Quantitative Tests for Market Power
Measures of firm concentration by themselves are not good indicators of market power. In general, the successful exercise of market power depends on a number of factors, not just market share or concentration. Thus a full competition analysis must look at a range of factors.
With those qualifications in mind, quantitative measures of market concentration or market power are often used in assessing the effect of horizontal mergers, as one component of competition analysis. For example, in the United States competition authorities use the Herfindahl-Hirschman Index to screen mergers, and identify those that warrant further examination.
Several different techniques are available for measuring the level of firm concentration in a market, as a potential indicator of market power.
The Hirschman-Herfindahl Index (HHI) is based on the total number and size distribution of firms in an industry. It is computed as the sum of the squares of the market shares of all firms in the industry. The HHI ranges from 0 in a market with many very small firms, to 10 000 in a pure monopoly. For example, suppose a market has four firms with market shares of 50, 30, 10, and 10 percent, respectively. The HHI for that market is 2,500 %20 900 %20 100 %20 100 = 3,600. 
In the United States, competition authorities use the HHI to evaluate the potential effects of a merger on market concentration. The United States Horizontal Merger Guidelines  set thresholds for the change in the HHI to determine whether a horizontal merger has the potential to generate market power and reduce competition. The Guidelines start by defining a pre-merger market as being:
- Unconcentrated if the HHI is less than 1,000,
- Moderately concentrated if the HHI is between 1,000 and 1,800, and
- Concentrated if the HHI is above 1,800.
If, as a result of a horizontal merger, the HHI increases by less than 100 points in a moderately concentrated market or by less than 50 points in a concentrated market, that merger is considered to be “safe.”
If the merger increases the HHI by more than these thresholds, it is examined further to determine its likely effect on competition.
The European Union’s Guidelines on the Assessment of Horizontal Mergers  are similar.
- There are unlikely to be horizontal competition concerns in a market with a post-merger HHI below 1,000.
- Similarly, there are unlikely to be horizontal competition concerns in a merger with a post-merger HHI between 1,000 and 2,000 and a delta below 250, or a merger with a post-merger HHI above 2,000 and a delta below 150, except in the presence of special circumstances that are set forth in the Guidelines.
Concentration ratios can also be used to measure the degree of market concentration. Concentration ratios measure the combined market share of a given number of large firms. For example, the four-firm concentration ratio gives the combined market share of the largest four firms in an industry, as a proportion of the total size of the industry. The higher the ratio, the more concentrated the industry, and the greater the potential for market power.
Indexes of Market Power
The Lerner Index measures the extent to which a given firm’s prices exceed marginal costs. It is measured as the difference between the price of a good or service and its marginal cost, expressed as a proportion of the price:
The Lerner Index is higher, the greater the mark-up in price over marginal cost. However, a high Lerner Index does not necessarily mean the firm in question is exercising market power. Prices may exceed marginal costs for a number of legitimate reasons. In the telecommunications sector at least some prices must exceed marginal costs to cover the high fixed costs of networks.
In practice, the Lerner Index can be problematic to calculate. This is particularly true in industries such as telecommunications where calculating a firm’s marginal cost of production for a given service can be difficult.
Economists use a modified version of the Lerner Index called L2:
The parameters in the Modified Lerner Index are:
- The firm’s price (P),
- The firm’s marginal or incremental cost (MC),
- The firm’s market share (S),
- The market price elasticity of demand (). This measures the countervailing power of consumers — their willingness to do without the product or service if the price increases,
- The firm price elasticity of demand (). This measures consumers’ willingness to substitute products from other suppliers, as well as doing without the product entirely, when the firm increases the price, and
- The supply elasticity of the competitive fringe (f). This measures the change in the amount supplied by existing or new competitors due to a change in the dominant firm’s price.
Higher values of this index indicate greater market power. The value of the L2 index value rises as:
- Market share increases,
- Market price elasticity of demand falls, and/or
- Competitors’ supply elasticity falls.
The impact of a “high” or rising market share on market power could be offset by high or rising values for either or both elasticities. Alternatively, a firm with a relatively “low” market share could have market power if either or both elasticities were low as well. For example even a firm with a low market share can enjoy temporary economic rents by introducing an innovation or through superior customer service. For a while at least, consumers may be less inclined to substitute rivals’ products, and competitors may be unwilling or unable to match the firm’s action.
 The HHI may also be calculated using proportions, rather than percentages. Using proportions, the HHI for the example above would be calculated as follows: HHI = 0.25 %20 0.09 %20 0.01 %20 0.01 = 0.36. Using this approach, definitions of unconcentrated, moderately concentrated, and concentrated markets given in the United States Horizontal Merger Guidelines would be: less than 0.1, 0.1 to 0.18, and above 0.18, respectively.
Organisation for Economic Co-Operation and Development, Glossary of Industrial Organisation Economics and Competition Law