Question

Given that ∑p₀q₀ = 220, ∑p₀q₁ = 380, ∑p₁q₁ = 350 and Marshall-Edgeworth’s Price Index Number is 150, find Laspeyre’s Price Index Number.

Answer 1

Given:

∑p₀q₀ = 220,

∑p₀q₁ = 380,

∑p₁q₁ = 350 and

P₀₁ (M − E) = 150

To find:

P₀₁(L) = ?

We have

`P_01(M - E) = (sum p_1q_0 + sum p_1q_1)/(sum p_0q_0 + sum p_0q_1) xx 100`

∴ `150 = (sum p_1q_0 + 350)/(220 + 380) xx 100`

∴ `150 = (sum p_1q_0 + 350)/600 xx 100`

∴ `(150 xx 600)/100 = sum p_1q_0 + 350`

∴ 150 × 6 = ∑p₁q₀ + 350

∴ 900 = ∑p₁q₀ + 350

∴ ∑p₁q₀ = 900 − 350

∴ ∑p₁q₀ = 550

`P_01(L) = (sum p_1q_0)/(sum p_0q_0) xx 100`

= `550/220 xx 100` 

= 2.5 × 100

= 250

Hence, Laspeyre’s Price Index Number is 250.