# Solve the following problem : Given that ∑p0q0=130,∑p1q1=140,∑p0q1=160,and∑p1q0=200, find Laspeyre’s, Paasche’s, Dorbish-Bowley’s, and Marshall-Edgeworth’s Price Index Numbers. - Mathematics and Statistics

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Solve the following problem :

Given that sum "p"_0"q"_0 = 130, sum "p"_1"q"_1 = 140, sum "p"_0"q"_1 = 160, and sum "p"_1"q"_0 = 200, find Laspeyre’s, Paasche’s, Dorbish-Bowley’s, and Marshall-Edgeworth’s Price Index Numbers.

#### Solution

Given,
sum"P"_0"q"_0 = 130, sum"p"_0"q"_1 = 160,
sum"p"_1"q"_1 = 140, sum"p"_1"q"_0 = 200

Laspeyre’s Price Index Number:

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

= (200)/(130) xx 100 = 153.85

Laspeyre’s Price Index Number:

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

= (140)/(160) xx 100 = 87.5

Dorbish-Bowley’s Price Index Number:

P01(D–B) = ("P"_01("L") + "P"_01("P"))/(2)

= (153.85 + 87.5)/(2) = 120.68

Marshall-Edgeworth’s Price Index Number:

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

= (200 + 140)/(130 + 160) xx 100
= 117.24

Concept: Construction of Index Numbers - Weighted Aggregate Method
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Chapter 5: Index Numbers - Miscellaneous Exercise 5 [Page 93]

#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 5 Index Numbers
Miscellaneous Exercise 5 | Q 4.16 | Page 93
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