Indices Calculation
Illustration: - construct index numbers of price from the following data by applying
Laspeyres method,
Paasche method
Bowley's method,
Fisher's ideal method, and
Marshall-Edgeworths method.
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2006
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2007
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Commodity
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Price
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Quantity
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Price
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Quantity
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A
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2
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8
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4
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6
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B
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5
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10
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6
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5
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C
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4
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14
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5
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10
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D
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2
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19
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2
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13
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Solution: -
Calculation of various indices
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Commodity
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2006 price qty.
P0 q0
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2007 prices qty.
P1 q1
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P1q0 P0q0 P1q1 P0q1
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A
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82
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46
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32 16 24
12
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B
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105
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65
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60 50 30
25
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C
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144
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510
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70 56 50
40
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D
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192
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213
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38 38 26
26
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∑p1q0 =200, ∑P0q0 =160, ∑p1q1 =130, ∑p0q1 =103
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Laspeyres method:
p01 = ∑p1q0 / ∑p0q0 x 100; where ∑p1q0 = 200, ∑p0q0 = 160
p01 = 200/160 x 100 = 125.
Paasche's method:
p01 = ∑p1q1 / ∑p0q1 x 100; where ∑p1q1 = 130, ∑p0q1 = 103
p0i = 130 / 103 x 100= 126.21
Bowley's method:
p01 = ∑p1q0/∑p0q0 + ∑p1q1/∑p0q1 / 2 +100 = 200/160 + 130/103 / 2 +100
= 1.25 + 1.262 / 2 x 100 = 126.2 / 2 x 100 = 125.6
Or p0i = L + P / 2 = 125 + 126.2 / 2 = 125.6
Fisher's ideal method:
p01 = √(∑)p1q0/∑p0q0 x ∑p1q1/∑p0q1 x 100 √200/160 x 130/102 x 100
= √1.578 x 100 = 1.2561 x 100 = 125.61
Marshall-Edgeworths method:
p01=∑(q0 + q1) p1 / ∑(q0 + q1) p0 x 100 = ∑p1q0 + ∑p1q1 / ∑p0q0 + ∑p0q1
= 200 + 130 / 160 +103 x 100 = 330/263 x 100 = 330/263 x 100 = 125.48