The Herfindahl Formula

HI

=

(Share 1)^2 + (Share 2)^2 + (Share 3)^2 + ... + (Share n)^2

• There terms in parentheses (Share 1, Share 2, etc.) are the market shares for each firm, that is, the total industry sales accounted for by each firm.


• The last term (Share n) indicates the market share of the last firm, which is labeled "n", because this is a general formula that works for an industry with any number of firms. For an industry with ten firms, this formula includes ten terms, and n is equal to ten. For an industry with twenty firms, this Herfindahl index includes twenty terms, and n is equal to twenty.


• The "^2" means the market share is being squared.

High, Medium, and Low

The Herfindahl index ranges from a low of 0, indicating perfect competition, to a higher of 10,000, indicating compete monopoly. Greater values mean greater concentration, less competition, and more market control held by individual firms.

• No Concentration: At the low end, a 0 Herfindahl index means perfect competition or at the very least monopolistic competition that is EXTREMELY competitive. The number of firms is so large that sum of the square of the market shares is 0.


• Total Concentration: At the high end, a 10,000 Herfindahl index means monopoly. This value is only achieved if one firm has a market share of 100 percent. Note that this is slightly different from four- and eight-firm concentration ratios, which can achieve a 100 percent value for oligopolistic industries.

• Low Concentration: A Herfindahl index of 0 to 1,000 is commonly interpreted as an industry with low concentration. Monopolistic competition falls into the bottom of this with oligopoly emerging near the upper end. While the correspondence is not exactly, generally speaking industries with concentration ratios between 0 percent and 50 percent, have Herfindahl index values between 0 and 1,000.


• Medium Concentration: A Herfindahl index of 1,000 to 1,800 percent is considered an industry with medium concentration. These industries are very much oligopoly. This level corresponds with concentration ratios between 50 percent and 80 percent.


• High Concentration: An industry with a Herfindahl index of 1,800 to 10,000 percent is viewed as highly concentration. Government regulators are usually most concerned with industries falling into this category. This level corresponds with concentration ratios between 80 percent and 100 percent.

The Shady Valley Soft Drink Industry

Soft Drink Sales

The market shares for each soft drink is listed in the third column of the table. OmniCola's 460 million annual sales gives it a market share of 23 percent. Juice-Up, with $350 million of sales, has a 17.5 percent market share. The twentieth, and least popular soft drink, which remains unnamed because almost nobody likes it, has $15 million a year in sales, and a market share of 0.75 percent.

The Herfindahl index is calculated by squaring each market share, then summing all twenty. The square of OmniCola's 23 percent market share is 529. The square of Juice-Up's 17.5 percent market share is 306.25. And the square of the 0.75 percent market share of the twentieth soft drink that almost no one in Shady Valley likes is 0.5625. Summing all twenty squared market shares generates an Herfindahl index of 1177.

This places the Shady Valley soft drink industry in the medium concentration range. The top few firms have some market control, but not a whole lot.

Sum of the Squares of Market Shares

In contrast, concentration ratios are based on the sum of unadjusted market shares and only use information for the top four or eight firms.

The squaring of the market shares does a couple of things for the Herfindahl index.

• First, it gives relatively more importance to firms with greater market shares. This is based on the presumption that firms with greater market shares have greater market control. Suppose for example, that the top two firms in a market have a combined 50 percent market share. The Herfindahl index is significantly different if the individual market shares are 40 percent and 10 percent than if they are 30 percent and 20 percent. The first combination contributes 1,700 points to the Herfindahl index and the second contributes only 1,300 points.


• Second, even though the Herfindahl index, in principle, includes every firm in the market, in practice the smallest firms have a minimal impact on the calculation and can be largely ignored. For example, firms with less than 1 percent market share add less than 1 point to the Herfindahl index, that falls in the range of 1,000 to 5,000 points.

The Pro of the Herfindahl Index

Suppose, for example, that sales of OmniColan increase from $460 million to $560 million, which causing an increase in market share to 28 percent. At the same time sales of Juice-Up decrease from $350 million to $250 million, which causes a decrease in market share to 12.5 percent. In this case, the Herfindahl index increases from 1177 to 1282.

However, these changes in sales and market shares have no affect on four-firm and eight-firm concentration ratios. The top four firms in the Shady Valley soft drink market account for 61.25 percent of industry sales before and after the change. The top eight firms also account for 78.5 percent of total industry sales before and after.

Yet, the increase in sales of OmniCola and market share, at the expense of Juice-Up, gives OmniCola more market control. This change in market control is reflected by the Herfindahl index, but not by either concentration ratio.

And a Couple of Cons

• The first problem is to find meaning in the numbers. While a four-firm concentration ratio of 61.25 percent MEANS that the top four firms in the industry account for 61.25 percent of total industry sales, what does an Herfindahl index of 1177 really mean? There is no obvious intuitive meaning to the Herfindahl index.


• Along this same line of thought, another problem with the Herfindahl index is the choice of squaring market shares. There is no particular reason, theoretical or otherwise, to square the market share for each firm. Squaring each share does give greater importance to firms with larger market shares, but these shares could just as easily be cubed, or raised to the fourth, fifth, or sixth power.


• A third problem with the Herfindahl index is that it requires a substantial amount of information, more than that for concentration ratios. The only information needed to calculate a four-firm concentration ratio is the market shares of the top four firms. However, to calculate a Herfindahl index, the market share for every firm in the industry is needed. In that some oligopolistic industries have a few large firms, and dozens, even hundreds of smaller firms, obtaining the needed information can be quite a chore.