Question

Construct cost of index number for 2016 on the basis of 2011 from the following data using Aggregate Expenditure Method and Family Budget Method.

Article	Quantity (kg.)	Prices in ₹
		2011	2016
A	10	20	30
B	7	21	28
C	5	20	25
D	2	10	12
E	2	6	8

Calculate Fisher's Ideal Index Number.

Answer 1

Aggregate expenditure Method

Article	Price in 2011 (p0)	Price in 2016 (p1)	Quantity (q0)	p0q0	p1q0
A	20	30	10	200	300
B	21	28	7	147	196
C	20	25	5	100	125
D	10	12	2	20	24
E	6	8	2	12	16
				Σp0q0 = 479	Σp1q0 = 661

Consumer price index for the year 2016
$=\frac{\mathrm{\Sigma }{p}_1{q}_0}{\mathrm{\Sigma }{p}_0{q}_0}\times 100=\frac{661}{479}\times 100=137.99=138$

Family Budget Method

Article	Price in 2011 (p0)	Price in 2016 (p1)	Price Relative (R) $R=\frac{p_1}{p_0}\times 100$	Quantity (q0)	p0q0 (W)	RW
A	20	30	150	10	200	30000
B	21	28	133.33	7	147	19599.51
C	20	25	125	5	100	12500
D	10	12	120	2	20	2400
E	6	8	133.33	2	12	1599.96
					ΣW = 479	ΣRW = 66099.47

Consumer price index for the year 2016

$=\frac{\mathrm{\Sigma R}W}{\Sigma W}=\frac{66099.47}{479}=137.99=138$