Unit 2: Index Numbers
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Unit 2: Index Numbers Note 1. This unit is purely formula based. 2. There is no problem that needs logic to interpret 3. Substitution of values into the right formula is all that is needed Price Relative πππππ π ππππ‘ππ£π (π) = π1 × 100 π0 p1 – price in current year p0 – price in base year Price Index Numbers (Unweighted) Simple Aggregative Method π01 = ∑ π1 × 100 ∑ π0 Simple Unweighted Arithmetic Mean π01 = ∑π π Unweighted Simple Geometric Mean π01 = π΄ππ‘ππππ ( ∑ ππππ ) π Price Index Numbers (Weighted) Laspeyre’s Price Index πΏ π01 = ∑ π1 π0 × 100 ∑ π0 π0 π π01 = ∑ π1 π1 × 100 ∑ π0 π1 Paasche’s Price Index Marshall-Edgeworth Price Index ππΈ π01 = ∑ π1 π0 + ∑ π1 π1 × 100 ∑ π0 π0 + ∑ π0 π1 Dorbish – Bowley’s Price Index π·π΅ π01 =( ∑ π1 π0 ∑ π1 π1 ) × 100 + ∑ π0 π0 ∑ π0 π1 Fisher’s Price Index πΉ π01 =√ ∑ π1 π0 ∑ π1 π1 × × 100 ∑ π0 π0 ∑ π0 π1 Kelly’s Price Index / Fixed Weight Index πΎ π01 = ∑ π1 π × 100 ∑ π0 π Weighted Avergage of Price Relatives a) Weighted AM π01 = ∑ ππ π b) Weighted GM π01 = π΄ππ‘ππππ ( ∑ πππππ ) ∑π Quantity Index Numbers (Weighted) Laspeyre’s Quantity Index πΏ π01 = ∑ π1 π0 × 100 ∑ π0 π0 π π01 = ∑ π1 π1 × 100 ∑ π0 π1 Paasche’s Quantity Index Marshall-Edgeworth Quantity Index ππΈ π01 = ∑ π1 π0 + ∑ π1 π1 × 100 ∑ π0 π0 + ∑ π0 π1 Dorbish – Bowley’s Quantity Index π·π΅ π01 =( ∑ π1 π0 ∑ π1 π1 ) × 100 + ∑ π0 π0 ∑ π0 π1 Fisher’s Quantity Index πΉ π01 =√ ∑ π1 π0 ∑ π1 π1 × × 100 ∑ π0 π0 ∑ π0 π1 Value Index Numbers π01 = ∑ π1 π1 × 100 ∑ π0 π0 Tests for Adequacy of Index Numbers Time Reversal Test π10 = 1 =1 π01 TRT is not satisfied by Laspeyre’s, Paasche’s and Dorbish Bowley’s index numbers. But it is satisfied by Marshall-Edgeworth, Fisher and Kelly index numbers Factor Reversal Test π01 × π01 = Only Fisher’s index satisfies factor reversal test. ∑ π1 π1 ∑ π0 π0 Cost of Living Index Number Aggregative Expenditure Method πΆππΌ = ∑ π1 π0 × 100 ∑ π0 π0 Family Budget Method πΆππΌ = ∑ ππ ∑π
