Laspeyre's price index uses as weights the:

Base year quantities. Σp₁q₀/Σp₀q₀ × 100.

Paasche's price index uses as weights the:

Current year quantities. Σp₁q₁/Σp₀q₁ × 100.

Fisher's price index number is:

√(L × P). Geometric mean of Laspeyre and Paasche.

Maharashtra State Board · HSC Commerce · Class 12 (Std XII)

Class 12 Maths and Statistics Part 2 Chapter 5: Index Numbers

Short notes, key concepts, quick revision and practice MCQs with answers

An index number measures the relative change in prices, quantities or values over time compared with a base period taken as 100. The chapter covers types and notation, simple and weighted aggregate methods, the Laspeyre, Paasche, Dorbish-Bowley, Marshall-Edgeworth, Walsh and Fisher indices, and cost of living index numbers.

Key concepts: Index Numbers

Index number: A statistical measure of the relative change in a variable (or group of variables) between a base period and a current period, expressed as a percentage with the base = 100.
Types and notation: Price, quantity and value index numbers. p₀, q₀ are base year price and quantity; p₁, q₁ are current year price and quantity. P₀₁ is the price index of the current year with respect to the base year.
Simple aggregate method: P₀₁ = Σp₁/Σp₀ × 100; quantity index Q₀₁ = Σq₁/Σq₀ × 100; value index V₀₁ = Σp₁q₁/Σp₀q₀ × 100.
Weighted aggregate method: P₀₁ = Σp₁w/Σp₀w × 100, where w is the weight given to each commodity.
Laspeyre and Paasche: Laspeyre (base year quantities as weights): Σp₁q₀/Σp₀q₀ × 100. Paasche (current year quantities): Σp₁q₁/Σp₀q₁ × 100.
Other weighted indices: Dorbish-Bowley = (Laspeyre + Paasche)/2. Marshall-Edgeworth = Σp₁(q₀ + q₁)/Σp₀(q₀ + q₁) × 100. Walsh = Σp₁√(q₀q₁)/Σp₀√(q₀q₁) × 100.
Fisher's ideal index: P₀₁(F) = √[(Σp₁q₀/Σp₀q₀) × (Σp₁q₁/Σp₀q₁)] × 100, the geometric mean of Laspeyre and Paasche.
Cost of living index: Measures the change in the cost of living of a particular class of people. Aggregate expenditure method: Σp₁q₀/Σp₀q₀ × 100. Family budget method: ΣIW/ΣW, where I = p₁/p₀ × 100 and W = p₀q₀.

Quick revision: important points

The index number of the base year is always 100.
Fisher's index lies between Laspeyre's and Paasche's.
Aggregate expenditure method is the same as Laspeyre's formula.
Real income = money income × 100/cost of living index.
Index numbers are called economic barometers.

Practice MCQs with answers

The index number of the base year is:
1. 0
2. 1
3. 100
4. 1000
Show answer
Answer: C. 100
The base is taken as 100.
If Σp₀ = 200 and Σp₁ = 250, the simple aggregate price index is:
1. 80
2. 125
3. 150
4. 50
Show answer
Answer: B. 125
250/200 × 100 = 125.
Laspeyre's price index uses as weights the:
1. Current year quantities
2. Base year quantities
3. Average quantities
4. Prices
Show answer
Answer: B. Base year quantities
Σp₁q₀/Σp₀q₀ × 100.
Paasche's price index uses as weights the:
1. Base year quantities
2. Current year quantities
3. Base year prices
4. Equal weights
Show answer
Answer: B. Current year quantities
Σp₁q₁/Σp₀q₁ × 100.
Fisher's price index number is:
1. (L + P)/2
2. √(L × P)
3. L × P
4. L/P
Show answer
Answer: B. √(L × P)
Geometric mean of Laspeyre and Paasche.

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