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Page No 362:

Question 1:

Construct the Index Number for 2011 with 2015 as base from the following prices of commodities by simple (Unweighted) aggregative method.

Commodities : A B C D E
Prices in ₹(2015) : 50 40 10 5 2
Prices in  ₹(2011) : 80 60 20 10 6
[Index Number = 164.48]

 

Answer:

Commodity Prices in 2015
(p0)
Prices in 2011
(p1)
A
B
C
D
E
50
40
10
  5
  2
80
60
20
10
  6
   ∑ p0 = 107  ∑ p1 = 176

p01=Σp1Σp0×100=176107=164.48

Thus, price index is 164.48.

Page No 362:

Question 2:

Using the following data and 2008 as the base period, compute simple aggregative price indices for the two fuels.

Item  Producer's Price (in ₹)
 2008 2009 2010
Coal ( ₹) 5 3 4
Crude oil ( ₹) 2 3 4

Answer:

Item Prices in 2008
(p0)
Prices in 2009
(p1)
Prices in 2010
(p2)
Coal
Crude oil
5
2
3
3
4
4
  p0 = 7 p1 = 6 p2 = 8

p01=Σp1Σp0×100=67×100=85.71p02=Σp2Σp0×100=87×100=114.28
Thus, index  number for 2009 is 85.71 and index number for 2010 is 114.28

Page No 362:

Question 3:

Calculate the index number for 2014 with 2013 as base from the following prices of the commodities by simple (unweighted) aggregative method.

Commodity and unit Price ( ₹)
(2013)
Price ( ₹)
(2014)
Butter per kg 20.00 22.00
Milk per litre 3.00 4.50
Cheese per Tin 18.00 19.80
Bread per Kg 2.00 3.80
Eggs per Dozen 4.00 4.50

Answer:

Commodity Prices in 2013
(p0)
Prices in 2014
(p1)
Butter
Milk
Cheese
Bread
Eggs
20
3
18
2
4
22
4.5
19.80
3.80
4.50
  p0 = 47 p1 = 54.6

p01=Σp1Σp0×100=54.647×100=546047=116.17
Thus, index number is 116.17.

Page No 362:

Question 4:

Calculate Quantity Index Numbers from the following data by simple aggregative method taking quantity of 2011 as base.

Commodity Quantity (in tons)
2011 2012 2013 2014 2015
A 0.30 0.33 0.36 0.36 0.39
B 0.25 0.24 0.30 0.32 0.30
C 0.20 0.25 0.28 0.32 0.30
D 2.00 2.40 2.50 2.50 2.60

[Quantity Index No. : 2012 = 117.1; 2013 = 125.1; 2014 = 127.3 ; 2015 = 130.5]

Answer:

Commodity Quantity in 2011
(q0)
Quantity in 
2012
(q1)
Quantity in 
2013
(q2)
Quantity in
2014
(q3)
Quantity in
2015
(q4)
A
B
C
D
0.30
0.25
0.20
2.00
0.33
0.24
0.25
2.4
0.36
0.30
0.28
2.50
0.36
0.32
0.32
2.50
0.39
0.30
0.30
2.60
  q0 = 2.75 q1 = 3.22 q2 = 3.44 q3 = 3.5 q4 = 3.59

q01=Σq1Σq0×100=3.222.75×100=117.1
Thus, quantity index for 2012 is 117.1.
q02=Σq2Σq0×100=3.442.75×100=125.1
Thus, quantity index for 2013 is 125.1.
q03=Σq3Σq0×100=3.52.75×100=127.3
Thus, quantity index for 2014 is 127.3.
q04=Σq4Σq0×100=3.592.75×100=3592.75=130.5
Thus, quantity index for 2015 is 130.5.



Page No 363:

Question 5:

Calcualte index number for 2017 on the base prices for 2013 from the following by average of price relative method.

Items : Bricks Timber Plaster Board Sand Cement
Price in  ₹ (2013) : 10 20 5 2 7
Price in  ₹ (2017) : 16 21 6 3 14
                                                                                               [Index No. = 147]

Answer:

Item Prices in 2013
(p0)
Prices in 2017
(p1
)
Price relatives of 2017 in
relation to 2013
p1p0×100
Brick 10 16 1610×100=160
Timber 20 21 2120×100=105
Plaster Board 5 6 65×100=120
Sand 2 3 32×100=150
Cement 7 14 147×100=200
      Σp1p0×100=735

p01=Σp1p0×100N=7355=147
Thus, index number is 147.

Page No 363:

Question 6:

Construct the index number for 2016 taking 2006 as base by price relative method using arithmetic mean.

Commodities : A B C D
Price in  ₹ (2006) : 10 20 30 40
Price in  ₹ (2016) : 13 17 60 70
                                                                                               [Index No. = 147.5]

Answer:

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By Board Grade
Curriculum
 
1 - CBSE
Grade
 
13 - XI-Commerce
Subject
 
16 - Economics
Textbook
 
7 - NM Shah (2018)
Unit
 
Type Unit Name
Chapter
 
9 - Introduction to Index Numbers
Slo
 
Select Slo
Exercise
Page No
363
Set No
1
Question No
6
Flow
6
Page Flow
Exercise Flow
Question
 
Calcualte index number for 2017 on the base prices for 2013 from the following by average of price relative method.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Items : Bricks Timber Plaster Board Sand Cement
Price in  ₹ (2013) : 10 20 5 2 7
Price in  ₹ (2017) : 16 21 6 3 14
 
                                                                                               [Index No. = 147]
 
Solution
 
Comment
 
Submit
Commodities Prices in 2006
(p0)
Prices in 2016
(p1)
p1p0×100
A 10 13 1310×100=130
B 20 17 1720×100=85
C 30 60 6030×100=200
D 40 70 7040×100=175
      Σp1p0×100=590

p01=Σp1p0×100N=5904=147.5
Thus, index number is 147.5

Page No 363:

Question 7:

Construct Index Number for each year from the following average annual wholesale prices of cotton with 2001 as base .

Year Wholesale Prices
(in ₹)
Year Wholesale Prices
(in ₹)
2001 75 2006 70
2002 50 2007 69
2003 65 2008 75
2004 60 2009 84
2005 72 2010 80
 

Answer:

Prices in 2001
(p0)
Prices in 2002
(p1)
Prices in
2003
(p2)
Prices in 2004
(p3)
Prices in 2005
 (p4)
Prices in 2006
 (p5)
Prices in 2007
(p6)
Prices in 2008
(p7)
Prices in 2009
(p8)
Prices in 2010
(p9)
75 50 65 60 72 70 69 75 84 80

p01=Σp1Σp0×100=5075×100=66.67p02=Σp2Σp0×100=6575×100=86.67p03=Σp3Σp0×100=6075×100=80p04=Σp4Σp0×100=7275×100=96p05=Σp5Σp0×100=7075×100=93.33p06=Σp6Σp0×100=6975×100=92p07=Σp7Σp0×100=7575×100=100p08=Σp8Σp0×100=8475×100=112p09=Σp9Σp0×100=8075×100=106.67

Page No 363:

Question 8:

The group indices of prices of commodities for second week of Sept. 2017 and the group weights are given below. Compute the index number by family budget method.

Group Weights Index
Food Article 31 473.6
Manufactures 30 390.2
Industrial Raw Material 18 510.2
Semi-Manufactures 17 403.3
Miscellaneous 4 624.4
 

Answer:

Group Weights
(w)
Index
(x)
wx
Food Article
Manufactures
Industrial Raw Material
Semi-Manufactures
Miscellaneous
31
30
18
17
4
473.6
390.2
510.2
403.3
624.4
14681.6
11706
9183.6
6856.1
2497.6
  w = 100   wx = 44924.9

WPI=ΣwxΣw=44924.9100=449.249
Thus, the index of wholesale prices is 449.29.

Page No 363:

Question 9:

Calculate price index number for 2016 of following data by weighted aggregative method using (a) Laspeyre's method, (b)  Paasche's method, (c) Fisher's method.
 

Commodity  Price
(2012)
Quantity
(2012)
 Price
(2016)
Quantity
(2016)
A 4 20 6 10
B 3 15 5 23
C 2 25 3 15
D 5 10 4 15
 

Answer:

Commodity Base Year Current Year  
Prices
p0
Quantity
q0
Prices
p1
Quantity
q1
p0q0 p0q1 p1q0 p1q1
A
B
C
D
4
3
2
5
20
15
25
10
6
5
3
4
10
23
15
40
80
45
50
50
40
69
30
200
120
75
75
40
60
115
45
160
          p0q0 = 225 p0q1 = 339 p1q0 = 310 p1q1 = 380



(a)
Laspeyre's method p01=Σp1q0Σp0q0×100                                  =310225×100=137.77
(b)
Paasche's method p01=Σp1q1Σp0q1×100                               =380339×100=112.09
(c)
Fisher's method p01=Σp1q1Σp0q1×Σp1q0Σp0q0×100                               =380339×310225×100=124.26
Note: As per the textbook, the price index using Paasche's method is 158.99 and Fisher's method is 148.1. However, as per the above solution the price index using Paasche's method should be 112.09 and Fisher's method should be 124.26.



Page No 364:

Question 10:

From the data given below , construct Laspeyre's , Paasche's and Fisher's price index and quantity index numbers with base 2015 and interpret.​

 
Commodity 2015 2016
Price
(₹)
Quantity
(Kg)
Price
(₹)
Quantity
(Kg)
A
B
C
4
3
8
2
5
2
6
2
4
3
1
6


 

Answer:

Commodity Base Year Current Year  
Price
p0
Quantity
q0
Price
p1
Quantity
q1
p0q0 p0q1 p1q0 p1q1
A
B
C
4
3
8
2
5
2
6
2
4
3
1
6
8
15
16
12
3
48
12
10
8
18
2
24
          p0q0 = 39 p0q1 = 63 p1q0 = 30 p1q1 = 44

Laspeyre's Price index =  Σp1q0Σp0q0×100=3039×100=76.92
Laspeyre's Quantity index = Σp0q1Σp0q0×100=6339×100=161.53

Paasche's Price index = Σp1q1Σp0q1×100=4463×100=69.84

Paasche's Quantity index = Σp1q1Σp1q0×100=4430×100=146.67

Fisher's Price index = Σp1q1Σp0q1×Σp1q0Σp0q0×100=4463×3039×100=73.29

Fisher's Quantity index =Σp1q1Σp1q0×Σp0q1Σp0q0×100=4430×6339×100=153.92
Note: As per the textbook, the quantity indices using Laspeyre's and Paasche's methods are 143.18 and 130. However, as per the above solution the quantity indices using Laspeyre's and Paasche's methods should be 161.53 and 146.67.

Page No 364:

Question 11:

Calculate weighted aggregative of actual  price index number and quantity index number from the following data using (i) Laspeyre's Method , and (ii) Paasche's Method and (iii) Fisher's Method and interpret them.
 

Commodity Base year Current Year
  Quantity
lbs.
Price 
per lb.
 Quantity
lbs.
Price 
​per lb.
Bread 6 40 paise 7 30 paise
Meat 4 45 paise 5 50 paise
Tea 0.5 90 paise 1.5 40 pAise
 

Answer:

  Base Year Current Year  
Quantity
q0
Price
p0
Quantity
q1
Price
p1
p0q0 p1q1 p1q0 p0q1
Bread
Meat
Tea
6
4
0.5
40
45
90
7
5
1.5
30
50
40
240
180
45
210
250
60
180
200
20
280
225
135
  p0q0 = 465 p1q1 = 520 p1q0 = 400 p0q1 = 640

(i) Price Index number
(a) Laspeyre's p01=Σp1q0Σp0q0×100=400465×100=86.02

(b) Paasche's p01=Σp1q1Σp0q1×100=520640×100=81.25
(c) Fisher's p01=Σp1q1Σp0q1×Σp1q0Σp0q0×100=520640×400465×100=83.60

(ii) Quantity Index number
(a) Laspeyre's q01=Σq1p0Σq0p0×100=640465×100=137.63

(b) Paasche's q01=Σq1p1Σq0p1×100=520400×100=130

(c) Fisher's q01=Σp0q1Σp0q0×Σp1q0Σp1q0×100=520400×640465×100=133.76

The price index number for current year is 86.02 and 81.25 as per Laspeyres's method and Paasche's method respectively. This implies that there is net decrease in the prices in current year by 13.98% and 18.75% from the base year as per Laspeyres's method and Paasche's method respectively.

The quantity index number for current year is 137.63 and 130 as per Laspeyres's method and Paasche's method respectively. This implies that there is net increase in the quantity demanded by 37.63% and 30% from the base year as per Laspeyres's method and Paasche's method respectively.
 

Page No 364:

Question 12:

Calculate price index number by weighted average of price relative method.

Commodity Price Base Year
(in ₹)
Price current year
( in ₹)
Quantity Base year 
(in Kg)
A 6.0 8.0 40
B 3.0 3.2 80
C 2.0 3.0 2
 
 

Answer:

Commodity
Price in Base Year (p0)

Price in Quantity Year
(
p1)

Quantity in Base Year
(
q0)
R=p1p0×100 V
(p0q0)
RV
A
B
C
6
3
2
8
3.2
3
40
80
20
133.33
106.67
150
240
240
40
31999.2
25600.8
6000
  V = 520 RV = 63600

Weighted Average of Price Relative Method

 Index number =ΣRVΣV                      =63600520                      =122.30
Thus, price index number is 122.30.

Page No 364:

Question 13:

Prepare consumer price index numbers from the following data for 2014 and 2013  taking 2012 as base.
 

Group Price
(in ₹)
2012 2013 2014
A 20.00 24.00 21.00
B 1.25 1.50 1.00
C 5.00 8.00 8.00
D 2.00 2.25 2.12

Give weights to four groups as 4, 3, 2 and 1 respectively.
 

Answer:

Price Index for 2013

Group p0
(2012)
p1
(2013)
W R=p1p0×100 WR
A
B
C
D
20
1.25
5
2
24
1.5
8
2.25
4
3
2
1
120
120
160
112.5
480
360
320
112.5
  W= 10   WR=1272.5

Index number=ΣWRΣW                    =1272.510                    =127.25
Thus, consumer price index for 2013 is 127.25.

Price Index number for 2014
Group p0
(2012)
p1
(2014)
W R=p1p0×100 WR
A
B
C
D
20
1.25
5
2
21
1
8
2.12
4
3
2
1
105
80
160
106
420
240
320
106
  W= 10   WR=1086

Index number=ΣWRΣW                    =108610                    =108.6
Thus, consumer price index for 2014 is 108.6.

Note: As per textbook, consumer index for 2014 is 109.78. However, as per the above solution, consumer index for 2014 should be 108.6.



Page No 365:

Question 14:

From the data given below construct the consumer price index number:

Commodity Price Relatives Weights
Food 250 45
Rent 150 15
Clothing 320 20
Fuel and Lighting 190 5
Miscellaneous 300 15
 

Answer:

Commodity Price relatives
(R)
Weights
(W)
WR
Food
Rent
Clothing
Fuel
Miscellaneous
250
150
320
190
300
45
15
20
5
15
11250
2250
6400
950
4500
  W = 100 WR = 25350

Index number=ΣWRΣW                     =25350100                     =253.50
Thus, the consumer price index number is 253.5.



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