Page 213 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes 1. Laspeyres’s Index: Laspeyres’ price index number uses base year quantities as weights.
Thus, we can write:

p q p q
P La 1i 0i 100 P La 1 0 100
01 or 01
p q p q
0i 0i 0 0
2. Paasche’s Index: This index number uses current year quantities as weights. Thus, we can
write

p q p q
P Pa 1i 1i 100 P Pa 1 1 100
01 or 01
p q p q
0i 1i 0 1
3. Fisher’s Ideal Index: As will be discussed later that the Laspeyres’s Index has an upward
bias and the Paasche’s Index has a downward bias. In view of this, Fisher suggested that an
ideal index should be the geometric mean of Laspeyres’ and Paasche’s indices. Thus, the
Fisher’s formula can be written as follows:

p q p q
P F P La P Pa 1 0 100 1 1 100
01 01 01
p q p q
0 0 0 1
p q p q
1 0 1 1
If we write L = and P = , the Fisher’s Ideal Index can also be written
p q p q
0 0 0 1
as P L P 100
01
4. Dorbish and Bowley’s Index: This index number is constructed by taking the arithmetic
mean of the Laspeyres’s and Paasche’s indices.

1 p q p q
P DB 1 0 100 1 1 100
01
2 p q p q
0 0 0 1

1 p q p q 1
1 1
1 0
100 L P 100
2 p q p q 2
0 0 0 1
5. Marshall and Edgeworth’s Index: This index number uses arithmetic mean of base and
current year quantities.

q q
p 0 1
1 2 p q q p q p q
P ME 100 1 0 1 100 1 0 1 1 100
01 q q p q q p q p q
p 0 1 0 0 1 0 0 0 1
0
2

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