Question

Calculate the weighted price relative index on the basis of the following data:

$\begin{array}{cccc}\text{Commodity}& \text{Quantity in 2011 (Units)}& \text{Price in 2011 (Rs)}& \text{Price in 2016 (Rs)}\\ A& 80& 5& 8\\ B& 65& 8& 14\\ C& 42& 12& 18\\ D& 37& 4& 5\\ E& 31& 4& 5\\ F& 15& 2& 4\end{array}$

Answer 1

Construction of Weighted Index Numbers

$\begin{array}{ccccccc}\text{Commodity}& \text{Weights}& \text{Price(Rs.)}& \text{Price(Rs.)}& \text{Value Weights}& \frac{P_1}{P_0}\times 100& RW\\ & q_0& 2011& 2016& \left(p_0{q}_0\right)& R& \\ & & p_0& p_1& W& & \\ A& 80& 5& 8& 400& 160& 64,000\\ B& 65& 8& 14& 520& 175& 91,000\\ C& 42& 12& 18& 504& 150& 75,600\\ D& 37& 4& 5& 148& 125& 18,500\\ E& 31& 4& 5& 124& 125& 15,500\\ F& 15& 2& 4& 30& 200& 6,000\\ & & & & \sum W=1,726& & \sum RW=2,70,600\end{array}$

Weighted Average of Price Relatives

$P_{01}=\frac{\sum RW}{\sum W}=\frac{2,70,600}{1,726}=156.77$

The index number of 156.77 shows the increase of 56.77% in prices in the year 2016 as compared to year 2011.