Question

Calculate Laspeyre's and Paasche's price index number on the basis of the following data:

$\begin{array}{cccccc}\text{Commodity}& A& B& C& D& E\\ \text{Base Year Price}\left(p_0\right)& 10& 25& 30& 15& 20\\ \text{Curreny Year Price}\left(p_1\right)& 15& 40& 45& 30& 25\\ \text{Base Year Quantity}\left(q_0\right)& 6& 10& 15& 20& 8\\ \text{Current Year Quantity}\left(q_1\right)& 8& 20& 12& 15& 6\end{array}$

Answer 1

$\begin{array}{ccccccccc}\text{Commodity}& P_0& Q_0& P_1& Q_1& P_0{Q}_0& P_1{Q}_0& P_0{Q}_1& P_1{Q}_1\\ A& 10& 6& 15& 8& 60& 90& 80& 120\\ B& 25& 10& 40& 20& 250& 400& 500& 800\\ C& 30& 15& 45& 12& 450& 675& 360& 540\\ D& 15& 20& 30& 15& 300& 600& 225& 450\\ E& 20& 8& 25& 6& 160& 200& 120& 150\\ & & & & & \sum P_0{Q}_0=1220& \sum P_1{Q}_0=1965& \sum P_0{Q}_1=1285& \sum P_1{Q}_1=2060\end{array}$

Laspeyre's Price Index:

$P_{01}=\frac{\sum P_1{Q}_0}{\sum P_0{Q}_0}\times 100=\frac{1965}{1220}\times 100=161.06$

Paasche's Price index :

$P_{02}=\frac{\sum P_1{Q}_1}{\sum P_0{Q}_1}\times 100=\frac{2060}{1285}\times 100=160.31$