# Market concentration (Herfindahl-Hirschman index)

## What is the Herfindahl-Hirschman index?

The Herfindahl index is a variation of the market concentration marketing metric. Instead of a simple sum of the market shares of the larger brands in the marketplace, the Herfindahl index applies a multiple (squared) effect to the difference in the market shares for all/most brands.

#### The Herfindahl-Hirschman index formula

The Herfindahl index is calculated by:

The sum of the squares of each brand’s market shares

Notes on the Herfindahl-Hirschman index

• Usually only the top 50 brands are included in the calculation of the index
• The maximum index score = 1 (which occurs in the case of a monopoly)
• The minimum index score = 1/number of brands (which occurs if all brands have an equal market share)

#### First Example of the Herfindahl-Hirschman index

Let’s use an example marketplace with five brands – their market shares are as follows:

• Brand A = 40% (0.40)
• Brand B = 30% (0.30)
• Brand C = 20% (0.20)
• Brand D = 7% (0.07)
• Brand E = 3% (0.03)

The Herfindahl index is the calculated by squaring each of the market shares as follows: 0.40 X 0.40 + 0.30 X 0.30 + 0.20 X 0.20 + 0.07 X 0.07 + 0.03 X 0.03 = 0.160 + 0.090 + 0.040 + 0.0049 + 0.0009 = 0.2958 = 0.30 (rounded)

Given that there are five brands in the market, the minimum Herfindahl index would be 1/5 = 0.20 – see below for how to use this index.

#### Second Example of the Herfindahl-Hirschman index

In this second example, let’s use five brands again, but this time have a more concentrated market, as follows:

• Brand A = 60% (0.60)
• Brand B = 30% (0.30)
• Brand C = 8% (0.08)
• Brand D = 1% (0.01)
• Brand E = 1% (0.01)

For this second example, the Herfindahl index is calculated as follows: 0.60 X 0.60 + 0.30 X 0.30 + 0.08 X 0.08 + 0.01 X 0.01 + 0.01 X 0.01 = 0.360 + 0.090 + 0.0064 + 0.0001 + 0.0001 = 0.4566= 0.46 (rounded)

And given that there are still five brands in the market, the minimum Herfindahl index in this example would also be 1/5 = 0.20 – see below for how to use this index.

#### Using the Herfindahl-Hirschman index scores

The H-index for market concentration is best used as a comparative measure. In the two examples above, the first market had an index score of 0.30 (max = 1, min = 0.20) and the second market had an index score of 0.46 (max = 1, min = 0.20). Therefore, the second market is far more concentrated that the first market.

The H-index removes the subjective decision of how many brands to include in the calculation, which is a limitation of the more basic approach to measuring market concentration.

As you can see from the two examples above; a firm with a large market share will add significantly to the overall index. However, relatively minor market shares will have very little impact. Therefore, several large players are required to generate a higher index score.

This index can be compared to the minimum score that could be generated it all brands were equal in market share. For example, a market with just ten brands, with each brand having a 10% market share – when multiplied by itself (squared) each market share becomes 10% X 10% = 0.01 and all 10 brands would add up to an index of just 0.10.

It is a relatively simple calculation to perform by a spreadsheet and once it is set up a can be tracked over time and several industries can be compared on this index.

Related topics

What is market concentration?

The free Excel template for calculating market concentration.

Posted on Categories Market Shares, Metrics