bus-stat-book1

Q1p 0 laspeyre s quantity index number q01l 100 q 0 p

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Unformatted text preview: 0 = 131. 0 Example 5: Calculate a suitable price index from the following data Commodity Quantity A B C Price 1996 2 5 3 20 15 8 1997 4 6 2 Solution: Here the quantities are given in common we can use Kelly’ s index price number and is given by Σp1q Kelly’ s Price index number = P01k = × 100 Σp 0 q 186 = × 100 = 133.81 139 Commodity A B C q 20 15 8 P0 2 5 3 P1 4 6 2 Total p0q 40 75 24 139 P1 q 80 90 16 186 Σp1q × 100 Σp 0 q IV. Weighted Average of Price Relative index. When the specific weights are given for each commodity, the weighted index number is calculated by the formula. Σpw Weighted Average of Price Relative index = Σw Where w = the weight of the commodity P = the price relative index Kelly’ s Price index number = P01k = 251 p1 × 100 p0 When the base year value P0q0 is taken as the weight i.e. W=P0q0 then the formula is p Σ 1 × 100 × p 0 q 0 p Weighted Average of Price Relative index = 0 Σp 0 q 0 Σp1q 0 = × 100 Σp 0 q 0 This is nothing but Laspeyre’ s formula. When the weights are taken as w = p0q1, the formula is p Σ 1 × 100 × p0 q1 p Weighted Average of Price Relative index = 0 Σp 0 q1 Σp1q1 = × 100 Σp 0 q1 This is nothing but Paasche’ s Formula. = Example 6: Compute the weighted index number for the following data. Commodity Price Weight Current Base year year A 5 4 60 B 3 2 50 C 2 1 30 Solution: Commodity P1 P0 W A B 5 3 4 2 60 50 252 P= p1 × 100 p0 125 150 PW 7500 7500 C 2 1 30 140 200 Weighted Average of Price Relative index = 6000 21000 Σpw Σw 21000 140 = 150 10.6 Quantity or Volume index number: Price index numbers measure and permit comparison of the price of certain goods. On the other hand, the quantity index numbers measure the physical volume of production, employment and etc. The most common type of the quantity index is that of quantity produced. Σq1p 0 Laspeyre’ s quantity index number = Q01L = × 100 Σq 0 p 0 Σq1p1 Paasche’ s quantity index number = Q01P = × 100 Σq 0 p1 = Fisher’ s quantity index number = Q01F = = L× P Σq1 p0 Σq1 p1 × × 100 Σq 0 p 0 Σq 0 p1 These formulae represent the quantity index in which quantities of the different commodities...
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