	40	8	10	2	16	`square`	160	`square`
IV	30	4	20	1	`square`	2	`square`	40
Total	–	–	–	–			390	`square`

Walsh’s price Index Number is

P₀₁(W) = `square/(sum"p"_0sqrt("q"_0"q"_1)) xx 100`

= `510/square xx 100`

= `square`

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`

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

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

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
Commodity	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
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`

If ∑ p0q0 = 140, ∑ p0q1 = 200, ∑ p1q0 = 350, ∑ p1q1 = 460, find Laspeyre’s, Paasche’s, Dorbish-Bowley’s and Marshall-Edgeworth’s Price Index Numbers. - Mathematics and Statistics

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If ∑ p0q0 = 140, ∑ p0q1 = 200, ∑ p1q0 = 350, ∑ p1q1 = 460, find Laspeyre’s, Paasche’s, Dorbish-Bowley’s and Marshall-Edgeworth’s Price Index Numbers. - Mathematics and Statistics

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