The Herfindahl-Hirschman Index is equal to
The sum of the K largest firms’ market shares
The sum of the squares of all firms’ market shares
The sum of all firms’ market shares
10,000 divided by K, where K is the number of firms
The Correct Answer and Explanation is:
Correct Answer:
The sum of the squares of all firms’ market shares
Explanation:
The Herfindahl-Hirschman Index (HHI) is a commonly used measure of market concentration and is especially relevant in antitrust and competition analysis. It helps assess the degree of competition within a market and is widely used by government regulators such as the U.S. Department of Justice and the Federal Trade Commission.
Definition:
The HHI is calculated by summing the squares of the market shares of all firms in the market. Each firm’s market share is expressed as a percentage (ranging from 0 to 100), and then squared before summing. Mathematically: HHI=s12+s22+s32+…+sn2HHI = s_1^2 + s_2^2 + s_3^2 + \ldots + s_n^2
Where:
- sis_i is the market share of firm ii, expressed as a whole number percentage (e.g., 30% as 30, not 0.30).
- nn is the number of firms in the market.
Example:
Suppose there are four firms in a market with the following market shares:
- Firm A: 40%
- Firm B: 30%
- Firm C: 20%
- Firm D: 10%
Then: HHI=402+302+202+102=1600+900+400+100=3000HHI = 40^2 + 30^2 + 20^2 + 10^2 = 1600 + 900 + 400 + 100 = 3000
Interpretation:
- An HHI below 1,500 indicates a competitive market.
- An HHI between 1,500 and 2,500 suggests moderate concentration.
- An HHI above 2,500 indicates a highly concentrated market.
Why Squared?
Squaring gives greater weight to larger firms, highlighting the dominance of big players and making it easier to distinguish between market structures with similar numbers of firms but differing levels of concentration.
Other Options – Why They’re Incorrect:
- “Sum of the K largest firms’ market shares” does not reflect squaring or total concentration.
- “Sum of all firms’ market shares” is always 100%.
- “10,000 divided by K” is a formula only valid in a perfectly equal market (each firm has equal share), not a general rule.