Solve the following problem : Given that ∑p1q1=300,∑p0q1=320,∑p0q0 = 120, and Marshall- Edgeworth’s Price Index Number is 120, find ∑p1q0 and Paasche’s Price Index Number.

Question

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.

Sum

Solution

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

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 + 320) 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

Paasche’s Price Index Number:

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

= `(300)/(320) xx 100`
= 93.75

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Construction of Index Numbers - Weighted Aggregate Method

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Q 4.17 Q 4.16 Q 4.18

Chapter 5: Index Numbers - Miscellaneous Exercise 5 [Page 93]

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

Chapter 5 Index Numbers
Miscellaneous Exercise 5 | Q 4.17 | Page 93

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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)`

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Solve the following problem : Given that ∑p1q1=300,∑p0q1=320,∑p0q0 = 120, and Marshall- Edgeworth’s Price Index Number is 120, find ∑p1q0 and Paasche’s Price Index Number.

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Solve the following problem : Given that ∑p1q1=300,∑p0q1=320,∑p0q0 = 120, and Marshall- Edgeworth’s Price Index Number is 120, find ∑p1q0 and Paasche’s Price Index Number.

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