Sandeep Garg Solutions for Class 11 Economics Chapter 9 - Index Numbers

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Sandeep Garg Solutions Class 11 – Chapter 9

Question 1

Arrange an index number for the year 2015 on the basis of 2010 using the simple aggregative method:

Goods Unit Cost
2011 2016
Potato Kilo 100 500
Tomato Kilo 400 250
Onion Kilo 200 400
OIl litre 4 5
Fabric meter 2 3

ANSWER:

Goods 2010 Price

(P0)

2015 Price

(P1)

Potato

Tomato

Onion

OIl

Fabric

100

400

200

4

2

500

250

400

5

3

ΣP0 = 702 ΣP1 = 928

P01 = \(\frac{\sum P_{1}}{\sum P_{0}}\, X\, 100\)

P01 = \(\frac{928}{702}\, X\, 100\)

P01 = 132

Question 2

Form an index number using 2010 price:

Items P Q R S T U
Prices (2011) 220 50 370 110 70 90
Prices (2016) 250 80 500 130 72 100

ANSWER:

Items Price in 2011

(P0)

Price in 2016

(P1)

P

Q

R

S

T

U

220

50

370

110

70

90

250

80

500

130

72

100

ΣP0 = 910 ΣP1 = 1152

P01 = \(\frac{\sum P_{1}}{\sum P_{0}}\, X\, 100\)

P01 = \(\frac{1152}{910}\, X\, 100\)

P01 = 126.59

Question 3

Prepare an index number for 2014 on the basis of 2010 from the below data using aggregate expenditure method.

Particulars Quantity (kg.) Prices
2010 2014
G 9 21 25
H 6 20 22
I 4 19 23
J 3 9 10
K 3 5 9

Answer:

Article 2010 Price

(P0)

2014 Price

(P1)

Quantity

(Q0)

P0Q0 P1Q0
G

H

I

J

K

21

20

19

9

5

25

22

23

10

9

9

6

4

3

3

189

120

76

27

15

225

132

92

30

27

ΣP0Q0 = 427 ΣP1Q0 = 506

The consumer price index for the year 2014 is

\(\frac{\sum P_{1}Q_{0}}{\sum P_{0}Q_{0}}\,\, \times 100\) \(\frac{506}{427}\, X\, 100\)

= 118

Question 4

Calculate the consumer index number by using the family budget method.

Items Quantity Base Price Year Current Price Year
Rent 45 200 225
Food 20 300 350
Clothing 8 150 175
Fuel 10 100 110
Misc. 17 200 250

Answer:

Items Base Price Year (P0) Current Price Year

(P1)

\(R \,=\, \frac{P_{0}}{P_{1}} \, \times \, 100\) Quantity

(Q0)

P0Q0

(A)

RA
Rent 200 225 88.8 45 9000 799200
Food 300 350 85.7 20 6000 514200
Clothing 150 175 85.7 8 1200 685
Fuel 100 110 90.9 10 1000 1909
Misc. 200 250 80 17 3400 1360
ΣA= 20600 ΣRA = 1317354

The consumer price index for the current year

\(\frac{\sum RA}{\sum A} = \frac{1317354.6}{20600} = 63.94\)

Question 5

Arrange an index for 2015 taking 2010 using a simple average of price relatives method

Items A B C D
Year 2010 Price 20 40 50 70
Year 2015 Price 30 50 70 90

Answer:

Items Year 2010 Price (P0) Year 2015 Price (P1) Price Relative=

\(\frac{P0}{P1}\) X 100
A 20 30 66.6
B 40 50 80
C 50 70 71.42
D 70 90 87.5
index number 1

= 75

Simple Average of Price Relatives
index number 2

P01 =

= 18.75

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