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Index Numbers – CBSE NCERT Study Resources

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11th

11th - Economics

Index Numbers

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Overview of the Chapter

This chapter introduces the concept of Index Numbers, which are statistical measures designed to show changes in a variable or a group of related variables over time or space. Index Numbers are widely used in economics to compare economic variables such as price levels, production, and employment.

Index Number: An index number is a statistical measure that expresses the relative change in price, quantity, or value compared to a base period.

Types of Index Numbers

Index Numbers can be classified into the following types:

  • Price Index: Measures changes in the price level of goods and services.
  • Quantity Index: Measures changes in the volume of goods produced or consumed.
  • Value Index: Measures changes in the total monetary value of production or consumption.

Construction of Index Numbers

The construction of Index Numbers involves the following steps:

  1. Selection of the base year.
  2. Selection of commodities or items.
  3. Collection of price or quantity data.
  4. Calculation of price relatives or quantity relatives.
  5. Assigning appropriate weights to items.
  6. Aggregating the data to compute the index.

Base Year: The year against which comparisons are made. It is assigned an index value of 100.

Methods of Constructing Index Numbers

There are two main methods for constructing Index Numbers:

  • Simple Index Numbers: Uses an unweighted average of price or quantity relatives.
  • Weighted Index Numbers: Assigns weights to items based on their importance. Common methods include Laspeyres, Paasche, and Fisher's Ideal Index.

Uses of Index Numbers

Index Numbers are used for various purposes, including:

  • Measuring inflation or deflation.
  • Adjusting wages and salaries for cost of living.
  • Comparing economic conditions across regions or time periods.
  • Formulating government policies.

Limitations of Index Numbers

Despite their usefulness, Index Numbers have certain limitations:

  • Selection of an appropriate base year can be challenging.
  • Changes in quality of goods are not always reflected.
  • They may not represent all sections of society accurately.

All Question Types with Solutions – CBSE Exam Pattern

Explore a complete set of CBSE-style questions with detailed solutions, categorized by marks and question types. Ideal for exam preparation, revision and practice.

Very Short Answer (1 Mark) – with Solutions (CBSE Pattern)

These are 1-mark questions requiring direct, concise answers. Ideal for quick recall and concept clarity.

Question 1:
Define Index Numbers.
Answer:

Index numbers measure relative changes in economic variables over time.

Question 2:
What is the base year in index numbers?
Answer:

The reference year against which changes are calculated.

Question 3:
Name two types of index numbers.
Answer:
  • Price Index
  • Quantity Index
Question 4:
Give one use of Wholesale Price Index (WPI).
Answer:

Measures inflation at the wholesale level.

Question 5:
What is the formula for Laspeyres Price Index?
Answer:

(ΣP₁Q₀ / ΣP₀Q₀) × 100

Question 6:
Differentiate between simple and weighted index numbers.
Answer:

Simple ignores item importance, weighted considers it.

Question 7:
Why is Fisher's Ideal Index called 'ideal'?
Answer:

It combines Laspeyres and Paasche indices for accuracy.

Question 8:
What is the limitation of index numbers?
Answer:

They may not reflect qualitative changes.

Question 9:
Calculate index number if current price is ₹120 and base price is ₹100.
Answer:

(120/100) × 100 = 120

Question 10:
How does WPI differ from CPI?
Answer:

WPI tracks wholesale prices, CPI tracks retail prices.

Question 11:
What is chain base method in index numbers?
Answer:

Comparing each year to the previous year.

Question 12:
Give an example of quantity index.
Answer:

Index of industrial production (IIP).

Question 13:
What is the purpose of deflating a series?
Answer:

To remove inflation effects from data.

Question 14:
Define Index Numbers in economics.
Answer:

An Index Number is a statistical measure designed to show changes in a variable or a group of related variables over time, geographical locations, or other criteria. It simplifies complex data into a single value for easy comparison.

Question 15:
What is the base year in the context of index numbers?
Answer:

The base year is a reference year against which changes in the index are measured. It is assigned an index value of 100, and all future or past values are compared to this benchmark.

Question 16:
Name the two main types of Index Numbers.
Answer:

The two main types are:
1. Price Index (measures changes in price levels)
2. Quantity Index (measures changes in quantity produced or consumed).

Question 17:
What is the purpose of using weights in index numbers?
Answer:

Weights are used to assign importance to different items in the index. They ensure that more significant items have a greater impact on the index value, reflecting their real-world relevance.

Question 18:
Give the formula for Laspeyres Price Index.
Answer:

The formula is:
Laspeyres Price Index = (Σ(P₁ × Q₀) / (Σ(P₀ × Q₀)) × 100
where P₁ is current year price, P₀ is base year price, and Q₀ is base year quantity.

Question 19:
What does a Consumer Price Index (CPI) of 120 indicate?
Answer:

A CPI of 120 means that the general price level has increased by 20% compared to the base year. It reflects inflation or the rising cost of living.

Question 20:
Why is the Fisher's Ideal Index called 'ideal'?
Answer:

Fisher's Ideal Index is called 'ideal' because it combines Laspeyres and Paasche indices, eliminating their biases. It satisfies both time reversal and factor reversal tests.

Question 21:
What is the time reversal test in index numbers?
Answer:

The time reversal test checks if an index number reverses correctly when the base and current years are swapped. Mathematically, Index₁₂ × Index₂₁ = 1.

Question 22:
How is the Wholesale Price Index (WPI) different from the Consumer Price Index (CPI)?
Answer:

WPI tracks price changes at the wholesale level (goods traded between businesses), while CPI measures retail price changes affecting consumers directly.

Question 23:
What is the chain base method in index numbers?
Answer:

The chain base method updates the base year periodically, linking each new index to the previous one. This ensures the index remains relevant over long periods.

Question 24:
Calculate the simple aggregative price index if ΣP₁ = 450 and ΣP₀ = 400.
Answer:

Simple Aggregative Price Index = (ΣP₁ / ΣP₀) × 100
= (450 / 400) × 100
= 112.5

Question 25:
What is the commodity substitution bias in index numbers?
Answer:

Commodity substitution bias occurs when consumers switch to cheaper alternatives due to price rises, but the index (like Laspeyres) fails to account for this, overestimating inflation.

Question 26:
Define Index Number in Economics.
Answer:

An Index Number is a statistical measure that shows changes in a variable or a group of related variables over time, relative to a base period. It helps in comparing economic data like prices, production, or employment.

Question 27:
Give one limitation of using Index Numbers.
Answer:

Index Numbers may not account for quality changes in goods/services over time, leading to inaccurate comparisons.

Question 28:
Differentiate between Wholesale Price Index (WPI) and Consumer Price Index (CPI).
Answer:

WPI tracks price changes at the wholesale level (bulk transactions), while CPI measures retail price changes affecting consumers directly.

Question 29:
How is the Paasche Price Index calculated?
Answer:

The formula is:
Index = (ΣP₁Q₁ / ΣP₀Q₁) × 100
where Q₁ = current year quantities. It uses current-year weights.

Question 30:
What role do Index Numbers play in policymaking?
Answer:

They help governments and businesses analyze inflation, adjust wages/pensions, and formulate economic policies based on price/quantity trends.

Very Short Answer (2 Marks) – with Solutions (CBSE Pattern)

These 2-mark questions test key concepts in a brief format. Answers are expected to be accurate and slightly descriptive.

Question 1:
What is the purpose of using a base year in index numbers?
Answer:

The base year serves as a reference point for comparison. It is assigned an index value of 100, and all future or past values are measured relative to it, making trends easier to analyze.

Question 2:
Differentiate between simple index number and weighted index number.
Answer:

Simple Index Number gives equal importance to all items, while Weighted Index Number assigns different weights based on their significance. For example, in price indices, essential goods may have higher weights.

Question 3:
Name any two commonly used price indices in India.
Answer:

Two widely used price indices in India are:
1. Consumer Price Index (CPI)
2. Wholesale Price Index (WPI)

Question 4:
Why is the Laspeyres Index considered a weighted index?
Answer:

The Laspeyres Index uses base-year quantities as weights, giving importance to items based on their consumption in the base period. This makes it a weighted index.

Question 5:
Calculate the simple price index for 2026 if the current year price is ₹120 and the base year price is ₹100.
Answer:

Formula: Simple Price Index = (Current Year Price / Base Year Price) × 100

Calculation:
= (120 / 100) × 100
= 120

Question 6:
What does a Consumer Price Index (CPI) of 115 indicate?
Answer:

A CPI of 115 means that the general price level has increased by 15% compared to the base year (100). It reflects inflation or rising living costs.

Question 7:
Explain the term chain base index.
Answer:

A chain base index updates the base year periodically (e.g., annually) to reflect recent trends more accurately, unlike fixed-base indices that use a single base year.

Question 8:
List two limitations of index numbers.
Answer:

1. Quality changes are ignored—index numbers may not account for improvements in product quality.
2. Selection bias—the choice of items or weights can skew results.

Question 9:
How is the Paasche Index different from the Laspeyres Index?
Answer:

The Paasche Index uses current-year quantities as weights, while the Laspeyres Index uses base-year quantities. Paasche reflects current consumption patterns better.

Question 10:
Give an example of how index numbers are used in policymaking.
Answer:

Governments use CPI to adjust wages, pensions, or tax brackets to account for inflation, ensuring fair economic adjustments.

Short Answer (3 Marks) – with Solutions (CBSE Pattern)

These 3-mark questions require brief explanations and help assess understanding and application of concepts.

Question 1:
Explain the steps involved in constructing a Consumer Price Index (CPI).
Answer:

Steps:
1. Selection of base year: Choose a representative year for comparison.
2. Identification of commodities: Include essential goods/services consumed by a specific group.
3. Collection of price data: Gather prices of selected items for base and current years.
4. Assigning weights: Allocate importance to each item based on expenditure patterns.
5. Calculation: Use the formula: CPI = (Σ(P₁ × Q₀) / Σ(P₀ × Q₀)) × 100, where P₁ = current price, P₀ = base price, Q₀ = base quantity.

Question 2:
Why is the Fisher's Ideal Index considered a better measure than other indices?
Answer:

Fisher's Ideal Index is the geometric mean of Laspeyre's and Paasche's indices, addressing their individual biases.
Advantages:

  • It satisfies the time reversal and factor reversal tests, ensuring consistency.
  • Minimizes overestimation (Laspeyre's) and underestimation (Paasche's) by averaging both.
  • Provides a more balanced representation of price changes.
Example: If Laspeyre's = 120 and Paasche's = 110, Fisher's = √(120 × 110) ≈ 114.89.

Question 3:
Describe the limitations of using Index Numbers in economic analysis.
Answer:

Limitations:

  • Base-year dependency: Results may vary if the base year is outdated or unrepresentative.
  • Quality changes ignored: Does not account for improvements/deterioration in product quality.
  • Limited scope: May exclude informal sector data, leading to incomplete analysis.
  • Weighting issues: Fixed weights (e.g., in Laspeyre's) may not reflect current consumption patterns.

Despite these, index numbers remain vital for trend analysis.

Question 4:
Calculate the Simple Aggregative Price Index for 2025 using the following data (Base year: 2020):
Item A: ₹50 (2020), ₹60 (2025)
Item B: ₹30 (2020), ₹45 (2025)
Item C: ₹20 (2020), ₹25 (2025)
Answer:

Formula: Simple Aggregative Index = (ΣP₁ / ΣP₀) × 100
Steps:
1. Sum of base-year prices (ΣP₀) = 50 + 30 + 20 = ₹100.
2. Sum of current-year prices (ΣP₁) = 60 + 45 + 25 = ₹130.
3. Index = (130 / 100) × 100 = 130.
Interpretation: Prices increased by 30% in 2025 compared to 2020.

Question 5:
Define Index Numbers and explain their significance in economics.
Answer:

An Index Number is a statistical measure designed to show changes in a variable or a group of related variables over time or space. It is expressed as a percentage relative to a base period.

Significance:

  • Helps in measuring inflation or deflation through price indices like CPI or WPI.
  • Used for comparative analysis of economic data across different time periods or regions.
  • Assists policymakers in formulating economic policies based on trends.

Question 6:
Differentiate between Laspeyre's and Paasche's Price Index with suitable examples.
Answer:

Laspeyre's Price Index uses base-year quantities as weights, making it suitable for analyzing price changes with fixed consumption patterns.
Example: Calculating inflation for a fixed basket of goods in 2020 using 2015 quantities.

Paasche's Price Index uses current-year quantities as weights, reflecting changes in consumption patterns.
Example: Measuring price changes in 2025 using quantities consumed in 2025.

Key difference: Laspeyre's tends to overstate inflation, while Paasche's understates it due to weight differences.

Question 7:
Differentiate between Simple Index Number and Weighted Index Number with examples.
Answer:

Simple Index Number assigns equal importance to all items in the index. For example, calculating the price index of three commodities (A, B, C) by averaging their price changes without considering their relative importance.

Weighted Index Number assigns different weights to items based on their significance. For example, in the Consumer Price Index (CPI), food items may have higher weights than luxury goods because they occupy a larger share of household expenses.

Key differences:

  • Simple index treats all items equally, while weighted index considers their importance.
  • Weighted index is more accurate for economic analysis.

Question 8:
Explain the Laspeyres Price Index formula and its application.
Answer:

The Laspeyres Price Index measures price changes using base-period quantities as weights. Its formula is:

Laspeyres Index = (Σ(P₁ × Q₀) / (Σ(P₀ × Q₀)) × 100
Where:
P₁ = Current year prices
P₀ = Base year prices
Q₀ = Base year quantities

Application:

  • It is widely used to calculate inflation by comparing current prices with base-year prices.
  • Useful for assessing cost of living adjustments.
  • Assumes consumption patterns remain constant (a limitation).

Question 9:
What are the limitations of using Index Numbers in economic analysis?
Answer:

Limitations of Index Numbers include:

  • Base year bias: Choosing an unrepresentative base year can distort comparisons.
  • Quality changes: Index numbers may not account for improvements or deteriorations in product quality.
  • Limited scope: They may exclude important variables, leading to incomplete analysis.
  • Weighting issues: Incorrect weights can misrepresent economic realities.
  • Homogeneity assumption: They assume uniform behavior across items, which may not hold true.

Despite these, they remain essential tools for economic measurement.

Question 10:
Describe the steps involved in constructing a Consumer Price Index (CPI).
Answer:

Steps to construct Consumer Price Index (CPI):
1. Select the base year: A representative year for comparison.
2. Identify the basket of goods and services: Includes items typically consumed by households.
3. Assign weights: Based on expenditure patterns (e.g., food gets higher weight).
4. Collect price data: Track current prices of items in the basket.
5. Calculate the index: Use the formula:
CPI = (Σ(P₁ × Q₀) / Σ(P₀ × Q₀)) × 100
6. Review periodically: Update basket and weights to reflect changing consumption habits.

Question 11:
How does the Paasche Price Index differ from the Laspeyres Price Index?
Answer:

The Paasche Price Index uses current-year quantities as weights, while the Laspeyres Price Index uses base-year quantities. The Paasche formula is:
Paasche Index = (Σ(P₁ × Q₁) / Σ(P₀ × Q₁)) × 100

Key differences:

  • Laspeyres is easier to compute as base-year quantities are fixed.
  • Paasche reflects current consumption patterns but requires frequent updates.
  • Laspeyres tends to overstate inflation, while Paasche understates it.

Economists often use a combination of both for balanced analysis.

Long Answer (5 Marks) – with Solutions (CBSE Pattern)

These 5-mark questions are descriptive and require detailed, structured answers with proper explanation and examples.

Question 1:
Explain the Laspeyres Price Index with its formula. Discuss its advantages and limitations in measuring inflation.
Answer:
Theoretical Framework

The Laspeyres Price Index measures price changes using a fixed basket of goods from the base year. Its formula is: LPI = (ΣP₁Q₀ / ΣP₀Q₀) × 100, where P₁ and P₀ are current and base year prices, and Q₀ is base year quantity.


Evidence Analysis
  • Advantage: Reflects consumption patterns of the base year, useful for historical comparisons.
  • Limitation: Overestimates inflation by ignoring substitution effects (e.g., consumers switch to cheaper alternatives).

Critical Evaluation

Our textbook shows it’s widely used in India’s WPI, but fails to account for new products. For example, smartphones weren’t included in 2004-05 base year.

Question 2:
Compare Paasche’s Index and Fisher’s Ideal Index. Which is more reliable for policymaking and why?
Answer:
Theoretical Framework

Paasche’s Index uses current year quantities (PI = (ΣP₁Q₁ / ΣP₀Q₁) × 100), while Fisher’s Ideal Index is the geometric mean of Laspeyres and Paasche.


Evidence Analysis
IndexAdvantageLimitation
PaascheReflects current consumptionUnderestimates inflation
FisherBalances both biasesComplex calculations

Critical Evaluation

Fisher’s Index is more reliable as it eliminates formula bias. For example, India’s CPI now uses it for accurate inflation tracking.

Question 3:
Analyze how chain-based index numbers overcome the limitations of fixed-base methods. Provide two examples.
Answer:
Theoretical Framework

Chain-based indices update the basket annually, unlike fixed-base methods. They use overlapping data to maintain continuity.


Evidence Analysis
  • Example 1: US CPI shifted to chain-based in 2002 to include tech products like streaming services.
  • Example 2: India’s IIP now uses 2011-12 as a flexible base to capture industrial changes.

Critical Evaluation

We studied that this method reduces substitution bias. However, frequent updates may cause comparability issues over long periods.

Question 4:
Why is the Consumer Price Index (CPI) considered a better measure of inflation than the Wholesale Price Index (WPI)? Support with data.
Answer:
Theoretical Framework

CPI reflects retail price changes affecting households, while WPI tracks wholesale market trends.


Evidence Analysis
IndexCoverage2023 Inflation Rate (India)
CPIFood, housing, services5.7%
WPIRaw materials only-0.5%

Critical Evaluation

CPI is superior as it includes services (e.g., healthcare), which constitute 60% of household budgets per our textbook.

Question 5:
Critically evaluate the use of index numbers in economic planning. How do they assist in GDP calculation?
Answer:
Theoretical Framework

Index numbers simplify complex data into trends, aiding comparisons like real GDP growth by adjusting for inflation.


Evidence Analysis
  • Role 1: Deflators (e.g., GDP deflator) convert nominal GDP to real GDP.
  • Role 2: Help compare sectoral growth (e.g., IIP for manufacturing).

Critical Evaluation

While useful, our textbook highlights limitations—base year revisions (e.g., India’s 2011-12 shift) disrupt time-series consistency.

Question 6:
Compare Paasche’s Index and Fisher’s Ideal Index using a table. Which is more suitable for dynamic economies? Justify.
Answer:
Theoretical Framework

Paasche’s Index uses current-year quantities, while Fisher’s Ideal Index is the geometric mean of Laspeyres and Paasche.


Evidence Analysis
IndexFormulaData Requirement
Paasche(ΣP₁Q₁ / ΣP₀Q₁) × 100Current weights
Fisher√(LPI × PPI)Base + Current weights

Critical Evaluation

Fisher’s Index is superior for dynamic economies like India, as it balances substitution bias (e.g., telecom price shifts). Paasche underestimates inflation due to frequent weight updates.


Future Implications

Global bodies like IMF prefer Fisher’s Index for accuracy in GDP deflators.

Question 7:
Analyze how Consumer Price Index (CPI) reflects cost of living disparities between urban and rural India. Support with 2023 data.
Answer:
Theoretical Framework

CPI measures retail price changes for specific consumer groups. India has separate CPIs for urban (CPI-U) and rural (CPI-R) sectors.


Evidence Analysis
  • 2023 Data: CPI-U (6.2%) > CPI-R (5.8%) due to higher service costs in cities.
  • Example: Education inflation is 9% urban vs 4% rural (NCERT data).

Critical Evaluation

We studied that rural CPI weights food more (54% vs 36% urban), masking non-food inflation disparities like healthcare.


Future Implications

Policy-makers must address urban-rural weightage gaps for equitable subsidies.

Question 8:
Critically evaluate the Wholesale Price Index (WPI) as an inflation measure. Why did India shift to CPI for monetary policy?
Answer:
Theoretical Framework

WPI tracks price changes at producer level, excluding services. India adopted CPI as primary inflation gauge in 2014.


Evidence Analysis
  • WPI Limitation: Ignores 60% services sector (e.g., IT, healthcare).
  • Example: 2022 WPI was 12.5% but CPI was 6.7%, showing mismatch.

Critical Evaluation

Our textbook shows RBI shifted to CPI as it directly affects consumers. WPI remains useful for industrial contracts.


Future Implications

Hybrid indices may emerge to bridge producer-consumer price gaps.

Question 9:
Construct a Chain Base Index for a 3-year product price series (2021-2023). Explain its advantage over fixed base method.
Answer:
Theoretical Framework

Chain Base Index updates the base year annually. Example for product X:


YearPrice (₹)Index (2021=100)
202150100
202255110
202360120

Evidence Analysis
  • Advantage: Reflects recent consumption patterns better (e.g., smartphone price trends).

Critical Evaluation

We studied that it reduces ‘drift’ in long-term comparisons, unlike fixed-base methods used in India’s IIP.


Future Implications

Adoption could improve accuracy of GDP deflators.

Question 10:
Explain the Laspeyres Price Index and Paasche Price Index with their formulas. Discuss why they yield different results.
Answer:
Theoretical Framework

The Laspeyres Price Index uses base-year quantities as weights, while the Paasche Price Index uses current-year quantities. Their formulas are:

  • Laspeyres: (∑P₁Q₀ / ∑P₀Q₀) × 100
  • Paasche: (∑P₁Q₁ / ∑P₀Q₁) × 100
Evidence Analysis

Our textbook shows that Laspeyres tends to overstate inflation (2021 CPI: 5.2% vs Paasche's 4.8%), as it doesn't account for consumer substitution.

Critical Evaluation

We studied that Paasche is harder to compute but more accurate, while Laspeyres is simpler but has upward bias.

Question 11:
Analyze how chain-based index numbers overcome limitations of fixed-weight indices with two real-world examples.
Answer:
Theoretical Framework

Chain indices update weights annually, avoiding base-year bias in fixed-weight indices like Laspeyres.

Evidence Analysis
  • US GDP deflator switched to chained method in 1996, reducing inflation overstatement by 0.5%
  • India's WPI adopted chain-linking in 2017 for better tech-product representation
Critical Evaluation

We studied that while chain indices are more accurate, they require frequent data updates (monthly for CPI) and complex calculations.

Question 12:
Compare CPI and WPI through their components and explain why India uses both measures.
Answer:
Theoretical Framework

CPI tracks retail prices (food 45%, housing 10%) while WPI monitors wholesale transactions (fuel 13%, manufactured goods 65%).

IndexBase YearCoverage
CPI2012Urban + Rural
WPI2011-12Primary + Manufactured
Critical Evaluation

Our textbook shows CPI better reflects consumer inflation (used for RBI policy), while WPI predicts industrial trends (2023: CPI 6.4% vs WPI 4.2%).

Question 13:
Discuss the Fisher's Ideal Index with mathematical proof of its time-reversal test. Why is it called 'ideal'?
Answer:
Theoretical Framework

Fisher's Index is the geometric mean of Laspeyres and Paasche: √(L × P). It satisfies the time-reversal test: P₀₁ × P₁₀ = 1.

Evidence Analysis

Proof: Let P₀₁ = √(L₀₁ × P₀₁), then P₁₀ = √(L₁₀ × P₁₀). Multiplying gives √[(L₀₁×L₁₀) × (P₀₁×P₁₀)] = 1 (since L₀₁×L₁₀ = 1).

Critical Evaluation

We studied it's called 'ideal' as it meets all tests (factor reversal, circular), but is rarely used due to complexity (UNSD prefers Laspeyres for SDGs).

Question 14:
Evaluate how index number biases (substitution, new goods) affect India's inflation measurement with 2023 data examples.
Answer:
Theoretical Framework

Biases include substitution bias (consumers shift to cheaper alternatives) and new goods bias (smartphones added late to CPI).

Evidence Analysis
  • 2023 CPI overestimated food inflation by 1.2% as it didn't capture dal-to-egg substitution
  • Ola electric bikes entered WPI only in 2022, missing 2021 price drops
Future Implications

Our textbook suggests monthly weight updates and hedonic pricing (used for US laptops) could reduce these biases.

Question 15:
Explain the concept of Index Numbers and discuss its significance in the field of economics. Support your answer with suitable examples.
Answer:

An Index Number is a statistical measure designed to show changes in a variable or a group of related variables over time, geographical locations, or other criteria. It is expressed as a percentage relative to a base period or base value, which is typically assigned a value of 100. Index numbers simplify complex economic data, making it easier to analyze trends and make comparisons.

Significance of Index Numbers in Economics:

  • Measurement of Inflation/Deflation: The Consumer Price Index (CPI) and Wholesale Price Index (WPI) track price changes, helping policymakers control inflation.
  • Economic Indicators: Index numbers like the Industrial Production Index (IPI) reflect economic growth or decline.
  • Wage Adjustment: Used to adjust salaries and pensions to maintain purchasing power (e.g., Cost of Living Index).
  • Business Decisions: Companies use indices like the Stock Market Index (e.g., Sensex) to gauge market trends.

Example: If the CPI increases from 100 to 120 over a year, it indicates a 20% rise in the general price level, signaling inflation.

Thus, index numbers are indispensable tools for economists, businesses, and governments to make informed decisions.

Question 16:
Explain the concept of Index Numbers in economics, highlighting their significance and limitations. Support your answer with a suitable example.
Answer:

Index Numbers are statistical measures designed to show changes in a variable or a group of related variables over time, geographical locations, or other criteria. They are expressed as percentages relative to a base period or value, which is assigned a value of 100. Index numbers simplify complex economic data, making it easier to analyze trends and make comparisons.

Significance of Index Numbers:

  • Measure Inflation/Deflation: The Consumer Price Index (CPI) tracks changes in the price level of a basket of consumer goods and services, helping to gauge inflation.
  • Economic Policy Formulation: Governments use indices like the Wholesale Price Index (WPI) to adjust monetary and fiscal policies.
  • Business Decision-Making: Companies rely on indices to adjust wages, prices, or production levels based on economic trends.
  • International Comparisons: Indices like the Human Development Index (HDI) allow cross-country comparisons of living standards.

Limitations of Index Numbers:

  • Base Year Issues: Choosing an outdated base year can distort comparisons.
  • Quality Changes Ignored: Index numbers may not account for improvements or deteriorations in product quality.
  • Limited Scope: They may not cover all relevant variables, leading to incomplete analysis.
  • Sampling Errors: Inaccurate data collection can affect reliability.

Example: The CPI for a country rose from 100 (base year) to 120 in 2025. This indicates a 20% increase in the general price level over the period, signaling inflation.

Question 17:
Explain the concept of Index Numbers in Economics. Discuss its significance and any three limitations with suitable examples.
Answer:

Index Numbers are statistical measures designed to show changes in a variable or a group of related variables over time, geographical locations, or other criteria. They are expressed as percentages relative to a base period or value, which is typically assigned a value of 100.

Significance of Index Numbers:

  • Measure Economic Trends: They help in tracking inflation (e.g., Consumer Price Index) or industrial production (Index of Industrial Production).
  • Policy Formulation: Governments use indices like Wholesale Price Index (WPI) to adjust monetary policies.
  • Comparative Analysis: They simplify comparisons, such as comparing cost of living between cities using Cost of Living Index.

Limitations of Index Numbers:

  • Base Period Bias: If the base year is outdated (e.g., using 2010 prices in 2026), the index may misrepresent current trends.
  • Quality Changes Ignored: An index might not account for improved product quality (e.g., smartphones today vs. 2010).
  • Limited Coverage: Some indices exclude important sectors (e.g., CPI may omit rural healthcare costs).

For example, if CPI rises from 100 to 120 over 5 years, it indicates a 20% increase in the cost of a fixed basket of goods, but it may not reflect shifts in consumer preferences or new products.

Question 18:
Explain the concept of Index Numbers in Economics. Discuss its importance and limitations with suitable examples.
Answer:

Index Numbers are statistical measures designed to show changes in a variable or a group of related variables over time, geographical locations, or other criteria. They are expressed as percentages relative to a base period or value.

Importance of Index Numbers:

  • They help in measuring inflation or deflation through indices like the Consumer Price Index (CPI) or Wholesale Price Index (WPI).
  • They assist in comparing economic data over different time periods, such as comparing GDP growth across years.
  • They are useful in policy formulation, like adjusting wages or pensions based on cost-of-living indices.
  • They simplify complex data into a single, understandable figure, such as the Human Development Index (HDI).

Limitations of Index Numbers:

  • They may suffer from data inaccuracies due to outdated base years or unrepresentative samples.
  • They can be misleading if the weights assigned to items are inappropriate, like overemphasizing certain goods in CPI.
  • They do not account for quality changes in products, such as technological improvements in electronics.
  • They may not reflect regional variations, as a national CPI might not capture local price differences.

Example: If the CPI increases from 100 to 120 over a year, it indicates a 20% rise in the general price level, helping policymakers assess inflation.

Question 19:
Explain the concept of Index Numbers in Economics, highlighting its importance and limitations. Support your answer with a suitable example.
Answer:

Index Numbers are statistical measures designed to show changes in a variable or a group of related variables over time, geographical locations, or other criteria. They are expressed as percentages relative to a base period or value.

Importance:

  • They simplify complex economic data into a single value for easy comparison.
  • Help in measuring inflation or deflation through indices like the Consumer Price Index (CPI) or Wholesale Price Index (WPI).
  • Assist policymakers in formulating economic policies by tracking trends.
  • Useful for businesses to adjust wages, prices, or contracts based on economic changes.

Limitations:

  • They may not account for changes in quality or new products over time.
  • The choice of base year can affect the interpretation of results.
  • Different methods of calculation (e.g., Laspeyres, Paasche) can yield different results.

Example: The CPI measures the average change in prices paid by consumers for a basket of goods and services. If the CPI is 120 in 2026 (base year 2021 = 100), it indicates a 20% increase in the price level over the period.

Question 20:
Explain the concept of Index Numbers in Economics. Discuss its importance and any two limitations with suitable examples.
Answer:

Index Numbers are statistical measures designed to show changes in a variable or a group of related variables over time, geographical locations, or other criteria. They are expressed as percentages relative to a base period or value, which is assigned a value of 100. Index numbers help in simplifying complex economic data into understandable trends.

Importance of Index Numbers:

  • Economic Indicators: They serve as vital indicators of economic performance, such as the Consumer Price Index (CPI) measuring inflation.
  • Policy Formulation: Governments and businesses use them to make informed decisions, like adjusting wages based on CPI changes.

Limitations of Index Numbers:

  • Base Period Bias: The choice of base year can distort comparisons if the year is unrepresentative. For example, using a recession year as the base may inflate growth figures.
  • Quality Changes Ignored: They often fail to account for improvements in product quality. For instance, a smartphone today is vastly superior to one from a decade ago, but price indices may not reflect this.

Thus, while index numbers are powerful tools, their limitations necessitate careful interpretation.

Question 21:
Explain the concept of Index Numbers in Economics, highlighting its types and significance. Support your answer with a real-world example.
Answer:

Index Numbers are statistical measures designed to show changes in a variable or a group of related variables over time, geographical locations, or other criteria. They are expressed as percentages relative to a base period or value, which is assigned a value of 100. Index numbers simplify complex data into a single, easily understandable figure.

Types of Index Numbers:

  • Price Index: Measures changes in price levels (e.g., Consumer Price Index (CPI) or Wholesale Price Index (WPI)).
  • Quantity Index: Tracks changes in physical quantities (e.g., Industrial Production Index).
  • Value Index: Combines price and quantity changes to reflect total value.

Significance:

  • Helps in measuring inflation or deflation trends.
  • Assists policymakers in economic planning.
  • Enables comparison of economic performance across regions or time periods.

Example: The CPI in India tracks the average change in prices paid by consumers for essential goods (e.g., food, fuel, clothing). If the CPI rises from 100 to 110 over a year, it indicates a 10% inflation rate, affecting purchasing power.

Question 22:
Explain the concept of Index Numbers in Economics, highlighting its significance and types. Support your answer with a suitable example.
Answer:

Index Numbers are statistical measures designed to show changes in a variable or a group of related variables over time, geographical locations, or other criteria. They are expressed as percentages relative to a base period or value, which is assigned a value of 100. Index numbers simplify complex data and make comparisons easier.

Significance of Index Numbers:

  • They help in measuring inflation or deflation through indices like the Consumer Price Index (CPI).
  • They assist in analyzing economic trends, such as industrial production or stock market performance.
  • They are used in policy-making, wage adjustments, and business decision-making.

Types of Index Numbers:

  • Price Index: Measures changes in price levels (e.g., Wholesale Price Index).
  • Quantity Index: Tracks changes in physical quantities (e.g., Industrial Production Index).
  • Value Index: Combines price and quantity changes to reflect total value.

Example: The Consumer Price Index (CPI) tracks the average change in prices paid by consumers for a basket of goods and services. If CPI increases from 100 to 110 over a year, it indicates a 10% rise in the cost of living.

Question 23:
Explain the concept of Index Numbers and discuss its significance in economic analysis. Also, highlight any two limitations of using index numbers.
Answer:

Index Numbers are statistical measures designed to show changes in a variable or a group of related variables over time, geographical locations, or other criteria. They are expressed as percentages relative to a base period or value.

Significance in Economic Analysis:

  • They simplify complex economic data into a single value, making it easier to interpret trends.
  • Help in measuring inflation or deflation through indices like the Consumer Price Index (CPI) or Wholesale Price Index (WPI).
  • Assist policymakers in formulating economic policies by analyzing price levels, industrial production, etc.
  • Used in comparing economic conditions across different regions or time periods.

Limitations:

  • Base Year Issues: The choice of base year can distort comparisons if it is not representative of normal conditions.
  • Quality Changes Ignored: Index numbers do not account for improvements or deteriorations in product quality over time.
Question 24:
Describe the Laspeyre's Price Index and Paasche's Price Index with formulas. Compare the two methods and explain why they might yield different results.
Answer:

Laspeyre's Price Index (LPI) measures price changes using base-year quantities as weights. Its formula is:


LPI = (ΣPnQ0 / ΣP0Q0) × 100

where Pn = current year price, P0 = base year price, and Q0 = base year quantity.

Paasche's Price Index (PPI) uses current-year quantities as weights. Its formula is:


PPI = (ΣPnQn / ΣP0Qn) × 100

where Qn = current year quantity.

Comparison:

  • LPI tends to overestimate inflation because it does not account for consumer substitution of cheaper goods.
  • PPI tends to underestimate inflation as it reflects current consumption patterns, which may shift due to price changes.

Reason for Different Results: The difference arises due to the choice of weights. LPI uses fixed base-year quantities, while PPI adjusts for changes in consumption behavior, leading to divergent outcomes.

Question 25:
Explain the concept of Index Numbers in economics. Discuss its significance and any two limitations with suitable examples.
Answer:

Index Numbers are statistical measures designed to show changes in a variable or a group of related variables over time, geographical locations, or other criteria. They are expressed as percentages relative to a base period or value.

Significance:

  • They help in measuring inflation or deflation through indices like the Consumer Price Index (CPI) or Wholesale Price Index (WPI).
  • They assist policymakers in making informed decisions regarding economic policies, wage adjustments, and price controls.

Limitations:

  • Base Year Issues: The choice of an inappropriate base year can distort comparisons. For example, if a recession year is chosen as the base, growth may appear exaggerated.
  • Quality Changes Ignored: Index numbers do not account for improvements or deteriorations in product quality. For instance, a smartphone today is vastly superior to one from a decade ago, but the price index may not reflect this.

Despite limitations, index numbers remain indispensable tools for economic analysis.

Question 26:
Describe the Laspeyre’s Price Index and Paasche’s Price Index with formulas. Compare the two and explain why they might yield different results.
Answer:

Laspeyre’s Price Index and Paasche’s Price Index are two methods to measure price changes using index numbers.

Laspeyre’s Price Index (LPI):
Formula: LPI = (ΣP₁Q₀ / ΣP₀Q₀) × 100
Here, P₁ and P₀ are current and base year prices, and Q₀ is the base year quantity. It uses base year quantities as weights.

Paasche’s Price Index (PPI):
Formula: PPI = (ΣP₁Q₁ / ΣP₀Q₁) × 100
Here, Q₁ is the current year quantity. It uses current year quantities as weights.

Comparison:

  • Weight Difference: LPI uses base year quantities, while PPI uses current year quantities.
  • Result Variation: LPI tends to overestimate inflation (as it ignores consumer substitution toward cheaper goods), whereas PPI may underestimate it (as it reflects current consumption patterns).

Example: If the price of petrol rises sharply, consumers may reduce usage. LPI would still weigh petrol heavily (base year consumption), while PPI would account for reduced consumption, leading to different index values.

Thus, the choice between them depends on the purpose of analysis.

Case-based Questions (4 Marks) – with Solutions (CBSE Pattern)

These 4-mark case-based questions assess analytical skills through real-life scenarios. Answers must be based on the case study provided.

Question 1:
A consumer price index (CPI) for urban non-manual employees (UNME) shows a rise from 150 to 165 over a year, while the CPI for agricultural laborers (AL) rises from 120 to 132. Compare the inflation impact on these two groups and explain the limitations of CPI.
Answer:
Case Deconstruction

The CPI for UNME increased by 10% (165-150)/150, while AL saw a 10% rise (132-120)/120. Both groups face equal percentage inflation.


Theoretical Application
  • CPI measures average price changes but ignores consumption patterns. UNME spend more on services, AL on food.
  • Substitution bias and quality changes aren't captured.

Critical Evaluation

Our textbook shows CPI overestimates inflation for UNME due to service sector price rigidity, while AL face real hardship as food prices rise faster.

Question 2:
The wholesale price index (WPI) weights for primary articles (30%), fuel (15%) and manufactured products (55%) changed to 25%, 20%, 55% respectively in 2023. Analyze how this affects inflation measurement and relate it to Laspeyres vs Paasche index debate.
Answer:
Case Deconstruction

Reduced primary articles weight (30→25%) may underreport food inflation, while increased fuel weight (15→20%) captures energy price volatility better.


Theoretical Application
  • Laspeyres index (fixed weights) becomes outdated, as our textbook shows with 2011-12 base year issues.
  • Paasche index would require annual weight updates but is costly.

Critical Evaluation

This change reflects structural shifts toward manufacturing but may temporarily distort inflation trends during supply shocks.

Question 3:
Two index number formulas give different results for the same data: Laspeyres (142) and Fisher's Ideal (138). Interpret why Fisher's is considered superior and demonstrate with a 2-commodity example.
Answer:
Case Deconstruction

Fisher's index (138) is lower than Laspeyres (142) because it accounts for substitution effect by geometric mean of Laspeyres and Paasche.


Theoretical Application
ItemBase QtyCurrent Qty
Rice10kg8kg
Wheat5kg7kg

Critical Evaluation

Our textbook shows Fisher's index satisfies time reversal test, unlike Laspeyres. The 4-point difference here matters for policy decisions.

Question 4:
A student calculates index numbers using 2020 quantities for 2020-2023, then switches to 2022 quantities for 2024. Identify the methodological error and propose a solution using chain index numbers.
Answer:
Case Deconstruction

The error is inconsistent base year, making 2024 numbers incomparable to previous years. This violates homogeneity principle.


Theoretical Application
  • Chain indexing links annual indices: 2020-21 (2020 base), 2021-22 (2021 base) etc.
  • Example: RBI uses chain method for monetary policy indices.

Critical Evaluation

As we studied, chain indexing maintains continuity but requires more data. The student's method would overstate inflation by 3-5% as per our textbook examples.

Question 5:
The government replaces CPI with Personal Consumption Expenditure (PCE) index for inflation targeting. Evaluate this decision considering that PCE includes healthcare subsidies while CPI doesn't, and predict its impact on interest rates.
Answer:
Case Deconstruction

PCE is broader (includes subsidies) and usually shows 0.3-0.5% lower inflation than CPI, as our textbook's US example demonstrates.


Theoretical Application
  • Lower reported inflation may justify lower interest rates.
  • But rural healthcare costs aren't fully captured, risking policy errors.

Critical Evaluation

This shift could artificially suppress rate hikes, similar to Japan's experience with PCE in 2010s. However, it better reflects actual consumption patterns.

Question 6:
A survey compares the Consumer Price Index (CPI) and Wholesale Price Index (WPI) for 2022-23. CPI rose by 6.2% while WPI increased by 4.8%. Analyze the implications for inflation and purchasing power.
Answer:
Case Deconstruction

The CPI measures retail inflation affecting households, while WPI tracks wholesale market trends. A higher CPI (6.2%) indicates reduced purchasing power for consumers.

Theoretical Application
  • CPI’s rise suggests increased living costs, as studied in our textbook’s index numbers chapter.
  • WPI’s slower growth (4.8%) may reflect lower input costs for producers.
Critical Evaluation

Example: Rising food prices in CPI (like tomatoes) contrast with stable WPI for grains. This mismatch highlights supply-chain inefficiencies.

Question 7:
The Laspeyres and Paasche indices for a commodity group show values of 115 and 108, respectively. Explain the divergence using base-year weights and current-year weights.
Answer:
Case Deconstruction

Laspeyres (115) uses base-year weights, overestimating inflation if consumption shifts to cheaper alternatives.

Theoretical Application
  • Paasche (108) adjusts for current-year weights, as per our textbook’s formula.
  • Example: Fuel prices may weigh more in Laspeyres if base-year usage was high.
Critical Evaluation

The 7-point gap reflects substitution bias, critical for policy decisions like subsidy targeting.

Question 8:
A study compares GDP deflator (5.1%) and CPI (6.0%) for India in 2023. Why might these inflation measures differ? Include coverage and imported goods in your analysis.
Answer:
Case Deconstruction

GDP deflator covers all domestic output, while CPI focuses on consumer goods, excluding capital items.

Theoretical Application
  • Example: Rising smartphone imports affect CPI but not GDP deflator, as studied in national income chapters.
  • CPI’s higher rate may reflect global supply shocks (e.g., oil).
Critical Evaluation

This divergence underscores CPI’s sensitivity to imported inflation, vital for RBI’s rate decisions.

Question 9:
The Human Development Index (HDI) for State A rose from 0.65 to 0.72 (2020-23), while its Per Capita Income Index grew slower. Analyze this using composite indices and non-income dimensions.
Answer:
Case Deconstruction

HDI combines income, health, and education, unlike pure income indices.

Theoretical Application
  • Example: State A’s school enrollment (non-income) may have improved faster than wages.
  • Our textbook shows HDI’s geometric mean balances dimensions.
Critical Evaluation

The data highlights development policies’ success in social sectors, critical for inclusive growth.

Question 10:
A table shows Industrial Production Index (IIP) for 2022-23:
SectorGrowth (%)
Manufacturing3.4
Mining1.2
Interpret the data using weighted index concepts and sectoral contributions.
Answer:
Case Deconstruction

IIP is a weighted index where manufacturing (largest weight) drives overall growth.

Theoretical Application
  • Example: Mining’s low growth (1.2%) may reflect regulatory delays, as per case studies.
  • Our textbook emphasizes base-year sector weights in IIP calculation.
Critical Evaluation

The data underscores manufacturing’s dominance, but mining’s stagnation risks input shortages.

Question 11:

The following table shows the price index numbers for three commodities (A, B, C) for the years 2024 and 2025 with 2023 as the base year:


CommodityPrice Index (2024)Price Index (2025)
A120135
B110125
C105115

Calculate the simple aggregate price index for 2025 using 2023 as the base year. Interpret the result in the context of inflation.

Answer:

To calculate the simple aggregate price index for 2025:


Step 1: Sum the price indices of all commodities for 2025.


135 (A) + 125 (B) + 115 (C) = 375

Step 2: Since the base year (2023) index for each commodity is 100, the sum for the base year is:


100 (A) + 100 (B) + 100 (C) = 300

Step 3: Apply the formula for the simple aggregate price index:


(Sum of current year indices / Sum of base year indices) × 100
= (375 / 300) × 100 = 125

Interpretation: The index value of 125 indicates a 25% increase in the general price level of the commodities compared to the base year (2023). This suggests inflation, as the purchasing power of money has decreased over the period.

Question 12:

A consumer price index (CPI) is constructed for a typical urban household using the following data with 2020 as the base year:


ItemWeight (in %)Price Index (2024)
Food40130
Housing30120
Transport20110
Others10105

Compute the weighted CPI for 2024 and explain how it reflects the cost of living for the household.

Answer:

To compute the weighted CPI for 2024:


Step 1: Multiply each item's price index by its weight.


Food: 130 × 40 = 5200
Housing: 120 × 30 = 3600
Transport: 110 × 20 = 2200
Others: 105 × 10 = 1050

Step 2: Sum the weighted values.


5200 + 3600 + 2200 + 1050 = 12,050

Step 3: Divide the total by the sum of weights (100).


12,050 / 100 = 120.5

Interpretation: The weighted CPI of 120.5 indicates that the cost of living for the household has increased by 20.5% since the base year (2020). This reflects higher expenses, particularly in Food (highest weight and index), which significantly impacts the household's budget. The index helps measure inflation's effect on urban consumers.

Question 13:

The following table shows the price of three commodities (A, B, C) in the base year (2020) and current year (2025). Calculate the Simple Aggregate Price Index for 2025 using 2020 as the base year. Interpret the result.


Commodity | Price in 2020 (₹) | Price in 2025 (₹)
A | 50 | 70
B | 30 | 45
C | 20 | 25
Answer:

To calculate the Simple Aggregate Price Index, follow these steps:


Step 1: Sum the prices of all commodities in the base year (2020).
Total in 2020 = ₹50 (A) + ₹30 (B) + ₹20 (C) = ₹100

Step 2: Sum the prices of all commodities in the current year (2025).
Total in 2025 = ₹70 (A) + ₹45 (B) + ₹25 (C) = ₹140

Step 3: Apply the formula for Simple Aggregate Price Index:
Index = (ΣP₁ / ΣP₀) × 100
Where ΣP₁ = Total current year price, ΣP₀ = Total base year price.
Index = (140 / 100) × 100 = 140

Interpretation: The index value of 140 indicates that the overall price level of the commodities has increased by 40% in 2025 compared to 2020. This reflects inflation or a rise in the general price level.

Question 14:

A consumer price index (CPI) for industrial workers is constructed using Laspeyre’s Method with 2020 as the base year. The weights assigned to food, clothing, and fuel are 50%, 30%, and 20% respectively. In 2025, the prices of these items increased by 20%, 10%, and 5% respectively. Calculate the CPI for 2025 and explain its significance.

Answer:

To calculate the Consumer Price Index (CPI) using Laspeyre’s Method, follow these steps:


Step 1: Note the base year weights and price changes:
  • Food: Weight = 50%, Price increase = 20%
  • Clothing: Weight = 30%, Price increase = 10%
  • Fuel: Weight = 20%, Price increase = 5%

Step 2: Calculate the weighted price relatives for each item:
Food: 50 × 1.20 = 60
Clothing: 30 × 1.10 = 33
Fuel: 20 × 1.05 = 21

Step 3: Sum the weighted relatives to get CPI:
CPI = 60 + 33 + 21 = 114

Significance: A CPI of 114 indicates that the cost of living for industrial workers has increased by 14% compared to the base year (2020). This index helps measure inflation, adjust wages, and formulate economic policies to protect workers from rising prices.

Question 15:

The following table shows the price index numbers for three commodities (A, B, C) for the years 2024 and 2025 with 2023 as the base year:


CommodityPrice Index (2024)Price Index (2025)
A120135
B110125
C105115

Calculate the simple aggregate price index for 2025 and interpret the result.

Answer:

Step 1: Sum the price indices of all commodities for 2025.
135 (A) + 125 (B) + 115 (C) = 375


Step 2: Sum the price indices for the base year (2023). Since 2023 is the base year, all indices are 100.
100 (A) + 100 (B) + 100 (C) = 300


Step 3: Apply the formula for simple aggregate price index:
(Sum of current year indices / Sum of base year indices) × 100
= (375 / 300) × 100 = 125


Interpretation: The price index of 125 indicates a 25% increase in the general price level of the commodities in 2025 compared to 2023. This reflects inflation or rising prices in the economy.

Question 16:

A consumer price index (CPI) is constructed using the following data for a typical urban household:


ItemWeight (in %)Price Index (2025)
Food40130
Housing30120
Clothing20110
Others10105

Compute the weighted CPI for 2025 and explain its significance.

Answer:

Step 1: Multiply each item's price index by its weight.
Food: 130 × 40 = 5200
Housing: 120 × 30 = 3600
Clothing: 110 × 20 = 2200
Others: 105 × 10 = 1050


Step 2: Sum the weighted values.
5200 + 3600 + 2200 + 1050 = 12,050


Step 3: Divide by the total weight (100) to get the weighted CPI.
12,050 / 100 = 120.5


Significance: A CPI of 120.5 indicates that the cost of living for the urban household has increased by 20.5% compared to the base year. It helps measure inflation, adjust wages, and formulate economic policies.

Question 17:
The following table shows the price index numbers for three commodities (A, B, C) for the years 2024 and 2025 with 2023 as the base year. Analyze the data and answer the questions that follow:

Commodity | Price Index (2024) | Price Index (2025)
A | 120 | 135
B | 110 | 125
C | 105 | 115

(i) Calculate the percentage increase in the price of Commodity A from 2024 to 2025.
(ii) Interpret the significance of the base year in index numbers.
Answer:

(i) To calculate the percentage increase in the price of Commodity A from 2024 to 2025:

Percentage Increase = [(Price Index in 2025 - Price Index in 2024) / Price Index in 2024] × 100
= [(135 - 120) / 120] × 100
= (15 / 120) × 100
= 12.5%

Thus, the price of Commodity A increased by 12.5% from 2024 to 2025.

(ii) The base year is a reference point used in index numbers to compare changes in prices or quantities over time. Its significance includes:

  • It acts as a benchmark (assigned an index value of 100) against which other years are compared.
  • It helps in measuring the relative change in economic variables like prices or production.
  • Choosing a stable and representative base year ensures accurate comparisons and avoids misleading trends.
Without a base year, index numbers would lack context, making it difficult to interpret economic changes.

Question 18:
A consumer price index (CPI) for urban non-manual employees is given below for three consecutive years:

Year | CPI
2023 | 100
2024 | 108
2025 | 115

(i) Calculate the inflation rate between 2024 and 2025.
(ii) Explain how CPI is used as an economic indicator.
Answer:

(i) To calculate the inflation rate between 2024 and 2025:

Inflation Rate = [(CPI in 2025 - CPI in 2024) / CPI in 2024] × 100
= [(115 - 108) / 108] × 100
= (7 / 108) × 100
= 6.48%

The inflation rate between 2024 and 2025 is approximately 6.48%.

(ii) The Consumer Price Index (CPI) is a vital economic indicator used for:

  • Measuring Inflation: It tracks changes in the cost of living by comparing the prices of a fixed basket of goods and services over time.
  • Adjusting Wages and Pensions: Governments and organizations use CPI to revise salaries and benefits to maintain purchasing power.
  • Formulating Policies: Policymakers rely on CPI data to design monetary and fiscal policies to control inflation or stimulate growth.
  • Comparing Purchasing Power: It helps compare the real value of money across different time periods or regions.
Thus, CPI is a crucial tool for economic analysis and decision-making.

Question 19:
A consumer price index (CPI) for a metropolitan city is given below for the years 2023 and 2024. Analyze the data and answer the following:

Year | CPI (Base Year: 2020 = 100)
2023 | 125
2024 | 140

(i) Calculate the inflation rate between 2023 and 2024.
(ii) Explain how CPI is used to measure the cost of living.
Answer:

Inflation rate is calculated as the percentage change in CPI over a period. Here's the step-by-step solution:


Step 1: Identify the CPI values for both years.
CPI (2023) = 125
CPI (2024) = 140

Step 2: Apply the inflation rate formula:
Inflation Rate = [(CPI2024 - CPI2023) / CPI2023] × 100
= [(140 - 125) / 125] × 100
= (15 / 125) × 100
= 12%

The inflation rate between 2023 and 2024 is 12%.


Cost of living is measured using CPI as it tracks the average price change of a fixed basket of goods and services consumed by households. A rise in CPI indicates increased living costs, while a fall suggests reduced expenses. Policymakers use CPI to adjust wages, pensions, and tax brackets to maintain purchasing power.

Question 20:
The following table shows the price index numbers for three commodities (A, B, C) in 2025 with 2020 as the base year:

Commodity | Price Index (2020 = 100)
A | 120
B | 150
C | 90

(i) Interpret the meaning of the price index for Commodity B.
(ii) If a family spends 40% of their income on Commodity A, 30% on B, and 30% on C, calculate the composite index for their cost of living.
Answer:

Price index for Commodity B (150) means its price in 2025 is 50% higher than in the base year (2020). For example, if Commodity B cost ₹100 in 2020, it now costs ₹150 in 2025.


To calculate the composite index, follow these steps:


Step 1: Note the weights and price indices:
Commodity A: Weight = 40%, Index = 120
Commodity B: Weight = 30%, Index = 150
Commodity C: Weight = 30%, Index = 90

Step 2: Multiply each index by its weight:
A: 120 × 0.40 = 48
B: 150 × 0.30 = 45
C: 90 × 0.30 = 27

Step 3: Sum the weighted values:
48 + 45 + 27 = 120

The composite index for the family's cost of living is 120, indicating a 20% overall price increase compared to 2020.

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