Question

If ∑ p₀q₀ = 120, ∑ p₀q₁ = 160, ∑ p₁q₁ = 140, ∑ p₁q_o = 200, find Laspeyre’s, Paasche’s, Dorbish-Bowley’s and Marshall-Edgeworth’s Price Index Numbers.

Answer 1

Given,
`sum"P"_0"q"_0 = 120, 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)/(120) xx 100` = 166.67

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)`

= `(166.67 + 87.5)/(2)` = 127.085

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)/(120 + 160) xx 100`
= 121.43