The Herfindahl index, known as the Herfindahl–Hirschman Index or HHI, measures the size of firms in relation to the industry they operate in. Thus, it provides insight into how concentrated a market is, and is used in antitrust lawsuits to determine how much market power a given firm has.
This is the equation used to calculate HHI. It may look complicated, but it really isn’t so let’s break it down.
The highest possible HHI is 10,000, because a firm with 100% market share will simply swap out “100” for S and square it (100*100), rendering a score of 10,000. This the case for HHI in a monopoly setting.
So, you can induct that in the formula, n represents the number of firms in the market and S represents the market share of each of those firms.
So, basically, the formula is synonymous to: Firm 1’s market size² + Firm 2’s market size² + Firm N’s market size².
Now, note the following about what different HHI’s mean:
- An HHI index below 100 is considered a highly competitive market.
- 100 to 1000 is considered a moderately unconcentrated market.
- 1000 to 1800 is considered a moderately concentrated market.
- Over 1800 is a highly concentrated market.
Thus, in antitrust mergers or cases, plaintiffs may point to the HHI of the companies looking to merge. Let’s now consider a few examples:
Example 1
We have two firms in a market that are looking to merge. Firm A controls 18% of the market, and Firm B controls 9% of the market. There are also firms C, D, E and F, which respectively control 22%, 20%, 16%, and 15% of the market. What are the pre and post-merger HHI’s? Will the merger go through?
Pre-merger:
18² + 9² + 22² + 20² + 16² + 15² = 1,770
Post-merger (Firm A and B merge):
27² + 22² + 20² + 16² + 15² = 2,094
So, the merger will not go through, because it pushes the HHI above the critical level of 1,800.
Example 2
Consider a market in which Firm A controls 67% of the market and Firm B controls 33% of the market. The government wants to break Firm A into 4 equal pieces. Will this be enough to make the market competitive?
Pre-merger HHI:
67² + 33² = 5578
Post-merger HHI:
16.75² + 16.75² + 16.75² + 16.75² + 33² = 2211.25
Hence, no, the market will still be considered concentrated if Firm A is broken up into four equal pieces.
That’s all for our introduction to the HHI! Let me know in the comments if you would like to see any additions to this article, or further articles on similar subjects.
