# Index Numbers

This page contains the NCERT Statistics for Economicsclass 11 chapter 7 Index Numbers from the book Statistics for Economics. You can find the solutions for the chapter 7 of NCERT class 11 Statistics for Economics, for the Short Answer Questions, Long Answer Questions and Projects/Assignments Questions in this page. So is the case if you are looking for NCERT class 11 Statistics for Economics related topic Index Numbers question and answers.
EXERCISES
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: (i) weighted index
An index number that takes into account the relative importance of the items it measures is known as a weighted index. This type of index assigns weights to different items to reflect their significance or relevance in the overall measure. This is in contrast to a simple aggregative index or a simple average of relatives, which do not differentiate between the importance of the items they include. The weighted index is more precise as it considers the varying impact of different items, making it a crucial tool in economic analysis and policy making.
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: (i) base year
In most weighted index numbers, the weights assigned to different items typically pertain to the base year. This approach involves using the importance or relevance of items as it was in the base year to calculate the index. The rationale behind this is to measure changes over time from a consistent point of reference, which is the base year in this case. This method ensures that the index reflects how different elements have evolved from a fixed historical point, providing a clear picture of change over time.
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: (i) small
When a commodity has a small weight in an index, the impact of a change in its price on the overall index will be small. This is because the weight assigned to a commodity in an index reflects its relative importance or significance in the calculation of the index. Therefore, a commodity with a lesser weight contributes less to the overall index value. Consequently, any price changes in such commodities will have a proportionately smaller effect on the index as a whole, compared to commodities with greater weights.
4.
A consumer price index measures changes in
(i)
retail prices ✔
(ii)
wholesale prices
(iii)
producers prices
A consumer price index measures changes in: (i) retail prices
A Consumer Price Index (CPI) is specifically designed to measure changes in retail prices. The CPI is a statistical estimate constructed using the prices of a sample of representative items whose prices are collected periodically. It is used to track the changes in the cost of a basic basket of goods and services purchased by a typical consumer. This index is crucial in understanding the inflation rate experienced by consumers in their day-to-day living expenses and is a key indicator of the economic health of a country.
The CPI differs from wholesale prices, which are tracked by the Wholesale Price Index (WPI), and producer prices, which are measured by the Producer Price Index (PPI). While WPI and PPI focus on the cost of goods at the wholesale level and the production level respectively, CPI exclusively measures the average change over time in the prices paid by urban consumers for a market basket of consumer goods and services.
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 the consumer price index for industrial workers is: (i) Food
Within the Consumer Price Index (CPI) for industrial workers, the item with the highest weight is typically ‘Food’. This is because food constitutes a significant portion of the average industrial worker’s expenses. The CPI is designed to measure the average change over time in the prices paid by consumers for a basket of goods and services, and given the essential nature of food, it usually carries more weight compared to other categories like housing or clothing.
This allocation of weights in the CPI reflects the spending patterns of the population segment in question, in this case, industrial workers. Since a larger portion of their income is likely to be spent on food, changes in food prices have a more significant impact on their overall cost of living, hence the higher weight in the CPI.
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: (i) wholesale price index
It is important to note that both the Wholesale Price Index (WPI) and the Consumer Price Index (CPI) are used for calculating inflation, but in many contexts, especially in India, the WPI has been traditionally used as a primary measure of inflation.
The WPI measures the changes in the prices of goods at the wholesale level. In many economies, including India, WPI has been a crucial indicator for inflationary trends because it reflects the prices paid by manufacturers and wholesalers and is therefore seen as a precursor to retail inflation, which is measured by the CPI.
However, it’s worth noting that different countries may prefer different indices based on their economic structures and policy focuses. While WPI is commonly used in some countries, others might rely more on CPI or even the Producer Price Index (PPI) for measuring inflation.
7.
Why do we need an index number?
The need for an index number is explained as follows:
Measuring Changes in a Group of Related Variables: An index number is a statistical tool used to measure changes in the magnitude of a group of related variables. This is essential in economics and statistics to understand trends and patterns over time.
Simplifying Complex Data: Index numbers help in simplifying and summarizing a large amount of data. They provide a single figure that represents changes in a set of variables, making it easier to comprehend and analyze complex information.
Comparative Analysis: They enable comparative analysis over different time periods or between different entities. For instance, comparing the cost of living between two different years or the economic performance of different countries.
Economic Policy and Decision Making: Index numbers are widely used in economic policy making. For example, the Consumer Price Index (CPI) is used in wage negotiation and formulating income policies, while the Wholesale Price Index (WPI) is used in assessing inflationary trends.
Adjusting Economic Variables: They are also used to adjust other economic variables for the effects of inflation. For example, GDP and national income are often adjusted using price index numbers to reflect real, rather than nominal, values.
Sectoral Analysis: Specific index numbers like the Industrial Production Index (IPI) provide insights into sector-specific performance, aiding in targeted policy-making and sectoral analysis.
8.
What are the desirable properties of the base period?
The desirable properties of the base period are as follows:
1
Normalcy: The base year should be a normal year, free from any abnormal or extraordinary economic events. This means it should not be a year with extreme economic conditions like a recession or a boom.
2
Recentness: The base year should be relatively recent to ensure that the data is relevant and reflects current economic conditions. A base year that is too far in the past may not accurately represent current economic realities due to changes over time.
3
Stability: The base period should be characterized by stability in the economy. This stability ensures that the base year provides a solid and reliable foundation for comparison over time.
4
Availability of Data: There should be comprehensive and reliable data available for the base year. The accuracy and completeness of data are crucial for constructing meaningful index numbers.
5
Representativeness: The base year should be representative of the period under study. It should reflect the typical conditions of the period, ensuring that the index numbers derived are meaningful and applicable.
These properties are essential to ensure that the base period provides a suitable and reliable point of reference for constructing index numbers, which are used for various economic analyses and policy-making decisions.
9.
Why is it essential to have different CPI for different categories of consumers?
The necessity of having different Consumer Price Indexes (CPI) for different categories of consumers is explained as follows:
Varying Consumption Patterns: Different categories of consumers have distinct consumption patterns. For instance, the spending habits of urban consumers may significantly differ from those of rural consumers.
Diverse Income Levels: Income levels vary among different consumer groups, which influences their spending behavior. A CPI for industrial workers would differ from one for agricultural labourers due to the difference in their income and expenditure patterns.
Specific Needs and Preferences: Different consumer categories have unique needs and preferences. The basket of goods and services used to calculate CPI for one group may not be relevant for another group.
Accurate Measurement of Inflation: To accurately measure inflation for a specific group, it is essential to consider the goods and services that are most relevant to that group. A general CPI might not accurately reflect the inflation experienced by different consumer categories.
Targeted Policy Making: Different CPIs allow for more targeted economic policies. Policymakers can address the specific needs of different groups more effectively when they have detailed information about each group’s inflation rate.
Equitable Economic Analysis: Having different CPIs ensures a more equitable and inclusive approach to economic analysis, acknowledging the diversity in consumer behavior and needs across different segments of the population.
These reasons highlight the importance of having different CPIs for different consumer categories, ensuring that inflation measurement is accurate, relevant, and useful for economic analysis and policy-making.
10.
What does a consumer price index for industrial workers measure?
The Consumer Price Index (CPI) for industrial workers measures the following:
Change in Retail Prices: The CPI for industrial workers specifically tracks the change in retail prices of a basket of goods and services. This basket is representative of the typical purchases made by industrial workers.
Cost of Living: The index measures the cost of living for industrial workers. It reflects how the prices of goods and services that are essential for their daily life change over time.
Inflation Impact: The CPI for industrial workers is a key indicator of the inflation experienced by this particular group. It shows how the purchasing power of industrial workers is affected by price changes.
Wage Negotiation and Policy Making: This index is crucial for wage negotiation and formulating income policies for industrial workers. It helps in understanding the economic pressures faced by this segment of the workforce and aids in making informed decisions regarding their wages and benefits.
Economic Analysis: The CPI for industrial workers is also used for broader economic analysis, providing insights into the economic conditions affecting the industrial sector’s workforce.
11.
What is the difference between a price index and a quantity index?
The differences between a price index and a quantity index are as follows:
Aspect
Price Index
Quantity Index
Definition
Measures the average change in prices of a basket of goods and services over time.
Measures the change in the quantity of goods and services produced or consumed.
Focus
Concentrates on the price aspect of goods and services.
Focuses on the physical quantity or volume of goods and services.
Purpose
Used to track inflation or deflation in an economy.
Used to measure changes in economic output or consumption.
Usage
Helps in adjusting salaries, pensions, and formulating economic policies related to inflation.
Used to assess economic growth, productivity, and consumption patterns.
Representation
Expressed in terms of prices.
Expressed in terms of physical units or adjusted for inflation.
Examples
Consumer Price Index (CPI), Wholesale Price Index (WPI).
Industrial Production Index, Gross Domestic Product (GDP) based on quantities.
12.
Is the change in any price reflected in a price index number?
No. The change in any individual price is not directly reflected in a price index number. Instead, a price index number represents the average change in prices of a selected basket of goods and services. Here’s a detailed explanation:
Selective Representation: A price index number reflects the average change in prices of a specifically chosen basket of goods and services, rather than every price change in the economy.
Basket of Goods Approach: The index is based on a basket of goods and services that represents typical consumption for a particular segment of the population.
Weighted Impact: Changes in prices are incorporated into the index as a weighted average, meaning the influence of a price change depends on the item’s weight in the basket.
Limited Scope: The price index does not capture every price change in the economy, only those that occur within the selected basket of goods and services.
General Trend Indicator: The index reflects the overall trend of prices for the chosen basket, rather than individual price movements.
13.
Can the CPI for urban non-manual employees represent the changes in the cost of living of the President of India?
No. The Consumer Price Index (CPI) for urban non-manual employees cannot accurately represent the changes in the cost of living of the President of India. Here’s why:
Different Consumption Patterns: The President of India, due to their unique position and lifestyle, is likely to have consumption patterns that are significantly different from those of urban non-manual employees. The basket of goods and services used to calculate the CPI for urban non-manual employees may not be representative of the President’s consumption.
Income and Expenditure Levels: The President’s income and expenditure levels are vastly different from those of urban non-manual employees. This disparity means that the impact of price changes on the President’s cost of living would be different from the impact on urban non-manual employees.
Specific Needs and Lifestyle: The President’s role comes with specific needs and a lifestyle that includes elements not covered in the typical CPI basket for urban non-manual employees. This includes aspects related to security, protocol, and official duties, which are not part of the average urban non-manual employee’s life.
Purpose of CPI: The CPI is designed to reflect the general inflation experienced by a specific group. It is not tailored to the unique circumstances of individuals, especially those in high-ranking positions like the President.
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 & lighting
15
20
House rent
30
40
Misc
35
65
To calculate the weighted index number for the cost of living for 2005 with 1980 as the base, we use the following tabulated calculations:
Items
Base Period Price
(in 1980)
Current Period Price
(in 2005)
Price Ratio
{R = \dfrac{P_1}{P_0} × 100}
(in %)
Weight
{W}
Weighted Price Ratio
{W × R}
Food
100
200
{\dfrac{200}{100} × 100 = 200}
75
15,000
Clothing
20
25
{\dfrac{25}{20} × 100 = 125}
10
1,250
Fuel & Lighting
15
20
{\dfrac{20}{15} × 100 = 133.33}
5
666.67
House Rent
30
40
{\dfrac{40}{30} × 100 = 133.33}
6
800
Misc
35
65
{\dfrac{65}{35} × 100 = 185.71}
4
742.84
Total
{∑W = 100}
{∑RW = 18,459.51}
Now, the Weighted Index Number for the cost of living (CPI) is calculated
CPI
{= \dfrac{∑WR}{∑R}}
{= \dfrac{18,459.51}{100}}
= 184.59
Therefore, the weighted index number for the cost of living for 2005 with 1980 as the base is 184.59. This indicates that the cost of living has increased by approximately 84.59% from 1980 to 2005 for the workers in the industrial center, considering the given items and their weights.
15.
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
My comments on the table showing the Index of Industrial Production (IIP) with the base year 1993-94 are as follows:
Overall Growth: The General Index shows significant growth from 130.8 in 1996-97 to 189.0 in 2003-2004. This indicates a substantial increase in industrial production over this period.
Sectoral Analysis:
Mining and Quarrying: This sector, with a weight of 10.73%, shows growth from 118.2 to 146.9. The growth is notable but not as pronounced as in other sectors. This could indicate moderate development or expansion in mining and quarrying activities.
Manufacturing: The manufacturing sector, having the highest weight of 79.58%, shows a significant increase from 133.6 to 196.6. This substantial growth reflects robust development in manufacturing, which is a critical component of the industrial sector.
Electricity: With a weight of 10.69%, the electricity sector grew from 122.0 to 172.6. This growth is crucial as it indicates not only the expansion of electricity generation capacity but also potentially reflects the growing demand for electricity in the economy.
Implications for the Economy: The overall growth in the IIP suggests a positive trend in the industrial sector during this period. The manufacturing sector’s significant growth could imply advancements in technology, increased investment, and possibly a rise in both domestic and international demand for manufactured goods.
Weightage and Impact: The varying weights of different sectors in the IIP indicate their relative importance in the industrial sector. The high weightage of manufacturing underscores its significant impact on the overall index.
Policy Insights: These trends can provide valuable insights for policymakers. For instance, the robust growth in manufacturing might encourage further investment in this sector, while the relatively slower growth in mining and quarrying might prompt a review of policies affecting this sector.
16.
Try to list the important items of consumption in your family.
Here’s a list of important items of consumption in my family:
1.
Food and Groceries:
Rice, Wheat, and other cereals
Vegetables and Fruits
Milk and Dairy Products
Meat, Fish, and Eggs
Cooking Oil and Spices
2.
Utilities:
Electricity
Water
Cooking Gas
3.
Housing:
Rent or Mortgage Payments
Maintenance and Repairs
4.
Healthcare:
Medicines
Doctor’s Consultation Fees
5.
Education:
School/College Fees
Books and Stationery
Online Learning Resources
6.
Clothing:
Everyday Wear
Formal Attire
Seasonal Clothing like Winter Wear
7.
Transportation:
Fuel for Vehicles
Public Transport Fares
8.
Communication:
Mobile Phone Bills
Internet Charges
9.
Entertainment and Recreation:
Movie and Event Tickets
Subscription Services (like streaming platforms)
Sports and Hobby Equipment
10.
Household Items:
Cleaning Supplies
Toiletries and Personal Care Products
11.
Miscellaneous:
Savings and Investments
These items represent the typical consumption pattern of my family, covering essential needs like food, shelter, healthcare, and education, along with other aspects like transportation, communication, and recreation. This list can vary depending on the specific lifestyle and priorities of different families.
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 be raised to maintain the same standard of living if the CPI is 400?
To determine by how much the salary should be raised to maintain the same standard of living, given that the Consumer Price Index (CPI) is 400, we can follow these steps:
1.
Understand the CPI: A CPI of 400 implies that the cost of living has increased by 4 times (400%) since the base year.
2.
Calculate the Adjusted Salary: To maintain the same standard of living, the salary should also increase by the same rate as the CPI. So, the salary in the current year should be 4 times the base year salary.
3.
Base Year Salary: ₹ 4,000 per annum.
4.
Required Current Year Salary: {₹~4,000 × 4 = ₹~16,000} per annum.
5.
Current Actual Salary: ₹ 6,000 per annum.
6.
Salary Shortfall:
The difference between the required current year salary and the actual current year salary.
{₹~16,000 - ₹~6,000 = ₹~10,000}
Therefore, to maintain the same standard of living as in the base year, the person’s salary should be raised by ₹ 10,000 per annum from the current salary of ₹ 6,000.
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?
To find the percentage of the total weight given to food, we can use the formula for the Consumer Price Index (CPI) which is a weighted average of the prices of a basket of consumer goods and services. The formula is:
{\text{CPI} = \dfrac{∑(\text{Price Index of Item} × \text{Weight of Item})}{∑\text{Weights}}}
Given that:
CPI for June 2005 = 125
Food Index = 120
Index of Other Items = 135
Let the weight of food be {W} and the weight of other items be {1 - W} (since the total weight is 1 or 100%)
The CPI can be rewritten as:
{125 = \dfrac{(120 × W) + (135 × (1 - W))}{1}}
Solving for {W}:
{125 = 120W + 135 - 135W}
{⇒ 125 = 135 - 15W}
{⇒ 15W = 135 - 125}
{15W = 10}
{⇒ W}
{= \dfrac{10}{15}}
{= \dfrac{2}{3}}
≅ 0.67
Converting to percentage:
{0.67 × 100\% = 67\%}
Therefore, the percentage of the total weight given to food in the CPI calculation for June 2005 is approximately 67%.
So, obviously the weightage given to other items is 33% (This is just additional information and is not asked for in the problem)
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 ₹) 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?
To calculate the cost of living index for the year 2004 compared with 1995, we will create a table that includes the base period price (1995), the current period price (2004), the price ratio {R = \dfrac{P_1}{P_0} × 100}, the weight {W}, and the weighted price ratio {W × R}. Here’s the table:
Expenses on items
Base Period Price (1995)
Current Period Price (2004)
Price Ratio
{R = \dfrac{P_1}{P_0} × 100}
(in %)
Weight
{W}
Weighted Price Ratio
{W × R}
Food
1400
1500
{\dfrac{1500}{1400} × 100 = 107.14}
35
107.14 × 35 = 3749.90
Fuel
200
250
{\dfrac{250}{200} × 100 = 125.00}
10
125.00 × 10 = 1250.00
Clothing
500
750
{\dfrac{750}{500} × 100 = 150.00}
20
150.00 × 20 = 3000.00
Rent
200
300
{\dfrac{300}{200} × 100 = 150.00}
15
150.00 × 15 = 2250.00
Misc.
250
400
{\dfrac{400}{250} × 100 = 160.00}
20
160.00 × 20 = 3200.00
{∑W = 100}
{∑WR = 13449.90}
To find the cost of living index, we sum up the weighted price ratios and divide by the sum of the weights, then multiply by 100. The sum of the weights is 100 (since they are percentages), so the cost of living index is the sum of the weighted price ratios divided by 100.
{\text{Cost of Living Index }= \dfrac{13449.90}{100} = 134.50}
Therefore, the cost of living index for the year 2004 as compared with 1995 is 134.50, indicating a 34.50% increase in the cost of living.
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?
I have recorded the daily expenditure, quantities bought, and prices paid per unit of my family’s daily purchases over two weeks. Here’s a summarized version of the data:
Week 1:
Item
Quantity Bought
Price per Unit
(in ₹)
Total Expenditure
(in ₹)
Rice (kg)
2
40
80
Vegetables (kg)
3
30
90
Milk (liters)
7
50
350
Eggs (dozen)
1
60
60
2
25
50
Week 2:
Item
Quantity Bought
Price per Unit
(in ₹)
Total Expenditure(in ₹)
Rice (kg)
2
42
84
Vegetables (kg)
3
35
105
Milk (liters)
7
52
364
Eggs (dozen)
1
65
65
2
28
56
Calculation of CPI (Consumer Price Index):
Item
Price in Week 1
Price in Week 2
Price Ratio
{R = \dfrac{P_1}{P_0} × 100}
(in %)
Weight
Weighted Price Ratio
{W × R}
Rice (kg)
40
42
{\dfrac{42}{40} × 100 = 105}
30
3150
Vegetables (kg)
30
35
{\dfrac{35}{30} × 100 = 116.67}
25
2916.75
Milk (liters)
50
52
{\dfrac{52}{50} × 100 = 104}
20
2080
Eggs (dozen)
60
65
{\dfrac{65}{60} × 100 = 108.33}
15
1624.95
25
28
{\dfrac{28}{25} × 100 = 112}
10
1120
{∑W = 100}
{∑WR = 10891.7}
{\text{CPI for Week 2 }= \dfrac{10891.7}{100} = 108.92}
Analysis Based on CPI:
Increase in Cost of Living: The CPI of 108.92 for Week 2 indicates that the cost of living has increased by approximately 8.92% compared to Week 1.
Budget Impact: The increase in CPI reflects a significant impact on our family budget. Essential items like rice and vegetables, which have higher weights, saw notable price increases, leading to a higher overall expenditure.
Savings Consideration: With the rise in prices, particularly of heavily weighted items like rice and vegetables, our ability to save has been affected, as more income is now allocated to cover these essential expenses.
Adapting to Price Changes: The noticeable increase in CPI has prompted our family to be more mindful of our spending. We are considering alternative shopping strategies, such as seeking discounts or buying less expensive brands, to manage our budget effectively.
This exercise of calculating the CPI with weighted items provided a deeper insight into how specific price changes in essential commodities can significantly impact a family’s overall cost of living and financial planning.
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?
Analysis:
(i) Comment on the Relative Values of the Index Numbers:
Consistent Increase: All three indices show a consistent increase over the years. This indicates rising prices in general, affecting both industrial workers and agricultural labourers.
CPI for Industrial Workers: The CPI for industrial workers shows a significant increase from 313 in 1995-96 to 500 in 2003-04. This suggests a substantial rise in the cost of living for industrial workers over this period.
CPI for Agricultural Labourers: The CPI for agricultural labourers also shows a steady increase, though the rate of increase is slightly lower than that for industrial workers. It moves from 234 in 1995-96 to 331 in 2003-04.
WPI (Wholesale Price Index): The WPI, which measures the price of goods at the wholesale level, also increases but at a different rate compared to the CPIs. It starts at 121.6 in 1995-96 and reaches 175.9 in 2003-04.
(ii) Are They Comparable?
Different Base Years: The indices have different base years (1982 for industrial workers, 1986-87 for agricultural labourers, and 1993-94 for WPI). This makes direct comparison challenging because each index measures price changes relative to its own base year.
Different Focus: Each index measures different aspects of the economy. CPI for industrial workers and agricultural labourers measure the cost of living for specific groups, while WPI measures wholesale price levels.
Comparability for Trends: While direct numerical comparison may not be meaningful due to different base years, these indices can be compared in terms of trends. They all show an upward trend, indicating general inflation in the economy.
Policy Implications: For policy-making, these indices provide valuable insights into how inflation affects different sectors of the economy. Policymakers can use this information to address specific needs of industrial workers, agricultural labourers, and the wholesale market.
In conclusion, while the CPI for industrial workers, CPI for agricultural labourers, and WPI are not directly comparable in terms of their numerical values due to different base years and focus areas, they are comparable in terms of understanding the overall inflationary trends in the economy.
22.
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:
Item
Monthly
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.
The calculation of the average GST rate makes use of the formula for weighted average. In this case, the weights are the shares of expenditure on each category of goods. The total weight is equal to the total expenditure of the family. And the variables are the GST rates.
Category
Expenditure Weight (w)
GST Rate (x)
WX
Category 1
2000
0
0
Category 2
200
0.05
10
Category 3
100
0.12
12
Category 4
200
0.18
36
Category 5
1000
0.28
280
3500
338
The mean GST rate as far as this family is concerned is (338)/ (3500) = 0.966 i.e. 9.66%
To calculate the average GST rate for the family’s expenditure, we use the formula for weighted average. The weights are the expenditures on each category of goods, and the variables are the GST rates.
Data Given:
Item
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
Calculation of Weighted Average GST Rate:
First, we categorize the items based on their GST rates and sum their expenditures:
Category
Items
Total Expenditure
Category 1 (0% GST):
Cereals, Eggs, Fish, Meat
= ₹ 1500 + ₹ 250 + ₹ 250
= ₹ 2000
Category 2 (5% GST):
Medicines, Biogas, Transport
= ₹ 50 + ₹ 50 + ₹ 100
= ₹ 200
Category 3 (12% GST):
Butter, Babool, Tomato Ketchup
= ₹ 50 + ₹ 10 + ₹ 40
= ₹ 100
Category 4 (18% GST):
Biscuits, Cakes, Pastries, Branded Garments
= ₹ 75 + ₹ 25 + ₹ 100
= ₹ 200
Category 5 (28% GST):
Vacuum Cleaner, Car
= ₹ 1000
Now, we calculate the weighted GST for each category:
Category
Expenditure Weight
{(W)}
GST Rate
{(X)}
{WX}
1
2000
0
0
2
200
0.05
10
3
100
0.12
12
4
200
0.18
36
5
1000
0.28
280
Total
3500
338
Mean GST Rate Calculation:
The mean GST rate is calculated as the total weighted GST divided by the total expenditure:
Mean GST Rate
{= \dfrac{338}{3500}}
= 0.0966
≅ 9.66%
Therefore, the average GST rate as far as this family is concerned is approximately 9.66%. This calculation provides an insight into the overall tax burden on the family’s expenditure based on the GST rates applicable to different categories of goods they consume.