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

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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

या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?

Q 1.04 Q 1.03 Q 1.05

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

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

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

संबंधित प्रश्‍न

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

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

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.

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

Fill in the blank :

Paasche’s Price Index Number is given by _______.

Fill in the blank :

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

Walsh’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 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:

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

If Laspeyre’s and Dorbish’s Price Index Numbers are 150.2 and 152.8 respectively, find Paasche’s Price Index Number.

Choose the correct alternative:

The formula P₀₁ = `(sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100` is for

Marshall-Edgeworth's Price Index Number is given by ______

The average of Laspeyre’s and Paasche’s Price Index Numbers is called ______ Price Index Number

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
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)

`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.

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`

Calculate Walsh’s Price Index Number.

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