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## NCERT Solutions for Class 11 Economics Chapter 8 – Index Numbers

#### Question 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

An index number which accounts for the relative importance of the items is known as weighted index
An index number in which different items of the series are accorded weight age according to their relative importance is known as Weighted Index Numbers. It is the weighted average of the prices of different goods.

#### Question 2:

In most of the weighted index numbers the weight pertains to
(i) base year
(ii) current year
(iii) both base and current year

In most of the weighted index numbers, the weight pertains to current year.
In the Weighted Method of calculating index numbers, different goods are accorded weights according to the quantity brought. Laspeyre's method uses base year's quantities as weights, Paasche's method uses current year's quantities as weights and Fisher’s method uses both base year as well as current year's quantities as base.

#### Question 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

The impact of change in the price of a commodity with little weight in the index will be small
A lesser important commodity is assigned lower weight as it would not have a significant effect of price change.

#### Question 4:

A consumer price index measures changes in
(i) retail prices
(ii) wholesale prices
(iii) producers prices

A consumer price index measures changes in retail prices.
Consumer Price Index (CPI) is used to measure changes in the cost of living in which the retail prices of consumer goods and services are obtained. It measures the average changes in the retail prices.

#### Question 5:

The item having the highest weight in consumer price index for industrial workers is
(i) Food
(ii) Housing
(iii) Clothing

The item having the highest weight in consumer price index for industrial workers is food
The weight schemes in CPI for Industrial Workers include food, pan, supari, tobacco, fuel and lighting, housing, clothing, and miscellaneous expenses. The food being the most important component has the highest weight. It implies that the food price changes have a significant impact on the CPI.

#### Question 6:

In general, inflation is calculated by using
(i) wholesale price index
(ii) consumer price index
(iii) producers' price index

In general, inflation is calculated by using Wholesale Price Index.
Wholesale Price Index measures the relative changes in the prices of the commodities traded in the wholesale markets. It assesses situations of overall demand and supply in the market. It focuses on the rate of inflation in the economy.

#### Question 7:

Why do we need an index number?

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, salaries and allowances.

#### Question 8:

What are the desirable properties of the base period?

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.

#### Question 9:

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

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.

#### Question 10:

What does a consumer price index for industrial workers measure?

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.

#### Question 11:

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

 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.

#### Question 12:

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

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.

#### Question 13:

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

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.

#### Question 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

 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

#### Question 15:

 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

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.

#### Question 16:

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

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

#### Question 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 rise to maintain the same standard of living if the CPI is 400?

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.

#### Question 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?

 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%

#### Question 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 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 2004 as compared with 1995?

 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.

#### Question 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?

 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.

#### Question 21:

Given the following data:
 Year CPI of Industrial Workers (1982 = 100) CPI of Urban Non-manual Employees (1984-85 = 100) CPI of Agricultural Labourers (1986-87 = 100) WPI (1993-94 = 100) 1995–96 313 257 234 121.6 1996–97 342 283 256 127.2 1997–98 366 302 264 132.8 1998–99 414 337 293 140.7 1999–00 428 352 306 145.3 2000–01 444 352 306 155.7 2001–02 463 390 309 161.3 2002–03 482 405 319 166.8 2003–04 500 420 331 175.9
SourceEconomic Survey, Government of India 2004-2005
(i) Calculate the inflation rates using different index numbers.
(ii) Comment on the relative values of the index numbers.
(iii) Are they comparable?

(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 Non-manual Employees (1984-85 =100) Inflation Rate (in %) 1995–96 257 1996–97 283 1997–98 302 1998–99 337 1999–00 352 2000–01 352 2001–02 390 2002–03 405 2003–04 420
c)
 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
d)
 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
(ii) 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.

(iii) 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.

Courtesy : CBSE