Which of the following concentration indices is larger?The concentration ratio C2 in an industry with 3 identical firmsConcentration indices depend on the industry, thus it cannot be said a priori which concentration index is larger. The Herfindahl index in an industry with 2 identical firmsThe entropy index in an industry with 2 identical firms
Question
Which of the following concentration indices is larger?The concentration ratio C2 in an industry with 3 identical firmsConcentration indices depend on the industry, thus it cannot be said a priori which concentration index is larger. The Herfindahl index in an industry with 2 identical firmsThe entropy index in an industry with 2 identical firms
Solution
The concentration ratio (C2) in an industry with 3 identical firms would be 2/3 or approximately 0.67, since the concentration ratio is the sum of the market shares of the largest firms in the industry, in this case, the two largest firms out of three identical ones.
The Herfindahl index in an industry with 2 identical firms would be 1, since the Herfindahl index is the sum of the squares of the market shares of all firms in the industry, and in this case, each firm has a market share of 1/2, so the Herfindahl index would be (1/2)^2 + (1/2)^2 = 1/4 + 1/4 = 1/2.
The entropy index in an industry with 2 identical firms would also be 1, since the entropy index is a measure of diversity and in this case, there is no diversity as both firms are identical.
Therefore, the Herfindahl index and the entropy index are larger than the concentration ratio C2 in an industry with 3 identical firms.
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