Chapter 8 Index Numbers Solutions
Question - 11 : - What is the difference between a price index and a quantity index?
Answer - 11 : -
The difference between a price index and a quantity index is as follows
- Price index numbers measure and allow for comparison of the prices of certain goods while quantity index number measure the changes in the physical volume of production, construction or employment.
- Price index numbers are more widely used as compared to quantity index numbers.
- Price index is known as unweighted index number while quantity index number is known was weighted index numbers.
Question - 12 : - Is the change in any price reflected in a price index number?
Answer - 12 : -
No, the change in any price is not reflected in a price index number. Price index numbers measure and permit comparison of the prices of certain goods included in the basket being used to compare prices in the base period with prices in the current period. Moreover, an equal rise in the price of an item with large weight and that of an item with low weight will have different implications for the overall change in the price index.
Question - 13 : - Can the CPI number for urban non-manual emplyees represent the changes in the cost of living of the President of India?
Answer - 13 : -
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 an average non-manual employee does not consist of the items that would be a part of the consumption basket 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 weghted index number for cost of living for 2005 with 1980 as the base.
Answer - 14 : - 
Question - 15 : - Read the following table carefully and give your comments.
Answer - 15 : -
Index of Industrial Production Base 1993-94
The following conclusions can be made by analysing the above table
- Manufacturing industry has the highest weight of 79.58% in Index of Industrial Production (IIP) while mining and quarrying and electricity industries account for 10.73% and 10.69% respectively.
- Manufacturing Industry has registered the highest growth among all industrial sectors in both the years 1996-97 and 2003-04.
- Mining and quarrying has registered the lowest growth rate in both the years.
- The General Index shows that industrial increased by 30.8% in 1996.-97 as compared to 1993-94 and by 89% in 2003-04.
Question - 16 : - Try to list the important items of consumption in your family.
Answer - 16 : -
(This is a general example. You can use the actual consumption items in your family).
The following items constitute the total consumption needs for a family
- Food
- Clothing
- House-Rent/EMI of Housing loan
- Education
- Electricity
- Entertainment and recreation
- Miscellaneous expenses
Question - 17 : - 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 rise to maintanin the same standard of living if the CPI is 400?
Answer - 17 : -
Base CPI = ₹ 100
Current CPI = ₹400
Base Year Salary = ₹ 4,000
Current Year Salary = ₹ 6,000
When Base CPI is ₹100, then the salary is = ₹ 4,000
Current salary equivalent to base year salary = (Base year salary/100) × CPI of current year
When Current CPI is ₹ 400, then the salary should be
Thus, his salary should be X 16,000 to maintain his purchasing power. Therefore, in the current year his salary should increase by ₹ 16,000 – ₹ 6,000 = ₹ 10,000 so as to maintain the same level of living in the current year as that of the base year.
The consumer price index for June, 2005 was 125. The food index was 120 and that of other items
What is the percentage of the total weight given to food?
Answer - 18 : - 
Let the total weight = 100
W1 denotes weight of food
W2 denotes weight of other items
So,
Multiplying both sides of Eq. (i) by 135 and subtracting Eq. (ii) from (i) we get
Substituting the value of in the Eq. (i), we get
W1 + W2 = 100
or 6667 + W2 = 100
W2 = 33.33
Therefore, percentage of total weight given to food is 66.67% and other items 33.33%.
An enquiry into the budgets of the middle class families in a certain city gave the following information
What is the cost of living index of 2004 as compared with 1995?
Answer - 19 : - 
Cost of Living Index = 134.50
Thus, the price 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?
Answer - 20 : -
This is a practical exercise. Record the daily expenditure, quantities bought and prices paid per unit of the daily purchases of your family for two weeks and try to analyse if quantities purchased decrease with rise in price of the respective items and also note if the percentage change in quantity brought about by a percentage change in price differ for different types of items.