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Construct index numbers of prices of the...

Construct index numbers of prices of the items in the year 2018 from the following data by:
(i) Laspeyre's Method,
(ii) Paasche's Method, and
(iii) Fisher's Method.

Text Solution

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(i) Laspeyre's Method: `P_(01)=(Sigmap_(1)q_(0))/(Sigmap_(0)q_(0))xx100`
`=(660)/(635)xx100=103.94`
(ii) Paasche's Method: `P_(01)=(Sigmap_(1)q_(1))/(Sigmap_(0)q_(1))xx100`
`=(1,560)/(1,450)xx100=107.59`
(iii) Fisher's Method: `P_(01)=sqrt((Sigmap_(1)q_(0))/(Sigmap_(0)q_(0))xx(Sigmap_(1)q_(1))/(Sigmap_(0)q_(1)))xx100`
`=sqrt((660)/(635)xx(1,560)/(1,450))xx100`
`=sqrt(1.03xx1.07)xx100`
`=sqrt(1.1021)xx100`
`=1.05 xx100=105`
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