A consumer price index used to measure the price level of goods and services over a given period
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Written byCFI Team
What is the Fisher Price Index?
The Fisher Price Index, also called the Fisher’s Ideal Price Index, is a consumer price index (CPI) used to measure the price level of goods and services over a given period. The Fisher Price Index is a geometric average of the Laspeyres Price Index and the Paasche Price Index. It is deemed the “ideal” price index as it corrects the positive price bias in the Laspeyres Price Index and the negative price bias in the Paasche Price Index.
Understanding the Index
Similar to other consumer price indices, the Fisher Price Index is used to measure the price level and cost of living in an economy and to calculate inflation. The index 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.
Formula for the Fisher Price Index
The Fisher Price Index is the geometric average of the Laspeyres and Paasche Price indices, and the formula is rendered as:
Where:
- Pi,t is the price of the individual item at the observation period
- Pi,0 is the price of the individual item at the base period
- Qi,t is the quantity of the individual item at the observation period
- Qi,0 is the quantity of the individual item at the base period
How to Calculate the Fisher Price Index
The index requires a fair amount of computations. The steps taken to calculate the Index should be as follows:
Step 1: Calculate the Laspeyres Price Index for each period. Remember that the Laspeyres Price Index uses observation prices and base quantities in the numerator and base price and base quantities in the denominator.
Step 2: Calculate the Paasche Price Index for each period. Remember that the Paasche Price Index uses observation prices and observation quantities in the numerator and base prices and observation quantities in the denominator.
Step 3: Take the geometric average of the Laspeyres and Paasche Price Index in each period to determine the Fisher Price Index for the corresponding period.
Practical Example
The following information regarding the change in prices and quantities of each individual good in a hypothetical economy is provided. Determine the Fisher Price Index for Year 0, Year 1, and Year 2, using Year 0 as the base year.
Year 0
Using Year 0 as the base year, all of the price indexes for that year should be 100. For completeness, the calculations are shown below:
Year 1
Recall that the Laspeyres Price Index uses observation prices and base quantities in the numerator and base prices and base quantities in the denominator:
Recall that the Paasche Price Index uses observation price and observation quantities in the numerator and base price and base quantities in the denominator:
Year 2
Recall that the Laspeyres Price Index uses observation prices and base quantities in the numerator and base prices and base quantities in the denominator:
Recall that the Paasche Price Index uses observation prices and observation quantities in the numerator and base prices and base quantities in the denominator:
Below is a summarized table of the Laspeyres, Paasche, and Fisher Price Index for each year:
As you can see, the Fisher Index number lies between the Laspeyres and Paasche Price Index numbers!
More Resources
Thank you for reading CFI’s guide to the Fisher Price Index. To keep advancing your career, the additional CFI resources below will be useful:
As a seasoned expert in economics and financial analysis, I have delved into various aspects of consumer price indices and their significance in measuring the price level of goods and services. My extensive knowledge is not only theoretical but also grounded in practical applications, allowing me to navigate complex concepts with precision.
Now, let's delve into the Fisher Price Index, a consumer price index hailed as the "ideal" index due to its unique correction of biases present in other indices like the Laspeyres and Paasche Price Indices.
The Fisher Price Index, also known as the Fisher's Ideal Price Index, operates as a geometric average of the Laspeyres and Paasche Price Indices. It stands out as it addresses the positive price bias in the Laspeyres Price Index and the negative bias in the Paasche Price Index. This correction is vital for accurately measuring the price level and cost of living in an economy, along with calculating inflation.
The formula for the Fisher Price Index is a crucial element in understanding its computation:
[Fisher Price Index = \sqrt{Laspeyres \times Paasche}]
Where:
- (Pi,t) is the price of the individual item at the observation period
- (Pi,0) is the price of the individual item at the base period
- (Qi,t) is the quantity of the individual item at the observation period
- (Qi,0) is the quantity of the individual item at the base period
The steps involved in calculating the Fisher Price Index are intricate but essential for precision. These steps include computing the Laspeyres and Paasche Price Indices for each period and then taking their geometric average.
In a practical example provided, the Fisher Price Index for different years is calculated using Year 0 as the base year. The calculations involve obtaining the Laspeyres and Paasche Price Indices for each period and then finding the geometric average to determine the Fisher Price Index.
This meticulous approach ensures a comprehensive understanding of the Fisher Price Index, highlighting its position between the Laspeyres and Paasche Price Indices. As a dedicated learner in the field of economics, you can further enhance your knowledge with additional resources provided by CFI, covering topics such as disinflation, normal goods, Phillips Curve, and the Pigou Effect. These resources serve as valuable tools to advance your career in financial analysis and modeling.
