Chapter 18 of 18

100%

CBSE Class 11 Economics★ 6-8 marks · CBSE Class 11 Economics (Statistics for Economics) Chapter 8

Index Numbers

How do we measure INFLATION? How do we compare the cost of living across time? The answer: INDEX NUMBERS — the Consumer Price Index (CPI), Wholesale Price Index (WPI), and Index of Industrial Production (IIP). CBSE Class 11 Economics (Statistics for Economics) Chapter 8.

⏱ 16 min readHard difficulty✓ Free · NCERT-aligned

Ask AI about this

🔤Build your vocabulary from this chapterLexiGenome mines the key words, explains them in your language, and schedules them with spaced repetition.Mine words →

By the end of this chapter you'll be able to…

1Explain what an index number is and why the base year value is set at 100
2Calculate a simple aggregative price index and a simple average of price relatives
3Compute Laspeyres, Paasche, and Fisher's Ideal Price Index from given price and quantity data
4Describe the Consumer Price Index (CPI) and Wholesale Price Index (WPI) — what each measures, who compiles it, and its current base year
5State five limitations of index numbers including base year selection, substitution bias, and quality changes

💡

Why this chapter matters

Index numbers ARE the economy's vital signs — the CPI measures inflation, the WPI tracks wholesale prices, and the IIP measures industrial output. Every time you hear 'inflation is 5%', you are hearing the CPI index. This chapter explains how these numbers are constructed and what they mean.

Before you start — revise these

A 5-minute refresher here will save you 30 minutes of confusion below.

🔗

Measures of Central Tendency

Weighted average concept (used in Laspeyres and Paasche) builds on the weighted mean formula

Index Numbers

"An index number is a compass that tells you which way prices are moving — and how fast."

1. Chapter Overview

INDEX NUMBERS are statistical devices that measure CHANGES in a variable or group of variables over TIME, SPACE, or both. This chapter covers: what index numbers ARE, how they're CONSTRUCTED (base year, weighted vs unweighted), the MAJOR INDEXES used in India (CPI, WPI, IIP, Sensex), and the limitations of index numbers.

2. What Is an Index Number?

A number that measures the RELATIVE CHANGE in a variable (or group of variables) compared to a BASE PERIOD
Base period value = 100. Current period = 120 → 20% increase over the base period.
Index numbers are essentially PERCENTAGES with the % sign removed

Why Index Numbers?

Measure inflation: CPI, WPI — how much have prices risen?
Measure economic performance: IIP — is industrial output growing?
Cost of living adjustments: DA (Dearness Allowance) for government employees is linked to CPI
Stock market: Sensex, Nifty — how is the market performing relative to a base?
Policy decisions: RBI uses CPI to decide interest rates

3. Construction of an Index Number

Step 1: Choose the Base Year

The REFERENCE year against which all other years are compared
Should be: a 'NORMAL' year (no wars, famines, pandemics, extreme economic events)
Should be: relatively RECENT (to remain relevant)
Current CPI base year: 2012
Current WPI base year: 2011-12

Step 2: Select the Items

What goods/services does the index cover?
For CPI: a BASKET of goods and services that a typical consumer buys (food, housing, transport, education, health, etc.)
The basket is determined by CONSUMPTION SURVEYS

Step 3: Choose the Weights

Not all items are equally important. Food is a BIGGER share of a poor household's budget than of a rich household's.
Weighted index: Each item's price change is weighted by its IMPORTANCE in the basket
Weights come from: consumer expenditure surveys (for CPI), production and trade data (for WPI)

Step 4: Choose the Formula

Simple (Unweighted) Methods

Simple Aggregative: P₀₁ = (ΣP₁ / ΣP₀) × 100. Sum of current prices ÷ Sum of base prices. Problem: no weighting. All items treated equally.
Simple Average of Price Relatives: Average of individual price ratios.

Weighted Methods

Laspeyres' Index: Uses BASE PERIOD quantities as weights. P₀₁ = Σ(P₁Q₀) / Σ(P₀Q₀) × 100. Tends to OVERSTATE inflation (doesn't account for substitution away from expensive items).
Paasche's Index: Uses CURRENT PERIOD quantities. P₀₁ = Σ(P₁Q₁) / Σ(P₀Q₁) × 100. Tends to UNDERSTATE inflation.
Fisher's Ideal Index: Geometric mean of Laspeyres AND Paasche. √(Laspeyres × Paasche). Considered the BEST — but requires more data.

4. Major Indexes in India

Consumer Price Index (CPI)

Measures CHANGE in RETAIL PRICES of goods and services consumed by households
Compiled by: NSO (National Statistical Office)
Types: CPI-Rural, CPI-Urban, CPI-Combined
Used for: measuring INFLATION from the consumer's perspective. RBI uses CPI for inflation targeting (target: 4% ± 2%).

Wholesale Price Index (WPI)

Measures CHANGE in WHOLESALE PRICES (at the producer/wholesale level, not retail)
Compiled by: Office of the Economic Adviser, Ministry of Commerce
Covers: primary articles, fuel and power, manufactured products
WPI inflation vs CPI inflation: They can DIFFER because they cover different baskets at different levels of the supply chain

Index of Industrial Production (IIP)

Measures CHANGE in the VOLUME of industrial production
Compiled by: CSO (Central Statistics Office)
Sectors: mining, manufacturing, electricity

Sensex and Nifty

Stock market indexes. Sensex (BSE — 30 stocks). Nifty (NSE — 50 stocks).
Measure overall market performance

5. Issues and Limitations of Index Numbers

Base year: Must remain RELEVANT. Consumption patterns CHANGE over time. An outdated base year gives a misleading index.
Basket selection: Whose consumption? Urban middle class? Rural poor? Indexes DIFFER by the basket.
Quality changes: A phone today is NOT the same as a phone in 2012 (the CPI base year). Price increases may reflect QUALITY IMPROVEMENT, not pure inflation.
New products: Smartphones, OTT subscriptions, data packs — not in the basket when base year was set. The basket AGES.
Substitution bias: When the price of one item rises, consumers switch to cheaper alternatives. Fixed-weight indexes (Laspeyres) ignore this → overstate inflation.

6. Exam Focus

Definition of index number — relative change from base year
Steps in construction — base year, items, weights, formula
Laspeyres vs Paasche vs Fisher — formulas and tendencies
CPI, WPI, IIP — what each measures, who compiles, base year
Inflation targeting — RBI uses CPI (4% ± 2%)
Limitations — base year, basket, quality, new products, substitution bias

7. Conclusion

Index numbers are the THERMOMETERS of the economy:

CPI: Measures the fever (inflation) as felt by CONSUMERS. RBI watches it obsessively.
WPI: Measures wholesale prices. Useful for producers and policymakers.
IIP: Measures the PULSE of industry.
CONSTRUCTION: Base year, basket, weights, formula. Each choice MATTERS.
LIMITATIONS: Index numbers are INDISPENSABLE — but they are APPROXIMATIONS, not truths.

'When you hear "inflation is 5%", you're hearing the voice of the Consumer Price Index. Index numbers turn the chaos of millions of prices into a single, readable number.'

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Simple Aggregative Price Index

P₀₁ = (ΣP₁ / ΣP₀) × 100

Ratio of sum of current year prices to sum of base year prices × 100; simple but gives equal weight to all items regardless of importance

Simple Average of Price Relatives

P₀₁ = [Σ(P₁/P₀ × 100)] / N

Average of individual price relatives; each item's price ratio is treated equally; N = number of items

Laspeyres Price Index

P₀₁ = (ΣP₁Q₀ / ΣP₀Q₀) × 100

Base year quantities (Q₀) used as weights; tends to OVERSTATE inflation because it ignores consumer substitution away from expensive items

Paasche Price Index

P₀₁ = (ΣP₁Q₁ / ΣP₀Q₁) × 100

Current year quantities (Q₁) used as weights; tends to UNDERSTATE inflation; requires collecting current quantity data each period (expensive)

Fisher's Ideal Price Index

P₀₁ = √(Laspeyres × Paasche) = √[(ΣP₁Q₀/ΣP₀Q₀) × (ΣP₁Q₁/ΣP₀Q₁)] × 100

Geometric mean of Laspeyres and Paasche; called 'Ideal' because it satisfies both time reversal and factor reversal tests; considered the most accurate

Inflation Rate from Index

Inflation Rate = [(Current Period Index − Previous Period Index) / Previous Period Index] × 100

Change in CPI from one period to the next gives the inflation rate; e.g., CPI rises from 150 to 157.5 → inflation = 5%

⚠️

Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Confusing Laspeyres (base year quantities) with Paasche (current year quantities)

✓ Laspeyres uses Q₀ (base year quantities) for BOTH current and base year price calculations. Paasche uses Q₁ (current year quantities) for BOTH. Memory trick: Laspeyres = Last year (base) quantities; Paasche = Present (current) quantities.

WATCH OUT

✗ Not multiplying by 100 in index number formulas

✓ ALL index number formulas must end with × 100. The base period index = 100 by convention. Omitting ×100 gives a decimal (like 1.08) instead of an index (like 108) — this is an index, not a ratio.

WATCH OUT

✗ Confusing CPI and WPI — saying both measure the same inflation

✓ CPI measures RETAIL prices paid by consumers; compiled by NSO; current base year 2012. WPI measures WHOLESALE prices at producer/wholesale level; compiled by Office of the Economic Adviser (Ministry of Commerce); base year 2011-12. They can diverge significantly.

NCERT exercises (with solutions)

Every NCERT exercise from this chapter — what it covers and how many questions to expect.

Ex 8

Exercise 8

Calculation of simple and weighted price indexes, Laspeyres, Paasche, Fisher; CPI and WPI descriptions; limitations; base year selection

Questions

Practice problems

Try each one yourself before tapping "Show solution". Active recall > rereading.

Q1EASY· simple-aggregative

Calculate the Simple Aggregative Price Index for the following data (Base year 2020, Current year 2024): Item A: P₀ = 10, P₁ = 12. Item B: P₀ = 20, P₁ = 25. Item C: P₀ = 30, P₁ = 36.

▶ Show solution

Simple Aggregative Price Index = (ΣP₁ / ΣP₀) × 100. ΣP₁ = 12 + 25 + 36 = 73. ΣP₀ = 10 + 20 + 30 = 60. P₀₁ = (73 / 60) × 100 = 121.67. Interpretation: Prices in 2024 are 21.67% higher than in 2020 (base year). Limitation: This index gives equal weight to all items regardless of how much consumers spend on them.

Q2MEDIUM· laspeyres-paasche

Calculate Laspeyres and Paasche Price Indexes from the following data: Item A: P₀ = 5, P₁ = 6, Q₀ = 100, Q₁ = 90. Item B: P₀ = 10, P₁ = 12, Q₀ = 50, Q₁ = 60.

▶ Show solution

Laspeyres Index (base year quantities): ΣP₁Q₀ = (6×100) + (12×50) = 600 + 600 = 1200. ΣP₀Q₀ = (5×100) + (10×50) = 500 + 500 = 1000. Laspeyres = (1200/1000) × 100 = 120. Paasche Index (current year quantities): ΣP₁Q₁ = (6×90) + (12×60) = 540 + 720 = 1260. ΣP₀Q₁ = (5×90) + (10×60) = 450 + 600 = 1050. Paasche = (1260/1050) × 100 = 120. Note: Here both are equal at 120. In general, Laspeyres ≥ Paasche because consumers substitute toward cheaper goods, reducing the actual cost of living below what the Laspeyres formula suggests.

Q3HARD· fisher-ideal

Using the data: Item A: P₀=4, P₁=5, Q₀=60, Q₁=50. Item B: P₀=8, P₁=10, Q₀=40, Q₁=45. Item C: P₀=12, P₁=15, Q₀=30, Q₁=25. Calculate (a) Laspeyres Index, (b) Paasche Index, (c) Fisher's Ideal Index. State why Fisher's Index is called 'Ideal'.

▶ Show solution

(a) Laspeyres Index: ΣP₁Q₀ = (5×60)+(10×40)+(15×30) = 300+400+450 = 1150. ΣP₀Q₀ = (4×60)+(8×40)+(12×30) = 240+320+360 = 920. Laspeyres = (1150/920)×100 = 125. (b) Paasche Index: ΣP₁Q₁ = (5×50)+(10×45)+(15×25) = 250+450+375 = 1075. ΣP₀Q₁ = (4×50)+(8×45)+(12×25) = 200+360+300 = 860. Paasche = (1075/860)×100 = 125. (c) Fisher's Ideal = √(Laspeyres × Paasche) = √(125 × 125) = √15625 = 125. Why 'Ideal': Fisher's Index is called 'Ideal' because it satisfies two important mathematical tests: (1) Time Reversal Test: P₀₁ × P₁₀ = 1 — if you compute the index forward and backward in time, the results are consistent. (2) Factor Reversal Test: the product of the price index and quantity index equals the value index. Neither Laspeyres nor Paasche individually satisfies both tests, but Fisher's (their geometric mean) does. It is also free from the upward bias of Laspeyres and the downward bias of Paasche.

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•Index number: measures relative change from base period; base year = 100; a value of 120 means 20% rise from base
•Simple Aggregative: (ΣP₁/ΣP₀) × 100 — no weighting; treats all items equally regardless of importance
•Laspeyres = (ΣP₁Q₀/ΣP₀Q₀) × 100 — base year quantities; tends to OVERSTATE inflation (substitution bias)
•Paasche = (ΣP₁Q₁/ΣP₀Q₁) × 100 — current year quantities; tends to UNDERSTATE inflation; costly to compute
•Fisher's Ideal = √(Laspeyres × Paasche); satisfies time reversal and factor reversal tests; most accurate
•CPI: measures retail consumer prices; compiled by NSO; base year 2012; RBI uses CPI for 4% inflation target
•WPI: measures wholesale prices; compiled by Office of Economic Adviser (Ministry of Commerce); base year 2011-12
•Five limitations: outdated base year, basket composition, quality changes, new products not covered, substitution bias

CBSE marks blueprint

Where the marks come from in this chapter — so you can plan your prep.

Typical chapter weightage: 6-8 marks

Question type	Marks each	Typical count	What it tests
Short Answer	3	1	CPI vs WPI description, limitations of index numbers, or base year selection criteria
Long Answer	6	1	Full calculation of Laspeyres, Paasche, and Fisher's Index from a data table with interpretation

Prep strategy

Practise Laspeyres and Paasche calculations from a table — set up columns P₁Q₀, P₀Q₀, P₁Q₁, P₀Q₁ clearly; each column earns computation marks separately
Memorise the CPI and WPI details: what each measures, who compiles it, and its base year — these are guaranteed short-answer marks
Know all five limitations of index numbers as a list: base year problem, basket selection, quality changes, new products, substitution bias

Where this shows up in the real world

This chapter isn't just an exam topic — it lives in the world around you.

India's CPI and RBI's Inflation Targeting

Every month, NSO releases the CPI-Combined figure. If it rises above 6% (the upper tolerance band), RBI raises interest rates (repo rate) to cool inflation. If it falls below 2%, RBI cuts rates to stimulate growth. Index numbers directly control the price of money.

Dearness Allowance (DA) for Government Employees

India's 1 crore+ central government employees and 60+ lakh pensioners receive Dearness Allowance (DA) twice a year. DA is calculated as a percentage of basic salary based on the All India CPI for Industrial Workers (CPI-IW). A rise in CPI-IW triggers a DA hike — a direct application of index numbers in public finance.

Exam strategy

Battle-tested tips from teachers and toppers for this chapter.

For Laspeyres/Paasche calculation: set up a neat 5-column table (Item, P₀, P₁, Q₀, Q₁, P₁Q₀, P₀Q₀, P₁Q₁, P₀Q₁) — this is the clearest format for examiners and ensures you don't mix up the formula
Fisher's Index: show the two intermediate results (Laspeyres = X, Paasche = Y) before writing Fisher = √(X×Y) — partial marks are given for each intermediate step
Limitation questions: write 5 limitations as a numbered list with one sentence explanation each; never write them as a paragraph
CPI vs WPI: keep a side-by-side comparison (what it measures, who compiles it, base year, use) — tables score better than prose for this type of comparison question

Going beyond the textbook

For olympiad aspirants and curious learners — topics that build on this chapter.

Study the Marshall-Edgeworth Index: uses the average of base and current year quantities as weights — a compromise between Laspeyres and Paasche; P₀₁ = Σ[(Q₀+Q₁)P₁] / Σ[(Q₀+Q₁)P₀] × 100
Explore the Divisia Index — a continuous-time index that avoids the substitution bias of both Laspeyres and Paasche; used in central bank research for constructing monetary aggregates

Where else this chapter is tested

CBSE board isn't the only one — other exams test this chapter too.

CBSE Class 11 BoardHigh

CUETHigh

Class 12 Economics (Indian Economy)Medium

AI helpers for this chapter

Generate more practice on the fly, or have the chapter explained at a different level.

⚡

Generate 5 more questions

Fresh MCQs + short-answer items based on this chapter, plus answer keys.

🧠

Explain at a different level

Re-explain the chapter at the level you actually want.

📝 My notes

Saved on this device — sign in to sync · how this works

0/600

Questions students ask

The real ones — pulled from the Q&A community and tutor sessions.

CPI measures the prices actually paid by consumers for goods and services — it reflects the cost of living directly. WPI measures wholesale/producer prices, which don't always pass through to consumers immediately. Since the RBI's mandate is price stability for the common person, CPI (specifically CPI-Combined) is the appropriate measure. The current RBI inflation target is 4% ± 2% band.

Laspeyres uses BASE year quantities — quantities from before prices changed. When prices rise, consumers substitute toward cheaper goods (buy less of the expensive ones). Laspeyres doesn't account for this substitution, so it calculates the cost of buying the OLD basket at NEW prices — overstating the true cost increase. Paasche uses CURRENT year quantities — after substitution has already happened. This understates the cost increase because it weights the new (lower) quantities more heavily.

Practice more, ask doubts, find a tutor

CBSE Class 11 mock tests

CBSE Class 11 PYQs

Ask in Q&A

Economics flashcards

Related chapters

Students who read Index Numbers usually read these next.

Indian Economy on the Eve of Independence

What was the state of the Indian economy after 200 years of British rule? This chapter paints the picture: a prosperous pre-colonial economy transformed into a supplier of raw materials and a market for British goods — stagnant, impoverished, and de-industrialised. CBSE Class 11 Economics (Indian Economic Development) Chapter 1.

Indian Economy 1950–1990 (Planning and Mixed Economy)

Independent India chose a MIXED ECONOMY path — socialism + capitalism, planning + markets. This chapter covers the Five Year Plans, the Industrial Policy Resolution of 1956, the Green Revolution, and the debate: did India's 'planned development' succeed or fail? CBSE Class 11 Economics (Indian Economic Development) Chapter 2.

Liberalisation, Privatisation and Globalisation (LPG Reforms 1991)

In 1991, India almost DEFAULTED on its foreign loans. The crisis forced a RADICAL change: the LPG reforms. This chapter explains why India reformed, what the reforms were, and their impact — the winners, the losers, and the ongoing debate. CBSE Class 11 Economics (Indian Economic Development) Chapter 3.

Poverty

Who is poor? How is poverty MEASURED (poverty line)? Why does poverty persist? And what has India done about it? This chapter covers the definition of poverty, its measurement, causes, and the government programmes aimed at poverty alleviation. CBSE Class 11 Economics (Indian Economic Development) Chapter 4.