Question

The following data relate to the prices and quantities of 4 commodities in the years 2011-12 and 2016-17. Construct the index numbers of price for the year 2016-17 by using 2011-12 the base year by: (i) Laspeyre's method, (ii) Paasche's method, (iii) Fisher's ideal method:

Commodity	2011-12		2016-17
	Price (in ₹) p0	Quantity q0	Price (in ₹)	Quantity q1
A	5	100	6	150
B	4	80	5	100
C	2.5	60	5	72
D	12	30	9	33

Answer 1

Commodity	p0	q0	p1	q1	p0q0	p0q1	p1q0	p1q1
A	5	100	6	150	500	750	600	900
B	4	80	5	100	320	400	400	500
C	2.5	60	5	72	150	180	300	360
D	12	30	9	33	360	396	270	297
Total					1330	1726	1570	2057

(i) Laspeyre's Method

$P_{01}=\frac{\mathrm{\Sigma }{p}_1{q}_0}{\mathrm{\Sigma }{p}_0{q}_0}\times 100=\frac{1570}{1330}\times 100=118.05$

(ii) Paasche's Method

$P_{01}=\frac{\mathrm{\Sigma }{p}_1{q}_1}{\mathrm{\Sigma }{p}_0{q}_1}\times 100=\frac{2057}{1726}\times 100=119.18$

(iii) Fisher's Method

$$\begin{gathered} P_{01}=\sqrt{\frac{\mathrm{\Sigma }{p}_1{q}_0}{\mathrm{\Sigma }{p}_0{q}_0}\times \frac{\mathrm{\Sigma }{p}_1{q}_1}{\mathrm{\Sigma }{p}_0{q}_1}}\times 100 \\ \mathrm{or},P_{01}=\sqrt{\frac{1570}{1330}\times \frac{2057}{1726}}\times 100 \\ \mathrm{or},P_{01}=\sqrt{\frac{3229490}{2295580}}\times 100 \\ \mathrm{or},P_{01}=1.1860\times 100 \\ \Rightarrow P_{01}=118.60 \end{gathered}$$