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`

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 6 120 180 II 10 5 50 5 25 5 50 250 III 40 8 10 2 16 4 160 40 IV 30 4 20 1 4 2 60 40 Total – – – – 390 510 Walsh’s price Index Number is P01(W) = `(sum"p"_1sqrt("q"_0"q"_1))/(sum"p"_0sqrt("q"_0"q"_1)) xx 100` = `510/390 xx 100` = 130.77

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

Question

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`

Chart

Fill in the Blanks

Solution

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	6	120	180
II	10	5	50	5	25	5	50	250
III	40	8	10	2	16	4	160	40
IV	30	4	20	1	4	2	60	40
Total	–	–	–	–			390	510

Walsh’s price Index Number is

P₀₁(W) = `(sum"p"_1sqrt("q"_0"q"_1))/(sum"p"_0sqrt("q"_0"q"_1)) xx 100`

= `510/390 xx 100`

= 130.77

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Construction of Index Numbers - Weighted Aggregate Method

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Chapter 2.5: Index Numbers - Q.5

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

Chapter 2.5 Index Numbers
Q.5 | Q 1

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
L	4	16	3	19
M	6	16	8	14
N	8	28	7	32

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).

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

Find x in the following table if Laspeyre’s and Paasche’s Price Index Numbers are equal.

Commodity	Base Year		Current year
Commodity	Price	Quantity	Price	Quantity
A	2	10	2	5
B	2	5	x	2

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 _______.

Fill in the blank :

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

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.