Question

4. Calculate the index numbers from the following data using:
(i) Laspeyre's method,
(ii) Paasche's method,
(iii) Fisher's ideal method:

Commodity	Base year		Current year
	Price (in ₹) p 0	Quantity q0	Price (in ₹) p1	Quantity q1
A	8	100	10	120
B	4	60	5	80
C	10	20	12	25
D	12	25	15	30
E	3	5	4	6

Answer 1

	Base Year		Current Year
Commodity	Price p0	Quantity q0	Price p1	Quantity q1	p0q0	p0q1	p1q0	p1q1
A	8	100	10	120	800	960	1000	1200
B	4	60	5	80	240	320	300	400
C	10	20	12	25	200	250	240	300
D	12	25	15	30	300	360	375	450
E	3	5	4	6	15	18	20	24
					Σp0q0 = 1555	Σp0q1 = 1908	Σp1q0 = 1935	Σp1q1 = 2374

(i) Laspeyre's Method

$p_{01}=\frac{\mathrm{\Sigma }{p}_1{q}_0}{\mathrm{\Sigma }{p}_0{q}_0}\times 100=\frac{1935}{1555}\times 100=124.44$

(ii) Paasche's Method

$p_{01}=\frac{\mathrm{\Sigma }{p}_1{q}_1}{\mathrm{\Sigma }{p}_0{q}_1}\times 100=\frac{2374}{1908}\times 100=124.42$

(iii) Fisher's Method

$$\begin{gathered} p_{01}=\sqrt{\frac{\mathrm{\Sigma }{p}_1{q}_0}{\mathrm{\Sigma }{p}_0{q}_0}\times \frac{\Sigma p_1{q}_1}{\Sigma p_0{q}_1}}\times 100 \\ \mathrm{or},p_{01}=\sqrt{\frac{1935}{1555}\times \frac{2374}{1908}}\times 100 \\ \Rightarrow p_{01}=\sqrt{\frac{4593690}{2966940}}\times 100=124.43 \end{gathered}$$