Index Numbers - Class 11 Economics - Chapter 7 - Notes, NCERT Solutions & Extra Questions
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Notes - Index Numbers | Class 11 Statistics For Economics | Economics
Comprehensive Notes on Index Numbers for Class 11 Students
Index numbers are a powerful statistical tool used to measure changes over time. This article will provide comprehensive notes on index numbers, particularly beneficial for Class 11 students. We will explore their definition, types, methods of calculation, and practical applications in economics.
Introduction to Index Numbers
Definition and Importance
An index number is a statistical measure that shows changes in a variable or group of related variables over time. These are expressed as percentages and enable easy comparison between different time periods or categories. Index numbers simplify the representation of data, making it easier to comprehend and analyse trends.
Real-life Examples and Applications
- Measuring inflation through Consumer Price Index (CPI).
- Tracking stock market performance via Sensex.
- Assessing changes in industrial production using Index of Industrial Production (IIP).
What is an Index Number?
Statistical Device and Definitions
An index number summarises the relative changes in a group of related variables. It offers a single figure which represents the average change of specified elements over different periods or their comparison across categories, such as prices of commodities or quantities of outputs.
Types of Index Numbers
- Price Index Numbers: Measure changes in the price of a basket of goods and services.
- Quantity Index Numbers: Track changes in the volume of production, construction, or employment.
- Value Index Numbers: Measure changes in the value or monetary worth.
Construction of Index Numbers
Aggregative Method
This method involves summing up the current prices of all items and comparing them with the sum of prices in the base period.
Example Calculation: $$ \text{Simple Aggregative Price Index} = \left( \frac{\sum P1}{\sum P0} \right) \times 100 $$
Weighted Aggregative Method
In this method, weights are assigned to items based on their importance.
Example Calculation: $$ \text{Weighted Aggregative Price Index} = \left( \frac{\sum(P1 \times Q0)}{\sum(P0 \times Q0)} \right) \times 100 $$
Method of Averaging Relatives
This method uses average relatives when multiple items are involved.
Example Calculation: $$ \text{Price Index Number using Price Relatives} = \left( \frac{1}{n} \sum \left( \frac{P1}{P0} \times 100 \right) \right) $$
graph TD
A[Construction of Index Numbers] --> B[Aggregative Method]
A --> C[Weighted Aggregative Method]
A --> D[Method of Averaging Relatives]
Different Types of Index Numbers
Consumer Price Index (CPI)
CPI measures changes in retail prices and is also known as the cost of living index.
Calculation Method and Example: $$ \text{CPI} = \left( \frac{\sum (W \times R)}{\sum W} \right) $$ Where (R) is the price relative and (W) is the weight of each item.
Wholesale Price Index (WPI)
WPI indicates changes in the general price level, primarily excluding services.
Example Calculation: WPI compares prices at the wholesale level, reflecting broader economic price changes.
Index of Industrial Production (IIP)
IIP measures the change in the volume of the industrial sector's production.
Calculation Method and Example: $$ \text{IIP} = \left( \frac{\sum(q_{i1} \times W_i)}{\sum W_i} \right) \times 100 $$ Where (q_{i1}) is the quantity relative for year 1 compared to the base year.
Issues in the Construction of Index Numbers
Selection of Items
Choose items that accurately represent the category being measured.
Choice of Base Period
Select a base year that is normal and recent to avoid skewed results.
Formula Choice
Choosing the correct formula, such as Laspeyre's or Paasche's index, is crucial depending on the study's nature.
graph TD
A[Issues in Index Construction] --> B[Selection of Items]
A --> C[Choice of Base Period]
A --> D[Formula Choice]
A --> E[Source of Data]
Source of Data
Ensure the data used is reliable, whether primary or secondary.
Important Index Numbers in India
- Consumer Price Index Numbers for Industrial Workers
- All-India Consumer Price Index Numbers for Agricultural Labourers
- Wholesale Price Index
- Index of Industrial Production
Applications of Index Numbers in Economics
Inflation Measurement
Index numbers like CPI and WPI help measure inflation by comparing current prices with the base period.
Example Calculation: $$ \text{Inflation Rate} = \left( \frac{Xt - Xt-1}{Xt-1} \right) \times 100 $$
Determining Real Wage and Purchasing Power
Index numbers help in calculating real wage and the purchasing power of money.
Example: $$ \text{Real Wage} = \left( \frac{\text{Money Wage}}{\text{Cost of Living Index}} \right) \times 100 $$
Conclusion
Index numbers provide a simple yet powerful means of understanding changes in economic variables over time. From measuring price changes to production levels, they offer essential insights that aid in policymaking and economic analysis.
Additional Resources
- Textbooks: Class 11 Economics textbooks provide detailed explanations and examples.
- Online Tools: Websites like the Reserve Bank of India offer data and tools for calculating various index numbers.
Understanding and effectively using index numbers can significantly enhance your analytical skills in economics and help you excel in your Class 11 studies.
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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
The index number that accounts for the relative importance of the items is known as a weighted index.
So, the correct option is:
(i) weighted index
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 either the base year or the current year. Specifically:
Laspeyre's Index uses weights from the base year.
Paasche's Index uses weights from the current year.
Thus, the correct answers are:
(i) base year and (ii) current year.
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
This is because a commodity with little weight has less influence on the overall index number.
A consumer price index measures changes in
(i) retail prices
(ii) wholesale prices
(iii) producers prices
A consumer price index (CPI) measures changes in retail prices.
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 Food.
You can see this from the given weights:
Food and beverages: 45.86%
Housing: 10.07%
Clothing & footwear: 6.53%
Given these weights, it is clear that Food occupies the largest proportion.
In general, inflation is calculated by using
(i) wholesale price index
(ii) consumer price index
(iii) producers' price index
Inflation can be calculated using several different indices, depending on what aspect of the economy is being measured. The most commonly used indices for calculating inflation are:
Wholesale Price Index (WPI)
Consumer Price Index (CPI)
Producers' Price Index (PPI)
Let's briefly examine each one:
1. Wholesale Price Index (WPI)
The WPI measures the changes in the price of goods sold and traded in bulk by wholesalers. It does not include services and may exclude some retail-level items. The WPI is used to determine the inflation at the level of producers or wholesalers.
2. Consumer Price Index (CPI)
The CPI measures the average change in retail prices of a basket of goods and services consumed by households. It represents the cost of living and is often used as the main indicator of inflation for consumers. Different countries calculate CPI based on different baskets of goods and services that reflect the consumption patterns of their population.
3. Producers' Price Index (PPI)
The PPI measures the average change in prices received by domestic producers for their output. Unlike the CPI, the PPI measures price changes from the perspective of the producer rather than the consumer. It includes prices of items at various stages of production.
How These Indices Are Used to Calculate Inflation
WPI: Provides a measure of price changes at the wholesale level.
CPI: Indicates the cost of living by measuring price changes at the retail level.
PPI: Shows changes in the price that producers receive for their goods, indicating early inflationary trends.
Calculation Formulas
Wholesale Price Index (WPI)
The inflation rate based on WPI can be calculated as:
$$ \text{Inflation Rate} = \frac{\text{WPI}{\text{current period}} - \text{WPI}{\text{base period}}}{\text{WPI}_{\text{base period}}} \times 100 $$
Consumer Price Index (CPI)
The CPI inflation rate can be calculated similarly:
$$ \text{Inflation Rate} = \frac{\text{CPI}{\text{current period}} - \text{CPI}{\text{base period}}}{\text{CPI}_{\text{base period}}} \times 100 $$
Producers' Price Index (PPI)
The PPI inflation rate follows the same basic calculation as WPI and CPI:
$$ \text{Inflation Rate} = \frac{\text{PPI}{\text{current period}} - \text{PPI}{\text{base period}}}{\text{PPI}_{\text{base period}}} \times 100 $$
In summary, each of these indices provides a unique perspective on inflation, and they can be used together to get a comprehensive understanding of inflationary trends in the economy.
Why do we need an index number?
Index numbers are crucial statistical tools that help measure and summarize changes in complex data sets over different time periods. They simplify complex data patterns into single, understandable figures, facilitating comparisons over time or between different sectors or regions. For example, index numbers like the Consumer Price Index (CPI) or the Wholesale Price Index (WPI) are pivotal in tracking inflation, vital for economic policy and decision-making. Additionally, they enable understanding trends in sectors like manufacturing with the Industrial Production Index, helping businesses and policymakers gauge economic health and inform strategies.
What are the desirable properties of the base period?
The desirable properties of the base period are:
Normalcy: The base period should be as normal as possible, meaning it should be free from any extreme values or events (like wars, natural disasters, economic crises) that could distort the average conditions.
Recency: The base period should not be too far in the past because the consumption patterns and economic conditions of an old base year may not accurately reflect current conditions.
Representativeness: The base period should be typical and representative of the conditions you are measuring, ensuring that comparisons are meaningful.
Stability: The period should not show any abnormal fluctuations that would make it unfit for comparison with other periods.
These properties help ensure that the index number provides a meaningful and accurate picture of the change being measured.
Why is it essential to have different CPI for different categories of consumers?
Different categories of consumers have distinct spending patterns and priorities, making it crucial to have separate Consumer Price Indexes (CPIs). For instance, agricultural laborers, industrial workers, and service employees might allocate their budgets differently across food, housing, healthcare, etc. Creating specific CPIs ensures that they accurately reflect the real inflation each group experiences based on their typical expenditures. This targeted approach helps in formulating more effective wage policies and social security measures, as well as in safeguarding the purchasing power of diverse demographic groups, thereby addressing economic disparities more efficiently.
What does a consumer price index for industrial workers measure?
A Consumer Price Index (CPI) for industrial workers measures the average change in retail prices of goods and services consumed by industrial workers.
For instance, consider the statement that the CPI for industrial workers with base year set to 2001 (=100) is 277 in December 2014. This means that if an industrial worker spent ₹100 in 2001 to buy a typical basket of goods and services, they would need ₹277 in December 2014 to purchase an identical basket.
Thus, the CPI reflects the relative cost of maintaining a certain standard of living over time by monitoring the changes in prices of a representative basket of goods and services that industrial workers typically buy.
What is the difference between a price index and a quantity index?
A price index and a quantity index are both types of index numbers but they measure different changes in data related to economic variables. Here’s a breakdown of their differences:
Price Index:
Purpose: Measures and permits comparison of the prices of certain goods.
Usage: Common examples include the Consumer Price Index (CPI) and the Wholesale Price Index (WPI).
Construction: Often takes the ratio of the price of a group of goods in the current period to the price in a base period and expresses it as a percentage.
Interpretation: An increase in the price index indicates a rise in the price level of the selected group of goods, suggesting inflation if it persists for a period.
Quantity Index:
Purpose: Measures the changes in the physical volume of production, construction, or employment.
Usage: Commonly used to assess the output in different sectors, such as the Index of Industrial Production (IIP).
Construction: Takes the ratio of the quantity of goods produced in the current period to the quantity produced in a base period, expressed as a percentage.
Interpretation: An increase in the quantity index signifies an increase in output or physical quantity.
Example Explanation:
Price Index: If the CPI for a particular year is 150, it means that the consumer prices have increased by 50% compared to the base year. This helps in understanding inflation and the rising cost of living.
Quantity Index: If the IIP shows an index of 120, it indicates that the industrial production has increased by 20% compared to the base year. This helps in understanding the growth in production capacity.
Is the change in any price reflected in a price index number?
Not necessarily. The change in any single price is not directly reflected in a price index number. A price index number, such as the Consumer Price Index (CPI) or Wholesale Price Index (WPI), represents the average change in prices of a group of commodities over time.
To give a clearer picture:
A price index number measures the general trend of price changes for a basket of selected items rather than individual items.
The importance or weight given to each item in the basket affects its influence on the overall index. For example, a large rise in the price of an important commodity like food will have more impact on the index compared to a rise in the price of a less significant good.
Therefore, it’s crucial to look at the weight and significance of the item in the basket to determine its impact on the price index number.
Can the CPI for urban non-manual employees represent the changes in the cost of living of the President of India?
No, the CPI for urban non-manual employees (CPI-UNME) cannot accurately represent the changes in the cost of living for the President of India. The CPI-UNME is designed to track changes in the cost of living for a specific group of urban workers and includes items and weights that reflect their consumption patterns.
The President of India likely has a very different consumption pattern:
Expenditure categories (types of goods and services consumed) will differ significantly.
The budget allocation and spending priorities may be quite distinct.
Thus, it is important to use an index that properly reflects the consumption basket specific to the President for a more accurate measurement of changes in their cost of living.
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 prepare the weighted index number for cost of living for 2005 with 1980 as the base year, we use the weighted formula:
$$ \mathrm{CPI} = \frac{\Sigma W_i \left(\frac{P_{1i}}{P_{0i}} \times 100\right)}{\Sigma W_i} $$
Given the prices and weights:
Item | 1980 Price ( P_0 ) | 2005 Price ( P_1 ) | Weight ( W ) |
---|---|---|---|
Food | 100 | 200 | 75 |
Clothing | 20 | 25 | 10 |
Fuel & Lighting | 15 | 20 | 5 |
House Rent | 30 | 40 | 6 |
Misc | 35 | 65 | 4 |
We plug these into the formula:
$$ \mathrm{CPI} = \frac{75 \left(\frac{200}{100}\right) + 10 \left(\frac{25}{20}\right) + 5 \left(\frac{20}{15}\right) + 6 \left(\frac{40}{30}\right) + 4 \left(\frac{65}{35}\right)}{75 + 10 + 5 + 6 + 4} $$
This calculates to:
$$ \mathrm{CPI} = \frac{75 \times 2 + 10 \times 1.25 + 5 \times 1.33 + 6 \times 1.33 + 4 \times 1.86}{100} = 184.6 $$
This means that the cost of living has increased by 84.6% from 1980 to 2005.
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 | 10.73 | 118.2 | 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 |
Comments on the Index of Industrial Production (Base Year: 1993-94)
The table provided shows the Index of Industrial Production (IIP) for different sectors between the years 1996-97 and 2003-2004 with the base year set to 1993-94 (IIP base year = 100). Here's a detailed analysis of the data for each sector:
Industry | Weight in % | 1996-97 | 2003-2004 |
---|---|---|---|
General index | 10.73 | 118.2 | 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 |
General Index:
1996-97: The General Index was 118.2.
2003-04: The General Index rose to 189.0.
This indicates an overall increase of approximately 59.9% from 1996-97 to 2003-04.
Mining and Quarrying:
1996-97: The index was 118.2.
2003-04: The index grew to 146.9.
This sector experienced an increase of about 24.3% over the period.
Manufacturing:
1996-97: The index stood at 133.6.
2003-04: The index escalated to 196.6.
This marks a significant growth of approximately 47.1% in the manufacturing sector.
Electricity:
1996-97: The index was 122.0.
2003-04: The index increased to 172.6.
This denotes an increase of about 41.5% in the electricity sector.
Summary Observations:
Overall Growth: There has been substantial growth across all sectors from 1996-1997 to 2003-2004.
Manufacturing Sector Dominance: The manufacturing sector, which carries the most significant weight (79.58%), showed a notable increase, implying that it might have been the primary driver of the overall growth in industrial production during this period.
Electricity Sector: This sector, although having a smaller weight compared to manufacturing, showed robust growth.
Mining and Quarrying: This sector exhibited the lowest growth rate among all sectors listed, which indicates slower relative progress.
The Industrial Production has generally improved significantly over the assessed period, with the manufacturing sector leading in growth, which is essential for the overall industrialization and economic progress of the country.
Try to list the important items of consumption in your family.
Sure! Here is a list of some essential items of consumption typically used by a family:
Category | Item |
---|---|
Food and Beverages | Groceries (e.g., rice, wheat, oil) |
Fruits and vegetables | |
Milk and dairy products | |
Meat, fish, and poultry | |
Snacks and beverages | |
Housing | Rent or mortgage payments |
Utilities | Electricity and water bills |
Gas | |
Transportation | Fuel |
Public transport fare | |
Vehicle maintenance | |
Clothing | Everyday wear |
Shoes | |
Healthcare | Medicines |
Doctor visits | |
Education | School/college fees |
Books and stationery | |
Miscellaneous | Internet services |
Mobile phone charges | |
Entertainment (e.g., movies, dining out) |
These items can vary between families depending on their lifestyle, income level, and specific needs.
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 ?
The adjusted salary needed to maintain the same standard of living, given a CPI of 400, is Rs 24,000 per annum.
Summary:
Base Year Salary: Rs 4,000
Current Year Salary: Rs 6,000
CPI: 400
Adjusted Salary to maintain the same standard of living: Rs 24,000
So, his salary should be raised to Rs 24,000.
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?
The weight given to food $(W_f)$ is $\frac{200}{3} $, approximately:
$$ W_f = \frac{200}{3} \approx 66.67 $$
Thus, the percentage of the total weight given to food is approximately 66.67%.
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 15% | Rent 20% | Misc 20% |
Price (in Rs) in 2004 | 1500 | 250 | 750 | 300 | 400 |
Price (in Rs) in 1995 | 1400 | 200 | 500 | 200 | 250 |
The weighted products are calculated as follows:
Item | Weight (%) ( W ) | Price Relative ( R ) (in %) | ( W ) × ( R ) |
---|---|---|---|
Food | 35 | 107.14 | 3749.9 |
Fuel | 10 | 125 | 1250 |
Clothing | 15 | 150 | 2250 |
Rent | 20 | 150 | 3000 |
Misc | 20 | 160 | 3200 |
Now, sum the weighted products and the total weights.
$$ \Sigma (W \times R) = 3749.9 + 1250 + 2250 + 3000 + 3200 = 13449.9 $$
$$ \Sigma W = 35 + 10 + 15 + 20 + 20 = 100 $$
Finally, calculate the overall CPI:
$$ \mathrm{CPI} = \frac{\Sigma (W \times R)}{\Sigma W} = \frac{13449.9}{100} = 134.499 $$
So, the Consumer Price Index (CPI) is 134.499, indicating that the cost of living has increased by 34.499% compared to the base year 1995.
What is the cost of living index during the year 2004 as compared with 1995 ?
It appears that specific data on the cost of living index for India in 2004 and 1995 is not directly available.
However, from the given material, you can calculate the cost of living index if you have the necessary data. The Consumer Price Index (CPI) is typically used for this purpose. The formula for calculating the CPI is:
$$ \text{CPI} = \frac{\Sigma (W \cdot R)}{\Sigma W} $$
where (W) is the weight of a particular item and (R) is the price relative.
Given the available data for the years you are interested in, you could use this formula to calculate the required cost of living index.
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?
To analyze how the price change has affected your family, we'll need to record and process the data related to daily expenditures, quantities bought, and prices paid per unit for each item over two weeks. Here’s a step-by-step approach to achieve this:
Step 1: Record Daily Data
Create a table to record the daily data as follows:
Table: Daily Expenditure and Prices
Date | Commodity | Quantity Bought (units) | Price per Unit (Rs) | Total Expenditure (Rs) |
---|---|---|---|---|
DD/MM/YYYY | Item A | Q1 | P1 | E1 |
Item B | Q2 | P2 | E2 | |
... | ... | ... | ... | ... |
Total | Sum(E1...En) |
Step 2: Calculate Total Expenditure for Each Day
For every day, sum up the total expenditure for all items recorded.
Step 3: Compile Data for Two Weeks
Aggregate the data for two weeks to see the total quantity bought, average price per unit, and total expenditure over these two weeks.
Table: Weekly Summary
Week | Total Quantity Bought (units) | Average Price per Unit (Rs) | Total Expenditure (Rs) |
---|---|---|---|
Week 1 | Sum(Q1...Qn) | Avg(P1...Pn) | Sum(E1...En) |
Week 2 | Sum(Q1...Qn) | Avg(P1...Pn) | Sum(E1...En) |
Step 4: Calculate Price Index
To see how the prices have changed over these two weeks, you can compute a price index using the formula for a simple aggregative price index for each week:
$$ \text{Price Index} = \frac{\sum \text{(Price of commodities in current week)}}{\sum \text{(Price of commodities in base week)}} \times 100 $$
Assume the first week as the base week:
( \text{P}_{0} ) = Sum of average prices per unit in Week 1.
( \text{P}_{1} ) = Sum of average prices per unit in Week 2.
$$ \mathrm{P}{01} = \frac{\sum P{1}}{\sum P_{0}} \times 100 $$
Step 5: Analysis and Impact
Based on the price index calculated:
If $ P_{01} > 100$, prices have risen in Week 2 compared to Week 1.
If $ P_{01} < 100 $, prices have decreased in Week 2 compared to Week 1.
Example of Calculation
Consider you have summarized the data as:
Week 1:
Total quantity bought: 150 units
Average price per unit: Rs 10
Total expenditure: Rs 1500
Week 2:
Total quantity bought: 160 units
Average price per unit: Rs 12
Total expenditure: Rs 1920
Price Index:
$$ \mathrm{P}_{01} = \left(\frac{12}{10} \right) \times 100 = 120 $$
This price index of 120 indicates that prices have risen by 20% from Week 1 to Week 2.
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 | 161.4 |
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?
(i) Comment on the Relative Values of the Index Numbers
The given table presents three different index numbers over several years: CPI of industrial workers $(1982=100)$, CPI of agricultural laborers $(1986-87=100)$, and WPI $(1993-94=100)$.
CPI for Industrial Workers:
Starting at 313 in 1995-96 and increasing to 500 by 2003-04.
This index increases steadily, indicating that the cost of living for industrial workers was rising consistently during this period.
CPI for Agricultural Labourers:
Starting at 234 in 1995-96 and increasing to 331 by 2003-04.
This index also shows a steady increase, indicating rising costs for agricultural laborers, although at a relatively slower pace compared to industrial workers.
WPI (Wholesale Price Index):
Starting at 121.6 in 1995-96 and increasing to 175.9 by 2003-04.
The WPI reflects a general rise in the wholesale prices of goods over these years.
(ii) Are They Comparable?
Index Numbers' Comparability:
Base Years:
The CPI for Industrial Workers uses 1982 as its base year.
The CPI for Agricultural Labourers uses 1986-87 as its base year.
The WPI uses 1993-94 as its base year.
Because these indices use different base years, they are not directly comparable. The indices reflect changes relative to their specific base years, making it difficult to compare the absolute values directly without adjustment.
Purpose and Scope:
CPI for Industrial Workers reflects changes relevant to industrial workers, primarily in urban settings.
CPI for Agricultural Labourers reflects changes relevant to agricultural laborers, mainly in rural settings.
WPI indicates changes in the general price level of wholesale goods, without specific reference to consumer categories.
The scope and intended purpose of these indices are also different, further complicating direct comparison.
Normalization for Comparison:To make these indices comparable, you might need to normalize them to a common base year or express them as percentages of their respective base years. This way, any comparison would provide insight into relative changes from a common point of reference.
In summary, while these indices provide valuable information about price changes over time, they are not directly comparable due to differences in base years and targeted populations. Adjustments or normalizations would be needed for a meaningful comparison.
The monthly expenditure (Rs.) of a family on some important items and the Goods and Services Tax (GST) rates applicable to these items is as follows:
item | Monthly Expense(Rs) | GST Rate $\%$ |
---|---|---|
Cereals | 1500 | 0 |
Eggs | 250 | 0 |
Fish, Meat | 250 | - |
Medicines | 50 | 5 |
Biogas | 50 | 5 |
Transport | 100 | 5 |
Butter | 50 | 12 |
Babool | 10 | 12 |
Tomato Ketchup | 40 | 12 |
Biscuit | 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 average tax rate for the family can be calculated as follows:
Using the formula:
$$ \text{Average Tax Rate} = \frac{\text{Total GST Paid}}{\text{Total Expenditure}} \times 100 $$
From the given data,
Total GST Paid = (250 \times 0.05 + 50 \times 0.05 + 100 \times 0.05 + 50 \times 0.12 + 10 \times 0.12 + 40 \times 0.12 + 75 \times 0.18 + 25 \times 0.18 + 100 \times 0.18 + 1000 \times 0.28)
Total Expenditure = (1500 + 250 + 250 + 50 + 50 + 100 + 50 + 10 + 40 + 75 + 25 + 100 + 1000)
After performing the above calculation, we get:
$$ \text{Average Tax Rate} = 0.09405 \times 100 = 9.405% $$
Thus, the average tax rate for the family is approximately 9.405%.
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