Question

Construct and index of prices using 2004 as the base year and Price Relatives Method:

Goods	Weight	2004	2017	2018
A B C	5 3 2	10 5 4	12 6 5	14 8 7

Answer 1

Construction of Price Index for the year 2017

Goods	Weight (W)	2004 Price (P0)	2017 Price (P1)	$\mathit{R}\mathbf{=}\frac{{\mathit{P}}_{\mathbf{1}}}{{\mathit{P}}_{\mathbf{0}}}\mathbf{\times }\mathbf{100}$	RW
A	5	10	12	$\frac{12}{10}\times 100=120$	600
B	3	5	6	$\frac{6}{5}\times 100=120$	360
C	2	4	5	$\frac{5}{4}\times 100=125$	250
	ΣW = 10				ΣRW = 1210

$$\begin{gathered} P_{01}=\frac{\Sigma RW}{\Sigma W} \\ \mathrm{or},P_{01}=\frac{1210}{10}=121 \end{gathered}$$


Construction of Price Index for the year 2018

Goods	Weight (W)	2004 Price (P0)	2018 Price (P2)	$\mathit{R}\mathbf{=}\frac{{\mathit{P}}_2}{{\mathit{P}}_{\mathbf{0}}}\mathbf{\times }\mathbf{100}$	RW
A	5	10	14	$\frac{14}{10}\times 100=140$	700
B	3	5	8	$\frac{8}{5}\times 100=160$	480
C	2	4	7	$\frac{7}{4}\times 100=175$	350
	ΣW = 10				ΣRW = 1530

$$\begin{gathered} P_{02}=\frac{\mathrm{\Sigma }RW}{\mathrm{\Sigma }W} \\ \mathrm{or},P_{02}=\frac{1530}{10}=153 \end{gathered}$$