Concentration ratio and Herfindahl-Hirschman index

What is the ideal measure of market power, and why is it rarely used?

In theory you would estimate the elasticity of demand . If demand is very elastic, the market is close to perfect competition. If demand is inelastic, firms may have market power.

In practice this is hard. Observed prices and quantities are the equilibrium of demand and supply together (the endogeneity problem), so demand and supply must be estimated as a pair. Time-series data may span years in which the market structure changed. Cross-section data are costly to collect, and results depend on the model chosen. So analysts and regulators use simpler measures.

Market power

• Ideal measure: elasticity of demand Know the idea very elastic = near perfect competition; inelastic = market power
  • Endogeneity observed price and quantity are equilibrium points of demand and supply together
  • Time-series estimates market structure may have changed
  • Cross-section estimates costly data; results depend on model choices
• Practical: N-firm concentration ratio Memorize sum of the top N shares
• Practical: Herfindahl-Hirschman index Memorize sum of squared shares

How do you calculate the concentration ratio and the HHI?

The concentration ratio for the N largest firms adds their market shares. It runs from 0 (perfect competition) to 100% (monopoly).

$$CR_N = s_1 + s_2 + \cdots + s_N$$

The Herfindahl-Hirschman index (HHI) squares the shares first, with shares written as decimals, so that a monopoly scores 1.

$$HHI_N = s_1^2 + s_2^2 + \cdots + s_N^2 \quad (\text{shares as decimals})$$

If M firms share the market equally, the HHI is 1/M. That gives a handy reading: 1/HHI is roughly the number of equal-sized firms the market behaves like.

$$HHI = \frac{1}{M} \;\Rightarrow\; M = \frac{1}{HHI}$$

Exam tip Check the question: top N or all firms? Percent or decimal? Squared or not?

What happens to each measure in a merger?

Suppose firms 3 and 4 (18% and 12%) merge into one with 30%. The new top four are 30, 30, 22 and 8.

Squaring gives big shares extra weight, so mergers among large firms move the HHI more. Here the four-firm ratio rises by about 10% (82 to 90) while the four-firm HHI rises by about 27% (0.1852 to 0.2348). The gap grows when the merging firms are the leaders, and the concentration ratio can then barely change at all. That is why regulators favor the HHI when assessing mergers.

$$\Delta HHI = 2\,s_1\,s_2$$

When two firms with shares $s_1$ and $s_2$ combine, the squared term $(s_1 + s_2)^2$ replaces $s_1^2 + s_2^2$, so the all-firm HHI rises by $2s_1s_2$. Check it: 2 × 0.18 × 0.12 = 0.0432, which is exactly 0.24 − 0.1968. The shortcut applies to the all-firm HHI. A top-N HHI can change by a different amount, because the list of leading firms changes.

What do concentration measures miss?

Limitations

• Barriers to entry Memorize the threat of entry can discipline a sole incumbent
• Elasticity of demand Memorize neither measure estimates it directly
• Concentration ratio ignores mergers among leaders Memorize it barely moves when two large firms combine
• Market definition geography and substitutes change every number

• Neither measure captures barriers to entry. A sole incumbent facing easy entry may still price competitively, because a potential entrant is enough to discipline it. Picture the only bike-rental shop in a seaside town, where a rival could start trading from a van within weeks: the shop keeps its prices modest to give the rival no reason to come.
• Neither measures the elasticity of demand directly.
• The concentration ratio barely moves when two large firms merge, while the HHI reacts more.
• Market definition changes every number: geography, and what counts as a substitute.

So a high concentration measure is a prompt for further analysis, not proof of pricing power. An analyst should still ask how easy entry would be and how sensitive buyers are to price.

Regulators care about these numbers because market power can lead to higher prices and lower output, which is inefficient for the market as a whole. Many countries have competition law to preserve competition. An analyst who hears of a proposed merger should always consider whether regulators may block it.

Go deeper HHI on a 0 to 10,000 scale

Regulators usually quote the HHI with shares in whole percents squared, so a monopoly scores 10,000 and the payments market above scores about 1,968. The CFA curriculum uses decimals, with a monopoly at 1. The two scales differ by a factor of 10,000, so check which one a question uses before comparing with any threshold.

Go deeper Why 1 ÷ HHI is only approximate

If all M firms have equal shares, the HHI is exactly 1/M. With unequal shares, 1 ÷ HHI gives the number of equal-sized firms that would produce the same HHI. Unless the shares are equal, it is smaller than the actual number of firms, because small firms contribute almost nothing once squared. The payments market has seven firms but behaves like about five.