# Concentration ratio

For the chemistry and biology concept, see Dilution ratio.

In economics, a concentration ratio is a measure of the total output produced in an industry by a given number of firms in the industry. The most common concentration ratios are the CR4 and the CR8, which means the market share of the four and the eight largest firms. Concentration ratios are usually used to show the extent of market control of the largest firms in the industry and to illustrate the degree to which an industry is oligopolistic.[1]

The standard tools of competition economists and competition authorities to measure market concentration are the Herfindahl index (HHI) and the concentration ratios (CR(n)).[2] These two are known as the traditional structural measures of market concentration (based on market shares). The concentration of firms in an industry is of interest to economists, business strategists and government agencies.[3]

## Two common ratios

• The Four-Firm Concentration Ratio measures the total market share of the four largest firms in an industry.
• The Eight-Firm Concentration Ratio measures the total market share of the eight largest firms in an industry.

Usually, these two common ratios are comparable from industry to industry, while concentration ratios for other numbers of firms can be also calculated.[1]

## Calculation

The concentration ratio is the percentage of market share held by the largest ${\displaystyle m}$ firms in an industry.

${\displaystyle CR_{m}=\sum _{i=1}^{m}s_{i}}$

Therefore it can be expressed as:

${\displaystyle CR_{m}=s_{1}+s_{2}+\ldots +s_{m}{,}}$

where ${\displaystyle s_{i}}$ is the market share and ${\displaystyle m}$ defines the ${\displaystyle m^{th}}$ firm.[4]

## Concentration levels

Concentration ratios range from 0 to 100 percent. The levels reach from no, low or medium to high to "total" concentration.
[1]

No concentration
0% means perfect competition or at the very least monopolistic competition. If for example CR4=0 %, the four largest firm in the industry would not have any significant market share.
Low concentration
0% to 50%. This category ranges from perfect competition to an oligopoly.
Medium concentration
50% to 80%. An industry in this range is likely an oligopoly.
High concentration
80% to 100%. This category ranges from an oligopoly to monopoly.
Total concentration
100% means an extremely concentrated oligopoly. If for example CR1= 100%, there is a monopoly.

## Problems

The definition of the concentration ratio does not use the market shares of all the firms in the industry and does not provide the distribution of firm size. It also does not provide a lot of detail about competitiveness of the industry. The concentration ratios just provide a sign of the oligopolistic nature of an industry and indicate the degree of competition.[1][3] The Herfindahl index provides a more complete picture of industry concentration than does the concentration ratio.

## Concentration ratios in United Kingdom

UK industries with the highest five-firm concentration ratios include the following:[5]

• Sugar: 99%
• Tobacco products: 99%
• Gas distribution: 82%
• Oils and fats: 88%
• Confectionery: 81%
• Coal extraction: 79%
• Soft drinks and mineral waters: 75%
• Pesticides: 75%
• Weapons and ammunition: 77%

UK industries with the lowest five-firm concentration ratios include the following:[5]

• Metal forging, pressing etc.: 4%
• Plastic products: 4%
• Furniture: 5%
• Construction: 5%
• Structural metal products: 6%
• Wholesale distributions: 6%
• General purpose machinery: 8%
• Wood and wood products: 9%

## Electricity specific measures

As to account for the specificities of electricity markets the specific structural measures are calculated. The Herfindahl index and the concentration ratios focus on the market shares of companies, but these measures identify the "pivotalness" of companies to meeting the demand on the system. A company that is very pivotal can be said to have a high market power.[2]

### Pivotal Supplier Index (PSI)

The Pivotal Supplier Index considers the demand in addition to the supply side. At the most basic level, the PSI answers the question if a particular supplier, the "pivotal supplier", is needed to supply the demand: would it be possible to supply the prevalent demand also without this supplier or is he mandatory?[4]

The Pivotal Supplier Index is expressed as the following:

PSI = I[Cx > Σni=I Ci - Total Consumption]
where Cx is the capacity of the potential pivotal supplier and the sum of Ci the capacity of all suppliers. The function I[.] is the indicator function, which takes the value 1 if the expression "." contained in it is true.

An equivalent expression is the following:

PSI = I[Total consumption > Σi≠xCi ]
where the sum of capacities is taken over all suppliers apart from x.

The PSI is a binary indicator that can be calculated hourly. If the supplier Cx is needed to supply the demand, it is pivotal and the index takes the value "1". If he is not pivotal, it takes the value "0".[4]

### Residual Supply Index (RSI)

The Residual Supply Index is a simple and effective tool in monitoring market power. It is the non-binary alternative to the PSI.[4]
The Residual Supply Index is expressed as:

RSI = (Σn1 Ci - Cx)/Last
where Cx is the capacity of the analysed supplier and the sum of Ci the capacity of all suppliers.

Receiving a result bigger than 100% is an indication that the supplier x should have little influence on the price. With a RSI smaller than 100%. the supplier x could easily practise market power. The RSI has the advantage over the PSI to be not binary and for this reason it can better indicate the increase of the structural market power.[4]

## Notes

1. ^ a b c d Concentration Ratios, 16 December 2009
2. ^ a b
3. ^ a b Industry Concentration, 20 October 2009
4. Lang, C:Marktmacht und Marktmachtmessung im deutschen Großhandelsmarkt für Strom, Deutscher Universitätsverlag/GWF Fachverlag Gmbh, Wiesbaden 2007, S.8, S.9 - 11
5. ^ a b

## References

German

• Christoph Lang: Marktmacht und Marktmachtmessung im deutschen Großhandelsmarkt für Strom, Deutscher Universitätsverlag/GWF Fachverlag Gmbh, Wiesbaden 2007

English