Question

Calculate price index number for 2016 of following data by weighted aggregative method using (a) Laspeyre's method, (b) Paasche's method, (c) Fisher's method.

Commodity	Price (2012)	Quantity (2012)	Price (2016)	Quantity (2016)
A	4	20	6	10
B	3	15	5	23
C	2	25	3	15
D	5	10	4	15

Answer 1

Commodity	Base Year		Current Year
	Prices p0	Quantity q0	Prices p1	Quantity q1	p0q0	p0q1	p1q0	p1q1
A B C D	4 3 2 5	20 15 25 10	6 5 3 4	10 23 15 40	80 45 50 50	40 69 30 200	120 75 75 40	60 115 45 160
					∑p0q0 = 225	∑p0q1 = 339	∑p1q0 = 310	∑p1q1 = 380

(a)
$$\begin{gathered} \mathrm{Laspeyre}\text{'}\mathrm{s}\mathrm{method}\left(p_{01}\right)=\frac{\mathrm{\Sigma }{p}_1{q}_0}{\mathrm{\Sigma }{p}_0{q}_0}\times 100 \\ =\frac{310}{225}\times 100=137.77 \end{gathered}$$
(b)
$$\begin{gathered} \mathrm{Paasche}\text{'}\mathrm{s}\mathrm{method}\left(p_{01}\right)=\frac{\mathrm{\Sigma }{p}_1{q}_1}{\mathrm{\Sigma }{p}_0{q}_1}\times 100 \\ =\frac{380}{339}\times 100=112.09 \end{gathered}$$
(c)
$$\begin{gathered} \mathrm{Fisher}\text{'}\mathrm{s}\mathrm{method}\left(p_{01}\right)=\sqrt{\frac{\mathrm{\Sigma }{p}_1{q}_1}{\mathrm{\Sigma }{p}_0{q}_1}\times \frac{\mathrm{\Sigma }{p}_1{q}_0}{\mathrm{\Sigma }{p}_0{q}_0}}\times 100 \\ =\sqrt{\frac{380}{339}\times \frac{310}{225}}\times 100=124.26 \end{gathered}$$
Note: As per the textbook, the price index using Paasche's method is 158.99 and Fisher's method is 148.1. However, as per the above solution the price index using Paasche's method should be 112.09 and Fisher's method should be 124.26.