# Concentration indexes -&nbsp;Four firm concentration ratios, Herfindahl Hershman indexes (HHI)

Concentration Indices

Market concentration indices are measures of how fragmented a market is structured. Market structure varies from one extreme where perfect competition exists with many producers or sellers and easy market entry and exit. The other market extreme is a monopoly with effective barriers to entry of a competitor. The tendency toward a monopoly or a market with monopolistic characteristics or power is the focus of most studies using concentration indices (personal observation).

A common type of concentration index is the concentration ratio. Two examples of concentration ratios are the four-firm concentration ratio and the eight-firm concentration ratio. The four-firm concentration ratio is an indicator of the size (as measured by output or sales) of the four largest firms within an industry, compared to the output of the entire industry. It is determined as follows:

CR4 = (X1 + X2 + X3 + X4) / T

where Xn is the output of the nth largest firm and T is the total output of the industry. Likewise, the eight-firm concentration ratio is:

CR8 = (X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8) / T

The Herfindahl-Hirschman Index (HHI) is a market concentration index determined as follows:

HHI is 10,000 x [Summation from i 1 to n, of S sub-i squared)

where S is the proportion of market share for the ith firm. For an industry with a single firm (monopoly), this value would be 10,000. For an industry with two firms equally sharing the market, the value would be 5,000. This value was found by the following equation:
10,000 x [(0.5)^2 + (0.5)^2] = 5,000.

Any of the above indicators of market concentration, when used in isolation, can be misleading.

A weakness of the firm concentration ratios is that they only measure the concentration of a limited number of firms. For a given industry, if the four-firm concentration ratio was 0.50 and the eight-firm concentration ratio was 0.90, then ten years later, they are 0.60 and 0.80, has the industry become more or less concentrated?

A weakness with the HHI is that two dissimilar industry distributions can give similar values. An industry with seven (7) firms having the following market shares: 40%, 25%, 10%, 10%, 5%, 5%, and 5% will have HHI of 2,500. An industry with four (4) firms, each with 25% of the market will also have an HHI of 2,500.

The examples show that no single index or ratio should be used to evaluate an industry. The use of multiple indicators in unison is recommended.

Questions:

1. Calculate the four-firm concentration ratio of an industry with the following distribution of sales: 40%, 10%, 10%, 10%, 10%, 10%, 10%.
a. 100%
b. 80%
c. 70%
d. 40%

Answer: c, C4 is (40 + 10 + 10 + 10) / 100 equals 70%

2. Calculate the eight-firm concentration ratio of an industry with the following distribution of sales: 40%, 10%, 10%, 10%, 10%, 10%, 10%.
a. 100%
b. 80%
c. 70%
d. 40%

Answer: a, C8 equals (40 + 10 + 10 + 10 + 10 + 10 + 10 + 0) / 100 equals 100%

3. Calculate the HHI of an industry with the following distribution of sales: 40%, 10%, 10%, 10%, 10%, 10%, 10%.
a. 10,000
b. 4,000
c. 2,200
d. 2,000

Answer: c, HHI equals 10,000 x (0.40^2 + 0.10^2 + 0.10^2 + 0.10^2 + 0.10^2 + 0.10^2 + 0.10^2) 2,200

4. True or False: An HHI of 0 indicates a monopoly firm.

Answer: False; an HHI equal to 0 indicates a perfectly competitive firm (Managerial Economics and Business Strategy 5th Edition, MIcheal R. Baye)

5. What type of firm is very concentrated
a. monopoly
b. perfect competition
c. monopolistic competition

Answer: Monopoly (Managerial Economics and Business Strategy 5th Edition, MIcheal R. Baye)

6. Which concentration ratio measures all firms in an industry?
a. Rothschild Index
b. Herfindahl-Hirschman index
c. Jones Index
d. Hatman Concentration Ratio

Answer: A Herfinadahl-Hirschman index meansures all firms in an industry, as opposed to just a few. (Managerial Economics and Business Strategy 5th Edition, MIcheal R. Baye)

http://en.wikipedia.org/wiki/Herfindahl_index

http://www.finscope.co.za/documents/2005/BtswLaunch04_3.pdf (Real world example with financial institution concentration indices)