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This page provides complete NCERT exercise solutions for CBSE Class 11 Economics Chapter 8 — Index Numbers. Review the Key Concepts and formulas first, then attempt each numerical. Step-by-step working is shown for all index number calculations. Verify your answers against these solutions.
Key Concepts (Quick Recap)
- Index Number: a statistical measure showing relative change in a variable over time; expressed as a percentage
- Base Year: the reference year with index = 100; should be a normal year
- Price Relative: P₀₁ = (p₁/p₀) × 100 (price in current year relative to base year)
- Quantity Relative: Q₀₁ = (q₁/q₀) × 100
- Value Relative: V₀₁ = (p₁q₁)/(p₀q₀) × 100
- Simple Index Number: unweighted average of price relatives
- Weighted Index Number: uses weights (quantities or values)
- Laspeyres Index (L): base year quantities as weights
- P₀₁L = Σp₁q₀/Σp₀q₀ × 100
- Paasche Index (P): current year quantities as weights
- P₀₁P = Σp₁q₁/Σp₀q₁ × 100
- Fisher's Ideal Index (F): geometric mean of L and P
- P₀₁F = √(Lasp × Paas)
- Consumer Price Index (CPI): measures retail price changes; used for DA calculation
- CPI = ΣWI/ΣW where W = weight, I = price relative
- Wholesale Price Index (WPI): measures wholesale price changes; inflation indicator
- Tests of Index Numbers: Time Reversal Test (P₀₁ × P₁₀ = 1), Factor Reversal Test (P₀₁ × Q₀₁ = V₀₁)
- Uses of Index Numbers: measure inflation, adjust wages (DA), deflation of national income, compare cost of living
Intext Questions
Section 8.1 — Meaning and Types
Section 8.2 — Construction of Index Numbers
Chapter-End Exercise
Question 1
Calculate the price index number for 2024 with 2020 as base using:
| Commodity | Price 2020 (p₀) | Price 2024 (p₁) |
|---|---|---|
| A | 10 | 15 |
| B | 20 | 25 |
| C | 30 | 35 |
| D | 40 | 50 |
Answer (Simple Aggregate Method):
P₀₁ = Σp₁/Σp₀ × 100 = (15+25+35+50)/(10+20+30+40) × 100 = 125/100 × 100 = 125
Interpretation: Prices increased by 25% from 2020 to 2024.
Question 2
Calculate the price index using the simple average of price relatives method:
| Commodity | p₀ | p₁ | Price Relative (p₁/p₀ × 100) |
|---|---|---|---|
| A | 10 | 15 | 150 |
| B | 20 | 25 | 125 |
| C | 30 | 35 | 116.67 |
| D | 40 | 50 | 125 |
Question 3
Calculate Laspeyres index from the following data:
| Commodity | p₀ | q₀ | p₁ | q₁ |
|---|---|---|---|---|
| A | 10 | 50 | 15 | 40 |
| B | 20 | 30 | 25 | 35 |
| C | 30 | 20 | 35 | 25 |
| Commodity | p₁q₀ | p₀q₀ |
|---|---|---|
| A | 15×50 = 750 | 10×50 = 500 |
| B | 25×30 = 750 | 20×30 = 600 |
| C | 35×20 = 700 | 30×20 = 600 |
| Total | 2200 | 1700 |
Lasp = Σp₁q₀/Σp₀q₀ × 100 = 2200/1700 × 100 = 129.41
Question 4
Calculate Paasche index from the same data (Question 3).
| Commodity | p₁q₁ | p₀q₁ |
|---|---|---|
| A | 15×40 = 600 | 10×40 = 400 |
| B | 25×35 = 875 | 20×35 = 700 |
| C | 35×25 = 875 | 30×25 = 750 |
| Total | 2350 | 1850 |
Paas = Σp₁q₁/Σp₀q₁ × 100 = 2350/1850 × 100 = 127.03
Question 5
Calculate Fisher's Ideal Index from the Laspeyres and Paasche indices calculated above.
Fisher = √(Lasp × Paas) = √(129.41 × 127.03) = √16439.06 = 128.27
Question 6
Calculate the Consumer Price Index (CPI) from the following data:
| Group | Weight (W) | Price Relative (I) |
|---|---|---|
| Food | 40 | 150 |
| Clothing | 15 | 130 |
| Fuel | 10 | 120 |
| Rent | 20 | 140 |
| Misc | 15 | 110 |
| Group | W | I | WI |
|---|---|---|---|
| Food | 40 | 150 | 6000 |
| Clothing | 15 | 130 | 1950 |
| Fuel | 10 | 120 | 1200 |
| Rent | 20 | 140 | 2800 |
| Misc | 15 | 110 | 1650 |
| Total | 100 | 13600 |
CPI = ΣWI/ΣW = 13600/100 = 136
Interpretation: The cost of living has increased by 36% compared to the base year.
Question 7
What is the time reversal test? Which index numbers satisfy it?
Condition: P₀₁ × P₁₀ = 1
Fisher's Ideal Index satisfies this test because it is the geometric mean of Laspeyres and Paasche indices. Neither Laspeyres nor Paasche alone satisfies this test.
Question 8
What is the factor reversal test?
Condition: P₀₁ × Q₀₁ = V₀₁
Where P₀₁ = price index, Q₀₁ = quantity index, V₀₁ = (p₁q₁)/(p₀q₀) (value relative)
Fisher's Ideal Index satisfies this test, which is why it is called the "ideal" index.
Question 9
Explain the uses of index numbers.
1. Measure of inflation: CPI and WPI measure the rate of inflation in the economy. 2. Dearness Allowance: CPI is used to calculate DA for government employees and workers. 3. Deflation of national income: Index numbers convert nominal income into real income. 4. Comparison of cost of living: CPI helps compare living costs across cities and time. 5. Economic policy-making: Government uses index numbers for fiscal and monetary policy. 6. Business decisions: Firms use price indices for pricing, wage negotiations, and inventory management. 7. Stock market analysis: Sensex and Nifty are index numbers tracking stock prices. 8. Agricultural analysis: Agricultural price indices track farm product prices.
Question 10
What are the limitations of index numbers?
1. Based on samples: Not all items are included; index is based on a representative basket. 2. Choice of base year: A non-normal base year distorts the index. 3. Quality changes: Index does not account for changes in product quality over time. 4. New products: New items entering the market are not immediately included. 5. Weighting problems: Weights may become outdated as consumption patterns change. 6. International comparison: Different countries use different baskets and base years. 7. Not exact: Index numbers are approximate measures, not precise.
Question 11
Explain the difference between CPI and WPI.
| Basis | CPI | WPI |
|---|---|---|
| Full form | Consumer Price Index | Wholesale Price Index |
| Level | Retail prices | Wholesale prices |
| Coverage | Goods and services consumed by households | Goods traded at wholesale level |
| Services | Includes services | Generally excludes services |
| Use | Calculating DA, cost of living | Indicator of inflation |
| Frequency | Monthly | Weekly/Monthly |
| Published by | Labour Bureau / CSO | Office of Economic Adviser |
Question 12
Calculate the index number using weighted average of price relatives:
| Commodity | p₀ | p₁ | q₀ |
|---|---|---|---|
| A | 5 | 8 | 10 |
| B | 10 | 12 | 5 |
| C | 15 | 18 | 8 |
| Commodity | p₀ | p₁ | q₀ | Weight W = p₀q₀ | Price Relative I = (p₁/p₀)×100 | WI |
|---|---|---|---|---|---|---|
| A | 5 | 8 | 10 | 50 | (8/5)×100 = 160 | 8000 |
| B | 10 | 12 | 5 | 50 | (12/10)×100 = 120 | 6000 |
| C | 15 | 18 | 8 | 120 | (18/15)×100 = 120 | 14400 |
| Total | 220 | 28400 |
P₀₁ = ΣWI/ΣW = 28400/220 = 129.09
Internal Links
- [Chapter 8 Guide — Index Numbers](/school/cbse/class/11/economics/cbse-index-numbers)
- [All Class 11 Economics Solutions](/school/cbse/class/11/economics/solutions)
- [Class 11 Economics Subject Guide](/school/cbse/class/11/economics)