# Fisher Index  ## Fisher Price Index Definition

The Fisher Index is a consumer price index used to measure the increase in prices of goods and services over a period of time and is calculated as the geometric mean of the  and the .

### Fisher Index Formula

Fisher-Price Index = (LPI*PPI)^0.5

where,

LPI = Laspeyres Price Index = ∑(Pn,t) * (Qn,0) * 100 / (Pn,0) * (Qn,0)

PPI = Paasche Price Index = ∑(Pn,t) * (Qn,t) * 100 / (Pn,0) * (Qn,0) ,

where

• Pn,t is the price of the item at the nth period
• Pn,0 is the price of the  item at the base period
• Qn,t is the quantity of the item at the nth period
• Qi,0 is the quantity of the item at the base period

### Examples of Fisher-Price Index

Below are the examples of a fisher price index.

You can download this Fisher Index Excel Template here – Fisher Index Excel Template

#### Example #1

Let us find the Fisher-price Index for three items whose price and quantity sold are given for three years. For the current year designated as Year 0 the prices in dollars and the quantity are given as follows:

First, we will calculate the Fisher-price Index for Year 0 using Laspeyres Price Index and Paasche Price Index.

Laspeyres Price Index for Year 0 –

• For Year 0 the Laspeyres Price Index (LPI) = (20*15+10*20+15*25)*100/ (20*15+10*20+15*25)
• = 100

Paasche Price Index –

• Paasche Price Index = (20*15+10*20+15*25)*100/ (20*15+10*20+15*25)
• = 100

Fisher Price Index for Year 0 –

• Fisher Index(FPI) =  (100*100)^0.5
• = 100

Similarly, we find the indexes for Year 1 and 2 as given.

For Year 1

Laspeyres Price Index

• LPI = (22*15+11*20+26*25)*100/ (20*15+10*20+15*25)
• = 137.14

Paasche Price Index

• PPI = (22*20+11*20+26*17)*100/ (20*15+10*20+15*25)
• = 125.94

Fisher Index (FPI)

• FPI = (137.4*125.94)^0.5
• = 131.42

For Year 2

Laspeyres Price Index

• LPI = (24*15+12*20+8*25)*100/ (20*15+10*20+15*25)
• = 148.57

Paasche Price Index

• PPI = (24*12+12*20+28*15)*100/ (20*15+10*20+15*25)
• = 144

Fisher Index

• FPI = (148.57*144)^0.5
• = 146.27

We have given a tabular representation of the indexes in the following table.

#### Example #2

Let us take the case of three very commonly used fuels: petrol, diesel, and kerosene and calculate the price indices for three years.

The price in dollars and quantities in liters are shown in the following table.

We can see that the price of fuels increased in Year 1 and decreased in Year 2. Did you notice that the quantities also show a similar trend, which is not surprising as we know that oil and gas exploration companies often reduce production when the price of crude oil (the raw material) fall?

The table showing the values of the indices, in this case, is given below and can be derived exactly in the same manner as shown in the above example.

• FPI is often called the real index as it corrects for the upward bias of the Laspeyres Price Index and the downward bias of the Paasche Price Index by taking the geometric average of the two weighted indices. It uses both current year and base year quantities as weight.
• Although it is not very frequently used index owing to its structural complexity and the number of variables required, it has very widespread use in academic circles and research.