Sandeep Garg Solutions Class 11 Economics Chapter 9 - Index Numbers

Sandeep Garg Class 11 Economics Solutions Economics Chapter 9 – Index Numbers are illustrated by the professional economic educator from the contemporary edition of Sandeep Garg Economics Class 11 textbook solutions.

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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
2010 2015
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

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

 

= \(\frac{506}{427}\, X\, 100\)

= 118.50

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)

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

(Q0)

P0Q0

(W)

RW
Rent 200 225 112.5 45 9000 1012500
Food 300 350 116.66 20 6000 699960
Clothing 150 175 116.66 8 1200 139992
Fuel 100 110 110 10 1000 110000
Misc. 200 250 125 17 3400 425000
ΣW= 20600 ΣWI = 2387452

The consumer price index for the current year as per family budget method is:

\(\frac{\sum WI}{\sum W} = \frac{2387452}{20600} = 115.89\)

 

Question 5

Arrange an index for 2015 taking 2010 using a simple aggregate and price relatives method

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

Answer:

Simple Aggregate Method

Items 2010 Price
(P0)
2015 Price
(P
1)
A
B
C
D
20
40
50
70
30
50
70
90
ΣP0 = 180 ΣP1 = 240

simple aggregate formula

=  240/180 × 100

= 133.33

Price Relative Method

Items Year 2010 Price (P0) Year 2015 Price (P1) \(R \,=\, \frac{P_{1}}{P_{0}} \, \times \, 100\)
A 20 30 150
B 40 50 125
C 50 70 140
D 70 90 128.57
N= 4   index-numbers

= 543.57

Simple Average of Price Relatives
index number 2

P01 = 543.57/ 4

= 135.89

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