Question

Calculate Fisher’s index number to the following data. Also show that it satisfies Time Reversal Test.

Commodity	2016		2017
	Price (Rs.)	Quantity (kg)	Price (Rs.)	Quantity (kg)
Food	40	12	65	14
Fuel	72	14	78	20
Clothing	36	10	36	15
Wheat	20	6	42	4
Others	46	8	52	6

Answer 1

Commodity	2016 (Base year)		2017 (Current year)		p0q0	p0q1	p1q0	p1q1
	p0	q0	p1	q1
Food	40	12	65	14	480	560	780	910
Fuel	72	14	78	20	1008	1440	1092	1560
Clothing	36	10	36	15	360	540	60	540
Wheat	20	6	42	4	120	80	252	168
Others	46	8	52	6	68	276	416	312
Total					`sum"p"_0"q"_0` = 2336	`sum"p"_0"q"_1` =2896	`sum"p"_1"q"_0` = 2900	`sum"p"_1"q"_1` = 3490

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((2900 xx 3490)/(2336 xx 2896)) xx 100`

= `sqrt((10121000)/(6765056)) xx 100`

= `sqrt(1.4961) xx 100`

= `1.2232 xx 100`

= 122.32

Time Reserved Test: P₀₁ × P₁₀ = 1

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

= `sqrt((2900 xx 3490 xx 2896 xx 2336)/(2336 xx 2896 xx 3490 xx 2900)`

= 1