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Economics 4 Marks Question

Index Numbers · CBSE STD 11 Commerce (CBSE - English Medium). 38 questions.

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Question 14 Marks
Calculate weighted aggregative price index number from the following data using Paasche's method.
Commodity
Base Year
Current Year
Price (₹)
Quantity
Price (₹)
Quantity
A
10
30
12
50
B
8
15
10
25
C
6
20
6
30
D
4
10
6
20
Answer
Consturction of Index Number:
Commodity Base Year Current Year $p_0q_1$ $p_1q_1$
$p_0$ $q_0$ $p_1$ $q_1$
A 10 30 12 50 500 600
B 8 15 10 25 200 250
C 6 20 6 30 180 180
D 4 10 6 20 80 120
          $\Sigma\text{p}_0\text{q}_1=960$ $\Sigma\text{p}_1\text{q}_1=1150$
Paasche's Price Index Number $\text{P}_{01}=\frac{\Sigma\text{p}_1\text{q}_1}{\Sigma\text{p}_0\text{q}_1}\times100$
$=\frac{1150}{960}\times100$
$=119.79$
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Question 24 Marks
Salary of Rahul was ₹ 10,000 in base year. Current year's CPI is 225 and his salary is ₹ 21,000. Can he maintain same living standard as base year? Give reasons.
Answer
When salary of Rahul was ₹ 10,000 in base year, current year's salary is ₹ 21,000 and current year's CPI is 225, then it implies that the cost of living standard has risen by 125% whereas his salary has increased by 110%, therefore there is a gap of 15%. So, he cannot maintain same living standard as the base year, as he has been compensated by less than 15%.
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Question 34 Marks
Calculate weighted index number for $2016$ by weighted average of relative method for the following data:
Items Weight Price in 2015 (₹) Price in 2016 (₹)
A 10 100 161
B 7 200 210
C 15 50 60
D 9 20 30
E 10 10 14
Answer
Construction of Index number:
Items Weight Price in 2015 (₹) $p_0$ Price in 2016 (₹) $p_1$ $\text{I}\bigg(\frac{\text{p}_1}{\text{p}_0}\times100\bigg)$ IW
A 10 100 161 161 1610
B 7 200 210 105 735
C 15 50 60 120 1800
D 9 20 30 150 1350
E 10 10 14 140 1400
          $\Sigma\text{IW}=6895$
Weight Average of Price Relative Methode $\text{P}_{01}=\frac{\Sigma\text{IW}}{\Sigma\text{W}}=\frac{6895}{51}=135.2$
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Question 44 Marks
Read the following table carefully and give your comments.
INDEX OF INDUSTRIAL PRODUCTION BASE 1993–94
Industry Weight in % 1996–97 2003–2004
General index 100 130.8 189.0
Mining and quarrying 10.73 118.2 146.9
Manufacturing 79.58 133.6 196.6
Electricity 10.69 122.0 172.6
Answer
The following comments can be made from the given table:
  1. In the given table highest weight is given to manufacturing i.e. around 79.58% as compared to mining and quarrying and electricity whose weights are 10.73% and 10.69% respectively.
  2. As compared to the year 1993-94, general production has increased from 30.8% to 89% in 1996-97 and 2003-04 respectively.
  3. The manufacturing sector’s performance is the best in both the years as compared to other two sectors. It has risen around 63% from 1996-97 to 2003-04.
  4. The mining and quarrying sector is the least growing sector as compared to other sectors.
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Question 54 Marks
Calculate weighted aggregative price index with Laspeyre's method from following data.
Items Base year Price Current Year Price Base year Quantity Current Year Quantity
A 40 60 12 15
B 20 24 8 10
C 50 55 12 15
D 50 55 12 15
E 30 42 20 22
Answer
Items
Base Year Price $(p_0)$
Current Year price $(p_1)$
Base Year Quantity $(q_0)$
Current Year Quantity $(q_1)$
$p_1q_0$
$p_0q_0$
A
40
60
12
15
720
480
B
20
24
8
10
192
160
C
5
7
15
15
105
75
D
50
55
12
15
660
600
E
30
42
20
22
840
600
 
 
 
 
 
$\Sigma\text{p}_1\text{p}_0=2517$
$\Sigma\text{p}_0\text{q}_0=1915$
$\text{P}_{01}=\frac{\Sigma\text{p}_1\text{q}_1}{\Sigma\text{p}_0\text{q}_0}\times100$
$=\frac{2517}{1915}\times100=1.31\times100=131$
The price is said to have risen by $31\%$.
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Question 64 Marks
The price paid and quantities purchased by a household in base and current years are given below. Calculate the additional dearness allowance to be given to the household so as to fully compensate it for the price rise, using both the Laspeyre's and Paasche's index number.
Commodity
Base Year
Current Year
Price (₹)
Quntity
Price (₹)
Quntity
A
30
10
40
8
B
12
20
15
18
Answer
Commodity Base Year Current Year $p_0q_0$ $p_0q_1$ $p_1q_1$ $p_1q_1$
$p_0$ $q_0$ $p_1$ $q_1$
A 30 10 40 8 300 240 400 320
B 12 20 15 18 240 216 300 270
          $\Sigma\text{p}_0\text{q}_0=540$ $\Sigma\text{p}_0\text{q}_1=456$ $\Sigma\text{p}_1\text{q}_0=700$ $\Sigma\text{p}_1\text{q}_1=590$
Laspere's Index Number: $\frac{\Sigma\text{p}_1\text{q}_0}{\Sigma\text{p}_0\text{q}_0}\times100=\frac{700}{540}\times100=129.63$
Paasche's Index Number: $\frac{\Sigma\text{p}_1\text{q}_1}{\Sigma\text{p}_0\text{q}_0}\times100=\frac{590}{456}\times100=129.39$
Additional dearness allowance to be paid as per Laspeyre's Index Number = $29.63\%$.
Additional dearness allowance to be paid as per Paasche's Index Number = $29.39\%$.
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Question 74 Marks
Can the CPI for urban non-manual employees represent the changes in the cost of living of the President of India?
Answer
The CPI for the urban non-manual employees cannot represent the changes in the cost of living of the President of India. This is because the consumption basket of the non-manual employees consists of different items than those of the consumption basket of President of India. In fact, in India CPI for industrial workers is the most popular index. This is used by the government to regulate Dearness Allowance (D.A.) to compensate its employees against the price rise. Hence, the CPI for the industrial workers cannot represent the changes in the cost of living of the President of India.
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Question 84 Marks
Calculate weighted average of price relative index from the following data:
Item Weight (in %) Base Year Price (₹) Current Year Price (₹)
A 40 2 4
B 30 5 6
C 20 4 5
D 10 2 3
Answer
Construction of Index number:
Item Weight (W) Base Year Price (₹)$p_0$ Current Year Price (₹) $p_1$ $\text{I}\bigg(\frac{\text{p}_1}{\text{p}_0}\times100\bigg)$ IW
A 40 2 4 $\frac{4}{2}\times100=200$ 8000
B 30 5 6 $\frac{6}{5}\times100=120$ 3600
C 20 4 5 $\frac{5}{4}\times100=125$ 2500
D 10 2 3 $\frac{3}{2}\times100=150$ 1500
  $\Sigma\text{W}=100$       $\Sigma\text{IW}=15600$
$\text{P}_{01}=\frac{\Sigma\text{IW}}{\Sigma\text{W}}$
$=\frac{15600}{100}$
$=156$
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Question 94 Marks
A department store sells stereo systems, television sets and radios. The percentage distribution of the total sales volume (in ₹) is estimated as 30% stereos, 50% televisions and 20% radios. The price of one stereo, one television and one radio in 2009 was ₹ 20,000, ₹ 15,000 and ₹ 500 respectively, while their respective price in 2012 were ₹ 25,000, ₹ 20,000 and ₹ 800.
A weighted price index for 2012 with base 2009 is to be computed.
  1. Which index number formula is appropriate? Why?
  2. Compute the index.
Answer
  1. Here, weighted average of price relative method is appropriate because the relative importance or contribution of various products i.e., stereo systems, televisions and radios, to the total sales volume is to be considered.
Product Weight Price in 2009 (₹) Price in 2012 (₹) $\text{I}\bigg(\frac{\text{p}_1}{\text{p}_0}\times100\bigg)$ IW
Stereo 30 20,000 25,000 $\frac{25,000}{20,000}\times100=125$ 3,750
Television 50 15,000 20,000 $\frac{20,000}{15,000}\times100=133.3$ 6,665
Radio 20 500 800 $\frac{800}{500}\times100=160$ 3,200
    $\Sigma\text{W}=100$     $\Sigma\text{IW}=13,615$
Hence, thw weighted price index for 2012 with base 2009, is given by $\text{P}_{01}=\frac{\Sigma\text{IW}}{\text{W}}=\frac{13,615}{100}=136.15$
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Question 104 Marks
Explain the concept of deflating using index numbers.
Answer
Deflating means correcting or adjusting a value which has inflated. It makes allowances for the effect of price changes. When prices rise, the purchasing power of money declines. If the money incomes of people remain constant between two periods and prices of commodities are doubled the purchasing power of money is reduced to half. For example if there is an increase in the price of rice from ₹ 10/ kg in the year 1980 to ₹ 320/kg in the year 1982. Then a person can buy only half kilo of rice with ₹ 10. so the purchasing power of a rupee is only 50 paise in 1982 as compared to 1980. Thus the purchasing power of money $=\frac{1}{\text{ Price Index}}$ In times of rising prices the money wages should be deflated by the price index to get the figure of real wages. The real wages alone tells whether a wage earner is in better position or in worst position. For calculating real wage, the money wages or income is divided by the corresponding price index and multiplied by 100.$\text{i.e. Real wages}=\frac{\text{Money wages}}{\text{Price Index}}\times100 $
$\text{Thus Real wages Index}=\frac{\text{Real wage of current year }}{\text{Real wage of base year}}\times100.$
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Question 114 Marks
Given the following data:
Year
1995-96
1996-97
1997-98
1998-99
1999-2000
2000-01
2001-02
2002-03
WPI (1993-94)
121.6
127.2
132.8
140.7
145.7
155.7
161.3
166.8
Calculate the inflation rate and interpret the result.
Answer
Rate of Inflation $=\frac{\text{X}_\text{t}-\text{X}_\text{t-1}}{\text{X}_\text{t}-1}\times100.$
Inflation rate for different years are calculated as:
Year 1996-97 $=\frac{127.2-121.6}{121.6}\times100=4.6\%$
Year 1997-98 $=\frac{132.8-127.2}{127.2}\times100=4.40\%$
Year 1998-99 $=\frac{140.7-132.8}{132.8}\times100=5.94\%$
Year 1999-2000 $=\frac{145.7-140.7}{140.7}\times100=3.55\%$
Year 2000-01 $=\frac{155.7-145.7}{145.7}\times100=6.86\%$
Year 2001-02 $=\frac{161.3-155.7}{155.7}\times100=3.59\%$
Year 2002-03 $=\frac{166.8-161.3}{161.3}\times100=3.40\%$
There are many ups and down in the rate of inflation based on WPl.
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Question 124 Marks
The monthly expenditure (₹) of a family on some important items and the Goods and Services Tax (GST) rates applicable to these items is as follows:
Item Monthly Expense (₹) GST Rate %
Cereals 1500 0
Eggs 250 0
Fish, Meat 250 0
Medicines 50 5
Biogas 50 5
Transport 100 5
Butter 50 12
Babool 10 12
Tomato Ketchup 40 12
Biscuits 75 18
Cakes, Pastries 25 18
Branded Garments 100 18
Vacuum Cleaner, Car 1000 28
Calculate the average tax rate as far as this family is concerned.
Answer
The calculation of the average GST rate makes use of the formula for weighted average. In this case, the weights are the shares of expenditure on each category of goods. The total weight is equal to the total expenditure of the family. And the variables are the GST rates.
Category
Expenditure Weight (w)
GST Rate (x)
WX
Category 1
2000
0
0
Category 2
200
0.05
10
Category 3
100
0.12
12
Category 4
200
0.18
36
Category 5
1000
0.28
280
 
2500
 
338
The mean GST rate as far as this family is concerned is $\frac{(338)}{(3500)}=0.966\text{ i.e. }9.66\%$
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Question 134 Marks
What is an Index Number? Explain the difficulties or problems involved while constructing an Index Number.
Answer
An index number is a statistical device used for measuring changes in the magnitude of a group of related variables. Some of the difficulties or problems involved in the construction of index numbers are:
  1. Purpose of the index number is to be absolutely clear, in order to avoid confusion.
  2. Selection of the items to be included is to be done very carefully and suitably, in order to get a meaningful picture of the change involved.
  3. Selection of the source of data is also important. In case of primary data, not being used, the secondary data from the most reliable source should be chosen.
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Question 144 Marks
From the following data, construct a weighted index number for $2010$ with $2000$ as base year:
Items Weight Prices
2000 2010
Wheat 15 10 15
Rice 10 8 16
Pulses 5 5 10
Milk 4 2 4
Oil 6 4 6
Sugar 7 3 6
Salt 3 1 2
Answer
Items Weight % Weight Price Price relative $\Big(\frac{\text{p}_1}{\text{p} _0}\times100\Big)$
2000 $(p_0)$ 2011 $(p_1)$
Wheat 15 30 10 15 150
Rice 10 20 8 16 200
Pulses 5 10 5 10 200
Milk 4 8 2 4 200
Oil 6 12 4 6 150
Sugar 7 14 3 6 200
Salt 3 6 1 2 200
Weighted Price Index is:
$\text{p}_{01}=\frac{\Sigma\text{wi}\Big(\frac{\text{P}_{11}}{\text{P}_{01}}\times100\Big)}{\Sigma\text{wi}}$
$=\frac{30\times150+20\times200+10\times200+8\times200+12\times150+14\times200+6\times200}{100}$
$=\frac{4500+4000+2000+1600+1800+2800+1200}{100}$
$\text{p}_{01}=\frac{17900}{100}=179$
$\therefore$ The Price Index has risen by $79\%$.
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Question 154 Marks
Calculate Laspeyre's price index number from the following data.
Commodity
Price
Quantity Bought
2014
2015
2014
2015
X
50
52
10
12
Y
7
9
3
4
Z
3
5
7
7
Answer
Consturction of Index Number:
Commodity
2014 (Base Year)
2015 (Current Year)
$p_0q_0$
$p_1q_0$
$p_0$
$q_0$
$p_1$
$q_0$
X
50
10
52
12
500
520
Y
7
3
9
4
21
27
Z
3
7
5
7
21
35
 
 
 
 
 
$\Sigma\text{p}_0\text{q}_0=542 $
$\Sigma\text{p}_1\text{q}_0=582$
Laspeyre's Price Index Number:$\text{P}_{01}=\frac{\Sigma\text{p}_1\text{q}_0}{\Sigma\text{p}_0\text{q}_0}\times100=\frac{582}{542}\times100=107.38$
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Question 164 Marks
Find out the Price Index of the year 2018, assuming 2016 as the base year of the following data by using Simple Average of Price Relatives Method:
Commodity
Price in the year, 2016 (₹) per Qtl.
Price in the year, 2018 (₹) per Qtl.
Wheat
800
900
Sugar
1100
1200
Rice
400
600
Potato
500
700
Salt
300
500
Answer
Commodity
$p_0$
$p_1$
$\frac{\text{p}_0}{\text{p}_1}\times100$
Wheat
800
900
112.50
Sugar
1100
1200
109.60
Rice
400
600
150.00
Potato
500
700
140.00
Salt
300
500
166.66
 
 
 
$\Sigma\Big(\frac{\text{p}_1}{\text{p}_0}\times100\Big)=678.25$
$\text{P}_{01}=\frac{\Sigma\Big(\frac{\text{p}_1}{\text{p}_0}\times100\Big)}{\text{N}}=\frac{678.25}{5}=135.65$
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Question 174 Marks
Construct Index Number by Paasche’s method:
Commodity Year 2005 Year 2006
Price Quantity Price Quantity
A 2 8 4 6
B 5 10 6 5
C 4 14 5 10
D 2 19 2 13
Answer
Commodity $p_0$ $q_0$ $p_1$ $q_1$ $p_0q_1$ $p_1q_1$
A 2 8 4 6 12 24
B 5 10 6 5 25 30
C 4 14 5 10 40 50
D 2 19 2 13 26 26
          $\Sigma\text{p}_0\text{q}_1=103$ $\Sigma\text{p}_1\text{q}_1=130$
Paasches's Method $\text{P}_{01}=\frac{\Sigma\text{p}_1\text{q}_1}{\Sigma\text{p}_0\text{q}_1}\times100$
$=\frac{130}{103}\times100=126.21$
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Question 184 Marks
The price quotation of different commodities for 2014 and 2015 are given below. Calculate the index number for 2015 with 2014 as base year by using:
  1. Simple Average of Price Relative.
  2. Weighted Average of Price Relative.
Commodity Unit Weight Price ( ₹)
2014 2015
A Kg 5 2.00 4.50
B Qunintal 7 2.50 3.20
C Dozen 6 3.00 3.50
D Kg 2 1.00 1.80
Answer
Consturction of Index Number:
Commodity Weight (W) $p_0$ Price in 2015 $(p_1)$ $\text{I}\bigg(\frac{\text{p}_1}{\text{p}_0}\times100\bigg)$ IW
A 5 2.00 4.50 $\frac{4.50}{2.0}\times100=225$ 1125
B 7 2.50 3.20 $\frac{3.20}{2.50}\times100=128$ 896
C 6 3.00 3.50 $\frac{3.50}{3.00}\times100=116.67$ 700.2
D 2 1.00 1.80 $\frac{1.80}{1.00}\times100=180$ 360
n = 4 $\Sigma\text{W}=20$     $\Sigma\text{I}=649.67$ $\Sigma\text{IW}=3081.02$
  1. Simple Average of price Relative Method: $\text{P}_{01}=\frac{\Sigma\text{I}}{\text{n}}=\frac{649.67}{4}=162.42$
  2. Weight Average of Price Relative Method: $\text{P}_{01}=\frac{\Sigma\text{IW}}{\Sigma\text{W}}=\frac{3081.02}{20}=154.051$
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Question 194 Marks
Distinguish between simple and weighted aggregative method of constructing price index numbers.
Answer
  • Simple Aggregative Method: Is the simplest method of constructing unweighted price index. In this method, total of the current year prices for the various commodities is divided by the total of the base year prices and the quotient is multiplied by 100. Symbolically,
$\text{P}_{01}=\frac{\Sigma\text{p}_1}{\Sigma\text{p}_0}\times100.$

Weighted Aggregative Method: Is a method of constructing weighted price index numbers. Weights are assigned to various items in the index according to their relative importance. Here weights are quantity weights. Laspeyre has used base year quantities as weights. According to Laspeyre,

$\text{P}_{01}=\frac{\Sigma\text{p}_1\text{q}_0}{\Sigma\text{p}_0\text{q}_0}\times100.$

Paasche has used current year quantities as weights. According to Paasche,

$\text{P}_{01}=\frac{\Sigma\text{p}_1\text{q}_1}{\Sigma\text{p}_0\text{q}_1}\times100.$
  • In simple aggregative method, all the items are treated as having equal importance whereas in weighted aggregative method, all the items are treated as having difference in importance.
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Question 204 Marks
What kind of indices NIFTY, SENSEX, HDI and Producer Price Index?
Answer
Sensex: It is Index of Bombay stock exchange It has total 30 shares. Its recent index above 20000 however, it keeps fluctuating day to day.
Nifty: It is Index of National stock exchange. It has total 50 shares. Present index above 5000.
Human Development Index: It is prepared by UNDP for measuring development status of different countries. It is based on:
  1. Standard of living.
  2. Life expectancy.
  3. Educational Attainments.
Producer Price Index: 'This index number measures price changes from the producers' perspective. It uses only basic prices including taxes, trade margins and transport costs. A Working Group on Revision of Wholesale Price.
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Question 214 Marks
Give the uses of various index numbers in Economics.
Answer
The uses of various index numbers in economics:
  1. Consumer Price Index or cost of living index numbers are helpful in wage negotiation, formulation of income policy, price policy, taxation and general economic policy formulation.
  2. Wholesale Price Index is used to eliminate the effect of changes in prices on aggregates like national income, capital formation etc. It is usually used to measure the rate of inflation.
  3. Index of Industrial Production gives a quantitative figure about the changes in production in the industrial sector.
  4. Agricultural Production Index provides a ready reckoner of the performance of agricultural sector.
  5. Sensex is a useful guide for investors in the stock market.
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Question 224 Marks
Using the simple aggregative method, calculate the index number for the given data:
  A B C D
$P_1$ 15 22 20 27
$P_0$ 10 20 18 25
Answer
Construction of Index number:
Commodity
$p_o ($Base Year$)$
$p_1 ($Current Year$)$
A
10
15
B
20
22
C
18
20
D
25
27
 
$\Sigma\text{p}_0=73$
$\Sigma\text{p}_1=84$
$\text{P}_{01}=\frac{\Sigma\text{p}_1}{\Sigma\text{p}_0}\times100\Rightarrow\text{P}_{01}=\frac{84}{73}\times100=115.0$
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Question 234 Marks
Calculate the cost of living index from the following data:
Iteam
Price
Weight
Base Year
Current Year
Food
30
47
4
Fuel
8
12
1
Cloth
14
18
3
House Rent
22
15
2
Miscellancous
25
30
1
Answer
Item
Weight in % (W)
$p_0$
$q_1$
$\text{R}=\frac{\text{p}_1}{\text{p}_0}\times100$
WR
Food
36.4
30
47
156.67
5702.78
Fuel
9.1
8
12
150.00
1365.00
Cloth
27.3
14
18
128.57
3509.96
House Rent
18.1
22
15
68.18
1234.05
Miscellancous
9.1
25
30
120.00
1092.00
 
$\Sigma\text{W}=100.0$
 
 
 
$\Sigma\text{WR}=12903.79$
$\text{CPI}=\frac{\Sigma\text{WR}}{\Sigma\text{W}}=\frac{12903.79}{100}=129.03$
This shows that the cost of living has risen by 29% approximately.
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Question 244 Marks
Construct Index of Industrial Production (IIP) from the following data:
Industry
Output
Weights
Base year
Current Year
Manufacturing
122
300
85
Electrical Product
203
400
5
Mining and Quarrying
65
87
10
Answer
Industry
$q_0$
$q_1$
$\text{R}=\frac{\text{p}_1}{\text{p}_0}\times100$
W
WR
Manufacturing
122
300
245.90
85
20901.50
Electrical Product
203
400
197.04
5
985.20
Mining and Quarrying
65
87
133.84
10
1338.40
 
 
 
 
$\Sigma\text{W}=100$
$\Sigma\text{WR}=23225.1$
$\text{IIP}=\frac{\Sigma\Bigg(\frac{\text{q}_1}{\text{q}_0}\times100\Bigg)\text{W}}{\Sigma\text{W}}\ \text{or}\ \frac{\Sigma\text{WR}}{\Sigma\text{W}}$
$=\frac{23225.1}{100}=232.25$
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Question 254 Marks
Calculate Simple Aggregative Price Index on the basis of the following data:
Commodity
Prices in 2018
Prices in 2019
Rice
120
180
Wheat
80
100
Oil
300
400
Pulses
130
180
Suger
150
200
Answer
Commodity Prices in $2018 (p_0)$ Prices in $2019 (p_1)$
Rice 120 180
Wheat 80 100
Oil 300 400
Pulses 130 180
Suger 150 200
  $\Sigma\text{p}_0=780$ $\Sigma\text{p}_1=1,060$
$\text{P}_{01}=\frac{\Sigma\text{p}_1}{\Sigma\text{p}_0}\times100=\frac{1,060}{780}=135.89$
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Question 264 Marks
Calculate weighted average of price relative index from the following data:
Item
Weight in %
Base Year Price (₹)
Current Year Price (₹)
A
40
2
4
B
30
5
6
C
20
4
5
D
10
2
3
Answer
Item Weight (W) $p_0$ $p_1$ $\text{R}=\frac{\text{p}_1}{\text{p}_0}\times100$ WR
A 40 2 4 $\frac{4}{2}\times100=200$ 8000
B 30 5 6 $\frac{6}{5}\times100=120$ 3600
C 20 4 5 $\frac{5}{4}\times100=125$ 2500
D 10 2 3 $\frac{3}{2}\times100=150$ 1500
  $\Sigma\text{W}=100$       $\Sigma\text{WR}=15600$
$\text{P}_{01}=\frac{\Sigma\text{WR}}{\Sigma\text{W}}=\frac{15600}{100}=156$
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Question 274 Marks
Why is it essential to have different CPI for different categories of consumers?
Answer
CPI, Consumer price index is a measure of average change in retail prices. It indicates the average change in the price paid by the final consumer for specified quantity of goods and services over a period of time. Different classes are getting affected differently by a change in the price level because different people consume different types of goods, consumer’s habit differs from individual to individual, place to place, strata to strata, etc. So, it is essential to have different CPI for different categories of consumers because the nature of consumption basket of consumers from different economic status varies hugely.
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Question 284 Marks
What are the desirable properties of the base period?
Answer
The base period associated with an index number is a time period which is used as a basis for comparing changes in prices or quantities during a particular period of time.
Properties of the base period:
  1. Normal period: The base year should be a normal period, and a period in which unusual events took place should not be considered a base period because they are not suitable for comparative analysis.
  2. Avoid extreme values: Extreme values are not considered a base period for comparative analysis.
  3. Differences between base period and current period should not be too large: Index numbers are helpful in decision making and enables the government to formulate policies. The period should not be too far in the past as compared to the current period as the policies, economic and social conditions change over a period of time and cannot be considered a base year.
  4. Periodical updates: Base period should be updated periodically to understand the changes in taste and preferences for a particular commodity.
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Question 294 Marks
Distinguish between Lasperey's and Paasche's index numbers.
Answer
  1. In Lasperey's index number base year quantities are taken as the weights and in Paasche's index the current year quantities are taken as weights.
  2. From the practical point of view Lasperey's index is often proffered to Paasche's for the simple reason that Lasperey's index weights are the base year quantities and do not change from the year to the next. On the other hand Paasche's index weights are the current year quantities, and in most cases these weights are difficult to obtain and expensive.
  3. Lasperey's index number is said to be have upward bias because it tends to over estimate the price rise, where as the Paasche's index number is said to have downward bias, because it tends to under estimate the price rise.
  4. When the prices increase, there is usually a reduction in the consumption of those items whose prices have increased. Hence using base year weights in the Lasperey's index, we will be giving too much weight to the prices that have increased the most and the numerator will be too large. Due to similar considerations, Paasche's index number using given year weights under estimates the rise in price and hence has down ward bias.
  5. If changes in prices and quantities between the reference period and the base period are moderate, both Lasperey's and Paasche's indices give nearly the same values.
  6. Paasche's index number, because of its dependence on given year's weight, has distinct disadvantage that the weights are required to be revised and computed for each period, adding extra cost towards the collection of data.
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Question 304 Marks
Find out the price index of the year 2015 assuming 2014 as the base year of the following data by using simple average of price relative method.
Commodity Price in 2014 (₹) Per Quintal Price in 2015 (₹) Per Quintal
Wheat 800 900
Sugar 1100 1200
Rice 400 600
Potato 500 700
Salt 300 500
Answer
Consturction of Index Number:
Commodity
Price in $2014 (₹)$$(p_0)$
Price in $2015 (₹)$$(p_0)$
$\text{I}\bigg(\frac{\text{p}_1}{\text{p}_0}\times100\bigg)$
Wheat
800
900
112.50
Sugar
1100
1200
109.09
Rice
400
600
150.0
Potato
500
700
140.0
Salt
300
500
166.67
n = 5
 
 
$\Sigma\text{I}= 678.26$
$\text{P}_{01}=\frac{\Sigma\text{I}}{\text{n}}=\frac{678.26}{5}=135.652 $
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Question 314 Marks
Explain the importance of Consumer Price Index.
Answer
The Consumer Price Index (CPI) is one of the special type of price index as:
  1. It is useful in wage negotiations. The government grants additional dearness allowance to its employees on the basis of increase in CPI from time to time.
  2. It is helpful in the formation of wage policy, income policy, price policy, taxation and general economic policy.
  3. It is used to calculate the purchasing power of money.
  4. It is used to calculate the real wages or real income of a particular group. The formula used is:
Real Wages $=\frac{\text{Money wages}}{\text{Cost of living index number}}\times100$
  1. It is a good indicator of the movement of retail prices of most of essential commodities of daily use.
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Question 324 Marks
Explain simple average of relatives for the construction of index numbers. Explain its merits and demerits.
Answer
When this method is used to construct a price index number, first of all price relatives are obtained for the various items included in the index and then the average of these relatives is obtained using any one of the averages i.e. mean or median etc. When ARITHMETIC MEAN is used for averaging the relatives the formula for computing the index is:$\text{P}_{01}=\frac{1}{\text{n}}\sum\bigg(\frac{\text{p}_1}{\text{p}_0}\times100\bigg)$
When GEOMETRIC MEAN is used for averaging the relatives the formula for computing the index is$\text{P}_{01}\text{Antilog}=\bigg[\frac{1}{\text{n}}\sum\log\bigg(\frac{\text{p}_1}{\text{p}_0}\times100\bigg)\bigg]$
And price relative = $\frac{\text{P}_1}{\text{P}_0}\times100.$ Merits: It is not affected by the units in which prices are quoted It gives equal importance to all the items and extreme items don't affect the index number. The index number calculated by this method satisfies the unit test. Demerits: Since it is an unweighted average the importance of all items are assumed to be the same. The index constructed by this method doesn't satisfy all the criteria of an ideal index number. In this method one can face difficulties to choose the average to be used.
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Question 334 Marks
Distinguish between simple aggregative index and simple average of relatives.
Answer
S. No.
Simple aggregative method
Simple average of relatives
1.
This is the simplest method of constructing index numbers. When this method is used to construct a price index number the total of current year prices for the various commodities in question is divided by the total of the base year prices and the quotient is multiplied by 100.
$₹ \text{ Symbolically}\text{ P}_{01}=\frac{\sum\text{P}_1}{\sum\text{P}_0}\times100$
Where $P_o$ are the base year prices $P_1$ are the current year prices $P_{o1}$ is the price index number for the current year with reference to the base year.
When this method is used to construct a price index number, first of all price relatives are obtained for the various items included in the index and then the average of these relatives is obtained using any one of the averages i.e. mean or median etc.
$\text{P}_01=\frac{1}{\text{n}}\sum\bigg(\frac{\text{P}_1}{\text{P}_0}\times100\bigg)$
2.
Merits:
It is not affected by the units in which prices are quoted.
It gives equal importance to all the items and extreme items don't affect the index number.
The index number calculated by this method satisfies the unit test.
Merits:
It is simple to calculate and easy to understand.
It gives a rough idea of change.
3.
Demerits:
There are two main limitations of this method. The units used in the prices or quantity quotations have a great influence on the value of index.
No considerations are given to the relative importance of the commodities.
Demerits:
Since it is an unweighted average the importance of all items are assumed to be the same.
The index constructed by this method doesn't satisfy all the criteria of an ideal index number.
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Question 344 Marks
What weights are given to different industries in IIP?
Answer
The table given below shows broad industrial groupings and their weights.
S. No.
Broad Groupings
Weight in %
1.
Mining and Quarrying
10.47
2.
Manufacturing
79.36
3.
Electricit
10.17
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Question 354 Marks
What are the characteristics of an index number?
Answer
The characteristics of an index number are as follows:
  1. Index numbers are specialized averages: As we know an average is a single figure representing a group of figures. However to obtain an average the items must be comparable. For example the average weight of man, woman and children of a certain locality has no meaning at all. Furthermore the unit of measurement must be same for all the items. However, this is not so with index numbers. Index numbers also one type of averages which shows in a single figure the change in two or more series of different items which can be expressed in different units. For example while constructing a consumer price index number the various items which are use in construction are divided into broad heads namely food, clothing, fuel, lighting, house rent, and miscellaneous which are expressed in different units.
  2. Index numbers measures the net change in a group of related variables: Since index numbers are essentially averages, they describe in one single figure the increase or decrease in a group of related variables under study. The group of variables may be prices of set of commodities, the volume of production in different sectors etc.
  3. Index numbers measure the effect of changes over period of time: Index numbers are most widely used for measuring changes over a period of time. For example we can compare the agricultural production, industrial production, imports, exports, wages etc in two different periods.
  4. Index Numbers are expressed in percentages: The changes in magnitude are expressed in terms of percentages LE which are independent of the units release of measurement. This facilitates the comparison of two or more index numbers in different situations. However, percentage sign is never used.
  5. Index Numbers Measure the changes which are not capable of direct measurement: Index numbers are meant to study changes in the effects of such factors which cannot be measured directly. For example, cost of living cannot be measured in quantitative terms. Only relative change can be studies by studying certain other factors connected with it.
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Question 364 Marks
Find out Paasche's Price Index from the following data:
Iteam
Base Year
Current Year
Price
Quantity
Price
Quantity
A
10
8
20
10
B
35
6
40
9
C
30
20
32
25
D
40
5
44
6
Answer
Iteam
Base Year
Current Year
 $p_1q_1$ $p_0q_1$
Price $(p_0)$
Quantity $(q_0)$
Price $(p_1)$
Quantity $(q_1)$
A
10
8
20
10
 200 100
B
35
6
40
9
 360 315
C
30
20
32
25
 800 750
D
40
5
44
6
 264 240
          $\Sigma\text{p}_1\text{q}_1=1624$ $\Sigma\text{p}_0\text{q}_1=1405$
Paashe's Price Index $\text{P}_{01}=\frac{\Sigma\text{p}_1\text{q}_1}{\Sigma\text{p}_0\text{q}_1}\times100$
$\frac{1,624}{1,405}\times100=115.58$
$\therefore$ Paasche's price index of 115 is interpreted as a price rise of 16% approximately.
Using current period weights, the price is said to have risen by 16% approximately.
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Question 374 Marks
Given the following data:
Item Base year Current Year
Price (₹) Quntity Price (₹) Quntity
A 1 10 2 5
B 1 5 X 2
Answer
Find X, if the ratio between Laspeyre's and Paasche's index number is 28:27.
Items
Base Year
Current Year
$p_0q_0$
$p_0q_1$
$p_1q_1$
$p_1q_1$
$p_0$
$q_0$
  
$p_1$
$q_1$
A
1
10
2
5
10
20
5
10
B
1
5
X
2
5
5X
2
2X
 
 
 
 
 
$\Sigma\text{p}_0\text{q}_0=15$
$\Sigma\text{p}_0\text{q}_1=20+5\text{X}$
$\Sigma\text{p}_1\text{q}_0=7$
$\Sigma\text{p}_1\text{q}_1=10+2\text{X}$
Laspere's Price Index Number $\text{L}=\frac{\Sigma\text{p}_1\text{q}_0}{\Sigma\text{p}_0\text{q}_0}\times100=\frac{20+5\text{X}}{15}\times100$ Paasche's Price Index Number $\text{P}=\frac{\Sigma\text{p}_1\text{q}_0}{\Sigma\text{p}_0\text{q}_0}\times100=\frac{10+2\text{X}}{7}\times100$ On dividing equation (i) by (ii) we get$\frac{\text{L}}{\text{P}}=\frac{20+5\text{X}}{15}+\frac{10+2\text{X}}{7}=\frac{20+5\text{X}}{10+2\text{X}}\times\frac{7}{15}$
Given, $\frac{\text{L}}{\text{P}}=\frac{28}{27}\Rightarrow\frac{28}{27}=\frac{20+5\text{X}}{10+2\text{X}}\times\frac{7}{15}$$\Rightarrow\frac{28\times15}{27\times7}=\frac{20+5\text{X}}{10+2\text{X}}\Rightarrow\frac{20}{9}=\frac{20+5\text{X}}{10+2\text{X}}$
$\Rightarrow20(10+2\text{X})=9(20+5\text{X})\Rightarrow5\text{X}=20\Rightarrow\text{X}=4$
Thus, missing figure i.e. price of B in current year is ₹ 4.
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Question 384 Marks
Construct the index number by simple average of price relative method and by simple aggregative method:
Commodity
A
B
C
D
E
Price in 2014 (₹)
16
40
35
5.25
2
Price in 2015 (₹)
20
60
50
6.25
1.5
Answer
Construction of Index Number:
Commodity Price in 2014 (₹)($p_0)$ Price in 2015 (₹) ($P_1)$ $\text{I}\bigg(\frac{\text{p}_1}{\text{p}_0}\times100\bigg)$
A 16 20 125
B 40 60 150
C 35 50 142.9
D 5.25 6.25 119.05
E 2 1.50 75
n = 5 $\Sigma\text{p}_0=98.25$ $\Sigma\text{p}_1=137.75$ $\Sigma\text{I}=611.95$
  1. Simple Aggretive Methode of Price Relative Methode:
$\text{P}_{01}=\frac{\Sigma\text{I}}{\text{n}}=\frac{611.95}{5}=122.39$
  1. Simple Aggretive Methode:
$\text{P}_{01}=\frac{\Sigma\text{p}_1}{\Sigma\text{q}_0}\times100=\frac{137.75}{98.25}\times100=140.20$
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