Question

Calculate weighted aggregative of actual price index number and quantity index number from the following data using (i) Laspeyre's Method , and (ii) Paasche's Method and (iii) Fisher's Method and interpret them.

Commodity	Base year		Current Year
	Quantity lbs.	Price per lb.	Quantity lbs.	Price ​per lb.
Bread	6	40 paise	7	30 paise
Meat	4	45 paise	5	50 paise
Tea	0.5	90 paise	1.5	40 pAise

Answer 1

	Base Year		Current Year
	Quantity q0	Price p0	Quantity q1	Price p1	p0q0	p1q1	p1q0	p0q1
Bread Meat Tea	6 4 0.5	40 45 90	7 5 1.5	30 50 40	240 180 45	210 250 60	180 200 20	280 225 135
					∑p0q0 = 465	∑p1q1 = 520	∑p1q0 = 400	∑p0q1 = 640

(i) Price Index number
(a) Laspeyre's $p_{01}=\frac{\mathrm{\Sigma }{p}_1{q}_0}{\mathrm{\Sigma }{p}_0{q}_0}\times 100=\frac{400}{465}\times 100=86.02$

(b) Paasche's $p_{01}=\frac{\mathrm{\Sigma }{p}_1{q}_1}{\mathrm{\Sigma }{p}_0{q}_1}\times 100=\frac{520}{640}\times 100=81.25$
(c) Fisher's $p_{01}=\sqrt{\frac{\mathrm{\Sigma }{p}_1{q}_1}{\mathrm{\Sigma }{p}_0{q}_1}\times \frac{\mathrm{\Sigma }{p}_1{q}_0}{\mathrm{\Sigma }{p}_0{q}_0}}\times 100=\sqrt{\frac{520}{640}\times \frac{400}{465}}\times 100=83.60$

(ii) Quantity Index number
(a) Laspeyre's $q_{01}=\frac{\mathrm{\Sigma }{q}_1{p}_0}{\mathrm{\Sigma }{q}_0{p}_0}\times 100=\frac{640}{465}\times 100=137.63$

(b) Paasche's $q_{01}=\frac{\mathrm{\Sigma }{q}_1{p}_1}{\mathrm{\Sigma }{q}_0{p}_1}\times 100=\frac{520}{400}\times 100=130$

(c) Fisher's $q_{01}=\sqrt{\frac{\mathrm{\Sigma }{p}_0{q}_1}{\mathrm{\Sigma }{p}_0{q}_0}\times \frac{\mathrm{\Sigma }{p}_1{q}_0}{\mathrm{\Sigma }{p}_1{q}_0}}\times 100=\sqrt{\frac{520}{400}\times \frac{640}{465}}\times 100=133.76$

The price index number for current year is 86.02 and 81.25 as per Laspeyres's method and Paasche's method respectively. This implies that there is net decrease in the prices in current year by 13.98% and 18.75% from the base year as per Laspeyres's method and Paasche's method respectively.

The quantity index number for current year is 137.63 and 130 as per Laspeyres's method and Paasche's method respectively. This implies that there is net increase in the quantity demanded by 37.63% and 30% from the base year as per Laspeyres's method and Paasche's method respectively.