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 Laspeyres Index and the Paasche Price Index.

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:

Year 0 Year 1 Year 2
A B A B A B
Price  20 10 15 22 11 26 24 12 28
Quantity 15 20 25 20 20 17 25 20 15
Value 300 200 375 440 220 442 600 240 420

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 –

Fisher Index Example 1-1.png

  • 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 –

Fisher Index Example 1-2.png

  • 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 Example 1-3.png

  • 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 1-4

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.

Year 0 Year 1 Year 2
Petrol Diesel Kerosene Petrol Diesel Kerosene Petrol Diesel Kerosene
Price 60 70 50 65 78 52 50 65 45
Quantity 10 10 15 20 15 18 8 5 10
Value 600 700 750 1300 1170 936 400 325 450

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 Example 2-1.png

Advantages of the FPI

  • 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.

Disadvantages of the FPI

  • The only limitation of the FPI is it is a little more complex constructs than the other two.
  • The quantities of the future years have to be forecasted while in the case of Laspeyres Price Index only the future prices have to be found out.

Conclusion

Although the Fisher Index is the better of the three indices Laspeyres Price Index is more commonly used for inflation calculations. But if we can make an accurate forecast of future quantities of an item Fisher-price index gives a more accurate measure.

Recommended Articles

This has been a guide to FPI (Fisher Index). Here we discuss formula and examples of fisher price index along with advantages and disadvantages. You can learn more about accounting from the following articles –

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