Question

Construct the cost of living index for the year 2012 on the basis of 2004 from the following data and give your comments :

$\begin{array}{cccc}\text{Item}& \text{Price (in Rs) in}2004& \text{Price (in Rs) in 2012}& \text{Weights}\\ \text{Food}& 39& 47& 4\\ \text{Fuel}& 8& 12& 1\\ \text{Cloth}& 14& 18& 3\\ \text{Rent}& 12& 15& 2\\ \text{Other}& 25& 30& 1\end{array}$

Answer 1

$\begin{array}{cccccc}\text{Items}& {\text{P}}_0& {\text{P}}_1& \text{R}=\frac{P{}_1}{P{}_0}\times 100& \text{Weights}\left(W\right)& \text{Weighted Relative}\left(RW\right)\\ \text{Food}& 39& 47& 120.51& 4& 482.04\\ \text{Fuel}& 8& 12& 150& 1& 150\\ \text{Cloth}& 14& 18& 128.57& 3& 385.71\\ \text{Rent}& 12& 15& 125& 2& 250\\ \text{Other}& 25& 30& 130& 1& 130\\ & & & & \sum W=11& \sum \text{RW}=1387.75\end{array}$

Cost of living index = $\frac{\sum \text{RW}}{\sum \text{W}}=1387.75/11=126.16$

It shows that because cost of living has gone up by 26.16$\%$ in 2012 compared to 2004.