Question

Calculate Walsh’s Price Index Number.

Commodity	Base Year		Current Year
	Price	Quantity	Price	Quantity
I	10	12	20	9
II	20	4	25	8
III	30	13	40	27
IV	60	29	75	36

Answer 1

Commodity	Base Year		Current Year		q0q1	${\displaystyle \sqrt{{\text{q}}_0{\text{q}}_1}}$	${\displaystyle {\text{p}}_0\sqrt{{\text{q}}_0{\text{q}}_1}}$	${\displaystyle {\text{p}}_1\sqrt{{\text{q}}_0{\text{q}}_1}}$
	p0	q0	p1	q1
I	10	12	20	9	108	10.39	103.9	207.8
II	20	4	25	8	32	5.66	113.2	141.5
III	30	13	40	27	351	18.73	561.9	749.2
IV	60	29	75	36	1044	32.31	1938.6	2423.25
Total	-	-	-	-		-	2717.6	3521.75

From the table,

${\displaystyle \sum {\text{p}}_0\sqrt{{\text{q}}_0{\text{q}}_1}=2717.6,\sum {\text{p}}_1\sqrt{{\text{q}}_0{\text{q}}_1}=3521.75}$

Walsh’s Price Index Number:

${\displaystyle {\text{P}}_{01}\left(\text{W}\right)=\frac{\sum {\text{p}}_1\sqrt{{\text{q}}_0{\text{q}}_1}}{\sum {\text{p}}_0\sqrt{{\text{q}}_0{\text{q}}_1}}\times 100}$

${\displaystyle =\frac{3521.75}{2717.6}\times 100}$

= 129.59