NCERT Solutions for Class 11 Economics Chapter 7 - Index Numbers

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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:

It measures the changes in the price level.
It determines the change in the standard of living.
It helps in planning and decision making.
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:

The base year should neither be too short nor be too long.
The base year should neither be too near nor too far in the past.
It should be easily accesible and available.
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:

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

Quantity Index :

Quantity Index measures changes in the level of output or physical volume of production in the economy.
It takes into consideration the weights of goods assigned according to the quantity.
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

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

44. 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. Following are the evident points determined from the above table:

The General Index is comparatively higher in the year 2003-04 than 1996-97.
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.
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.
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

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

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.
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