# Calculate Laspeyre’s - Mathematics and Statistics

Chart
Sum

Calculate
a) Laspeyre’s
b) Passche’s
c) Dorbish-Bowley’s Price Index Numbers for following data.

 Commodity Base Year Current Year Price Quantity Price Quantity A 10 9 50 8 B 20 5 60 4 C 30 7 70 3 D 40 8 80 2

#### Solution

Construct the following table:

 Commodity Base Year Current Year p0q0 p1q0 p0q1 p1q1 p0 q0 p1 q1 I 10 9 50 8 90 450 80 400 II 20 5 60 4 100 300 80 240 III 30 7 70 3 210 490 90 210 IV 40 8 80 2 320 640 80 160 Total – – – – 720 1880 330 1010

From the table, sum"p"_0"q"_0 = 720, sum"p"_1"q"_0 = 1880, sum"p"_0"q"_1 = 330, sum"p"_1"q"_1 = 1010

a) Laspeyre’s Price Index Number:

P01(L) = (sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100

= 1880/720 xx 100

= 261.11

b) Paasche’s Price Index Number:

P01(P) = (sum"p"_1"q"_1)/(sum"p"_0"q"_1) xx 100

= 1010/330 xx 100

= 306.6

c) Drobish-Bowley’s Price Index Number:

P01(D-B) = ("P"_01("L") + "P"_01("P"))/2

= (261.11 + 306.06)/2

= 567.17/2

= 283.59

Concept: Construction of Index Numbers - Weighted Aggregate Method
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Chapter 2.5: Index Numbers - Q.4
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