CMA Foundation · Fundamentals of Business Mathematics and Statistics · Index Numbers and Time Series
Two items have base-year prices ₹10 (A) and ₹20 (B) with base quantities 4 and 3. In the current year prices are ₹20 (A) and ₹10 (B) with quantities 3 and 4. Using Laspeyres' formula with its own base weights each time, what is P01 × P10 and is the time reversal test satisfied?
The Laspeyres index forward is 1.1 and the reversed index, using current-year quantities as weights, is also 1.1. Their product is 1.21, which differs from one, so Laspeyres' formula fails the time reversal test here.
- A1.21; not satisfiedCorrect
- B1.00; satisfied
- C1.10; satisfied
- D2.20; not satisfied
Explanation
Laspeyres P01 = (20×4+10×3)/(10×4+20×3) = 110/100 = 1.1. For P10 the base is year 1: Σp0q1/Σp1q1 = (10×3+20×4)/(20×3+10×4) = 110/100 = 1.1. The product is 1.21, not 1, so the test fails.
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