# Herfindahl index

In economics, the Herfindahl index is a measure of the size of firms in relationship to the industry and an indicator of the amount of competition among them. It is defined as the sum of the squares of the market shares of each individual firm. As such, it can range from 0 to 10,000, moving from a very large amount of very small firms to a single monopolistic producer. Decreases in the Herfindahl index generally indicate a loss of pricing power and an increase in competition, whereas increases imply the opposite.

 Contents

## Example

The major benefit of the Herfindahl index in relationship to such measures as the concentration ratio is that it gives more weight to larger firms. Take, for instance, two cases in which the six largest firms produce 90 percent of the output:

• Case 1: All six firms produce 15%, and
• Case 2: One firm produces 80 percent while the five others produce 2 percent each.

We will assume that the remaining 10% of output is divided among 10 equally sized producers.

The six-firm concentration ratio would equal 90 percent for both case 1 and case 2, but in the first case competition would be fierce where the second case approaches monopoly. The Herfindahl index for these two situations makes the lack of competition in the second case strikingly clear:

• Case 1: Herfindahl index of 1360
• Case 2: Herfindahl index of 6430

This behavior rests in the fact that the market shares are squared prior to being summed, giving additional weight to firms with larger size.

Formula

[itex]H =\sum_{i=1}^n(\Pi_i)^2[itex]

with [itex]\Pi[itex] the market share of every firm in the market, and [itex]n[itex] being the number of firms.

There is also a normalised herfindahl index

## Problematics

The usefulness of this statistic to detect and stop harmful monopolies however is directly dependent on a proper definition of a particular market. For example, if the statistic were to look at a hypothetical financial services industry as a whole, and found that it contained 6 main firms with 15 percent market share apiece, then the industry would look non monpolistic. However, one of those firms handles 90 percent of the checking and savings accounts and physical branches (and overcharges for them because of its monopoly), and the others primarily do commercial banking and investments. In this scenario people would be suffering due to a market dominance by one firm. Thus it is important to accurately define the market being analyzed based on all circumstances.

Another potential problem with this statistic is that it does not take into account factors such as geography. For example, firms may have 20 percent market share each, but may occupy five areas of the country and thus do not face price competition between each other.

The United States uses the Herfindahl index to determine whether mergers are equitable to society; increases of over 100 points generally provoke scrutiny, although this varies from case to case. The Department of Justice considers Herfindahl indices between 1000 and 1800 to be moderately concentrated and indices above 1800 to be concentrated. As the market concentration increases, competition and efficiency decrease and the chances of collusion and monopoly increase.

• Herfindahl-Hirschman Index Calculator (http://www.unclaw.com/chin/teaching/antitrust/herfindahl.htm). Web tool for calculating pre- and post-merger Herfindahl index, with more detailed information about the Department of Justice horizontal merger guidelines.

## Intuition

In order to get a feel for the meaning of the index, it is often useful to look at the inverse of the index (or rather 10000 / Index). This can be interpreted as number of equally sized firms that operate in this market. Example: 5 companies that have a market share of 20% each lead to an index value of 2000 = 5 * 20^2. Dividing 10000 through 2000 gives the original result of 5.

• Art and Cultures
• Countries of the World (http://www.academickids.com/encyclopedia/index.php/Countries)
• Space and Astronomy

Information

• Clip Art (http://classroomclipart.com)