Difficulty: Introductory | Prerequisites: Percentages, squaring numbers.
The Herfindahl-Hirschman Index (HHI) is the standard measure of market concentration used by economists and competition authorities (including the U.S. Department of Justice). It summarises how "spread out" or "concentrated" market share is across firms. A higher HHI means more concentration and, typically, more market power. You will see it in oligopoly and antitrust chapters, and it appears regularly on exams as a quick calculation question.
The HHI is the sum of squared market shares (expressed as percentages) of every firm in the industry. It ranges from near 0 (many tiny firms) to 10,000 (pure monopoly). A higher number means a more concentrated market.
Herfindahl-Hirschman Index (HHI)
The sum of the squares of each firm's market share (in percentage terms) across all firms in the industry. Think of it as a single number that captures both the number of firms and the inequality in their sizes.
Market share
A firm's sales as a percentage of total industry sales. Calculated as (firm sales / total industry sales) x 100.
Market concentration
The degree to which a small number of firms account for a large proportion of total industry output or sales. High concentration suggests oligopolistic or monopolistic conditions.
HHI = \sum_{i=1}^{N} s_i^2where s_i is the market share of firm i in percentage terms, and N is the number of firms.
The industry has 6 firms with total sales of: 300, 150, 120, 90, 60, 30.
Total industry sales = 300 + 150 + 120 + 90 + 60 + 30 = 750.
Compute each firm's market share (as a percentage):
Firm 1: (300/750) x 100 = 40%
Firm 2: (150/750) x 100 = 20%
Firm 3: (120/750) x 100 = 16%
Firm 4: (90/750) x 100 = 12%
Firm 5: (60/750) x 100 = 8%
Firm 6: (30/750) x 100 = 4%
Square each share and sum:
40^2 = 1,600
20^2 = 400
16^2 = 256
12^2 = 144
8^2 = 64
4^2 = 16
HHI = 1,600 + 400 + 256 + 144 + 64 + 16 = 2,480
HHI below 1,500: the market is considered unconcentrated.
HHI between 1,500 and 2,500: moderately concentrated.
HHI above 2,500: highly concentrated.
This industry, with an HHI of 2,480, sits at the upper end of moderately concentrated, close to the highly concentrated threshold. The largest firm holds 40% of the market, which drives much of the index.
The U.S. Department of Justice and the Federal Trade Commission use the HHI to screen proposed mergers. A merger that pushes the HHI above 2,500 or increases it by more than 200 points is likely to receive close scrutiny.
Students sometimes use market shares as decimals (0.40) rather than percentages (40) when squaring. The standard convention in most textbooks (and this course) is to use percentage points, giving an HHI that ranges up to 10,000. If you use decimals, the maximum is 1.0, and the thresholds are different. Check what your professor expects.
Some students forget to square the shares and simply add them up. Adding raw shares always gives 100%; that tells you nothing about concentration.
A common error is squaring each firm's sales figures directly instead of first converting to market shares.
HHI calculations are easy marks on an exam. The arithmetic is straightforward, so the main risk is a careless mistake in the market-share conversion or squaring step.
Know the DOJ/FTC concentration thresholds (1,500 and 2,500). Short-answer questions may ask you to classify a market.
You may be asked: "What happens to the HHI if two firms merge?" Combine their sales, recompute shares, re-square.
True or False: A pure monopoly has an HHI of 10,000. (True. One firm with 100% share: 100^2 = 10,000.)
Fill in the blank: HHI is the sum of the ____ of each firm's market share. (squares.)
True or False: An industry with 10 firms of equal size has an HHI of 100. (False. Each firm has 10% share; HHI = 10 x 10^2 = 1,000.)
Q: Six firms have sales of 300, 150, 120, 90, 60, and 30. Calculate the HHI.
A: Total sales = 750. Market shares: 40%, 20%, 16%, 12%, 8%, 4%. HHI = 1600 + 400 + 256 + 144 + 64 + 16 = 2,480.
Q: Is this market concentrated?
A: With an HHI of 2,480, it falls in the moderately concentrated range (1,500 to 2,500), near the threshold for highly concentrated.
Q: If Firms 5 and 6 merge, what is the new HHI?
A: The merged firm has sales of 90 (60 + 30), so its share is 90/750 = 12%. New shares: 40%, 20%, 16%, 12%, 12%. New HHI = 1600 + 400 + 256 + 144 + 144 = 2,544. The market is now highly concentrated.
The HHI connects to the broader discussion of market structure and market power. In Cournot models, the number and size distribution of firms determines the markup over marginal cost, and the HHI can be shown to be directly related to the industry-level Lerner Index (a measure of price-cost margins). It also appears in antitrust economics and regulatory policy discussions.
Herfindahl-Hirschman Index, HHI, market concentration, market share, industry concentration, antitrust, merger screening, DOJ merger guidelines, FTC, Lerner Index, oligopoly, market power, number-equivalent firms, ECON 302, intermediate microeconomics, Penn State