Class 11 Economics Chapter 8 Index Number Question Answers

NCERT QUESTIONS AND ANSWERS 

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

(i) weighted index

(ii) simple aggregative index

(iii) simple average of relatives

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

(i) base year

(ii) current year

(iii) both base and current year

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

(i) small

(ii) large

(iii) uncertain

4. A consumer price index measures changes in

(i) retail prices

(ii) wholesale prices

(iii) producers prices

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

(i) Food

(ii) Housing

(iii) Clothing

6. In general, inflation is calculated by using

(i) wholesale price index

(ii) consumer price index

(iii) producers’ price index

Ans. 1.(i)  2.(i)  3.(i)  4.(i)  5.(i)  6.(i)

7. Why do we need an index number?

Ans. An index number is a statistical device that is used to measure the changes in the related variables. Its importance is explained in the following points:

1. To measure change in the price level

Index numbers measure and compare prices of different commodities with the help of Wholesale Price Index (WPI). It is widely used to measure the level of inflation in an economy.

2. 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 low standard of living and vice-versa.

3. 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 inflation rate with the help of consumer price index.

4. 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.

5. 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, salary and allowance.

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

Ans. The base period should have the following desirable properties:

1. The base year should not be either too short or too long: It should not be either less than a month or more than a year for calculation purpose.
2. The base year should not belong to too near or too far: Statisticians compare the current year’s conditions with the conditions in the base year. So, if the base year is too far from the current year, then the comparison becomes meaningless. Similarly, if the base year is too near to the current year, then comparison fails to capture the change in the taste, preferences, fashion, etc. Thus, in order to conduct a meaningful comparison, the base year should not be either too far or too near to the current year.
3. The base year should be so selected that the data for the same should be available: The data for a year should be available in order to regard that particular year to be the base year. This enables one to draw conclusions, inferences and for making comparisons.
4. The base period should be constantly updated: The base year should be constantly updated due to the changes in taste, preferences and fashion otherwise; the comparison becomes misleading or inconclusive.

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

Ans. The Consumer Price Index (CPI) in India includes the following three components:

1. CPI for Industrial Workers.
2. CPI for Urban Non-manual Employees.
3. CPI for Agricultural Labourers.

The three CIPs are calculated on regular basis to get the aggregate effect of the changes in retail prices. While the CPI for industrial workers and agricultural labourers are calculated and published by Labour Bureau, Shimla, the CPI for the urban non-manual employees is calculated and published by the Central Statistical Organisation (CSO). The rationale behind carrying out separate calculation of CPI for industrial and agricultural labourers and CPI for urban non-manual employees is that the consumption baskets of the former group (i.e. industrial workers and agricultural labourers) differs significantly from that of the later (i.e. urban non-manual employees). Thus, as the consumption pattern differs among the two groups and to assess the impact of the price change on the consumption pattern, CPI is calculated separately for each group.

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

Ans. A Consumer Price Index for Industrial Workers measures the impact of changes in the retail prices on the cost of living of industrial workers. In a country like India, CPI for industrial workers is estimated and published by the Labour Bureau, Shimla taking 1982 as the base year for the current series. In India, CPI for industrial workers is the most popular index and is used by the government to regulate Dearness Allowance (D.A.) to compensate its employees against the price rise.

The weight schemes in CPI for Industrial Workers include food, pan, supari, tobacco, fuel and lighting, housing, clothing, and miscellaneous expenses. Food being the most important component has the highest weight. Thus, it implies that the food price changes have a significant impact on the CPI.

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

Ans. ANSWER:

Price Index			Quantity Index
1.	Price Index Number is calculated by two methods, namely		1.	Quantity Index Number is calculated by two methods, namely
	a.	Simple Aggregative Method		a.	Weighted Average of Price Relative Method
	b.	Simple Average of Price Relative Method		b.	Weighted Aggregative Method.
2.	Price Index number is also known as Unweighted Index Number		2.	Quantity Index Number is also known as Weighted Index Number.
3.	Price Index Number takes into account the prices of the commodity of the base year as well as of the current year.		3.	Quantity Index takes into consideration the weights of goods assigned according to the quantity.

 

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. Index numbers of prices are not simply a statement of prices at different dates, but they present the estimates of relative changes in the prices over the years with reference to a particular base year.

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 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.

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

 

ANSWER:

Items	Price in 1980  P0	Price in 2005  P1	Weight   W		RW
Food	100	200	75		15,000
Clothing	20	25	10		1,250
Fuel and Lighting	15	20	5		666.65
House Rent	30	40	6		799.98
Misc.	35	65	4		742.84

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 Mining and Quarrying Manufacturing Electricity	100 10.73 79.58 10.69	130.8 118.2 133.6 122.0	189.0 146.9 196.6 172.6

Ans.

The following conclusions can be made by analysing the above table.

1. Manufacturing Industry has the highest weight of 79.58% as compared to the Mining and Quarrying and Electricity Industries that accounts for 10.73% and 10.69% respectively.
2. The production of Manufacturing Industry is higher than that of the Mining and Quarrying and Electricity Industries in both the years 1996-97 and 2003-04.
3. Mining and Quarrying has the least growth performance while that of the Manufacturing Industry is the highest.
4. The General Index is comparatively higher in the year 2003-04 than 1996-97

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

Ans. The following items constitute the total consumption needs of our family

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

17. If the salary of a person in the base year is Rs 4,000 per annum and the current year salary is Rs 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 = Rs 100

Current CPI = Rs 400

Base Year Salary = Rs 4,000

Current Year Salary = Rs 6,000

Thus, his salary should be Rs 16,000. Therefore, in the current year his salary should increase by Rs 10,000 (i.e. Rs 16,000 – Rs 6,000) so as to maintain the same level of living in the current year as that of the base year.

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.

Items	Index	Weights	WI
Food	120	W1	120 W1
Other Items	135	W2	135 W2

 

Let the total weight = 100

W1 denotes weight of food

W2 denotes weight of food other items

 

So, W1 + W2 = 100                             (i)

CPI = 125

12500 = 120 W1 + 135 W2                   (ii)

 

Subtracting equations (ii) from (i)

 

13500	=	135 W1	+	135 W2
12500	=	120 W1	+	135 W2
–		–		–
1000	=	15 W1

Substituting the value of W1 in the equation (i)

 

W1 + W2 = 100

Or, 66.67 + W2 = 100

W2 = 33.33

Percentage of total weights given to food is 66.67% and other items is 33.33%

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

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

 

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

Ans.

Items	Weight   W	Price in 1995 P0	Price in 2004 P1		WR
Food	35	1400	1500		3,749.90
Fuel	10	200	250		1,250
Clothing	20	500	750		3,000
Rent	15	200	300		2,250
Misc.	20	250	400		3,200

Cost of Living Index = 134.50

 

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

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?

Ans.

Week I
	Potato			Onion			Total Expenditure (Rs)
Days	Price (per kg) PWI	Quantity QWI	Expenditure PWI  QWI	Price (per kg) PWI	Quantity QWI	Expenditure PWI  QWI
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			Total Expenditure (Rs)
Days	Price (per kg) PWII	Quantity QWII	Expenditure PWII  QWII	Price (per kg) PWII	Quantity QWII	Expenditure PWII  QWII
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 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.

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

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)

Year	CPI of Industrial Workers (1982 = 100)	Inflation Rate (in %)
1995–96	313
1996–97	342
1997–98	366
1998–99	414
1999–00	428
2000–01	444
2001–02	463
2002–03	482
2003–04	500

 

b)

Year	CPI of Agricultural Labourers (1986-87=100)	Inflation Rate (in %)
1995–96	234
1996–97	256
1997–98	264
1998–99	293
1999–00	306
2000–01	306
2001–02	309
2002–03	319
2003–04	331

 

c)

Year	WPI (1993-94 =100)	Inflation Rate (in %)
1995–96	121.6
1996–97	127.2
1997–98	132.8
1998–99	140.7
1999–00	145.3
2000–01	155.7
2001–02	161.3
2002–03	166.8
2003–04	175.9

 

The inflation rate for industrial worker 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 given to different index 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 item 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.

Ans.

	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: 3383500 = 0.0966 or 9.66%