Question

Construct index numbers of prices of the items in the year 2013 from the following data by:
- Laspeyre's method
- Paasche's method
$$\begin{array}{ccccc}\text{Commodities}& \text{Price}\left(P_0\right)& \text{Quantity}\left(Q_0\right)& \text{Price}\left(P_1\right)& \text{Quantity}\left(Q_1\right)\\ & \left(2006\right)& \left(2006\right)& \left(2013\right)& \left(2013\right)\\ A& 10& 30& 12& 50\\ B& 8& 15& 10& 25\\ C& 6& 20& 6& 30\\ D& 4& 10& 6& 20\end{array}$$

Answer 1

$$\begin{array}{cccc}{P}_0{Q}_0& P_0{Q}_1& P_1{Q}_0& P_1{Q}_1\\ 300& 500& 360& 600\\ 120& 200& 150& 250\\ 120& 180& 120& 180\\ 40& 80& 60& 120\\ \sum 580& \sum 960& \sum 690& \sum 1150\end{array}$$
Laspeyre's price index: $P_{01}=\frac{\sum P_1{Q}_0}{\sum P_0{Q}_0}\times 100=\frac{690}{580}\times 100=118.96$
Paache's price index : $P_{01}=\frac{\sum P_1{Q}_1}{\sum P_0{Q}_1}\ast 100=\frac{1150}{960}\ast 100=119.79$