Question

The monthly per capita expenditure incurred by workers for an industrial centre during 1980 and 2005 on the following items are given below. The weights of these items are 75, 10, 5, 6 and 4 respectively. Prepare a weighted index number for cost of living for 2005 with 1980 as the base.

$\begin{array}{ccc}\text{Items}& \text{Price in 1980}& \text{Price in 2005}\\ \text{Food}& 100& 200\\ \text{Clothing}& 20& 25\\ \text{Fuel and Lighting}& 15& 20\\ \text{House rent}& 30& 40\\ \text{Miscellaneous}& 35& 65\end{array}$

Answer 1

$\begin{array}{cccccc}\text{Items}& \text{Price in 1980}\left(P_0\right)& \text{Price in 2005}\left(P_1\right)& \text{Weight}& R=\frac{P_1}{P_0}\times 100& \text{RW}\\ \text{Food}& 100& 200& 75& \frac{200}{100}\times 100=200& 15000\\ \text{Clothing}& 20& 25& 10& \frac{25}{20}\times 100=125& 1,250\\ \text{Fuel and Lighting}& 15& 20& 5& \frac{20}{15}\times 100=133.33& 666.65\\ \text{House Rent}& 30& 40& 6& \frac{40}{30}\times 100=133.33& 799.98\\ \text{Miscellanous}& 35& 65& 4& \frac{65}{35}\times 100=185.71& 742.84\\ & & & \sum W=100& & \sum RW=18,459.47\end{array}$

Cost of living (CPI ) = $\frac{\sum WR}{\sum W}=\frac{18459.47}{100}=184.59$