Concentration Idexes, Four Firm Concentration Ratio and Herfindahl-Hirschman Index (Steven W. Lee)

Concentration ratios measure the market structure within a particular industry, describing the amount of output of the largest firms relative to the total industry segement. There are two primary measures of concentration that are utilized.

The four-firm concentration ratio(C4) which illustrates the fraction of total industry output that is produced by the four largest firms in the industry.

C4 = (S1 + S2 + S3 + S4) / Sr

Where S1 = Market Revenue of the firm with the largest market share
S2 = Market Revenue of second largest firm
S3 = Market Revenue of third largest firm
S4 = Market Revenue of fourth largest firm
Sr = The total size of the market segment

When an industry is composed of very large number firms, each of which is very small, the four-firm concentration ratio is close to zero. When there are four or fewer firms in an industry the ratio will be 1. The closer to zero that the ratio is the less concentrated the industry is, while inversely the closer to 1 the more concentrated the industry is. (Baye 238)

S1 = Market Revenue of $20
S2 = Market Revenue of $15
S3 = Market Revenue of $13
S4 = Market Revenue of $9
Sr = The total size of the market segment $75

Thus four-firm concentration ratio is ($20 + $15 + $13 + $9) / $75 = 76%
This defines that the example is a highly concentrated industry with in excess of ¾ being controlled by four firms.

The second Hirshman-Herfindahl index(HHI) is the sum of the squared market share of all firms in the given industry multiplied by 10,000. (Baye 239) As such a highly concentrated industry will yield a index closer to 10,000 while an industry with low concentration will yield a number closer to 0.

S1 = Market Revenue of $20
S2 = Market Revenue of $15
S3 = Market Revenue of $13
S4 = Market Revenue of $9
S5 = Market Revenue of $7
S6 = Market Revenue of $7
S7 = Market Revenue of $4
Sr = The total size of the market segment $75

((S1/Sr)^2+(S2/Sr)^2+(S3/Sr)^2+(S4/Sr)^2+(S5/Sr)^2+(S6/Sr)^2+(S7/Sr)^2) X 10,000

(($20/$75)^2+($15/$75)^2+($13/$75)^2+($9/$75)^2+($7/$75)^2+($7/$75)^2+($4/$75)^2 )X 10,000
((0.26667)^2+(.20)^2+(.17333)^2+(.12)^2+(0.09333)^2+(0.09333)^2+(0.05333)^2 )X 10,000
(0.071113+0.04+0.030043+0.0144+0.00871+.00871+.002844) X 10,000
.17582 X 10,000 = 1,758.20

So based on the HHI, this industry would not be considered highly concentrated.

Comparative Overview:

Industrial economists generally regard the Hirshman-Herfindahl index as superior to the concentration ratio as a measure of market structure. A major advantage of the Hirshman-Herfindahl results from its sensitivity to both the number of firms and the relative firm size distribution. (Amato 39-52) The four-firm concentration ratio has a very serious drawback as a measure. It implicitly assumes the size distribution amoung the four firms is irrelevant, which obviously is flawed. Additionally it assumes that firms 5 thru N are irrelevant again another obvious flaw. As a result the Justice Department replaced C4 with HHI as its primary method of deliberation in 1982. (Calkins 402)

Both C4 and HHI fail to state the true concentration of a market that has significant foreign penetration, as on domestic market share is measured. HHI is highly responsive while C4 total disregards the symmetry or asymmetry as applicable of the market share distribution. For any given number of participants in a market, the HHI will be lowest when shares are equal, the highest when one firm has a relatively large share of the market. This sensitivity has a significant drawback as a small error in the estimation of the firms’ market position is amplified. (Calkins 404)

Second, C4 and HHI, are based on the entire United States, and as such market concentration may not be relevant to the competitive environment which may be much more of a regional or local market.(Baye 241)
Finally, the definition of the market segment may result in the index failing to include the complimentary or substitute industries that thereby ignore total market variability.(Baye 241).

1. A Herfindahl index of 10,000 suggests:
a. monopoly
b. monopolistic competition
c. perfect competition
d. oligopoly

2. Which of the Following is used to measure market structure?
a. four-firm concentration ratio
b. HHI (Herfindahl-Hirschman Index)
c. Dansby-Willig Preformanc Index
d. A. and B.

3. Based upon the following numbers we can conclude that:
Industry A Industry B
------------- ------------
C4 1 0
HHI 10,000 0

a. Industry A is a Monopoly
b. Industry B is a Monopoly
c. Neither Industry is perfectly competitive.
d. Neither Industry is a Monopoly

4. TRUE or FALSE : If the four-firm concentration ratio indicates that Industry A is more concentrated than Industry B then so will HHI.

5. Four-Firm concentration ratios and HHI; computed from national data:
a. will overstate the true level of concentration when there are foreign producers in the market.
b. will understate the true level of concentration when there are foreign producers in the market.
c. will overstate the true level of concentration when the markets are local.
d. None of the above.


1. A.
2. D.
3. A.
4. False
5. A.

Amato, Louis. "The Choice of Strutre Measure in Industrial Economics." Quarterly Journal of Business and Economics 34(2)(1995): 39-52.

Calkins, Stephen. "The New Merger Guidelines and the Herfindahl-Hirschman Index." California Law Review 71(402)(1983): 402-29.

Baye, Michael. Managerial Economics and Business Strategy. 6. New York, NY: McGraw-Hill Irwin, 2007.