Question

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

Commodity	Base Year		Current Year
	Price	Quantity	Price	Quantity
A	8	20	11	15
B	7	10	12	10
C	3	30	5	25
D	2	50	4	35

Answer 1

Commodity	Base Year		Current Year		p0q0	p1q0	p0q1	p1q1
	p0	q0	p1	q1
A	8	20	11	15	160	220	120	165
B	7	10	12	10	70	120	70	120
C	3	30	5	25	90	150	75	125
D	2	50	4	35	100	200	70	140
Total	-	-	-	-	420	690	335	550

From the table,

`sum "p"_0"q"_0 = 420, sum "p"_1"q"_0 = 690`

`sum "p"_0"q"_1 = 335, sum "p"_1"q"_1 = 550`

(i) Laspeyre’s Price Index Number:

`"P"_01 ("L") = (sum "p"_1"q"_0)/(sum "p"_0"q"_0) xx 100 = 690/420 xx 100 = 164.29`

(ii) Paasche’s Price Index Number:

`"P"_01 ("P") = (sum "p"_1"q"_1)/(sum "p"_0"q"_1) xx 100 = 550/335 xx 100 = 164.18`

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

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

`= (164.29  +  164.18)/2`

= 164.24

(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`

`= (690 + 550)/(420 + 335) xx 100`

`= 1240/755 xx 100`

= 164.24