The formula to calculate the Herfindahl Index (HI) is:
\[ \text{HI} = \sum_{i=1}^{n} (s_i)^2 \]
Where:
The Herfindahl Index, also known as the Herfindahl-Hirschman Index (HHI), is a measure of market concentration and competition among firms within an industry. It is calculated by squaring the market share of each firm competing in the market and then summing the resulting numbers. The index ranges from 0 to 10,000, with higher values indicating a higher level of market concentration and, therefore, less competition.
Let's assume there are three firms in the market with the following market shares:
Using the formula to calculate the Herfindahl Index:
\[ \text{HI} = (40)^2 + (30)^2 + (30)^2 = 1600 + 900 + 900 = 3400 \]
The Herfindahl Index (HI) is 3400.