Question

Construct index number by Price Relative Method taking 2004 as base year:

Price per Unit in ₹

Year	A	B	C	D
2004 2016 2017 2018	25 20 25 28	18 22 20 24	16 24 25 30	21 22 25 26

Answer 1

Here, we construct the index number for each of the years from 2016-2018.
Base Year 2004, Current year 2016

	2004 ( P0)	2016 (P1)	Price Relative = $\frac{P_1}{P_0}\times 100$
A	25	20	$\frac{20}{25}\times 100=80$
B	18	22	$\frac{22}{18}\times 100=122.22$
C	16	24	$\frac{24}{16}\times 100=150$
D	21	22	$\frac{22}{21}\times 100=104.76$
			∑ =456.96

According to the Price Relative Method, price index is calculated using the following formula.
$$\begin{gathered} P_{01}=\frac{\Sigma \left({\displaystyle \frac{P_1}{P_0}}\times 100\right)}{N} \\ \mathrm{Substituting}\mathrm{the}\mathrm{values}\mathrm{in}\mathrm{the}\mathrm{formula}. \\ {\mathrm{P}}_{01}=\frac{456.98}{4}=114.245 \end{gathered}$$
${\mathrm{P}}_{01}=\frac{456.98}{4}=114.245$
Base Year 2004, Current year 2017

	2004 (P0)	2017 (P1)	Price Relative = $\frac{P_1}{P_0}\times 100$
A	25	25	$\frac{25}{25}\times 100=100$
B	18	20	$\frac{20}{18}\times 100=111.11$
C	16	25	$\frac{25}{16}\times 100=156.25$
D	21	25	$\frac{25}{21}\times 100=119.04$
			∑= 486.4

$P_{01}=\frac{486.4}{4}=121.60$
Base Year 2004, Current Year 2018

	2004 (P0)	2018 (P1)	Price Relative = $\frac{P_1}{P_0}\times 100$
A	25	28	$\frac{28}{25}\times 100=280$
B	18	24	$\frac{24}{18}\times 100=133.33$
C	16	30	$\frac{30}{16}\times 100=187.5$
D	21	26	$\frac{26}{21}\times 100=123.80$
			∑ 556.63

$P_{01}=\frac{556.63}{4}=139.157$