Index Numbers for CA Foundation
Index numbers: simple and weighted price indices, Laspeyres, Paasche and Fisher, tests of adequacy, chain base, deflating and splicing.
Quantitative AptitudePaper 3, Statistics12 MCQs2 lessons2 flashcards3 memory tricks
What you'll learn
- Constructing index numbers
Calculate simple and weighted price indices. - Tests, chain base and uses
Apply tests of adequacy and practical adjustments.
Key formulas
| Price relative | p₁/p₀ × 100 |
|---|---|
| Simple aggregative | Σp₁/Σp₀ × 100 |
| Laspeyres | Σp₁q₀/Σp₀q₀ × 100 |
| Paasche | Σp₁q₁/Σp₀q₁ × 100 |
| Fisher | √(L × P) |
| Marshall–Edgeworth | Σp₁(q₀ + q₁)/Σp₀(q₀ + q₁) × 100 |
Concepts explained
Laspeyres, Paasche and Fisher
Weighted price indices: Laspeyres uses base year quantities, Paasche current year quantities, and Fisher takes the geometric mean of the two.
What it means
- Laspeyres = Σp₁q₀/Σp₀q₀ × 100.
- Paasche = Σp₁q₁/Σp₀q₁ × 100.
- Fisher = √(L × P): 'ideal', passes time and factor reversal tests.
- Laspeyres tends to overstate and Paasche to understate price rises.
- L = 125, P = 120
Answer: ≈ 122.47
- Σp₁q₀ = 110, Σp₀q₀ = 90
Answer: ≈ 122.22
Related terms
- Marshall–Edgeworth: uses q₀ + q₁ as weights
- Dorbish–Bowley: arithmetic mean of L and P
Exam tip: L for 'last' (base) quantities, P for 'present' quantities.
Simple index numbers and price relatives
An index number shows the relative change in a variable compared with a base period set at 100.
What it means
- Price relative = p₁/p₀ × 100.
- Simple aggregative = Σp₁/Σp₀ × 100.
- Simple average of relatives = Σ(p₁/p₀ × 100)/n.
- Base year should be normal (no unusual events).
- ₹40 → ₹50
Answer: 125
- Σp₀ 50, Σp₁ 60
Answer: 120
Related terms
- Quantity index: measures changes in quantities
- Value index: Σp₁q₁/Σp₀q₀ × 100
Exam tip: Always divide current by base, never the other way round.
Chain base, deflating and splicing
Chain indices compare each year with the previous one; deflating removes price effects; splicing joins series with different bases.
What it means
- Chain base: each year's link relative to the previous year.
- Real value = money value ÷ price index × 100.
- Splicing: joining two overlapping series into one.
- CPI measures the cost of living; used for DA and inflation.
- ₹15,000 with CPI 150
Answer: ₹10,000
- 12,000 → 18,000; CPI 100 → 160
Answer: Real wage fell to ₹11,250
Related terms
- WPI: wholesale price index
- Base shifting: new base index = old index ÷ new base's old index × 100
Exam tip: Deflate means divide by the price index and multiply by 100.
Memory tricks
Laspeyres: base year quantities; Paasche: current year quantities.
Fisher = √(L × P); passes time and factor reversal tests.
Real wage = money wage ÷ CPI × 100.
Try 3 CA Foundation-style questions
Q1. The total price of a basket is ₹50 in the base year and ₹60 in the current year. The simple aggregative price index is
- 120
- 83.33
- 110
- 60
Show answer
Answer: (1) 120
Index = Σp₁ / Σp₀ × 100 = 60/50 × 100 = 120.
Q2. Laspeyres' index is 125 and Paasche's index is 120. Fisher's ideal index is about
- 122.5
- 245
- 122.47
- 5
Show answer
Answer: (3) 122.47
Fisher = √(125 × 120) = √15,000 ≈ 122.47.
Q3. The consumer price index (cost of living index) is mainly used to
- measure industrial production
- value company shares
- calculate GDP at current prices only
- measure changes in the cost of living and adjust wages (dearness allowance)
Show answer
Answer: (4) measure changes in the cost of living and adjust wages (dearness allowance)
CPI tracks the prices of goods and services bought by households; it is used to measure inflation and revise DA.
Practise all 12 questions Free · explanations for every option · see where you go wrong