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, P01(M-E) = 120, `sum"p"_1"q"_1` = 300, `sum"p"_0"q"_0` = 120, `sum"p"_0"q"_1` = 320 P01(M-E) = `(sum"p"_1"q"_0 + sum"p"_1"q"_1)/(sum"p"_0"q"_0 + sum"p"_0"q"_1) xx 100` &there4; 120 = `(sum"p"_1"q"_0 + 300)/(120 + 130) xx 100` &there4; 120 = `(sum"p"_1"q"_0 + 300)/440 xx 100` &there4; `sum"p"_1"q"_0 + 300 = (120 xx 440)/100` &there4; `sum"p"_1"q"_0 + 300` = 528 &there4; `sum"p"_1"q"_0` = 528 – 300 &there4; `sum"p"_1"q"_0` = 228 Laspeyre’s Price Index Number: P01(L) = `(sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100` = `228/120 xx 100` = 190

Given P01(M-E) = 120, ∑p1q1 = 300, ∑p0q0 = 120, ∑p0q1 = 320, Find P01(L)

Question

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)

Sum

Solution

Given, P₀₁(M-E) = 120, `sum"p"_1"q"_1` = 300, `sum"p"_0"q"_0` = 120, `sum"p"_0"q"_1` = 320

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

∴ 120 = `(sum"p"_1"q"_0 + 300)/(120 + 130) xx 100`

∴ 120 = `(sum"p"_1"q"_0 + 300)/440 xx 100`

∴ `sum"p"_1"q"_0 + 300 = (120 xx 440)/100`

∴ `sum"p"_1"q"_0 + 300` = 528

∴ `sum"p"_1"q"_0` = 528 – 300

∴ `sum"p"_1"q"_0` = 228

Laspeyre’s Price Index Number:

P₀₁(L) = `(sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100`

= `228/120 xx 100`

= 190

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Commodity	Base Year		Current Year
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I	10	9	20	8
II	20	5	30	4
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A	2	10	2	5
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Choose the correct alternative :

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Commodity	Base year		Current year
	Price p₀	Quantity q₀	price p₁	Quantity q₁
A	20	18	30	15
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D	12	10	18	10

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

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A	5	3	10	3
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Commodity	Base Year		Current Year
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A	20	8	40	7
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Dorbish-Bowley's Price Index Number is the square root of the product of Laspeyre's and Paasche's Index Numbers.

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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`

Given P01(M-E) = 120, ∑p1q1 = 300, ∑p0q0 = 120, ∑p0q1 = 320, Find P01(L)

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Given P01(M-E) = 120, ∑p1q1 = 300, ∑p0q0 = 120, ∑p0q1 = 320, Find P01(L)

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