The Herfindahl-Hirschman Index is a way of measuring how competitive or concentrated an industry is. The market share of each firm in an industry is squared and then all those numbers are added up to get the HHI. This number can play a role in decisions by the Justice Department on mergers.
The Anheuser-Busch InBev and Grupo Modelo want to merge. They both make beer. Anheuser-Busch InBev has 39% of the market and Grupo Modelo has 7%. The increase in the HHI would be 2*39*7 = 546. That would raise the HHI to over 2800. The Justice Department wants to stop the merger becuase the increase in the HHI is too big for a highly concentrated industry. Competition would be hurt too much.
Click here to read the Justice Department complaint. It includes a nice pie chart showing the market shares of brewers. Miller is 2nd with 22%. So right now two firms have more than half the U. S. market. The Justice Department document also shows that in many local markets the HHI could be much higher. Most textbooks say an HHI of 1800 means a concentrated industry while this document uses 2500.
Click here to read a Wall Street Journal editorial about the merger from February that also mentions the HHI.