Question

Calculate Laspeyre's; Paasche's and Fisher's index numbers from the following data:

Commodity	Base year		Current year
	Price (in ₹) p0	Quantity q0	Price (in ₹)	Quantity q1
A	10	30	12	50
B	8	15	10	25
C	6	20	6	30
D	4	10	6	20

Answer 1

	Base Year		Current Year
Commodity	Price p0	Quantity q0	Price p1	Quantity q1	p0q0	p0q1	p1q0	p1q1
A	10	30	12	50	300	500	360	600
B	8	15	10	25	120	200	150	250
C	6	20	6	30	120	180	120	180
D	4	10	6	20	40	80	60	120
					Σp0q0 = 580	Σp0q1 = 960	Σp1q0 = 690	Σp1q1 = 1150

(i) Laspeyre's Method

$p_{01}=\frac{\mathrm{\Sigma }{p}_1{q}_0}{\mathrm{\Sigma }{p}_0{q}_0}\times 100=\frac{690}{580}\times 100=\frac{69000}{580}=118.965$

(ii) Paasche's Method

$p_{01}=\frac{\mathrm{\Sigma }{p}_1{q}_1}{\mathrm{\Sigma }{p}_0{q}_1}\times 100=\frac{1150}{960}\times 100=\frac{115000}{960}=119.79$

(iii) Fisher's Method

$$\begin{gathered} p_{01}=\sqrt{\frac{\mathrm{\Sigma }{p}_1{q}_0}{\mathrm{\Sigma }{p}_0{q}_0}\times \frac{\mathrm{\Sigma }{p}_1{q}_1}{\mathrm{\Sigma }{p}_0{q}_1}}\times 100 \\ \mathrm{or},p_{01}=\sqrt{\frac{690}{580}\times \frac{1150}{960}}\times 100 \\ \Rightarrow p_{01}=119.376 \end{gathered}$$