Question

Calculate the Laspeyre’s, Paasche’s and Fisher’s price index number for the following data. Interpret on the data.

Commodities	Base Year		Current Year
	Price	Quantity	Price	Quantity
A	170	562	72	632
B	192	535	70	756
C	195	639	95	926
D	1987	128	92	255
E	1985	542	92	632
F	150	217	180	314
7	12.6	12.7	12.5	12.8
8	12.4	12.3	12.6	12.5
9	12.6	12.5	12.3	12.6
10	12.1	12.7	12.5	12.8

Answer 1

Commodities	Base Year		Current Year		p0q0	p0q1	p1q0	p1q1
	p0	q0	p1	q1
A	170	562	72	632	95540	107440	40464	45504
B	192	535	70	756	102720	145152	37450	52920
C	195	639	95	926	124605	180570	60705	87970
D	1987	128	92	255	23936	47685	11776	23460
E	1985	542	92	632	100270	116920	49864	58144
F	150	217	180	314	32550	47100	39060	56520
7	12.6	12.7	12.5	12.8	160.02	161.28	158.75	160
8	12.4	12.3	12.6	12.5	152.52	155	154.98	157.5
9	12.6	12.5	12.3	12.6	157.50	158.80	153.75	155
10	12.1	12.7	12.5	12.8	153.67	154.90	158.75	160
Total					480244.71	645496.98	239945.23	325150.5

Lasperyre’s price Index number

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

= `239945.23/480244.71 xx 100`

= 49.96

Passhe's price index number

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

= `325150.5/645496.98 xx 100`

= 50.37

Fisher's price index number

`"P"_01^"F" = [sqrt((sum"p"_1"q"_0 xx sum"p"_1"q"_1)/(sum"p"_0"q"_0 xx sum"p"_0"q"_1))] xx 100`

= `[sqrt((239945.23 xx 325150.5)/(480224.71 xx 645496.98))] xx 100`

= `sqrt((3572000)/(1827840)) xx 100`

= `sqrt(1.9542) xx 100`

= `1.3979 xx 100`

= 139.79

= 139.8

Time reversal test

Test is satisfied when `"P"_01 xx "P"_10` = 1

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

= `sqrt((1900 xx 1880)/(1360 xx 1344))`

`"P"_10 = sqrt((sum"p"_0"q"_1 xx sum"p"_0"q"_0)/(sum"p"_1"q"_1 xx sum"p"_1"q"_0))`

= `sqrt((1344 xx 1360)/(1880 xx 1900))`

`"P"_01 xx "P"_10 = sqrt((1900 xx 1880 xx 1344 xx 1360)/(1360 xx 1344 xx 1880 xx 1900))`

= `sqrt(1)`

Hence Fisher’s Ideal Index satisfies Time reversal test