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NCERT Class 11 Economics Chapter 8 Index Numbers
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Index Numbers
Chapter: 8
PART – (A) STATISTICS FOR ECONOMICS
TEXTUAL QUESTION ANSWERS
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.
Ans: (a) Weighted index.
2. In most of the weighted index numbers the weight pertains to:
(a) Base year.
(b) Current year.
(c) Both base and current year.
Ans: (c) Both base and current year.
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.
Ans: (a) Small.
4. A consumer price index measures changes in:
(a) Retail prices.
(b) Wholesale prices.
(c) Producer prices.
Ans: (a) Retail prices.
5. The item having the highest weight in consumer price index for industrial workers is:
(a) Food.
(b) Housing.
(c) Clothing.
Ans: (a) Food.
6. In general, inflation is calculated by using:
(a) Wholesale price index.
(b) Consumer price index.
(c) Producers’ price index.
Ans: (a) Wholesale price index.
7. Why do we need an index number?
Ans: An index number is a statistical device which is used to measure the changes in the related variables.
Its importance is as follows:
(a) To measure change in the price level: Index numbers measure and compare prices of different commodities with the help of Wholesale Price Index. It is widely used to measure the level of inflation in an economy.
(b) To study a change in the standard of living: Index numbers help to assess the living standard of people. Cost of living index measures the relative cost of living over time. If the index number has a low value, then it implies that people have a low standard of living and vice-versa.
(c) Useful in planning and decision making: Index numbers serve as the most important tool for business communities for drafting various plans and designing various policies. It is useful for the government and the planners to work out the inflation rate with the help of the consumer price index.
(d) To determine the level of production: Index number of Industrial Production measures changes in the physical volume of production. Also, the production index is an important indicator to ascertain the output level.
(e) To help the government in framing policy: Index numbers are of great help to the government to frame fiscal and monetary policies. The government formulates policies regarding inflation, trade, income, salaries and allowances.
8. What are the desirable properties of the base period?
Ans: A base period should have the following properties:
(a) The base year should be a normal period and periods in which extraordinary events have occurred should not be taken as base periods as they are not appropriate for general comparisons.
(b) Extreme values should not be selected as base period.
(c) The period should not be too far in the past because comparison with the current period cannot be done with such a base year as policies, economic and social conditions change with time.
(d) The base period for any index number is updated.
9. Why is it essential to have different CPI for different categories of consumers?
Ans: The Consumer Price Index (CPI) in India includes three components: CPI for Industrial Workers, CPI for Urban Non-manual Employees, and CPI for Agricultural Labourers. These indices are calculated regularly to assess the aggregate impact of changes in retail prices. While the CPI for industrial workers and agricultural labourers is calculated and published by the Labour Bureau in Shimla, the CPI for urban non-manual employees is managed by the Central Statistical Organisation (CSO). Having separate CPIs for various consumer categories is crucial because consumption patterns and spending habits vary significantly among groups. Factors such as income level, age, and geographical location influence the types of goods and services consumers prioritize. For instance, low-income households typically spend a larger share of their income on necessities like food, whereas higher-income groups may allocate more resources to luxury goods and services. Separate CPIs ensure that the specific inflationary pressures faced by each group are accurately measured and addressed.
10. What does a consumer price index for industrial workers measure?
Ans: Consumer price index for industrial workers measures the average change in retail price of a basket of commodities which an industrial worker generally consumes. The Consumer price index for industrial workers is increasingly being considered the appropriate indicator of general inflation which shows the most accurate impact of price rise on the cost of living of common people.
The items included in CPI (Consumer Price index) for industrial workers are food, pan, supari, tobacco, fuel and lighting, housing, clothing, and miscellaneous expenses with food being accorded the highest weight. This implies that the food price change has a significant impact on the CPI.
11. What is the difference between a price index and a quantity index?
Ans:
| A price index | A quantity index |
| In its simplest form, adding the price of each stock in the index and dividing by the total number of companies determines the index’s value. | The quantity index is a ratio describing relative changes in the quantity of produced goods or services relative to the base period. |
12. Is the change in any price reflected in a price index number?
Ans: No, the change in any price is not reflected in a price index number. In fact, only the relative change or the percentage change in the price level is reflected in the price index number. Price index number is of limited use. The reason is that the units of measurement of the prices of various commodities are not the same. It is unweighted because the relative importance of the items has not been properly reflected. Thus, there are different index numbers for changes in the prices of different commodities.
13. Can the CPI for urban non-manual employees represent the changes in the cost of living of the President of India?
Ans: 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 an average non-manual employee does not consist of the items that would be a part of the consumption basket of the President of India.
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 and lighting | 15 | 20 |
| House Rent | 30 | 40 |
| Misc. | 35 | 65 |
Ans:
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 |
Ans: Based on the analysis of the table, we can conclude the following:
(i) The manufacturing industry holds the largest share in the Index of Industrial Production (IIP), accounting for 79.58%. In comparison, mining and quarrying make up 10.73%, and the electricity sector contributes 10.69%.
(ii) The manufacturing sector experienced the highest growth among all industrial sectors in both 1996-97 and 2003-04.
(iii) On the other hand, mining and quarrying recorded the lowest growth rate in both of these years.
(iv) The General Index indicates that industrial production grew by 30.8% in 1996-97 compared to 1993-94 and by 89% in 2003-04.
16. Try to list the important items of consumption in your family.
Ans: The following items constitute the total consumption needs for a family:
(i) Food.
(ii) Clothing.
(iii) House-Rent/EMI of Housing loan.
(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?
Ans: Base year salary = ₹ 4,000
Price Index of the Base year = 100
Current year salary = ₹ 6,000
Consumer price index of the current year = 400
His salary should rise to ₹ 16000 to maintain the same standard of living.
Formula of Calculation:
Thus, there should be a rise of ₹ 10,000 (16,000-6,000) in the salary of that person to maintain the same standard of living.
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?
Ans: Suppose the percentage of weight given to food = x
In this case percentage of weight given to other items would be = (100 – x)
Hence,
or 12, 500 = 120x + 13500 – 135x
or 15x = 13500 – 12500 = 1000
= 66.66%
Hence, percentage of the total weight given to food = 66.66%
19. An enquiry into the budgets of the middle class families in a certain eity gave the following information:
| Expenses on Itents | Food (35%) | Fuel (10%) | Clothing (20%) | Rent (15%) | Mise. (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?
Ans:
Cost of Living Index = 134.50
Thus, the price rose by 34.50% during 1995 and 2004.
20. Record the only 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?
Ans: The students are advised that they should enquire of their parents about the daily expenditure quantities bought and prices paid per unit of daily purchases of their family for two weeks. They will come to know that the rising prices of goods have affected that family very much.
For example:
| p₁q₁ | p₀q₁ |
| 108 | 90 |
| 126 | 112 |
| 190 | 152 |
| 126 | 90 |
| Σp₁q₁ = 550 | Σp₀q₁ = 444 |
∴ Price index of the 2ⁿᵈ week P₀₁ = 123.87, which means that price increased by 23.87% as compared to 1ˢᵗ week. Family has to increase its expenditure by 23.87% for maintaining the same level of living in the 1ˢᵗ week.
21. Given the following data:
| Year | CPI of industrial workers (1982 = 100) | CPI of agricultural labourers (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 |
(a) Comment on the relative values of the index numbers.
(b) Are they comparable?
Ans: (a) The inflation rate calculated using CPI industrial workers with the base year 1982 is the highest and inflation rate calculated using WPI with the base year 1993-94 is the least.
(b) No, the index numbers are not comparable because:
(i) Base periods for CPI of industrial workers, urban non-manual workers, agricultural labourers and WPI are different.
(ii) Commodities and their weightage in different index numbers may be different.
22. 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:
| Items | 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.
Ans:
| Category of goods/items | 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 |
| Total | ΣW = 3500 | ΣWX = 338 |
Average tax rate or Mean GST rate of the family
Important Note:
Category 1 includes the first three items with 0% GST rate.
Category 2 includes the 4ᵗʰ, 5ᵗʰ and 6ᵗʰ items with GST rate as 5%.
Category 3 includes the 7ᵗʰ, 8ᵗʰ and 9ᵗʰ items with GST rate as 12%.
Category 4 includes the 10ᵗʰ, 11ᵗʰ and 12ᵗʰ items with GST rate as 18%.
Category 5 includes the 13ᵗʰ item with GST rate as 28%.
