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Page No 12.46:

Question 1:

From the data given below, construct the index number for the year 2016 on the base of 2011 by simple aggregative method:

Commodities Unit Price (In ₹)
2011 2016
Wheat quintal 200 250
Rice quintal 300 400
Pulses quintal 400 500
Milk litre 2 3
Clothing meter 4 5

Answer:

Commodity Price in 2011
(P0)
Price in 2016
(P1)
Wheat
Rice
Pulses
Milk
Clothing
200
300
400
2
4
250
400
500
3
5
  ΣP0 = 906 ΣP1 = 1158

P01=ΣP1ΣP0×100or, P01=1158906×100  P01=127.81



Page No 12.47:

Question 2:

Construct index numbers by (aggregative method) based on the price of 2011 from the following figures:

Items A B C D E F
Prices (2011) 200 60 350 100 60 80
Prices (2016) 240 90 600 110 62 90

Answer:

Items Price in 2011
(P0)
Price in 2016
(P1)
A
B
C
D
E
F
200
60
350
100
60
80
240
90
600
110
62
90
  ΣP0 = 850 ΣP1 = 1192

P01=ΣP1ΣP0×100or, P01 =1192850×100P01  =140.235

Page No 12.47:

Question 3:

Following are the prices of commodities in the year 2011 and 2016. Calculate the price index using price relatives method.

Commodity Prices in year 2011 Prices in 2016
A 45 55
B 60 70
C 20 30
D 50 75
E 85 90
F 120 130

Answer:

Commodity Price in 2011
(P0)
Price in 2016 (P1) Price Relative=P1P0×100
A 45 55 5545×100=122.22
B 60 70 7060×100=116.67
C 20 30 3020×100=150
D 50 75 7550×100=150
E 85 90 9085×100=105.88
F 120 130 130120×100=108.33
      Σ P1P0×100=753.1

P01=ΣP1P0×100Nor, P01=753.16 P01=125.515

Page No 12.47:

Question 4:

4. Calculate the index numbers from the following data using:
(i) Laspeyre's method,
(ii) Paasche's method,
(iii) Fisher's ideal method:

Commodity Base year Current year
Price (in ₹) p 0 Quantity q0 Price (in ₹) p1 Quantity q1
A 8 100 10 120
B 4 60 5 80
C 10 20 12 25
D 12 25 15 30
E 3 5 4 6

Answer:

  Base Year     Current Year  
Commodity Price
p0
Quantity
q0
Price
p1
Quantity
   q1      
p0q0 p0q1 p1q0 p1q1
A 8 100 10 120 800 960 1000 1200
B 4 60 5 80 240 320 300 400
C 10 20 12 25 200 250 240 300
D 12 25 15 30 300 360 375 450
E 3 5 4 6 15 18 20 24
          Σp0q0 = 1555 Σp0q1 = 1908 Σp1q0 = 1935 Σp1q1 = 2374

(i) Laspeyre's Method

p01=Σp1q0Σp0q0×100=19351555×100=124.44

(ii) Paasche's Method

p01=Σp1q1Σp0q1×100=23741908×100=124.42

(iii) Fisher's Method

p01=Σp1q0Σp0q0×Σp1q1Σp0q1×100or, p01    =19351555×23741908×100p01   =45936902966940×100=124.43

Page No 12.47:

Question 5:

Calculate Laspeyre's; Paasche's and Fisher's index numbers from the following data:

Commodity Base year Current year
Price (in ₹) p0 Quantity q0 Price (in ₹) Quantity q1
A 10 30 12 50
B 8 15 10 25
C 6 20 6 30
D 4 10 6 20

Answer:

  Base Year         Current Year  
Commodity Price
p0
Quantity
q0
Price
p1
Quantity
q1
p0q0 p0q1 p1q0 p1q1
A 10 30 12 50 300 500 360 600
B 8 15 10 25 120 200 150 250
C 6 20 6 30 120 180 120 180
D 4 10 6 20 40 80 60 120
          Σp0q0 = 580 Σp0q1 = 960 Σp1q0 = 690 Σp1q1 = 1150

(i) Laspeyre's Method

p01=Σp1q0Σp0q0×100=690580×100=69000580=118.965

(ii) Paasche's Method

p01=Σp1q1Σp0q1×100=1150960×100=115000960=119.79

(iii) Fisher's Method

p01=Σp1q0Σp0q0×Σp1q1Σp0q1×100or, p01    =690580×1150960×100  p01  =119.376



Page No 12.48:

Question 6:

The following table contains information from the eaw material purchase records of a small factory to the year 2011-12 and 2016-17:

Commodity 2011-12 2016-17
Price (₹/Unit) p0 Total Valule q0 Price (₹/Unit) Total Value q1
A 5 50 6 72
B 7 84 10 80
C 10 80 12 96
D 4 20 5 30
E 8 56 8 64
Calculate Fisher's Ideal Index Number.

Answer:

  Base Year 
      (2011-12)        
Current Year
(2016-17)
 
Commodity Price
p0
Quantity
q0
Price
p1
Quantity
q1
p0q0 p0q1 p1q0 p1q1
A 5 50 6 72 250 360 300 432
B 7 84 10 80 588 560 840 800
C 10 80 12 96 800 960 960 1152
D 4 20 5 30 80 120 100 150
E 8 56 8 64 448 512 448 512
          Σp0q0 = 2166 Σp0q1 = 2512 Σp1q0 = 2648 Σp1q1 = 3046

Fisher's Method

p01=Σp1q0Σp0q0×Σp1q1Σp0q1×100or,  p01  =26482166×30462512×100or,  p01  =80658085440992×100or,  p01  =1.4824×100or,  p01   =1.2175×100 p01   =121.75

Page No 12.48:

Question 7:

Calculate weighted average of price relative index number of prices for 2016 on the basis of 2011 from the following data:

Comity Quantity in 2011 Price (in ₹)2011 Price (in ₹) 2016
A 20 20 35
B 12 15 18
C 8 10 11
D 4 5 5
E 6 4 5

Answer:

Commodity
Quantity in 2011
(q0)

Weights

Price in 2011
(p0
)
 
Price in 2016
(
p1)
p0q0
(W)
R=p1p0×100
   
RW
A 20 20 35 400 175 70000
B 12 15 18 180 120 21600
C 8 10 11 80 110   8800
D 4 5 5 20 100    2000
E 6 4 5 24 125    3000
        ΣW = 704   ΣRW = 105400

Weighted Average of Price Relatives

p01=ΣRWΣW=105400704p01=149.715

Page No 12.48:

Question 8:

Construct cost of index number for 2016 on the basis of 2011 from the following data using Aggregate Expenditure Method and Family Budget Method.

Article Quantity (kg.) Prices in ₹
2011 2016
A 10 20 30
B 7 21 28
C 5 20 25
D 2 10 12
E 2 6 8
Calculate Fisher's Ideal Index Number.

Answer:

Aggregate expenditure Method
 
Article Price in 2011
(p0)
Price in 2016
(p1)
Quantity
(q0)
p0q0 p1q0
A 20 30 10 200 300
B 21 28 7 147 196
C 20 25 5 100 125
D 10 12 2 20  24
E 6 8 2 12 16
        Σp0q0 = 479 Σp1q0 = 661

Consumer price index for the year 2016
=Σp1q0Σp0q0×100=661479×100=137.99=138

 
Family Budget Method
 
Article Price in 2011
(p0)
Price in 2016
(p1)
Price Relative
(R)

R=p1p0×100
Quantity
(q0)
p0q0
(W)
RW
A 20 30 150 10 200 30000
B 21 28 133.33 7 147 19599.51
C 20 25 125 5 100 12500
D 10 12 120 2  20 2400
E 6 8 133.33 2 12 1599.96
          ΣW = 479 ΣRW = 66099.47

Consumer price index for the year 2016

=ΣRWΣW=66099.47479=137.99=138

Page No 12.48:

Question 9:

Calculate consumer price index number for the following data by aggregate expenditure and family budget Method.

Expenses Weights Price (in ₹) Base Year Price (in ₹) Current year
Food 45 300 350
Rent 20 200 225
Fuel 8 100 110
Clothing 10 150 175
Misc. 17 250 300

Answer:

Aggregate expenditure Method
 
Expenses Price in Base Year
(p0)
Price in Current Year
(p1)
Quantity
(q0)
p0q0 p1q0
Food 300 350 45 13500 15750
Rent 200 225 20 4000 4500
Fuel 100 110 8 800 880
Clothing 150 175 10 1500 1750
Misc. 250 300 17 4250 5100
        Σp0q0 = 24050 Σp1q0 = 27980

Consumer price index for the current year

=Σp1q0Σp0q0×100=2798024050×100=116.34
 
Family Budget Method

 
Expenses Price in Base Year
(p0)
Price in Current Year
(p1)
R=p1p0×100 Quantity
(q0)
p0q0
(W)
RW
Food 300 350 116.67 45 13500 1575045
Rent 200 225 112.5 20 4000 450000
Fuel 100 110 110 8   800   88000
Clothing 150 175 116.67 10 1500 175005
Misc. 250 300 120 17 4250 510000
          ΣW= 24050 ΣRW = 2798050

Consumer price index for the current year

=ΣRWΣW=279805024050=116.34



Page No 12.49:

Question 10:

Construct the index of industrial production from the following data:

Commodity Output (in tonnes) Weights
2011-12 2016-17
Mining 120 180 25
Electrical Products 200 290 45
Manufactured Goods 150 220 30

Answer:

 
Industry
Output in 2011-12
(q0)

Output in 2016-17
(q1)


Weights
(W)

 
q1q0×100 q1q0×100W
Mining 120 180 25 150 3750
Electrical Products 200 290 45 145 6525
Manufactured Goods 150 220 30 146.67 4400.1
      ΣW=100   14675.1

Index Number of Industrial Production =Σ q1q0×100WΣW=14675.1100=146.75

Page No 12.49:

Question 11:

Calculate the cost of living index number for 2016 taking 2012 as base year from the following data by family budget Method.

Times Quantity (in kg.) Price 2012 (in ₹/kg) Price 2016 (in ₹/kg)
A 15 10.00 12.00
B 20 16.50 20.00
C 8 6.00 7.50
D 12 15.00 16.00
E 10 8.00 11.50

Answer:

Family Budget Method
 
Items Price Price Relative
(R)
Quantity    
2012
(p0)
2016
(p1)
R=p1p0×100 2012
(q0)
p0q0
(W)
RW
A 10.00 12.00 120.00 15 150 18000.0
B 16.50 20.00 121.21 20 330 39999.3
C   6.00  7.50 125.00  8  48   6000.0
D 15.00 16.00 106.67 12 180 19200.6
E   8.00 11.50 143.75 10  80 11500.0
          ΣW = 788 ΣRW = 94699.9

Cost of Living Index=ΣRWΣW=94699.9788=120.18

Page No 12.49:

Question 12:

The following data relate to the prices and quantities of 4 commodities in the years 2011-12 and 2016-17. Construct the index numbers of price for the year 2016-17 by using 2011-12 the base year by: (i) Laspeyre's method, (ii) Paasche's method, (iii) Fisher's ideal method:

Commodity 2011-12 2016-17
Price (in ₹) p0 Quantity q0 Price (in ₹) Quantity q1
A 5 100 6 150
B 4 80 5 100
C 2.5 60 5 72
D 12 30 9 33

Answer:

Commodity p0 q0 p1 q1 p0q0 p0q1 p1q0 p1q1
A 5 100 6 150 500 750 600 900
B 4 80 5 100 320 400 400 500
C 2.5 60 5 72 150 180 300 360
D 12 30 9 33 360 396 270 297
Total         1330 1726 1570 2057

(i) Laspeyre's Method

P01=Σp1q0Σp0q0×100=15701330×100=118.05

(ii) Paasche's Method

P01=Σp1q1Σp0q1×100=20571726×100=119.18

(iii) Fisher's Method

P01=Σp1q0Σp0q0×Σp1q1Σp0q1×100or, P01=15701330×20571726×100or, P01 =32294902295580×100or, P01 =1.1860×100P01 =118.60

Page No 12.49:

Question 13:

Calculate the index number for 2016 with 2012 as base using the weighted average of price relative method for the following data:

Commodity Quantity (in units) 2012 Price (in ₹)2012 Price (in ₹)2016
A 2 12 24
B 8 8 12
C 4 15 27
D 5 6 18
E 1 10 12

Answer:

Commodity 2012
q0
2012
p0
2016
p1

p0q0
(W)

 

Price Relative (R)=
p1p0×100
 
RW
A 2 12 24 24 200 4800
B 8 8 12 64 150 9600
C 4 15 27 60 180 10800
D 5 6 18 30 300 9000
E 1 10 12 10 120 1200
        ΣW = 188   ΣRW = 35400

Weighted Average of Price Relatives

P01=ΣRWΣW=35400188=188.297



Page No 12.50:

Question 14:

Construct an index for the year 2016 taking 2011 as base by simple average of price relatives method

Items P Q R S
Price (in ₹) 30 50 70 90
Price (in ₹) 40 60 80 100

Answer:

Items Price in 2011
(P0)
Price in 2016
(P1)
Price Relative=
p1p0×100
P 30 40 133.33
Q 50 60 120
R 70 80 114.29
S 90 100 111.11
      Σ p1p0×100=478.73

Simple Average of Price Relatives

P01=Σ p1p0×100N=478.734=119.68

Page No 12.50:

Question 15:

Using Paasche's formula, compute the quantity index for the year 2016 with 2011 as base year.

Commodity Quantify (in Units) Value (in ₹)
2011 2016 2011 2016
A 5 100 6 150
B 100 150 500 900
C 80 100 320 500
D 60 72 150 360
E 30 33 360 297

Answer:

 
Commodity
Quantity in 2011
(q0)

Quantity in 2016
(q1)
Price in 2011
(p0)
Price in
2016
(p1)
q1p1 q0p1
A 5 100 6 150   15000    750
B 100 150 500 900 135000 90000
C 80 100 320 500 50000 40000
D 60 72 150 360 25920 21600
E 30 33 360 297   9801  8910
          235721 161260

Paasche's Index Numberq01 =Σq1 p1Σq0 p1×100 or,  q01 =235721161260×100 q01=146.17

Note: As per the textbook, the quantity index is 119.177. However, as per the above solution quantity index should be 146.17.



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