Question

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

Answer 1

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`

= 306.06

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