Find Laspeyre's index number, Paasche's index number, Fisher's index number

Item	Price0	Quantity0	Price1	Quantity1
A	10	20	12	22
B	8	16	8	18
C	5	10	6	11
D	4	7	4	8

Solution:

Item	`p_0`	`q_0`	`p_1`	`q_1`	`p_1q_0`	`p_0q_0`	`p_1q_1`	`p_0q_1`
A	10	20	12	22	240	200	264	220
B	8	16	8	18	128	128	144	144
C	5	10	6	11	60	50	66	55
D	4	7	4	8	28	28	32	32
---	---	---	---	---	---	---	---	---
Total					`456`	`406`	`506`	`451`

1. Laspeyre's index number

`I_L=(sum p_1q_0)/(sum p_0q_0) xx 100`

`=(456)/(406) xx 100`

`=112.32`

Thus, there is a rise of `(112.32-100)=12.32%` in prices

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2. Paasche's index number

`I_P=(sum p_1q_1)/(sum p_0q_1) xx 100`

`=(506)/(451) xx 100`

`=112.2`

Thus, there is a rise of `(112.2-100)=12.2%` in prices

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3. Fisher's index number

`I_F=sqrt(I_L xx I_P)`

`=sqrt(112.3153 xx 112.1951)`

`=112.26`

Thus, there is a rise of `(112.26-100)=12.26%` in prices

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