Chapter 5 — Index Numbers
Key Concepts Quick Recap
| Index | Formula | Base/Current Quantities |
|---|---|---|
| Laspeyre's Price Index (L) | (Σp₁q₀ / Σp₀q₀) × 100 | Base year quantities (q₀) as weights |
| Paasche's Price Index (P) | (Σp₁q₁ / Σp₀q₁) × 100 | Current year quantities (q₁) as weights |
| Fisher's Ideal Index (F) | √(L × P) | Geometric mean of Laspeyre's and Paasche's |
| Simple Aggregative | (Σp₁ / Σp₀) × 100 | Unweighted |
| Simple Average of Relatives | (1/n)Σ(p₁/p₀) × 100 | Average of price relatives |
I. Choose the Best Answer (MCQs)
1. Laspeyre's price index uses weights based on: (a) Current year quantities (b) Base year quantities (c) Average of base and current quantities (d) No weights
2. Paasche's price index uses weights based on: (a) Base year quantities (b) Current year quantities (c) Average quantities (d) Median quantities
3. Fisher's ideal index is the: (a) Arithmetic mean of Laspeyre's and Paasche's (b) Geometric mean of Laspeyre's and Paasche's (c) Harmonic mean of Laspeyre's and Paasche's (d) Difference between Laspeyre's and Paasche's
4. The Time Reversal Test requires that: (a) P₀₁ = P₁₀ (b) P₀₁ × P₁₀ = 1 (c) P₀₁ + P₁₀ = 1 (d) P₀₁ − P₁₀ = 0
5. If Laspeyre's index = 120 and Paasche's index = 108, Fisher's ideal index is approximately: (a) 114 (b) 113.78 (c) 112 (d) 115
6. Consumer Price Index (CPI) measures: (a) Changes in production (b) Changes in the price level of goods and services bought by consumers (c) Changes in wholesale prices (d) Changes in export prices
7. An index number is always expressed: (a) As a percentage (b) As a ratio (c) In rupees (d) In kilograms
II. Short Answer Questions
Common Mistakes
- Confusing p₀, q₀ (base year) with p₁, q₁ (current year) in formulas.
- Computing Laspeyre's with q₁ instead of q₀.
- Forgetting to multiply by 100 at the end.
Exam Checklist
- Laspeyre's: q₀ weights; Paasche's: q₁ weights; Fisher's: √(L × P).
- Fisher's satisfies Time Reversal Test (P₀₁ × P₁₀ = 1) and Factor Reversal Test.
- CPI: measures consumer price inflation; base for DA revision.
- Index number always expressed with base = 100.