Question

From the data given below , construct Laspeyre's , Paasche's and Fisher's price index and quantity index numbers with base 2015 and interpret.​

Commodity	2015		2016
	Price (₹)	Quantity (Kg)	Price (₹)	Quantity (Kg)
A B C	4 3 8	2 5 2	6 2 4	3 1 6

Answer 1

Commodity	Base Year		Current Year
	Price p0	Quantity q0	Price p1	Quantity q1	p0q0	p0q1	p1q0	p1q1
A B C	4 3 8	2 5 2	6 2 4	3 1 6	8 15 16	12 3 48	12 10 8	18 2 24
					∑p0q0 = 39	∑p0q1 = 63	∑p1q0 = 30	∑p1q1 = 44

Laspeyre's Price index = $\frac{\mathrm{\Sigma }{p}_1{q}_0}{\mathrm{\Sigma }{p}_0{q}_0}\times 100=\frac{30}{39}\times 100=76.92$
Laspeyre's Quantity index = $\frac{\mathrm{\Sigma }{p}_0{q}_1}{\mathrm{\Sigma }{p}_0{q}_0}\times 100=\frac{63}{39}\times 100=161.53$

Paasche's Price index = $\frac{\mathrm{\Sigma }{p}_1{q}_1}{\mathrm{\Sigma }{p}_0{q}_1}\times 100=\frac{44}{63}\times 100=69.84$

Paasche's Quantity index = $\frac{\mathrm{\Sigma }{p}_1{q}_1}{\mathrm{\Sigma }{p}_1{q}_0}\times 100=\frac{44}{30}\times 100=146.67$

Fisher's Price index = $\sqrt{\frac{\mathrm{\Sigma }{p}_1{q}_1}{\mathrm{\Sigma }{p}_0{q}_1}\times \frac{\mathrm{\Sigma }{p}_1{q}_0}{\mathrm{\Sigma }{p}_0{q}_0}}\times 100=\sqrt{\frac{44}{63}\times \frac{30}{39}}\times 100=73.29$

Fisher's Quantity index =$\sqrt{\frac{\mathrm{\Sigma }{p}_1{q}_1}{\mathrm{\Sigma }{p}_1{q}_0}\times \frac{\mathrm{\Sigma }{p}_0{q}_1}{\mathrm{\Sigma }{p}_0{q}_0}}\times 100=\sqrt{\frac{44}{30}\times \frac{63}{39}}\times 100=153.92$
Note: As per the textbook, the quantity indices using Laspeyre's and Paasche's methods are 143.18 and 130. However, as per the above solution the quantity indices using Laspeyre's and Paasche's methods should be 161.53 and 146.67.