Page 231 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Unit 16: Methods—Simple (Unweighted) Aggregate Method and Weighted Aggregate Method

Notes
∑ pq
10
1. Laspeyres Method: P = × 100 ; where ∑ p q = 200, ∑ p q = 160
01 ∑ pq 10 00
00
200
P = × 100 = 125
01 160

∑ pq
11
2. Paasche’s Method: P = × 100 ; where ∑ p q = 130, ∑ p q = 103
01 ∑ pq 11 01
01
130
P = × 100 = 126.21
01 103

∑ pq + ∑ p q
1 1
10
∑ pq ∑ p q
3. Bowley’s Method: P = 00 01 × 100
01
2
200 + 130
160 103
= × 100
2

+
1.25 1.262 2.512
= × 100 = × 100 = 125.6
2 2
+
LP 125 + 126.2
P = = = 125.6
01 2 2
4. Fisher’s Ideal Method:

∑ pq ∑ pq 200 130
11
10
P = + × 100 = × × 100
01 ∑ pq ∑ pq 160 103
0 1
00
= 1.578 100× = 1.2561 × 100 = 125.61
5. Marshall-Edgeworth Method:
∑ ( q + q 1 ) 0 p 1 ∑ pq + 10 ∑ pq
11
P = ( × 100 =
01 ∑ q + q 1 ) 0 p 0 ∑ pq + 00 ∑ pq
01
+
200 130 330
= × 100 = × 100 = 125.48
+
160 103 263
Example 8: Compute Laspeyres, Paasche’s, Fisher’s and Marshall-Edgeworth’s Index Numbers
from the following data:
Item Base Year Current Year

Price (Rs.) Quantity Price (Rs.) Quantity
A 5 25 6 30
B 3 8 4 10
C 2 10 3 8
D 10 4 3 5

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