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.

Answer 1

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