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NCERT Solutions Class 11, Economics, Statistics for Economics, Chapter- 7, Index Numbers

For a comprehensive understanding of Class 11 Economics and to achieve excellence in board and competitive examinations, NCERT Solutions are crucial. These resources, developed by experts, focus on important chapter concepts and are tailored to the CBSE curriculum, providing vital assistance in your studies.

In these NCERT Solutions for Class 11 Economics, we have discussed all types of NCERT intext questions and exercise questions.

Concepts covered in Class 11 Economics, Statistics for Economics, Chapter- 7 Index Numbers, are-

  • Introduction
  • What Is an Index Number?
  • Construction of an Index Number
  • The Aggregative Method
  • Method of Averaging Relatives
  • Consumer Price Index
  • Consumer Price Index Number
  • Wholesale Price Index
  • Index of Industrial Production
  • Human Development Index
  • Sensex
  • Index in Economics

Our NCERT Solutions for Class 11 Economics feature in-depth explanations that facilitate homework and assignment completion. By gaining a solid understanding of each chapter’s concepts with these solutions, you’ll be ready to secure top marks in your exams. Embark on your journey to academic excellence today!

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NCERT Solutions Class 11, Economics, Statistics for Economics, Chapter- 7, Index Numbers

1. An index number which accounts for the relative importance of the items is known as:

(a) weighted index
(b) simple aggregative index
(c) simple average of relatives

Solution:

(a) weighted index

An index number in which different items of the series are accorded weightage in accordance with their relative importance is known as weighted index numbers.

2. In most of the weighted index numbers the weight pertains to:

(a) base year
(b) current year
(c) both base and current year

Solution:

(a) base year

While calculating weighted index numbers, the weight pertains to base year. This method uses the base period quantities as weights.

3. The impact of change in the price of a commodity with little weight in the index will be:

(a) small
(b) large
(c) uncertain

Solution:

(a) small

A lesser important commodity is assigned lower weight as it would not have a significant effect of price change.

4. A consumer price index measures changes in:

(a) retail prices
(b) wholesale prices
(c) producers prices

Solution:

(a) retail prices

Consumer Price Index is used to measure changes in the cost in which the retail prices of consumer goods and services are obtained.

Thus, it measures the average changes in the retail prices.

5. The item having the highest weight in consumer price index for industrial workers is:

(a) Food
(b) Housing
(c) Clothing

Solution:

(a) Food

The weight schemes in CPI for industrial workers include food, fuel, lighting, housing, clothing etc. The food is given the top most priority as this component has the highest weight. So, the changes in food price have a significant impact on the CPI.

6. In general, inflation is calculated by using:

(a) wholesale price index
(b) consumer price index
(c) producers’ price index

Solution:

(a) wholesale price index

WPI measures the relative changes in the prices of the commodities traded in the wholesale markets. It determines the situations of overall demand and supply in the market.

7. Why do we need an index number?

Solution:

An index number is a statistical device which is used for measuring the changes in the magnitude of a group of variables. 

It is a needful measurement because:

  1. It measures the changes in the price level.
  2. It determines the change in the standard of living.
  3. It helps in planning and decision making.
  4. It regulates the level of production.

8. What are the desirable properties of the base period?

Solution:

The base year must have the following desirable properties:

  1. The base year should neither be too short nor be too long.
  2. The base year should neither be too near nor too far in the past.
  3. It should be easily accessible and available.
  4. It should be constantly or routinely updated.

9. Why is it essential to have different CPI for different categories of consumers?

Solution:

It is important to have different CPIs for different categories of consumer because the consumption pattern of the general groups i.e., industrial workers, urban non-manual workers and agricultural labourers differ from each other. Thus, to determine the impact of the price change on the cost of living of the three groups, component items included in the index need to be given different weights for each of the group.

10. What does a consumer price index for industrial workers measure?

Solution:

Consumers Prince Index measures the average change in retail price over time in prices of a given basket of goods and services consumed by an industrial worker generally. In India, the CPI for Industrial workers is published by Labour Bureau, Shimla.

Consumer Price Index is now considered as the most appropriate indicator of general inflation to show the most accurate impact of price rise on the cost of living. The items included in CPI for industrial workers are food, pan, supari, tobacco, fuel and lighting, housing, clothing and miscellaneous expenses. Food has the largest/highest weight. Food being the most important category a rise in food price will have a significant impact on CPI.

11. What is the difference between a price index and a quantity index?

Solution:

Price Index:

  1. Price Index measures the general changes in prices of goods.
  2. It takes into account the prices of the commodity of the base year as well as of the current year.
  3. It is measured by two methods i.e.,
    • Simple Aggregate Method
    • Simple Average of Price Relative Method

Quantity Index:

  1. Quantity Index measures changes in the level of output or physical volume of production in the economy.
  2. It takes into consideration the weights of goods assigned according to the quantity.
  3. It is calculated by two methods, i.e.,
    • Weighted Average of Price Relative method
    • Weighted Aggregate Method.

12. Is the change in any price reflected in a price index number?

Solution:

No, the change in any price is not reflected in a price index as the prices of all goods and services do not change at the same rate. In fact, only the relative change or the percentage change in the price level is reflected in the price index number.

13. Can the CPI for urban non-manual employees represent the changes in the cost of living of the President of India?

Solution:

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 of the fact that the consumption basket of the non-manual employees consists of different items than those of the consumption basket of the President of India.

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14. The monthly per capita expenditure incurred by workers for an industrial centre during 1980 and 2005 on the following items are given below. The weights of these items are 75,10, 5, 6 and 4 respectively. Prepare a weighted index number for cost of living for 2005 with 1980 as the base.

Items Price in 1980 Price in 2005
Food 100 200
Clothing 20 25
Fuel & lighting 15 20
House rent 30 40
Misc 35 65

Solution:

Items 2005 P1 1980 P0 Weight W R = (P1/P0) × 100 WR
Food 200 100 75 (200/100) × 100 = 200 15000
Clothing 25 20 10 25/20 × 100 = 125 1250
Fuel and lighting 20 15 5 20/15× 100 = 133·33 666·65
House Rent 40 30 6 40/30 × 100 = 133·33 799·98
Misc. 65 35 4 65/35 × 100 = 185·71 742·84
ΣW = 100 ΣWR = 18459·47

 Cost of living (CPI) = \(\frac{\sum WR}{\sum W}\)

\(= \frac{18459.47}{100}\)

\(= 184.5947\)

15. 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

Solution:

Following are the evident points determined from the above table:

  1. The General Index is comparatively higher in the year 2003-04 than 1996-97.
  2. Manufacturing industry has the highest weight of 79·58% as compared to the mining and quarrying and Electricity Industries that account for 10·73% and 10·69% respectively.
  3. The production of the Manufacturing Industry is higher than that of the mining and Quarrying and Electricity in both the years 1996-97 and 2003-04.
  4. Mining and quarrying have the least growth performance while that of the manufacturing industry is the highest.

16. Try to list the important items of consumption in your family.

Solution:

The actual consumption items in any family are:

(i) Food
(ii) Clothing
(iii) House Rent
(iv) Education
(v) Electricity
(vi) Entertainment and recreation
(vii) Miscellaneous expenses

17. If the salary of a person in the base year is  4,000 per annum and the current year salary is  6,000, by how much should his salary be raised to maintain the same standard of living if the CPI is 400?

Solution:

Base CPI =  ₹100

Current CPI =  ₹400

Base Year Salary =  ₹4000

Current Year Salary =  ₹6000

When Base CPI is  ₹100.

Then, the salary is  ₹4000.

Thus,

When Base CPI is ₹100 then the salary will be ₹(\(\frac{4000}{100}\))

When Base CPI will be ₹400 then the salary will be ₹(\(\frac{4000}{100}\times400\)) = ₹16,000

If the Base CPI is  ₹400, then the salary of that person should be  ₹16,000.

So, accordingly, his salary should be raised by  ₹10,000 to maintain the standard of living as per the current CPI.

18. The consumer price index for June, 2005 was 125. The food index was 120 and that of other items 135. What is the percentage of the total weight given to food?

Solution:

Let the percentage of total weight given to food be x and 100 – x denotes the percentage of total weight given to other items.

\(CPI =\frac{(X + 120)+(100-X)\times135}{100}\)

\(\Rightarrow 125=\frac{(120x + 13500-135x)}{100}\)

\(\Rightarrow 12500=15x + 13500\)

\(\Rightarrow 15x = 13500- 12500\)

\(15x = 1000\)

\(x = \frac{1000}{15}\)

\(x = 66.67\)

Thus, the percentage of the total weight given to food is 66.67%.

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19. An enquiry into the budgets of the middle class families in a certain city gave the following information:

Expenses on items Food Fuel Clothing Rent Misc.
35% 10% 20% 15% 20%
Price (in ₹) in 2004 1500 250 750 300 400
Price (in ₹) in 1995 1400 200 500 200 250

What is the cost of living index during the year 2004 as compared with 1995?

Solution:

Items Expenses on items in % Price in (₹) 1995 P0 Price in (₹) 2004 P1 (R) = P1P0 × 100 (WR)
Food 35 1400 1500 1500/1400 × 100 = 107·14 3749·9
Fuel 10 200 250 250/200 × 100 = 125 1,250
Clothing 20 500 750 750/500 × 100 = 150 3,000
Rent 15 200 300 300/200 × 100 = 150 2,250
Misc. 20 250 400 400/250 × 100 = 160 3,200
ΣW = 100 ΣWR = 13,449·9

\(CPI = \frac{\sum WR}{\sum W} = \frac{13449.9}{100}\)

= 134.499 or 134.50

Cost of living index = 134.50.

Thus, the prices rose by 34.50% during 1995 and 2004.

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20. Record the daily expenditure, quantities bought and prices paid per unit of the daily purchases of your family for two weeks. How has the price change affected your family?

Solution:

Week I

Potato Onion
Days Price (per kg) PWI Quantity QWI Expenditure PWI QWI Price (per kg) PWI Quantity QWI Expenditure PWI QWI Total Expenditure (Rs)
Monday 10 1 10 20 1 20 30
Tuesday 9 1 9 19 1 19 28
Wednesday 11 1 11 21 1 21 32
Thursday 12 15 18 20 1 20 38
Friday 8 1 8 19 2 38 46
Saturday 10 2 20 18 15 27 47
Sunday 9 1 9 20 1 20 29
Week II
Potato Onion
Days Price (per kg) PWII Quantity QWII Expenditure PWII QWII Price (per kg) PWII Quantity QWII Expenditure PWII QWII Total
Expenditure (Rs)
Monday 9 1 9 20 1 20 29
Tuesday 10 1.5 15 22 1.5 33 48
Wednesday 12 1 12 21 1 21 33
Thursday 10 1 10 19 1 19 29
Friday 11 2 22 18 1 18 40
Saturday 12 1 12 20 1 20 32
Sunday 10 1 10 22 1.5 33 43

The household on Monday of week one (WI) spend Rs 30, by buying 1 kg of Potato and 1kg of Onion at Rs 10 and Rs 20 per kg respectively, whereas, the price of Potato on Monday of the week second (WII) has reduced from Rs 10 to Rs 9 resulting in the reduction in the expenditure incurred by the household. Therefore, we can conclude that the decrease in price leads to a decrease in expenditure given the quantity purchased. We can also analyze that the price and quantity purchased by the household shares a negative relationship with each other.

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21. Given the following data:

Year CPI of industrial workers (1982 = 100) CPI of agricultural laborers (1986–87 = 100) WPI (1993–94 = 100)
1995–96 313 234 121.6
1996–97 342 256 127.2
1997–98 366 264 132.8
1998–99 414 293 140.7
1999–00 428 306 145.3
2000–01 444 306 155.7
2001–02 463 309 161.3
2002–03 482 319 166.8
2003–04 500 331 175.9

(i) Comment on the relative values of the index numbers.

(ii) Are they comparable?

Solution:

(i) (a)

(b)

(c)

The inflation rate for the industrial workers with the base year 1982 is the highest and WPI with the base year 1993-94 has the least. 

(ii) No, the index numbers are not comparable because of the following reasons:

  1. Base periods for CPI of industrial workers, urban non-manual workers, agricultural labourers, and WPI are different.
  2. Commodities and their weightage are given to different indexes may vary from one index number to another. 

22. The monthly expenditure (Rs.) 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 (Rs) 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.

Solution:

Monthly Expenditure (w) GST Rate % (X) WX
Cereals 1500 0 0
Eggs 250 0 0
Fish, Meat 250 0 0
Medicines 50 5 2.5
Biogas 50 5 2.5
Transport 100 5 5
Butter 50 12 6
Babool 10 12 1.2
Tomato Ketchup 40 12 4.8
Biscuits 75 18 13.5
Cakes, Pastries 25 18 4.5
Branded Garments 100 18 18
Vacuum Cleaner, Car 1000 28 280
Total 3500 338

The average tax rate for this family: \(\frac{338}{3500} = 0.0966\) or 9.66%

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