# The market shares (in percentage terms) for the 12 firms that comprise an industry are 15, 12, 11, 10, 8, 7, 7, 6, 6, 6, 6, and 6. The Herfindahl index is __________ and the four-firm concentration...

The market shares (in percentage terms) for the 12 firms that comprise an industry are 15, 12, 11, 10, 8, 7, 7, 6, 6, 6, 6, and 6. The Herfindahl index is __________ and the four-firm concentration ratio is __________.

932; 48 percent

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### 1 Answer

The Herfindahl Index, also known as the Herfindahl-Hirschman Index (HHI) and the four firm concentration ratio are ways of measuring how concentrated a market is. That is, they are used to determine how much market power is in the hands of a few firms.

The HHI does this by squaring the market share of each firm in a given market and adding up the results. The greater the number, the more concentrated the market is because. For example, imagine that one firm has 90% of a market and another firm has 10%. The squares of these two market share numbers would be 8,100 and 100, adding up to 8,200. Meanwhile, if 10 firms each had 10%, the squares of their market shares would only add up to 1,000. If we take the numbers for the market shares of the twelve firms mentioned in the question and square them all, we come out with a total of 932. This is not a very concentrated market.

The four firm concentration ratio is even simpler to calculate. All you have to do is add up the market shares of the four largest firms in the market. In this case, the top four firms have 15, 12, 11, and 10 percent of the market, respectively. When we add those numbers up, we get 48, meaning that the four firms control 48% of the market. This is considered to be a fairly low number as well.

So, **our HHI for this market is 932 and our four firm concentration ratio is 48%**. Both of these are relatively low numbers.

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