Question

If Dorbish-Bowley's and Fisher's Price Index Numbers are 5 and 4, respectively, then find Laspeyre's and Paasche's Price Index Numbers.

Answer 1

Let Laspeyre’s Price Index Number P₀₁(L) = x

and Paasche’s Price Index Number P₀₁(P) = y

Dorbish-Bowley’s Price Index Number P₀₁(D-B) = 5

Fisher’s Price Index Number P₀₁(F) = 4

`("P"_01("L")  "P"_01("P"))/(2) = "P"_(01)("D"–"B")`

∴ `(x + y)/(2)` = 5

∴ x + y = 10           ...(i)

`sqrt("P"_01("L") xx "P"_01("P"))= "P"_01("F")`

∴ `sqrt(xy)` = 4

∴ xy = 16

∴ y = `(16)/x`

∴ `x + (16)/x` = 10      ...[From (i)]

∴ x² + 16 = 10x

∴ x² – 10x + 16 = 0

∴ x – 8x – 2x + 16 = 0

∴ x(x – 8) – 2(x – 8) = 0

∴ (x – 2) (x – 8)

∴ x = 2 or x = 8

If x = 2, then from equation (i), y = 8

If x = 8, then from equation (i), y = 2

∴ P₀₁(L) = 8 and P₀₁(P) = 2

or P₀₁(P) = 8 and P₀₁(L) = 2