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Unformatted text preview: by the sum of the prices of those
commodities by 100. Symbolically,
∑ p1
Simple aggregate price index = P01 =
× 100
∑ p0
243 Where , p1 = t otal prices for the current year
p0 = Total prices for the base year
Example 1:
Calculate index numbers from the following data by simple
aggregate method taking prices of 2000 as base.
Commodity A
B
C
D
Solution:
Commodity A
B
C
D
Total Price per unit
(in Rupees)
2000
2004
80
95
50
60
90
100
30
45 Price per unit
(in Rupees)
2000
2004
(P0)
(P1)
80
95
50
60
90
100
30
45
250
300 ∑ p1
× 100
∑ p0
300
=
× 100 = 120
250
10.5.2 Simple Average Price Relative index:
In this method, first calculate the price relative for the
various commodities and then average of these relative is obtained
by using arithmetic mean and geometric mean. When arithmetic
mean is used for average of price relative, the formula for
computing the index is
Simple aggregate Price index = P01 = 244 Simple average of price relative by arithmetic mean P01 = ∑ × 100 p0 n
p1 P1 = Prices of current year
P0 = Prices of base year
n = Number of items or commodities
when geometric mean is used for average of price relative, the
formula for obtaining the index is
Simple average of price relative by geometric Mean
p1 Σ log( p × 100) 0 P01 = Antilog n Example 2:
From the following data, construct an index for 1998 taking 1997
as base by the average of price relative using (a) arithmetic mean
and (b) Geometric mean
Commodity
Price in 1997
Price in 1998
A
50
70
B
40
60
C
80
100
D
20
30
Solution:
(a) Price relative index number using arithmetic mean
Commodity Price in 1997
(P0) A
B
C
D 50
40
80
20 Price in
1998
(P1)
70
60
100
30
Total
245 p1
× 100
p0
140
150
125
150
565 p Σ 1 × 100 p Simple average of price relative index = (P01) = 0
4
565
=
= 141.25
4
(b) Price relative index number using Geometric Mean
Commodity Price in Price in
p1
p
× 100 log( 1 ×100)
1998
1997
p0
p0
(P1)
(P0)
A
50
70
140
2.1461
B
40
60
150
2.1761
C
80
100
125
2.0969
D
20
30
150
2.1761
Total
8.5952
Simple average of price Relative index
p Σ log 1 x100 po (P01) = Antilog...
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 Winter '08
 Moshiri
 Business

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