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Page No 462:

Question 1:

Using Simple Aggregate Method and Price Relatives Method, find out index values for the year 2018 from the following data:
 

Items A B C D E
2004 Price (₹) 15 33 38 25 50
2018 Price (₹) 30 35 57 35 63

Answer:

Simple Aggregate Method
 

Items 2004 Price
(P0)
2018 Price
(P1)
A
B
C
D
E
15
33
38
25
50
30
35
57
35
63
  ΣP0 = 161 ΣP1 = 220

P01=ΣP1ΣP0×100or, P01=220161×100P01=136.64

Price Relative Method
 
Items 2004 Price
(P0)
2018 Price
(P1)
Price relative =P1P0×100
A 15 30 3015×100=200
B 33 35 3533×100=106.06
C 38 57 5738×100=150
D 25 35 3525×100=140
E 50 63 6350×100=126
N = 5     ΣP1P0×100=722.06

P01=ΣP1P0×100Nor, P01=722.065P01=144.412

Page No 462:

Question 2:

Find out index value by the Price Relative Method for the year 2018 from the following data:
 

Items A B C D E F G
2004 Price (₹) 100 10 5 4 1 2 3
2018 Price (₹) 100 9 4 2 1 2.50 2.25

Answer:

Items
 
2004 Price
(P0)

2018 Price
(P1)
Price relative =P1P0×100
A 100 100 100100×100=100
B 10 9 910×100=90
C 5 4 45×100=80
D 4 2 24×100=50
E 1 1 11×100=100
F 2 2.50 2.502×100=125
G 3 2.25 2.253×100=75
N = 7     ΣP1P0×100=620

P01=ΣP1P0×100Nor, P01=6207=88.57

Hence, Price Index = 88.57

Page No 462:

Question 3:

Construct an index number by Price Relatives Method using 2004 as base year:
 

Goods A B C D
2004 Price (₹) 8 10 15 20
2017 Price (₹) 10 12 18 22
2018 Price (₹) 12 14 20 25

Answer:

Goods 2004 Price
(P0)
2017 Price
(P1)
2018 Price
(P2)
Price relatives of 2017 in relation to 2004
P1P0×100
Price relatives of 2018 in relation to 2004
P2P0×100
A 8 10 12 108×100=125 128×100=150
B 10 12 14 1210×100=120 1410×100=140
C 15 18 20 1815×100=120 2015×100=133.33
D 20 22 25 2220×100=110 2520×100=125
= 4       ΣP1P0×100=475 ΣP2P0×100=548.33

P01=ΣP1P0×100N=4754=118.75P02=ΣP2P0×100N=548.334=137.08

Page No 462:

Question 4:

Construct and index of prices using 2004 as the base year and Price Relatives Method:
 

Goods Weight 2004 2017 2018
A
B
C
5
3
2
10
5
4
12
6
5
14
8
7

Answer:

Construction of Price Index for the year 2017
 

Goods Weight
(W)
2004 Price
(P0)
2017 Price
(P1)
R=P1P0×100 RW
A 5 10 12 1210×100=120 600
B 3 5 6 65×100=120 360
C 2 4 5 54×100=125 250
  ΣW = 10       ΣRW = 1210

P01=ΣRWΣWor, P01=121010=121


Construction of Price Index for the year 2018
 
Goods Weight
(W)
2004 Price
(P0)
2018 Price
(P2)
R=P2P0×100 RW
A 5 10 14 1410×100=140 700
B 3 5 8 85×100=160 480
C 2 4 7 74×100=175 350
  ΣW = 10       ΣRW = 1530

P02=ΣRWΣWor, P02=153010=153



Page No 488:

Question 1:

  Taking 2004 as base year, construct the index numbers of the years 2014 and 2018.
 

Year 2004 2014 2015 2016 2017 2018
Prices (₹) 10 14 16 20 22 24

Answer:

Year Price
2004 10
2014 14
2015 16
2016 20
2017 22
2018 24

Since, base year is given as 2004
P0 = 10
Index number for year 2014

Here, P1 = 14
P01=P1P0×100 = 1410×100 = 140

Index number for year 2018
Here, P1 = 24
Substituting the values in the formula
P01=2410×100=240



Page No 489:

Question 2:

Construct index number by Price Relative Method taking 2004 as base year:
 

Price per Unit in ₹
Year A B C D
2004
2016
2017
2018
25
20
25
28
18
22
20
24
16
24
25
30
21
22
25
26

Answer:

Here, we construct the index number for each of the years from 2016-2018.
Base Year 2004, Current year 2016

  2004
( P0)
2016
(P1)
Price Relative = P1P0×100
A 25 20 2025×100=80
B 18 22 2218×100=122.22
C 16 24 2416×100=150
D 21 22 2221×100=104.76
       =456.96

According to the Price Relative Method, price index is calculated using the following formula.
P01 = ΣP1P0×100NSubstituting the values in the formula.P01 =456.984 = 114.245
P01=456.984=114.245
Base Year 2004, Current year 2017
  2004
(P0)
2017
(P1)
Price Relative = P1P0×100
A 25 25 2525×100=100
B 18 20 2018×100 = 111.11
C 16 25 2516×100=156.25
D 21 25 2521×100=119.04
      = 486.4

P01=486.44=121.60
Base Year 2004, Current Year 2018
 
  2004
(P0)
2018
(P1)
Price Relative = P1P0×100
A 25 28 2825×100=280
B 18 24 2418×100=133.33
C 16 30 3016×100=187.5
D 21 26 2621×100=123.80
      556.63

P01=556.634=139.157

Page No 489:

Question 3:

Compute a Price Index for the following by (i) Simple Aggregative Method, and (ii) Average of Price Relative Method:
 

Commodities A B C D E F
Price in 2004 (₹) 20 30 10 25 40 50
Price in 2018 (₹) 25 30 15 35 45 55

Answer:

(i) Simple Aggregate Method
 

  2004
(P0)
2018
(P1)
A
B
C
D
E
F
20
30
10
25
40
50
25
30
15
35
45
55
  P0 = 175 P1 = 205

P01= ΣP1ΣP0 =205175×100=117.14
(ii) Price Relative Method
 
  2004
​(P0)
2018
​(P1)
Price Relative =P0P1×100
A 20 25 2520×100=125
B 30 30 3030×100=100
C 10 15 1510×100=150
D 25 35 3525×100=140
E 40 45 4540×100=112.5
F 50 55 5550×100=110
      ∑ = 737.5

P01=ΣP0P1×100N =737.56=122.91

Page No 489:

Question 4:

Construct price index number of the following data by using:
(i) Laspeyre's Method, (ii) Paasche's Method, and (iii) Fisher's Method.
 

Items Base Year Current Year
Quantity Price Quantity Price
A
B
C
D
3
7
4
6
5
4
7
6
2
5
3
5
8
6
10
7

Answer:

  q0 p0 p0q0 p1 q1 p1q1 p1q0 p0q1
A
B
C
D
3
7
4
6
5
4
7
6
15
28
28
36
8
6
10
7
2
5
3
5
16
30
30
35
24
42
40
42
10
20
21
30
      Σp0q0 =107     Σp1q1 =111 Σp1q0 =148 Σp0q1 =81

(i) Laspeyre's Price index:
P01=ΣP1q0ΣP0q0×100or, P01=148107×100=138.31

(ii) Paasche's Price index:
P01=ΣP1q1ΣP0q1or, P01=11181×100=137.04

(iii) Fisher's Price index:
P01=ΣP1q0ΣP0q0×ΣP1q1ΣP0q1×100or, P01= 148107×11181×100=137.67

Page No 489:

Question 5:

Construct an index number for the year 2018, taking 2004 as base year by any method you deem ideal:
 

Year Good I Good II Good III
Price Quantity Price Quantity Price Quantity
2004
2018
5
4
10
12
8
7
6
7
6
5
3
4

Answer:

  P0 q0 P1 q1 P0q0 P1q1 P0q1 P1q0
I
II
III
5
8
6
10
6
3
4
7
5
12
7
4
50
48
18
48
49
20
60
56
24
40
42
15
          ΣP0q0 =116 ΣP1q1 =117 ΣP0q1 =140 ΣP1q0 =97

Fisher's Method

P01=ΣP1q0ΣP0q0×ΣP1q1ΣP0q0×100or,P01= 97116×117140×100 =83.59



Page No 490:

Question 6:

Given the following data and taking 2004 as the base year, construct index of prices using:

(i) Laspeyre's Method, (ii) Paasche's Method, and (iii) Fisher's Method.
 

Year Commodities
A B C D
Price Quantity Price Quantity Price Quantity Price Quantity
2004
2018
24
30
8
10
9
10
3
4
16
20
5
8
10
9
3
4

Answer:

  P0 q0 P0q0 P1 q1 P1q1 P1q0 P0q1
A
B
C
D
24
9
16
10
8
3
5
3
192
27
80
30
30
10
20
9
10
4
8
4
300
40
160
36
240
30
100
27
240
36
128
40
      P0q0 = 329     P1q1 = 536 P1q0 =397 P0q1​ = 444

Laspeyre's Price index
P01=ΣP1q0ΣP0q0×100or,P01=397329×100 =120.66

Paasche's Price index
P01=ΣP1q1ΣP0q1×100or,P01= 536444×100 =120.72

Fisher's Price index
P01=ΣP1q0ΣP0q0×ΣP1q1ΣP0q0×100or,P01= 397329×536329×100 =120.65

Page No 490:

Question 7:

Construct a weighted index number of the following data using price relative method:
 

 Item A B C D E
 Base Year (Quantity) 24 14 8 4 8
 Base Year (Price) 2 4 6 10 5
 Current Year (Price) 3 5 9 12 5

Answer:

  P0 q0 P1 P0q0
​(W)
R=P1P0×100 RW
A 2 24 3 48 32×100=150 7200
B 4 14 5 56 54×100=125 7000
C 6 8 9 48 96×100=150 7200
D 10 4 12 40 1210×100=120 4800
E 5 8 5 40 55×100=100  4000
        ΣW =232   ΣRW =30,200

Weighted index number
P01=ΣRWΣW30,200232 or,P01 =130.17

Page No 490:

Question 8:

Find out the index number of the following data with Laspeyre's Method:
 

Commodity 2017 2018
Price Quantity Price Quantity
A
B
70
62
7
3
80
74
6
2

Answer:

  P0 q0 P0q0 P1 q1 P1q0
A
B
70
62
7
3
490
186
80
74
6
2
560
222
      P0q0 =676     P1q0782

Laspeyre's Price index
P01=ΣP1q0ΣP0q0×100or,P01=782676×100 =115.68

Page No 490:

Question 9:

Construct Index number of the following data with Laspeyre's and Paasche's Methods:
 

Commodity Base Year Current Year
Quantity Price Quantity Price
A
B
C
10
8
5
0.80
0.85
1.30
11
9
5.5
0.70
0.90
0.80

Answer:

  P0 q0 P0q0 P1 q1 P1q1 P0q1 P1q0
A
B
C
0.8
0.85
1.35
10
8
5
8
6.8
6.5
0.7
0.9
0.8
11
9
5.5
7.7
8.1
4.4
8.8
7.65
7.15
7
7.2
4
      ΣP0q0 = 21.3     ΣP1q1 = 20.2 ΣP0q1 = 23.60 ΣP1q0 = 18.2

Laspeyre's Price Index
P01=ΣP1q0ΣP0q0or, P01=18.221.3×100=85.44

Passche's Price index
P01=ΣP1q1ΣP0q1or,P01=20.223.60×100=85.59

Page No 490:

Question 10:

Construct index numbers of the following data by Fisher's Method:
 

Commodity Base Year Current Year
Price Value Price Value
A
B
C
D
E
3
5
6
4
8
18
35
42
32
24
7
10
11
6
9
10
100
55
60
36

Answer:


 
  P0 Value
(Base Year)

 
q0=ValueP0 P0q0 P1
Value
(Current Year)
q1 =ValueP1 P1q1 P1q0 P0q1
A
B
C
D
E
3
5
6
4
8
18
35
42
32
24
6
7
7
8
3
18
35
42
32
24
7
10
11
6
9
14
100
55
60
36
2
10
5
10
4
14
100
55
60
36
42
70
77
48
27
6
50
30
40
32
    151   ΣP0q0 = 151       ΣP1q1 = 265 ΣP1q0 = 264 ΣP0q1 = 158

Fisher's Price Index

P01=ΣP1q0ΣP0q0×ΣP1q1ΣP0q0×100or, P01=264151×265158×100=171.24



Page No 491:

Question 11:

Construct Cost of Living Index on the basis of the following data:
 

Items Price Weight
 Wheat
 Rice
 Maida
 Pulses
 Oil
241
150
200
170
125
10
4
2
2
2

Answer:

Items Price
(P)
Weights
(W)
PW
Wheat
Rice
Maida
Pulses
Oil
241
150
200
170
125
10
4
2
2
2
2410
600
400
340
250
    W=20 PW = 4000

Cost of living Index 
=PWW=4000620=200

Page No 491:

Question 12:

Construct Consumer Price Index Number with the help of the following data:
 

Consumer Items Price Weight
 Food
 Fuel
 Cloth
 House Rent
 Miscellaneous
125
120
66.67
120
150
40
10
25
15
10

Answer:

Items Price
(P)
Weights
(W)
PW
Food
Fuel
Cloth
House rent
Miscellaneous
125
120
66.67
120
150
40
10
25
15
10
5000
1200
16 66.75
1800
1500
    ΣW =100 ΣW =11166.75

Consumer price index
=PWW=111 66.75100=111.67       

Page No 491:

Question 13:

From the following data find Consumer Price Index or Cost of Living Index:
 

Items Quantity Consumed in Current Year Price in Base year Price in Current Year
 Rice
 Pulses
 Oil
 Clothing
 Housing
 Miscellaneous
30 qt
36 kg
24 l
72 metres
per month
per month
12
0.4
1.5
0.75
20
20
25
0.6
2.2
10
30
15

Answer:

Items q1 P0 P1 P1q1 P0q1
 Rice
 Pulses
 Oil
 Clothing
 Housing
 Miscellaneous
30
36
24
72
1
1
12
0.4
1.5
0.75
20
20
25
0.6
2.2
10
30
15
750
21.6
52.8
720
30
15
360
14.4
36
54
20
20
        ΣP1q1= 1589.4 ΣP0q1= 504.4

​Note that here we are given the current year quantities for different items. So, the Consumer Price Index is calculated using the following formula.

CPI=ΣP1q1ΣP0q1or, CPI =1589.4504.4×100=315.10

Page No 491:

Question 14:

Construct Cost of Living Index Number for the year 2018 from the following statistics:
 

Commodity 2004 Price 2004 Quantity 2018 Price
A
B
C
D
E
25
36
12
6
28
16.0
7.0
3.5
2.5
4.0
35
48
16
10
28

Answer:

  P0 q0 P1 P1q0 P0q0
A
B
C
D
E
25
36
12
6
28
16
7
3.5
2.5
4
35
48
16
10
28
560
336
56
25
112
400
252
42
15
112
        ΣP1q0 =821 ΣP0q0 =1089

Cost of Living Index

CPI=ΣP0q0ΣP1q0×100or,CPI =1089821×100=132.643



Page No 492:

Question 15:

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:

  q0 P0 P1 W = P0q0 P1q0 R=P1P0×100 WR
Rice 6 100 120 600 720 120100×100=120 72,000
Wheat 8 80 90 640 720 9080×100=112.5  72,000
Bajra 1 70 70 70 70 7070×100=100 70,000
Arhar 2 120 115 240 230 115120×100=95.83 22,999.2
Ghee 20 12 15 240 300 1512×100=125 30,000
Sugar 1 160 170 160 170 170160×100=106.25 17,000
        ΣP0q0 = 1950 ΣP1q0 = 2210   283999.2

(i) Aggregate expenditure method​

CPI=ΣP1q0ΣP0q0or, CPI =22101950×100=113.33


(ii) Family Budged Method
CPI=WRW=283999.21950=145.64

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

Page No 492:

Question 16:

Construct index number of industrial production in the year 2018 from the following data on the basis of 2005's production:
 

Industry Units 2005 2018 Weight
 Electrical and Electronics
 Metallurgical
 Mechanical
 Mining
 Textiles
 Miscellaneous
Mill. Nos.
Th. Tonnes
Th. Tonnes
Th. Tonnes
Mill. Mtrs.
Th. Tonnes
12
22
72
100
60
123
70
37
105
123
130
270
36
12
10
22
8
12

Answer:

Industry q0 q1 Weight
(W)
R=q1q0×100 WR
Electronics 12 70 36 7012×100=583.33 20999.88
Metallurgical 22 37 12 3722×100=168.18 2018.16
Mechanical 72 105 10 10572×100=145.83 1458.3
Mining 100 123 22 123100×100=123 2706
Textiles 60 130 8 13060×100=216.67 1733.36
Misce. 123 270 12 270123×100=219.51 2634.12
      W = 100   ∑ WR = 31549.82

Index number of Industrial Production
IIP=WRWor, IIP=31549.82100=315.50

Page No 492:

Question 17:

Construct index number of industrial production from the following data:
 

Item Units Production or Output Weight
Base year Current Year
 Mechanical
 Sugar and Tea
 Textile
 Mining
 Transportation
 Electricity and Electronics
 Mill. Nos.
 Th. Tonnes
 Mill. Mtrs.
 Th. Tonnes
 Mill. Nos.
 Mill. Nos.
237
62
572
165
335
87
400
150
820
200
727
323
5
10
35
15
20
15

Answer:

Item Base year
(q0
)
Current year
(q1)
Relatives valuesR=q1q0×100 Weight
(W)
WR
 Mechanical 237 400 168.78 5 843.85
 Sugar and Tea 62 150 241.19 10 2419.35
 Textile 572 820 143.35 35 5017.48
 Mining 165 200 121.21 15 1818.15
 Transportation 335 727 217.01 20 4340.2
 Electricity and electronics 87 323 371.26 15 5568.9
        W = 100 RW = 20008.3

Index number of Industrial Production
IIP=RWWor, IIP =20008.3100=200.08

Page No 492:

Question 18:

Construct index number of industrial production from the following data:
 

Industry Number of Items Weight
Base Year Current Year
Mining and Quarrying
Manufacturing
Electricity and Electronics
35
413
10
107
1225
27
10
85
5
 

Answer:

Industry Base year
(q0)
Current year
(q1)
Relatives values
R=q1q0×100
Weight
(W)
WR
 Mining and quarrying
 Manufacturing
 Electricity and electronics
35
413
10
107
1225
27
305.71
296.61
270
10
85
5
3057.1
25211.85
1350
        W = 100 RW = 29618.95

Index number
=RWW=29618.95100=296.19



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