Question

Calculate Laspeyre’s, Paasche’s, Dorbish-Bowley’s, and Marshall - Edgeworth’s Price index numbers.

Commodity	Base Year		Current Year
	Price	Quantity	Price	Quantity
I	10	9	20	8
II	20	5	30	4
III	30	7	50	5
IV	40	8	60	6

Answer 1

Commodity	Base Year		Current Year		p0q0	p1q0	p0q1	p1q1
	p0	q0	p1	q1
I	10	9	20	8	90	180	80	160
II	20	5	30	4	100	150	80	120
III	30	7	50	5	210	350	150	250
IV	40	8	60	6	320	480	240	360
Total	-	-	-	-	720	1160	550	890

From the table,

`sum "p"_0"q"_0 = 720, sum "p"_1"q"_0 = 1160`

`sum "p"_0"q"_1 = 550, sum "p"_1"q"_1 = 890`

(i) Laspeyre’s Price Index Number:

`"P"_01 ("L") = (sum "p"_1"q"_0)/(sum "p"_0"q"_0) xx 100`

`= 1160/720 xx 100`

= 161.11

(ii) Paasche’s Price Index Number:

`"P"_01 ("P") = (sum "p"_1"q"_1)/(sum "p"_0"q"_1) xx 100`

`= 890/550 xx 100`

= 161.82

(iii) Dorbish-Bowley’s Price Index Number:

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

`= (161.11  +  161.82)/2`

= 161.46

(iv) Marshall-Edgeworth’s Price Index Number:

`"P"_01 ("M- E") = (sum "p"_1"q"_0  +  sum "p"_1"q"_1)/(sum "p"_0"q"_0  +  sum "p"_0"q"_1) xx 100`

`= (1160 + 890)/(720 + 550) xx 100`

= 161.42