Page 232 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes Solution: Computation of Laspeyres, Paasche’s, Fisher’s Index

Item p q p q p q p q p q p q
0 0 1 1 1 0 0 0 1 1 0 1
A 5 25 6 30 150 125 180 150
B 3 8 4 10 32 24 40 30
C 2 10 3 8 30 20 24 16
D 10 4 3 5 12 40 15 50
∑ p q ∑ p q ∑ p q ∑ p q
01
00
11
10
= 224 = 209 = 259 = 246
∑ pq 224
10
Laspeyres Index: P = × 100 = × 100 = 107.17
01 ∑ pq 209
00
∑ pq 259
11
Paasche’s Index: P = × 100 = × 100 = 105.28
01 ∑ pq 246
01
Fisher’s Index: P = LP× = 107.17 105.28× = 106.22
01
∑ pq + 1 ( 0 q 1 ) ∑ pq + ∑ pq
Marshall-Edgeworth’s Index: P = × 100 = 10 11 × 100
01 ∑ pq + 0 ( q 1 ) 0 ∑ pq + 00 ∑ pq
01
+
224 259
= × 100 = 106.15
+
209 246
Example 9 : Prepare Index Number for 2010 on the basis of 2005, where the following information
is given:
Year Article I Article II Article III

Price Quantity Price Quantity Price Quantity

2005 5 10 8 6 6 4
2010 4 12 7 7 5 3

Solution : Fisher’s Ideal Index Number for 2010 —(Base 2005)

2005 (Base Year) 2010

Article Price Qnty. Price Qnty. p q p q p q p q
0 0 1 0 0 1 1 1
p q p q
0 0 1 1
I 5 10 4 12 50 40 60 48
II 8 6 7 7 48 42 56 49
III 6 4 5 3 24 20 18 15

122 102 134 112
( p q∑ 00 ) ( p q∑ 10 ) ( p q∑ 01 ) ( p q∑ 11 )

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