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# Symbolically the following relation should be

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Unformatted text preview: are weighted by their prices. Example 7: From the following data compute quantity indices by (i) Laspeyre’ s method, (ii) Paasche’ s method and (iii) Fisher’ s method. 2000 2002 Commodity Price Total Price Total value value A 10 100 12 180 B 12 240 15 450 253 C 15 225 17 340 Solution: Here instead of quantity, total values are given. Hence first find quantities of base year and current year, total value ie. Quantity = price Commodity p0 q0 P1 q1 p0q0 p0q1 p1q0 p1q1 A 10 10 12 15 100 150 120 180 B 12 20 15 30 240 360 300 450 C 15 15 17 20 225 300 255 340 565 810 675 970 Σq1p 0 × 100 Σq 0 p 0 810 = × 100 565 = 143.4 Σq1p1 Paasche’ s quantity index number = q01P = × 100 Σq 0 p1 970 = × 100 675 = 143.7 F Fisher’ s quantity index number = q01 = L × P Laspeyre’ s quantity index number = q01L = = 143.4 × 143.7 = 143.6 (or) q01F = Σq1 p0 Σq1 p1 × × 100 Σq 0 p 0 Σq 0 p1 810 970 × × 100 565 675 = 1.434 × 1.437 × 100 = 254 = 1.436 ×100 = 143.6 10.7 Tests of Consistency of index numbers: Several formulae have been studied for the construction of index number. The question arises as to which formula is appropriate to a given problems. A number of tests been developed and the important among these are 1. Unit test 2. Time Reversal test 3. Factor Reversal test 1. Unit test: The unit test requires that the formula for constructing an index should be independent of the units in which prices and quantities are quoted. Except for the simple aggregate index (unweighted) , all other formulae discussed in this chapter satisfy this test. 2. Time Reversal test: Time Reversal test is a test to determine whether a given method will work both ways in time, forward and backward. In the words of Fisher, “the formula for calculating the index number should be such that it gives the same ratio between one point of comparison and the other, no matter which of the two is taken as base”. Symbolically, the following relation should be satisfied. P01 × P10 = 1 Where P01 is the index for time ‘ 1’ as time ‘ 0’ as base and P10 is the index for time ‘ 0’ as time ‘ 1’ as base. If the product is not unity, the...
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## This note was uploaded on 01/18/2014 for the course BUS 100 taught by Professor Moshiri during the Winter '08 term at UC Riverside.

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