Assume that six firms comprising an industry have market shares of 30%, 30%, 10%, 10%, 10%, and 10%. The Herfindahl index for this industry is __________.

Question

2,000

2,200

1,600

100

Answer 1

The Herfindahl index (HI) is calculated by squaring the market shares of all firms in the industry and then summing those squares. The formula for the Herfindahl index is:

\[ HI = s_1^2 + s_2^2 + s_3^2 + s_4^2 + s_5^2 + s_6^2 \]

where \(s_i\) is the market share of firm \(i\) expressed as a percentage.

For the given market shares:

• Firm 1: 30% → \(30^2 = 900\)
• Firm 2: 30% → \(30^2 = 900\)
• Firm 3: 10% → \(10^2 = 100\)
• Firm 4: 10% → \(10^2 = 100\)
• Firm 5: 10% → \(10^2 = 100\)
• Firm 6: 10% → \(10^2 = 100\)

Now, summing these values:

\[ HI = 900 + 900 + 100 + 100 + 100 + 100 = 2200 \]

Thus, the Herfindahl index for this industry is 2,200.