How to Calculate the Herfindahl-Hirschman Index (HHI)

The Herfindahl-Hirschman Index (HHI) measures market concentration by summing the squares of market shares. For example, if two companies each have 30% market share, HHI = 30² + 30² = 1800. If these two companies merge, they become one company with 60% market share, so HHI = 60² = 3600. The increase in HHI is 3600 - 1800 = 1800. When five companies have equal market share (20% each), HHI = 5 × 20² = 2000. If two merge, HHI = 3 × 20² + 40² = 2800. This calculation helps assess how mergers affect market concentration and competition.

Three merger types: (1) Vertical integration—combining production stages to reduce transaction costs, (2) Horizontal integration—merging similar firms for economies of scale and market power, (3) Conglomerate mergers—combining different products for cash flow stability or managerial talent leverage. FTC/DOJ use HHI thresholds (2,500 for highly concentrated) to evaluate mergers. Horizontal mergers increasing HHI by 200 points may be blocked. Conglomerate mergers may lose specialization benefits without offsetting synergies.

The objective of horizontal merger analysis is to prevent consumers from being denied competition benefits through mergers that significantly increase market power. The analysis uses a before-and-after framework: assessing how competition changes from pre-merger state (Y) to post-merger state (X). The Commission conducts market power analysis through structural factors: defining relevant markets, calculating market shares, and estimating concentration indexes. The HHI (Herfindahl-Hirschman Index) sums squared market shares, providing nuanced concentration measurement. Thresholds guide analysis: HHI below 1000 = unconcentrated; 1000-2000 = moderately concentrated (concerns if delta ≥ 250); above 2000 = concentrated (concerns if delta ≥ 150). Exceptional intervention in unconcentrated markets may occur for killer acquisitions, innovative firms, cross-shareholdings, maverick acquisitions, or evidence of pre-existing collusion.

The HHI measures market concentration by summing squared market shares: HHI = Σ(s_i²). Pure monopoly yields 10,000; perfect competition yields 0. The Department of Justice applies three-tier guidelines: (1) Post-merger HHI < 1,000: presumed no concerns; (2) 1,000 ≤ HHI < 1,800: examine HHI change—if change exceeds 50-100 points, significant concerns arise; (3) Post-merger HHI > 1,800: mergers increasing HHI by over 100 points are typically blocked. Market definition is critical in litigation, with defense arguing broad definitions and prosecution arguing narrow ones.

The Herfindahl-Hirschman Index (HHI) measures market concentration by summing the squares of all firms' market shares in a market. A market is considered concentrated when HHI exceeds approximately 1800-2000. The change in HHI (delta HHI) after a merger indicates potential competition concerns. For example, a symmetric oligopoly with 5 firms each having 20% market share has HHI = 2000. Higher HHI indicates greater market power and potential merger concerns.

Concentration indices measure market structure and potential competitive harm. CR4 (Concentration Ratio for Top 4) calculates the top four firms' share of total sales—for example, firms with 150, 100, 80, and 70 million sales in a 450 million market yield 88.9% concentration. However, CR4 ignores the distribution of remaining firms. HHI (Herfindahl-Hirschman Index) sums squared market shares of all firms, providing a more comprehensive measure. For shares of 40%, 30%, 20%, 9%, and 1%, HHI equals 2982. When firms merge, HHI increases significantly—for instance, merging 20% and 9% shares yields HHI of 3342. According to American merger guidelines, HHI below 1,000 indicates unconcentrated markets, 1,000-1,800 moderately concentrated, and above 1,800 highly concentrated. Mergers significantly increasing HHI in concentrated markets are unlikely approved.

Concentration indices measure market dominance by major companies. The Concentration Ratio (CRn) calculates the percentage of total market share held by the N largest companies. The Herfindahl-Hirschman Index (HHI) sums the squares of each company's market share percentage: HHI = S1² + S2² + ... + Sn². For example, with companies A(40%), B(25%), C(15%), D(10%), E(10%): CR4 = 90% (four companies control 90% of market), HHI = 2650. High CR4 and HHI values indicate concentrated markets (oligopoly/monopoly), while low values indicate competitive markets. High concentration limits competition, creates barriers to entry, and allows dominant firms to influence prices and strategies.

Two primary measures of market concentration are CR4 and HHI. CR4 (Concentration Ratio for 4) measures the market share of the four largest companies in a market, calculated as the sum of their market shares. It is easy to calculate and widely used but ignores smaller companies and does not capture relative concentration between firms. HHI (Herfindahl-Hirschman Index) sums the squares of all companies' market shares, providing a more complete picture by considering the entire market. HHI gives greater weight to larger market shares, making it more sensitive to concentration changes and better at detecting merger effects. HHI ranges from 10,000 (perfect competition) to 100,000 (monopoly).

The Four Firm Concentration Ratio (CR4) measures market concentration by summing the market shares of the four largest firms in an industry. The Herfindahl-Hirschman Index (HHI) measures market concentration by squaring the market share of each firm and summing the results. For example, with market shares of 30%, 25%, 20%, 15%, and 10% for the remaining firms, the CR4 is 90% and the HHI is 2,150. With market shares of 25%, 25%, 20%, 25%, and 5%, the CR4 is 95% and the HHI is 2,300.

Industry concentration is measured using the four-firm concentration ratio (CR4) and the Herfindahl-Hirschman Index (HHI). CR4 calculates the percentage of total market sales accounted for by the four largest firms, ranging from 0 to 1. HHI squares each firm's market share, sums them, and multiplies by 10,000, giving more weight to larger firms. Both measures indicate competitive intensity - higher values mean fewer dominant players. However, HHI has limitations: it uses lagged data, excludes foreign competition, ignores local market concentration, and is sensitive to product definition. These metrics help regulators assess market competitiveness and identify potential anti-competitive behavior.

Collusion occurs when oligopolistic firms coordinate to maximize joint profits through information sharing and price coordination. This is illegal under US antitrust laws (Sherman Act 1890, Clayton Act 1914) because it harms consumers through higher prices and reduced output. The Department of Justice prosecutes such cases, and the Supreme Court consistently rules against consumer-harming practices. However, collusion is difficult to detect because firms avoid documentation. The gas station case (two stations raising prices to $7/gallon) demonstrates how even small markets can be prosecuted under these laws.

The video explains that tacit collusion is a fundamentally human behavior that AI has rediscovered. The risk is described in economic terms with 100 years of antitrust practice available, but traditional antitrust requires proof of explicit agreement, which doesn't exist in tacit collusion. The video describes this as a 'quantum problem' - agents are 'quantumly entangled' models producing identical solutions without any communication channel. They don't need a communication channel for collusion; they just need shared information and default settings.

Market collusion occurs when companies secretly agree to fix prices, quantities, or market conditions to maximize profits. The video provides concrete examples: sugar companies (CJ, Samyang, Daehan) controlled 89% of the market and colluded for 4 years, earning 3.288 trillion won with only 12% in fines. Chicken companies (16 firms) controlled 77% of the market and colluded for 12 years, earning 12 trillion won with only 1.4% in fines. High market concentration enables collusion by reducing detection risk. Companies calculate collusion as a rational investment because expected profits exceed expected punishment costs. The exclusive prosecution right creates a fundamental barrier to prosecution, as only the FTC can refer cases, and even when violations are confirmed, the FTC can choose only fines without criminal prosecution. This system has allowed companies to treat collusion as a business strategy rather than a crime.

Market power harms purchasers, reduces output, and creates dead weight loss. Natural monopolies (utilities) require price regulation by government agencies. Antitrust laws prohibit collusion but not monopoly power itself. Patent and copyright laws protect monopoly positions to incentivize innovation. The trade-off involves balancing dead weight loss against innovation benefits. Studies show industries with few buyers have 10% lower price-cost margins than competitive markets.

Firms achieve market power through collusion (joining rivals to restrict output/raise prices) or exclusion (foreclosing competitors through input or dealer arrangements). Both mechanisms ultimately restrict competition and raise prices, but differ in methodology. Collusion involves direct rival coordination; exclusion involves indirect competitor impairment. Both harm consumers and reduce efficiency, can occur separately or together, and can reinforce each other. Competition authorities investigate by examining market structure, discount policies, and likely effects on all parties. Critical principles include focusing on consumer harm rather than competitor welfare, testing theories against economic literature, and maintaining openness to potential efficiencies while rigorously assessing causation and prevalence of alleged anti-competitive conduct.