Problem:

Suppose that the 6 firms in an industry have total annual sales of $70 billion, $40 billion, $30 billion, $30 billion, $20 billion, and $10 billion.

1. What is the four-firm concentration ratio in this industry?
2. What is the Herfindahl index for this industry?
3. Suppose another industry has a Herfindahl index of 4000. What can you conclude about the relative competitiveness of these two industries?

Answer:

1. The four-firm concentration ratio is the ratio of the sales of the four largest firms in the industry relative to total industry sales, expressed as a percentage. In this industry, total sales are $200 billion and the top four combined have sales of $170 billion. The four-firm concentration ratio is then 170/200 = .85, or 85%.
2. The Herfindahl index is computed as the sum of the squared market shares for all firms in the industry. In this example, the 6 firms have market shares of 35%, 20%, 15%, 15%, $10%, and 5%. The index is 35² + 20² + 15² + 15² + 10² + 5² = 2200.
3. Larger index numbers correspond to more highly concentrated industries. Accordingly, firms in the second industry are likely to have more market power.