Professor Vipin 2014
Index Numbers
Index numbers are statistical measures designed to show changes in a variable or group of related
variables with respect to time, geographic location or other characteristics such as income,
profession, etc. A collection of index numbers for different years, locations, etc., is sometimes called
an index series.
Price Relative
If p0 and p1 are the prices of a commodity in the base year and in the current year respectively, the
price relative is
Price Index Numbers
1. Un-weighted
i.
Simple Average of Relatives
∑
(
ii.
∑
)
Simple aggregative index number
∑
∑
2. Weighted
i.
Weighted Average if relatives
∑
∑
(
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∑
∑
)
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Professor Vipin 2014
ii.
Weighted aggregative index numbers
Laspeyre’s Price Index Number
Paasche’s Price Index Number
Marshall Edgeworth Price Index Number
Dorbish Bowley Price Index Number
(
)
Fisher’s Price Index Number
√(
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)
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Professor Vipin 2014
Laspeyre’s Quantity Index Number
Paasche’s Quantity Index Number
Marshall Edgeworth Quantity Index Number
Dorbish Bowley Quantity Index Number
(
)
Fisher’s Quantity Index Number
√(
)
Tests for an Index Number
1. Time Reversal Test
P01 and P10 are ratios and must not be shown as percentages
Time reversal test is not satisfied by Laspeyre’s, Paasche’s and Dorbish Bowley indx numbers. It is
satisfied by Marshall Edgeworth and Fisher Index Number
2. Factor Reversal Test
∑
∑
Fisher Index number is the only index number that satisfies the factor reversal test.
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Professor Vipin 2014
1. Using the following data. Find
a) Price and Quantity index numbers
b) Time Reversal Test
c) Factor Reversal Test
Commodity
A
B
C
D
Price
Quantity
Base Current
Base Current
4
5
10
10
10
12
5
4
3
4
2
3
2
4
1
2
Problem Format
Commodity
p0
A
B
C
D
Total
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p1
q0
q1
p0q0
p0q1
p1q0
p1q1
∑p0q0
∑p0q1
∑p1q0
∑p1q1
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