# NCERT Solutions for Class 11 Economics Chapter 7 - Index Numbers

30. 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

Explanation:

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.

31. In most of the weighted index numbers the weight pertains to:
(a) base year
(b) current year
(c) both base and current year

Ans. (a) base year

Explanation:

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

32. 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

Explanation:

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

33. A consumer price index measures changes in:
(a) retail prices
(b) wholesale prices
(c) producers prices

Ans. (a) retail prices

Explanation:

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.

34. The item having the highest weight in consumer price index for industrial workers is:
(a) Food
(b) Housing
(c) Clothing

Ans. (a) Food

Explanation:

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.

35. In general, inflation is calculated by using:
(a) wholesale price index
(b) consumer price index
(c) producers’ price index

Ans. (a) wholesale price index

Explanation:

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.

36. Why do we need an index number?

Ans. 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.

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

Ans. 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 accesible and available.
4. It should be constantly or routinely updated.

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

Ans. 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.

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

Ans. 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.

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

Ans. 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.

41. 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 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.

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

43. 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

Ans .

 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

$$\text{Cost of living (CPI)}=\frac{\Sigma WR}{\Sigma W}=\frac{18459.47}{100}=184·5947.$$

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. 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.

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

Ans. 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

46. 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 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
$$be ₹(\frac{4000}{100})\\\text{When Base CPI will be ₹400 then the salary will}\\be ₹(\frac{4000}{100}×100)= ₹16,000.$$

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.

47. 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. Let the percentage of total weight given to food be x and 100 – x denotes the percentage of total weight given to other items.
$$CPI=\frac{(X+120)+(100-X)×135}{100}\\⇒125=\frac{(120x+13500-135x)}{100}\\⇒12500 = 15x + 13500\\⇒ 15x = 13500 – 12500\\15x = 1000\\x=\frac{1000}{15}\\x = 66.·67%$$
Thus, the percentage of the total weight given to food is 66·67%.

48. 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?

Ans.

 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

$$CPI=\frac{\Sigma WR}{\Sigma W}=\frac{13449.9}{100}\\=134·499 or 134·50.\\\text{Cost of living index} = 134·50.\\\text{Thus, the prices rose by }34·50\% \text{during 1995 and 2004.}$$

49. 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?

Ans. Do it yourself.

50. 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

Source: Economic Survey, 2004–2005, Government of India
(i) Comment on the relative values of the index numbers.
(ii) Are they comparable?

Ans. (i) (a) Inflation using CPI of Industrial Workers:

 Year CPI of Industrial Workers (1982 = 100) Inflation Rate (in %) = (A2-A1)/A1 × 100 1995-96 313 (313-100)/100 × 100 = 213 1996-97 342 (342-100)/100− × 100 = 242 1997-98 366 (366-100)/100 × 100 = 266 1998-99 414 (414-100)/100 × 100 = 314 1999-00 428 (428-100)/100 × 100 = 328 2000-01 444 (444-100)/100 × 100 = 344 2002-02 463 (463-100)/100 × 100 = 363 2002-03 482 (482-100)/100 × 100 = 382 2003-04 500 (500-100)/100 × 100 = 400

(b) Inflation using CPI of Agricultural labourers:

 Year CPI of Agricultural Labourers (1986-87 = 100) Inflation Rate (in %)=(A2-A1)/A1 × 100 1995-96 234 (234-100)/100 × 100 = 134 1996-97 256 (256-100)/100 × 100 = 156 1997-98 264 (264-100)/100 × 100 = 164 1998-99 293 (293-100)/100 × 100 = 193 1999-00 306 (306-100)/100 × 100 = 206 2000-01 306 (306-100)/100 × 100 = 206 2001-02 309 (309-100)/100 × 100 = 209 2002-03 319 (319-100)/100 × 100 = 219 2003-04 331 (331-100)/100 × 100 = 231

(c) Inflation using WPI:

 Year WPI (1993-94 = 100) Inflation Rate (in %)=(A2-A1)/A1 × 100 1995-96 121·6 (121.6-100)/100× 100 = 21·6 1996-97 127·2 (127.2-100)/100× 100 = 27·2 1997-98 132·8 (132.8-100)/100 × 100 = 32·8 1998-99 140·7 (140.7-100)/100 × 100 = 40·7 1999-00 145·3 (145.3-100)/100× 100 = 45·3 2000-01 155·7 (155.7-100)/100 × 100 = 55·7 2001-02 161·3 (161.3-100)/100 × 100 = 61·3 2002-03 166·8 (166.8-100)/100 × 100 = 66·8 2003-04 175·9 (175.9-100)/100·− × 100 = 75·9
1. Hence as calculated, the industrial worker with the base year 1982 turns out to be the highest and WPI with the base year 1993-94 turns out to be the least.
2. No, these index numbers are not comparable as the components of them differ from each category of index numbers.

51. 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.

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

The average tax rate for this family = ΣWX/ΣW
=338/3500
= 0·0966 or 9·66%.