The geometric mean of Laspeyre’s and Paasche’s price indices is called Fisher’s price Index. Fisher price index uses both current year and base year quantities as weight. This index corrects the positive bias inherent in the laspeyres index and the negative bias inherent in the paasche index. Fisher’s price index is also a weighted aggregative price index because it is an average (G.M) of two weighted aggregative indices. The computational formula for the fisher ideal price index is:

**Problem:** Construct Fisher’s price index for the data given below: (Base = 2004). Also show that fisher’s index is the geometric mean of laspeyre and paache indices.

**Solution:**

### Fisher’s index is the geometric mean of laspeyre and paache indices

To check that Fisher’s index is the geometric mean of Laspeyre and Paache indices, we have

Here,

Therefore,

Hence it is proved that Fisher’s index is the geometric mean of Laspeyre and Paache indices.

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So why is this a reasonable or useful way to describe production (as in the Federal Production Index)?

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