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NCERT Solution for Class 11 Commerce Statistics for Economics Chapter 8 - Index Numbers

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Exercise/Page

NCERT Solution for Class 11 Commerce Statistics for Economics Chapter 8 - Index Numbers Page/Excercise 118

Solution 1

The correct answer is option (i). An index number which accounts for the relative importance of the items is known as weighted index. Under this method, different items of the series are accorded different weightage based on their relative importance. This offers a much more realistic number.  

Solution 2

The correct answer is option (i). In most of the weighted index numbers, the weight pertains to base year as changing the weight every year is not so clear. Under this method, different items of the series are accorded different weightage based on their relative importance. Base year quantities as weights used in Laspeyres' method, current year quantities as weights used in Paasche's method and both base and current year quantities as weights used in Fisher's method.

Solution 3

The correct answer is option (i). The impact of change in the price of a commodity with little weight in the index will be small. This is because a commodity which has less value given low weight and no significant effect of price change.

Solution 4

The correct answer is option (i). The Consumer Price Index (CPI) measures changes in retail prices, and hence, it is also known as retail price index numbers. It measures the average changes in retail prices to show the accurate impact of price rise on the cost of living of the people.

Solution 5

The correct answer is option (i). The Consumer Price Index (CPI) for industrial workers includes the following items-food, pan, supari, tobacco, fuel and lighting, housing, clothing and other expenses. Of these, the item having the highest weight in CPI for industrial workers is food. This indicates that the change in the food price has significant impact on CPI. 

Solution 6

The correct answer is option (i). The wholesale price index (WPI) is a widely used price index as an indicator of the rate of inflation in the economy. This indicates the movement in prices of commodities in all trading transactions. This index is helpful in forecasting the demand and supply of commodities in the market.

NCERT Solution for Class 11 Commerce Statistics for Economics Chapter 8 - Index Numbers Page/Excercise 119

Solution 7

An index number is a statistical device to measure changes in the magnitude of a group of related variables.

Need for index number:

  1. Barometer of economic activity: Index number serves as a barometer for measuring the value of money. This helps to compare the value of money for different years and thus is able to feel the pulse of the economy.
  2. Useful to government in formulating policies: A change in the value of money has direct impact on public. Thus, the government formulates fiscal and monetary policies based on the result of index numbers. 
  3. Useful to fix wages: A revision in the money wage occurs in accordance with a proportionate change in the cost of living. Thus, the government revises wages based on the cost of living index number.
  4. Easy to understand the economic condition: Economic condition of a particular group can be analysed for two years. This helps understand whether the economic condition is improved or getting worse for them.
  5. Indicator of inflation: An increase in the index number indicates the rate at which the purchasing power of money is decreasing. Thus, it helps in calculating the rate of inflation in an economy. 
  6. Measures price-level changes: This helps to compare the prices of different commodities and to understand the general price-level changes in the economy. 

Solution 8

The base period associated with an index number is a time period which is used as a basis for comparing changes in prices or quantities during a particular period of time.

 

Properties of the base period:

  1. Normal period: The base year should be a normal period, and a period in which unusual events took place should not be considered a base period because they are not suitable for comparative analysis.
  2. Avoid extreme values: Extreme values are not considered a base period for comparative analysis.
  3. Differences between base period and current period should not be too large: Index numbers are helpful in decision making and enables the government to formulate policies. The period should not be too far in the past as compared to the current period as the policies, economic and social conditions change over a period of time and cannot be considered a base year.
  4. Periodical updates: Base period should be updated periodically to understand the changes in taste and preferences for a particular commodity. 

Solution 9

Three Consumer Price Index (CPI) numbers are constructed in India. They are

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

 

CPI reflects the average increase in the cost of commodities consumed by a class of people. This enables to maintain the same standard of living in the current year as in the base year. This is calculated every month to analyse the impact of changes in the retail price on the cost of living of these three categories of consumers.

It is essential to have different CPI for different categories of consumers because the consumption pattern of different categories varies widely, i.e. each category's consumption basket contains different items. Every consumer has his/her own taste and preferences, and hence, the consumption pattern of the same class of people differs from place to place. It helps determine the effect of rise and fall in prices of various commodities consumed by different classes of people living in different locations. Therefore, CPI is constructed separately for different classes of people.

Solution 10

The Consumer Price Index (CPI) for industrial workers measures the average change in retail price of a basket of commodities consumed by an industrial worker. It is considered an appropriate indicator of general inflation as it shows the accurate impact of price rise on the cost living of the people.  

CPI for industrial workers includes the following items-food, pan, supari, tobacco, fuel and lighting, housing, clothing and other expenses. Of these, the item having the highest weight in CPI for industrial workers is food. This indicates that the change in the food price has significant impact on CPI. 

Solution 11

 

Price Index

Quantity Index

  1. It measures general changes in prices between current year and base year.
  1. It measures average change in quantities and assists to compare changes in physical quantity of commodities produced and consumed.
  1. Two methods to calculate Price Index Number are

a. Simple aggregative method

b. Simple average of price relative method

  1. Two methods to calculate Quantity Index Number are

a. Weighted average of price relative method

b. Weighted aggregative method

  1. It is also known as unweighted index number.
  1. It is also known as weighted index number.
  1. It considers the prices of the commodity of both base year and current year.
  1. It considers the weights of commodity assigned according to the quantity.

Solution 12

No, the change in any price is not reflected in a price index number. This is because the price index number provides only relative changes. This implies that it reflects the relative changes in the prices over a period of time relevant to one particular year. 

Solution 13

No, the CPI number for urban non-manual employees cannot represent the changes in the cost of living of the President of India. The consumption pattern of the urban non-manual employees is different from the consumption pattern of the President of India.

Solution 14

Calculation of cost of living index for 2005 with 1980 as base year:

 

Therefore, the cost of living index (CPI) in the current year (2005) has increased by 84.59% as compared to the base year (1980). 

Solution 15

Observations from the given table:

  1. Index of industrial production shows that the manufacturing industry has the highest weight of 79.58%. Electricity and mining and quarrying industries account for only 10.73% and 10.69%, respectively.
  2. The manufacturing industry has the highest production of 133.6% in 1996-97 and 196.6% in 2003-04 among all other industries in both years.
  3. Growth of the mining and quarrying industry is comparatively lower among all industries.
  4. The general index of the industries shows an increase by 30.8% in 1996-97 as compared to 1993-94 and by 89% in 2003-04. 

Solution 16

Items of consumption in my family:

  1. Food
  2. Rented house
  3. Clothes
  4. Electricity
  5. Cooking fuel
  6. Education
  7. Transport 

Solution 17

  

Solution 18

Assume the total weight assigned to food is X and the total weight assigned to other items is (100 ­- X).

  

Solution 19

Calculation of cost of living index of 2004:

  

NCERT Solution for Class 11 Commerce Statistics for Economics Chapter 8 - Index Numbers Page/Excercise 120

Solution 20

 

Week 1

Days

Bread

 

Milk

 

Price per loaf

Quantity

Total expense

Price per litre

Quantity

Total expense

Monday

25

2

50

40

1

40

Tuesday

24

1

24

39

2

78

Wednesday

24

1.5

36

38

1.5

57

Thursday

23

2

46

40

1

40

Friday

24

1

24

39

2

78

Saturday

22

2.5

55

37

1

37

Sunday

24

2

48

39

1.5

58.5

 

 

 

283

 

 

330

 

Week 2

Days

Bread

 

Milk

 

Price per loaf

Quantity

Total expense

Price per litre

Quantity

Total expense

Monday

26

2

52

42

1

42

Tuesday

23

2

46

40

2

80

Wednesday

24

1.5

36

39

2

78

Thursday

25

2

50

39

1

39

Friday

26

1

26

40

2

80

Saturday

22

2.5

55

39

1

39

Sunday

23

2

46

39

1.5

58.5

 

 

 

307

 

 

358

 

The household expense on the first day of the week for bread was Rs 50 and the expense on the first day of the second week has increased to Rs 52 and the price of milk expenses increased from Rs 40 to Rs 42. Hence, the total expenditure has been increased from Rs 90 (50 + 40) to Rs 94 (52 + 42). Therefore, the increase in the price will lead to an increase in the household expense of a family.

Solution 21

  1.  
    1. Inflation using CPI of industrial workers  

  

    1. Inflation using CPI of urban non-manual employees  

  

    1. Inflation using CPI of agriculture labourers (1986-87 = 100) 

  

    1. Inflation using WPI (1993-94 = 100) 

  

  1. The inflation rate which is computed by using CPI industrial worker with the base year 1982 is the highest and the rate computed by using WPI with the base year 1993-94 is the least.
  2. No, the index numbers are not comparable. This is because the base periods used for CPI of industrial workers, urban non-manual employees, agricultural workers and WPI are different. Also, the commodities and its weightage in different index numbers may be different.  

Text Book Solutions

CBSE XI Commerce - Statistics for Economics

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