Solve the following

1. Calculate Price Index number from the given data:

Commodity	A	B	C	D
Price in 2005 (₹)	6	16	24	4
Price in 2010 (₹)	8	18	28	6

SOLUTION:-

Commodity	Price in 2005 (₹) P0	Price in 2010 (₹) P1
A	6	8
B	16	18
C	24	28
D	4	6
Total	∑P0 = 50	∑P1 = 60

⇒ Here, ∑P0 = 50 and ∑P1 = 60
Using Simple Aggregate Price Index formula
∴ Simple Aggregate Price Index = P1/P0 * 100
= 60/50 * 100
=120

2. Calculate Quantity Index number from the given data:

Commodity	P	Q	R	S	T
Base year quantities	170	150	100	195	205
Current year quantities	90	70	75	150	95

SOLUTION: –

Commodity	Base year quantities q0	Current year quantities q1
P	170	90
Q	150	70
R	100	75
S	195	150
T	205	95
Total	∑q0 = 820	∑q1 = 480

Quantity Index Number = q1/q0 * 100
= 480/820 *100
= 58.54.

3. Calculate Value Index number from the given data:

Commodity	Base year		Current year
Commodity	Price	Quantity	Price	Quantity
A	40	15	70	20
B	10	12	60	22
C	50	10	90	18
D	20	14	100	16
E	30	13	40	15

Solution: –

Commodity	Base year			Current year
	p0	q0	p0q0	p1	q1	p1q1
A	40	15	600	70	20	1400
B	10	12	120	60	22	1320
C	50	10	500	90	18	1620
D	20	14	280	100	16	1600
E	30	13	390	40	15	600
Total	∑p0q0	=	1890	∑p1q1	=	6540

value Index Number = p1q1/p0q0 * 100
= ∑p1q1/∑p0q0×100
= 6540/1890×100
= 346.03

4. A) Calculate Laaspeyre’s index from the given data:

Commodity	Base year		current year
Commodity	Price	Quantity	Price	Quantity
X	8	30	12	25
Y	10	42	20	16

Solution: –

Commodity	Base year		Current year
Commodity	p0	q0	p1	q1	p1q0	p0q0
X	8	30	12	25	360	240
Y	10	42	20	16	840	420
Total					1200	660

Laaspeyre’s index = p1q0/p0q0 * 100
= ∑p1q0/∑p0q0×100
= 1200/660×100
= 181.81

4. B Calculate Paasche’s index from the given data:

Commodity	Base year		current year
Commodity	Price	Quantity	Price	Quantity
X	8	30	12	25
Y	10	42	20	16

Solution: –

Commodity	Base year		Current year
Commodity	p0	q0	p1	q1	p1q1	p0q1
X	8	30	12	25	300	200
Y	10	42	20	16	320	160
Total					620	360

Paasche’s index = p1q1/p0q1
= ∑p1q1/∑p0q1×100
= 620/360×100
= 172.22