Write the formulae for Lasperey's, Paasche's and fisher's quantit… - Vidyadip

Question

Write the formulae for Lasperey's, Paasche's and fisher's quantity index numbers.

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Answer

Lasperey's method: This method is devised by Laspeyre in year 1871.It is the most important of all the types of index numbers. In this method the base year quantities are taken weights. The formula for constructing Lasperey's price index number is $\text{P}_\text{01La}=\frac{\sum\text{p}_1}{\sum\text{p}_0}\times100$ Paasche's method: It was determined by a German Statistician in 1874 in which he took the quantities of current year as weights. In this method the formula is given by$\text{P}^\text{Pa}_\text{01}=\frac{\sum\text{p}_1\text{q}_0}{\text{p}_0\text{q}_0}\times100$
Fisher's ideal method: Fishers price index number is given by root of the multiplication of the Laspeyer's and Paasche's index numbers. It is called ideal index.$\text{P}^\text{F}_{01}=\sqrt{\text{P}^\text{La}_{01}\text{P}^\text{Pa}_{01}}$
$=\sqrt{\frac{\sum\text{p}_1\text{q}_0}{\text{p}_0\text{q}_0}\times100\frac{\sum\text{p}_\text{i}\text{q}_1}{\sum\text{p}_0\text{q}_1}\times100}$
$=\sqrt{\frac{\sum\text{p}_\text{1}\text{q}_0\sum\text{p}_\text{1}\text{q}_1}{\sum\text{p}_\text{0}\text{q}_0\sum\text{p}_\text{0}\text{q}_1}}\times100$

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