Calculate Walsh’s Price Index Number. Commodity Base Year Current Year Price Quantity Price Quantity I 10 12 20 9 II 20 4 25 8 III 30 13 40 27 IV 60 29 75 36

Commodity Base Year Current Year q0q1 `sqrt("q"_0"q"_1)` `"p"_0 sqrt("q"_0"q"_1)` `"p"_1 sqrt("q"_0"q"_1)` p0 q0 p1 q1 I 10 12 20 9 108 10.39 103.9 207.8 II 20 4 25 8 32 5.66 113.2 141.5 III 30 13 40 27 351 18.73 561.9 749.2 IV 60 29 75 36 1044 32.31 1938.6 2423.25 Total - - - - - 2717.6 3521.75 From the table, `sum "p"_0 sqrt("q"_0"q"_1) = 2717.6, sum "p"_1 sqrt("q"_0"q"_1) = 3521.75` Walsh’s Price Index Number: `"P"_01 ("W") = (sum "p"_1 sqrt("q"_0"q"_1))/(sum "p"_0 sqrt ("q"_0"q"_1)) xx 100` `= 3521.75/2717.6 xx 100` = 129.59

Calculate Walsh’s Price Index Number.

प्रश्न

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

योग

उत्तर

Commodity	Base Year		Current Year		q₀q₁	`sqrt("q"_0"q"_1)`	`"p"_0 sqrt("q"_0"q"_1)`	`"p"_1 sqrt("q"_0"q"_1)`
Commodity	p₀	q₀	p₁	q₁	q₀q₁	`sqrt("q"_0"q"_1)`	`"p"_0 sqrt("q"_0"q"_1)`	`"p"_1 sqrt("q"_0"q"_1)`
I	10	12	20	9	108	10.39	103.9	207.8
II	20	4	25	8	32	5.66	113.2	141.5
III	30	13	40	27	351	18.73	561.9	749.2
IV	60	29	75	36	1044	32.31	1938.6	2423.25
Total	-	-	-	-		-	2717.6	3521.75

From the table,

`sum "p"_0 sqrt("q"_0"q"_1) = 2717.6, sum "p"_1 sqrt("q"_0"q"_1) = 3521.75`

Walsh’s Price Index Number:

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

`= 3521.75/2717.6 xx 100`

= 129.59

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Construction of Index Numbers - Weighted Aggregate Method

क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

Q 1.04 Q 1.03 Q 1.05

अध्याय 5: Index Numbers - Exercise 5.2 [पृष्ठ ८२]

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

अध्याय 5 Index Numbers
Exercise 5.2 | Q 1.04 | पृष्ठ ८२

संबंधित प्रश्न

Calculate Walsh’s Price Index Number.

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

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

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 ______.

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

Choose the correct alternative :

Fisher’s Price Number is given by

Choose the correct alternative :

Walsh’s Price Index Number is given by

Fill in the blank :

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

Walsh’s Price Index 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.

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.

`(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

Find x if Laspeyre’s Price Index Number is same as Paasche’s Price Index Number for the following data

Commodity	Base Year		Current Year
	Price p₀	Quantity q₀	Price p₁	Quantity q₁
A	3	x	2	5
B	4	6	3	5

Solve the following problem :

Given that `sum "p"_1"q"_1 = 300, sum "p"_0"q"_1 = 320, sum "p"_0"q"_0` = 120, and Marshall- Edgeworth’s Price Index Number is 120, find `sum"p"_1"q"_0` and Paasche’s Price Index Number.

Fisher's Price Index Number is given by ______.

Calculate Marshall-Edgeworth Price Index Number for following.

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

Find the missing price if Laspeyre’s and Paasche’s Price Index Numbers are equal for following data.

Commodity	Base Year		Current Year
Commodity	Price	Quantity	Price	Quantity
A	1	10	2	5
B	1	5	–	12

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)

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`

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`

Calculate Walsh’s Price Index Number.

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