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Question
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.
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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
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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`
