Question

Find the Consumer Price Index from the following data. Using
(i) Aggregative Expenditure Method, and
(ii) Family Budget Method.
Is there any difference between the two results?

Commodity	Quantity Consumed in the year 2004	Unit	Price in 2004 (₹)	Price in 2018 (₹)
Rice Wheat Bajra Arhar Desi Ghee Sugar	6 8 1 2 20 1	Quintal Quintal Quintal Quintal kg Quintal	100 80 70 120 12 160	120 90 70 115 15 170

Answer 1

	q0	P0	P1	W = P0q0	P1q0	$R=\frac{P_1}{P_0}\times 100$	WR
Rice	6	100	120	600	720	$\frac{120}{100}\times 100=120$	72,000
Wheat	8	80	90	640	720	$\frac{90}{80}\times 100=112.5$	72,000
Bajra	1	70	70	70	70	$\frac{70}{70}\times 100=100$	70,000
Arhar	2	120	115	240	230	$\frac{115}{120}\times 100=95.83$	22,999.2
Ghee	20	12	15	240	300	$\frac{15}{12}\times 100=125$	30,000
Sugar	1	160	170	160	170	$\frac{170}{160}\times 100=106.25$	17,000
				$\Sigma P_0{q}_0=1950$	$\Sigma P_1{q}_0=2210$		283999.2

(i) Aggregate expenditure method​

$$\begin{gathered} CPI=\frac{\Sigma P_1{q}_0}{\Sigma P_0{q}_0} \\ \mathrm{or},CPI\mathit{}=\frac{2210}{1950}\times 100=113.33 \end{gathered}$$


(ii) Family Budged Method
$CPI=\frac{\sum WR}{\sum W}=\frac{283999.2}{1950}=145.64$

Yes, there is a difference between the values calculated by the two methods.
Difference = 145.64 – 113.33 = 32.31