|Enforcement authorities and organizations|
In economics, market concentration is a function of the number of firms and their respective shares of the total production (alternatively, total capacity or total reserves) in a market. The market concentration ratio measures the concentration of the top firms in the market, this can be through various metrics such as sales, employment numbers, active users or other relevant indicators. In theory and in practice, market concentration is closely associated with market competitiveness, and therefore is important to various antitrust agencies when considering proposed mergers and other regulatory issues. Market concentration is important in determining firm market power in setting prices and quantities.
Market concentration is affected through various forces, including barriers to entry and existing competition. Market concentration ratios also allows users to more accurately determine the type of market structure they are observing, from a perfect competitive, to a monopolistic, monopoly or oligopolistic market structure.
Market concentration is related to industrial concentration, which concerns the distribution of production within an industry, as opposed to a market. In industrial organization, market concentration may be used as a measure of competition, theorized to be positively related to the rate of profit in the industry, for example in the work of Joe S. Bain.
An alternative economic interpretation is that market concentration is a criterion that can be used to rank order various distributions of firms' shares of the total production (alternatively, total capacity or total reserves) in a market.
There are various factors that affect the concentration of specific markets including which include; barriers to entry(high start-up costs, high economies of scale, brand loyalty), industry size and age, product differentiation and current advertising levels. There are also firm specific factors affecting market concentration, including: research and development levels, and the human capital requirements. 
Although fewer competitors doesn't always indicate high market concentration, it can be a strong indicator of the market structure and power allocation.
After determining the relevant market and firms, through defining the product and geographical parameters, various metrics can be employed to determine the market concentration. This can be quantified using the SSNIP test.
A simple measure of market concentration is to calculate 1/N where N is the number of firms in the market. A result of 1 would indicate a pure monopoly, and will decrease with the number of active firms in the market, and nonincreasing in the degree of symmetry between them. This measure of concentration ignores the dispersion among the firms' shares. This measure is practically useful only if a sample of firms' market shares is believed to be random, rather than determined by the firms' inherent characteristics.
Any criterion that can be used to compare or rank distributions (e.g. probability distribution, frequency distribution or size distribution) can be used as a market concentration criterion. Examples are stochastic dominance and Gini coefficient.
The most commonly used market concentration measures is the Herfindahl-Hirschman Index (HHI or H).
Where is the market share of firm i, and N is the number of firms in the relevant market. If using decimals, the HHI index can range from 1/N to 1. However when using percentages, a HHI can range from 1 to 10000. In most markets, a HHI below 1500 indicates a market with low concentration, a HHI of 5000 indicates a duopoly and a HHI of 10000 indicates a fully monopolised market.
Section 1 of the Department of Justice and the Federal Trade Commission's Horizontal Merger Guidelines is entitled "Market Definition, Measurement and Concentration" and states that the Herfindahl index is the measure of concentration that these Guidelines will use. The Department of Justice considers.
where N is usually between 3 and 5. Although CR can provide a quick insight into the overall market concentration, it is limited in providing an accurate representation of industry competition, as this ratio does not provide a measure for the concentration within the top n, as a merger between two firms would not increase the overall CR, but would increase overall market concentration using other measures.
|Type of Market||CR Range||HHHI Range|
|Monopoly||1||6000 - 10 000 (Depending on Region)|
|Oligopoly||0.5-1||2000-6000 (Depending on Region)|
|Monopolistic||0-0.5||0 - 2000 (Depending on Region)|
|Competitive||0-0.5||0 - 2000 (Depending on Region)|
Since the introduction of the Sherman Antitrust Act of 1890, in response to growing monopolies and anti-competitive firms in the 1880's, antitrust agencies regularly use market concentration as an important metric to evaluate potential violations of competition laws. Since the passing of the act, these metrics have also been used to evaluate potential mergers' effect on overall market competition and overall consumer welfare. The first major example of the Sherman Act being imposed on a company to prevent potential consumer abuse through excessive market concentration was in the 1911 court case of Standard Oil Co. of New Jersey v. United States where after determining Standard Oil was monopolising the petroleum industry, the court-ordered remedy was the breakup into 34 smaller companies.
Modern regulatory bodies state that an increase in market concentration can inhibit innovation, and have detrimental effects on overall consumer welfare.
The United States Department of Justice determined that any merger that increases the HHI by more than 200 proposes a legitimate concern to antitrust laws and consumer welfare . Therefore, when considering potential mergers, especially in horizontal integration applications, antitrust agencies will consider the whether the increase in efficiency is worth the potential decrease in consumer welfare, through increased costs or reduction in quantity produced. 
Modern examples of market concentration being utilised to protect consumer welfare include:
As an economic tool market concentration is useful because it reflects the degree of competition in the market. Understanding the market concentration is important for firms when deciding their marketing strategy. As well, empirical evidence shows that there exists an inverse relationship between market concentration and efficiency, such that firms display an increase in efficiency when their relevant market concentration decreases. 
There are game theoretic models of market interaction (e.g. among oligopolists) that predict that an increase in market concentration will result in higher prices and lower consumer welfare even when collusion in the sense of cartelization (i.e. explicit collusion) is absent. Examples are Cournot oligopoly, and Bertrand oligopoly for differentiated products. Historically, Bain's (1956) original concern with market concentration was based on an intuitive relationship between high concentration and collusion.
Although theoretical models predict a strong correlation between market concentration and collusion, there is little empirical evidence linking market concentration to the level of collusion in an industry. 
Although, not as common as the Herfindahl-Hirschman Index or Concentration Ratio metrics, various alternative measures of market concentration have been used.
(a) The Rosenbluth (1961) index (also Hall and Tideman, 1967):
(b) Comprehensive concentration index (Horwath 1970):
(d) The Linda index (1976)
(e) The U Index (Davies, 1980):
The "number of effective competitors" is the inverse of the Herfindahl index.
Terrence Kavyu Muthoka defines distribution just as functionals in the Swartz space which is the space of functions with compact support and with all derivatives existing. The Media:Dirac_Distribution or the Dirac function is a good example .