Question

Solve the following problem :

If ${\displaystyle \sum \text{p\_}0{\text{q}}_0=120,\sum {\text{p}}_0{\text{q}}_1=160,\sum {\text{p}}_1{\text{q}}_1=140,\text{and}\sum {\text{p}}_1\text{q}+0}$ = 200, find Laspeyre’s, Paasche’s Dorbish-Bowley’s and Marshall Edgeworth’s Price Index Number.

Answer 1

Given,
${\displaystyle \sum {\text{p}}_0{\text{q}}_0=120,\sum {\text{p}}_0{\text{q}}_1=160}$,
${\displaystyle \sum {\text{p}}_1{\text{q}}_1=140,\sum {\text{p}}_1{\text{q}}_0=200}$

Laspeyre’s Price Index Number:

P₀₁(L) = ${\displaystyle \frac{\sum {\text{P}}_1{\text{q}}_0}{\sum {\text{p}}_0{\text{q}}_0}\times 100=\frac{200}{120}\times 100}$ = 166.67

Paasche’s Price Index Number:

P₀₁(P) = ${\displaystyle \frac{\sum {\text{P}}_1{\text{q}}_1}{\sum {\text{p}}_0{\text{q}}_1}\times 100=\frac{140}{160}\times 100}$ = 87.5

Dorbish-Bowley’s Price Index Number:

P₀₁(D–B) = ${\displaystyle \frac{{\text{P}}_{01}\left(\text{L}\right)+{\text{P}}_{01}\left(\text{P}\right)}{2}}$

= ${\displaystyle \frac{166.67+87.5}{2}}$

= ${\displaystyle \frac{254.17}{2}}$
= 127.085

Marshall-Edgeworth’s Price Index Number:

P₀₁(M–E) = ${\displaystyle \frac{\sum {\text{p}}_1{\text{q}}_0}{\sum {\text{p}}_0{\text{q}}_0}\times 100}$

= ${\displaystyle \frac{200+140}{120+160}\times 100}$

= ${\displaystyle \frac{340}{280}\times 100}$
= 121.43