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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.
 Winter '08
 Moshiri
 Business

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