bus-stat-book1

316 1302 100 2 1 2168 100 2 1309 100 1309 b

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Unformatted text preview: ggested the following formula for constructing the index number Σp1q Kelly’ s Price index number = P01k = × 100 Σp 0 q q + q1 Where = q = 0 2 Here the average of the quantities of two years is used as weights Example 3: Construct price index number from the following data by applying 1. Laspeyere’ s Method 2. Paasche’ s Method 3. Fisher’ s ideal Method 2000 2001 Commodity Price Qty Price Qty A 2 8 4 5 B 5 12 6 10 C 4 15 5 12 D 2 18 4 20 Solution: Commodity A B C D p0 2 5 4 2 q0 8 12 15 18 p1 4 6 5 4 q1 5 10 12 20 248 p0q0 16 60 60 36 172 p0q1 10 50 48 40 148 p1q0 p1 q1 32 72 75 72 251 20 60 60 80 220 Σp1q 0 × 100 Σp 0 q 0 251 = × 100 = 145.93 172 Σp1q1 Paasche price index number = P01P = × 100 Σp 0 q1 220 = × 100 148 = 148 .7 Fisher’ s ideal index number = L × P Laspeyre’ s price index = P01L = = (145.9) × (148.7) = 21695.33 = 147 .3 Or Fisher’ s ideal index number = = = Σp1 q 0 Σp1q1 × × 100 Σp 0 q 0 Σp 0 q1 251 220 × × 100 172 148 (1.459) × (1.487) × 100 = 2.170 × 100 = 1.473 × 100 = 147.3 Interpretation: The results can be interpreted as follows: If 100 rupees were used in the base year to buy the given commodities, we have to use Rs 145.90 in the current year to buy the same amount of the commodities as per the Laspeyre’ s formula. Other values give similar meaning . Example 4: Calculate the index number from the following data by applying (a) Bowley’ s price index 249 (b) Marshall- Edgeworth price index Commodity A B C Base year Quantity Price 10 3 20 15 2 25 Current year Quantity Price 8 4 15 20 3 30 Solution: Commodity A B C q0 10 20 2 P0 3 15 25 q1 8 15 3 P1 4 20 30 p0q0 30 300 50 380 p0q1 24 225 75 324 p1q0 p1 q1 40 400 60 500 32 300 90 422 1 Σp1q 0 Σp1q1 + × 100 2 Σp 0 q 0 Σp 0 q1 1 500 422 + = × 100 2 380 324 1 = [1.316 + 1.302] ×100 2 1 = [ 2.168] ×100 2 = 1.309 × 100 = 130.9 (b) Marshall Edgeworths price index Number Σ(q 0 + q1 )p1 = P01ME = × 100 Σ(q 0 + q1 )p 0 500 422 = × 100 + 380 324 922 = ×100 704 (a) Bowley’ s price index number = 25...
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