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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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 Winter '08
 Moshiri
 Business

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