Question

Prepare consumer price index numbers from the following data for 2014 and 2013 taking 2012 as base.

Group	Price (in ₹)
	2012	2013	2014
A	20.00	24.00	21.00
B	1.25	1.50	1.00
C	5.00	8.00	8.00
D	2.00	2.25	2.12

Give weights to four groups as 4, 3, 2 and 1 respectively.

Answer 1

Price Index for 2013

Group	p0 (2012)	p1 (2013)	W	$\mathit{R}\mathit{=}\left(\frac{{\mathit{p}}_{\mathbf{1}}}{{\mathit{p}}_{\mathbf{0}}}\mathbf{\times }\mathbf{100}\right)$	WR
A B C D	20 1.25 5 2	24 1.5 8 2.25	4 3 2 1	120 120 160 112.5	480 360 320 112.5
			∑W= 10		∑WR=1272.5

$$\begin{gathered} \mathrm{Index}\mathrm{number}=\frac{\mathit{\Sigma }\mathit{W}\mathit{R}}{\mathit{\Sigma }\mathit{W}} \\ =\frac{1272.5}{10} \\ =127.25 \end{gathered}$$
Thus, consumer price index for 2013 is 127.25.

Price Index number for 2014

Group	p0 (2012)	p1 (2014)	W	$\mathit{R}\mathit{=}\left(\frac{{\mathit{p}}_{\mathbf{1}}}{{\mathit{p}}_{\mathbf{0}}}\mathbf{\times }\mathbf{100}\right)$	WR
A B C D	20 1.25 5 2	21 1 8 2.12	4 3 2 1	105 80 160 106	420 240 320 106
			∑W= 10		∑WR=1086

$$\begin{gathered} \mathrm{Index}\mathrm{number}=\frac{\mathit{\Sigma }\mathit{W}\mathit{R}}{\mathit{\Sigma }\mathit{W}} \\ =\frac{1086}{10} \\ =108.6 \end{gathered}$$
Thus, consumer price index for 2014 is 108.6.

Note: As per textbook, consumer index for 2014 is 109.78. However, as per the above solution, consumer index for 2014 should be 108.6.