# Herfindahl Index: Definition & Formula

Instructor: Toni Bonton

Toni has taught personal finance and is currently pursuing a doctorate in business administration.

This lesson is all about the Herfindahl Index, how it is used to calculate the market concentration of an industry and what the Herfindahl Index value means in a market.

## The Herfindahl Index

Tiki has always wanted to own her own business. After receiving quite a few rave reviews about her cupcakes at the office holiday party, Tiki decided to give some serious consideration to opening her own bakery.

Before Tiki can trade her computer for a stand mixer, there are a few things to consider. The first thing Tiki thought about was the concentration, or competitiveness, of the market. There are currently four other bakeries in Tiki's large metropolitan city: The Brown Sugar Shack, The Sugar Cookie Cafe, The Buttercup Buffet, and The Chocolate Croissant. The market share for each bakery is listed below:

To calculate the market concentration in Tiki's large metropolitan city, she will need to use the Herfindahl Index or HI, also known as the Herfindahl-Hirchman Index or HHI. The HI is a formula that uses the market share of each firm in a given market to calculate the concentration in that market by squaring the market share of each firm and adding them together. The sum of these values is the HI. Here is the formula:

HI = xa^2 + xb^2 + xc^2 +... + xn^2

Each variable represents the market share of a firm, where xn is the market share of the last firm, provided there is more than three firms. If there are four firms, xn is the value of the fourth firm. If there are seven firms, xn is the value of the seventh firm; therefore, xa would be the market share of the first firm, xb would equal the market share of the second firm, and so on until the market share of the last firm is calculated. Using the above formula, if there are only three firms, there would be no value for xn, as xa, xb, and xc would account for all three firms.

Now let's see it in action!

## Calculating the Data

First, assign values to each variable.

Next, calculate the HI by adding the values together.

1600 + 900 + 225 + 225 = 2,950

The baked goods market in Tiki's metropolitan city has an HI of 2,950. Let's do another one!

Tiki decides to expand her market research to the entire state. There are a total of ten bakeries, all with an equal market share of ten percent. Here's the equation:

HI = 10^2 + 10^2 + 10^2 + 10^2 + 10^2 + 10^2 + 10^2 + 10^2 + 10^2 + 10^2

or

HI = 100 + 100 + 100 + 100 + 100 + 100 + 100 + 100 + 100 + 100

The baked goods market for the entire state has an HI of 1000.

## Interpreting the Data

So what does the HI number really mean? The HI serves as a numerical picture of how firms in a given market are performing and the possibility of more competition. The HI of a market can be categorized into three types: unconcentrated, moderately concentrated, and highly concentrated.

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