Concentration indexes - Four firm concentration ratios, Herfindahl Hirschman indexes (HHI), Rothschild index, Lerner Index, Mergers ---- (See also Concentration's Ratio Index on Blackboard under Assignment tab
Joshua Jackson
What is a concentration ratio?
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 four and the eight largest firms within an industry. Concentration ratios are usually used to show the extent of market control of the largest firms in the industry. The concentration ratio indicates whether an industry is comprised of a few large firms or many small firms.
Concentration levels Those levels include:
No concentration - 0% concentration which means perfect competition or monopolistic competition
Low concentration - 0-50% which means perfect competition to oligopoly
Medium concentration - 50-80% which means oligopoly
High concentration - 80-100% which means oligopoly to monopoly
Total concentration - 100% which means an extremely concentrated oligopoly or if only one company then a monopoly
Concentration Ratio Problems
does not use the market shares of all the firms in the industry
does not provide the distribution of firm size
does not provide a lot of detail concerning competitiveness in an industry (vague information)
only provide general signs of oligopoly or monopoly in an industry
only indicates a vague degree of competition in an industry
Specificity vs. Vagueness
The problems outlined above from concentration ratios and to a lesser extent HHI (Herfindahl-Hirschman Index) are vague in nature. Some industries need more specificity in determining the market as displayed in the Electricity market. To account for the specificities needed in a usage market such as electricity, there are specificity measures that are utilized to determine how pivotal a company is in meeting the demand on the system (constituents within their industry). A company that is very pivotal can be said to have a high market power.
Pivotal Supplier Index (PSI)
The Pivotal Supplier Index considers both supply and demand. The PSI addresses who is the pivotal supplier in the market, if the supplier is meeting the needs of that market, could the market be satisfied without this "pivotal" supplier. 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 indicator that can be calculated hourly. If the company is needed to provide their supply it is seen as pivotal and if they are not needed they are not considered pivotal.
Residual Supply Index (RSI)
The Residual Supply Index is used to monitor market power. It is an alternative to the PSI as shown above.
The Residual Supply Index is expressed as:
RSI = (Σn1 Ci - Cx)/Last
where Cx is the capacity of the analyzed supplier and the sum of Ci the capacity of all suppliers.
If a company has a result of over 100% they have little influence on price, and consequently if their result is under 100% they can utilize their market power around setting price.
Four-Firm & Eight Firm Concentration Ratios
Two most common ratios used include:
The Four-Firm Concentration Ratio measures the total market share of the four largest firms in an industry. This ratio measures the percentage of sales of the four largest firms in the market divided by the total market sales. The larger the ratio, the less competition there is in the market; the smaller the ratio, the more competitive the market is. More specifically, a ratio of less than 40% is considered competitive; a ratio of more than 40% is considered an oligopoly. The following equation shows how to calculate the ratio:c4 (Four-Firm Concentration Ratio)=w1+w2+w3+w4, wi= Si/StSi is the sales of a single firm and St is equal to all firm’s sales. There are two deficiencies with the Four-Firm concentration ratio which include by design being deficient and not accounting for shifts in market share. The Four-Firm concentration ratio only accounts for 4 firms in an industry that could hold thousands. It also does not account for drastic swings in market share amongst the top 4 companies
The Eight-Firm Concentration Ratio measures the total market share of the eight largest firms in an industry. It holds the same deficiencies as the Four-Firm concentration ratio listed above.
Usually, these two common ratios are comparable from industry to industry.
What is the Herfindahl-Hirschman Index?
A common measure of market concentration. It is calculated by squaring the market share of each firm competing in a market, and then summing the resulting numbers. The HHI (Herfindahl-Hirschman Index) number can range from close to zero to 10,000. The HHI is expressed as:
HHI = s1^2 + s2^2 + s3^2 + ... + sn^2 (where sn is the market share of the ith firm).
The closer a market is to being a monopoly, the higher the market's concentration (and the lower its competition). If there was only one firm in an industry, that firm would have 100% market share, and the HHI would equal 10,000 (100^2), which is a monopoly. If there were thousands of firms competing (market share close to zero), the HHI would be close to zero, indicating nearly perfect competition.
The U.S. Department of Justice uses the HHI for evaluating mergers. The U.S. Department of Justice considers a market with a result of less than 1,000 to be a competitive marketplace; a result of 1,000-1,800 to be a moderately concentrated marketplace; and a result of 1,800 or greater to be a highly concentrated marketplace. As a general rule, mergers that increase the HHI by more than 100 points in concentrated markets raise antitrust concerns.
Rothschild Index The Rothschild Index provides a measure of the sensitivity to price of the demand for the product group as a whole relative to the sensitivity of the quantity demanded of a single firm to a change in its price. The Rothschild Index is given as: R = ET / EF Where ET is the elasticity of demand for the total market and EF is the elasticity of demand for the product of an individual firm.
The Rothschild Index can take on a value between 0 and 1. When the index is 1, the individual firm faces a demand curve that has the same sensitivity to price as the market demand curve. In contrast, when the elasticity of demand for an individual firm’s product is much greater, then the Rothschild Index is close to 0.
Lerner Index The Lerner Index, named after the economist Abba Lerner, describes a firm's market power. It is defined as:
L = (P - MC) / P
where P is the market price set by the firm and MC is the firm's marginal cost. The index ranges from a high of 1 to a low of 0, with higher numbers implying greater market power. For a perfectly competitive firm where P = MC, Learner Index equals to 0 and such a firm has no market power.When a firm charges a price that is higher than marginal cost, the Learner Index takes on a value greater than 0. Therefore, the Learner Index provides a measure of how much firms in an industry mark-up their prices over marginal cost. The higher the Learner Index, the greater the firm’s markup.
The Lerner Index is related to the markup charged by a firm. By re-arranging the Lerner Index formula in the following way
P = (1 / (1 - L)) MC
we can derive that 1 / (1 - L) is the markup factor. It defines the factor by which marginal cost is multiplied to obtain the price of the good.
Limitations of the Concentration Indexes Statistics and all other data should always be interpreted with caution and the concentration indexes are no exception. There are three potential limitations to interpretation of concentration indexes: 1.Concentration indexes are based on domestic market and exclude foreign imports, which tends to overstate the true level of concentration in industries with significant number of foreign producers. 2.Concentration indexes are based on national market. In many industries, the relevant markets are local and might be composed of only a few firms which tend to understate the actual level of concentration in the local markets. 3.Definition of product classes and aggregation across product classes can affect the concentration ratios. As a general rule, products that are close substitutes are considered to belong to a given industry class.
Multiple Choice Questions 1. As a general rule of thumb, the U.S. Department of Justice may scrutinize a proposed merger if the Herfindahl-Hirschman index is:
A. Above 1000 B. Below 1000 C. Above 1800 D. Below 1800 Answer: C. Above 1800 2. A firm has a marginal cost of $22 and charges a price of $35. The Lerner index for this firm is:
A. .37 B. .63 C. .59 D. .26 Answer: A. .37 (P-MC)/P = (35-22)/35 = .37
3. The concentration and Herfindahl-Hirschman indices computed by the U.S. Bureau of Census must be interpreted with caution because:
A. they may understate the actual level of concentration in markets served by foreign firms. B. national data tends to overstate the degree of concentration when the relevant markets are local. C. the definition of product classes used to define an industry affects the results. D. All of the Above Answer: C. the definition of product classes used to define an industry affects the results.
4. The index that measures the potential for a change in social welfare by examining the effect of small changes in industry output is the:
A. Concentration Ratio B. Lerner Index C. Rothschild Index D. Herfindahl Index Answer: C. Rothschild Index
5. Which of the following statements could be considered limitations to concentration indexes?
A.Industry’s market includes foreign contributors. B.Relevant markets are local. C.Product class includes products that are NOT close substitutes. D.All of the above. Answer: D. All of the Above References
Baye, Michael R.. Managerial Economics and Business Strategy. McGraw-Hill, 2010.
Domazlicky, Bruce, “From Theory to Reality: Concentration Ratios”, 2002
Elzinga, Kenneth G. and Mills, David E. The Lerner Index of Monopoly Power: Originsand Uses. American Economic Review: Papers & Proceedings, Vol. 101, No. 3, 2011.
Matthew Shapiro, “Measuring Market Power in U.S Industry”, National Bureau of Economic Research, 2008.
Miller, John Perry. "Business Concentration and Price Policy." Princeton University Press. pg. 117-138, 1985.
Joshua Jackson
What is a concentration ratio?
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 four and the eight largest firms within an industry. Concentration ratios are usually used to show the extent of market control of the largest firms in the industry. The concentration ratio indicates whether an industry is comprised of a few large firms or many small firms.
Concentration levels
Those levels include:
Concentration Ratio Problems
Specificity vs. Vagueness
The problems outlined above from concentration ratios and to a lesser extent HHI (Herfindahl-Hirschman Index) are vague in nature. Some industries need more specificity in determining the market as displayed in the Electricity market. To account for the specificities needed in a usage market such as electricity, there are specificity measures that are utilized to determine how pivotal a company is in meeting the demand on the system (constituents within their industry). A company that is very pivotal can be said to have a high market power.
Pivotal Supplier Index (PSI)
The Pivotal Supplier Index considers both supply and demand. The PSI addresses who is the pivotal supplier in the market, if the supplier is meeting the needs of that market, could the market be satisfied without this "pivotal" supplier. 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 indicator that can be calculated hourly. If the company is needed to provide their supply it is seen as pivotal and if they are not needed they are not considered pivotal.
Residual Supply Index (RSI)
The Residual Supply Index is used to monitor market power. It is an alternative to the PSI as shown above.
The Residual Supply Index is expressed as:
RSI = (Σn1 Ci - Cx)/Last
where Cx is the capacity of the analyzed supplier and the sum of Ci the capacity of all suppliers.
If a company has a result of over 100% they have little influence on price, and consequently if their result is under 100% they can utilize their market power around setting price.
Four-Firm & Eight Firm Concentration Ratios
Two most common ratios used include:
The Four-Firm Concentration Ratio measures the total market share of the four largest firms in an industry. This ratio measures the percentage of sales of the four largest firms in the market divided by the total market sales. The larger the ratio, the less competition there is in the market; the smaller the ratio, the more competitive the market is. More specifically, a ratio of less than 40% is considered competitive; a ratio of more than 40% is considered an oligopoly. The following equation shows how to calculate the ratio:c4 (Four-Firm Concentration Ratio)=w1+w2+w3+w4, wi= Si/StSi is the sales of a single firm and St is equal to all firm’s sales. There are two deficiencies with the Four-Firm concentration ratio which include by design being deficient and not accounting for shifts in market share. The Four-Firm concentration ratio only accounts for 4 firms in an industry that could hold thousands. It also does not account for drastic swings in market share amongst the top 4 companies
The Eight-Firm Concentration Ratio measures the total market share of the eight largest firms in an industry. It holds the same deficiencies as the Four-Firm concentration ratio listed above.
Usually, these two common ratios are comparable from industry to industry.
What is the Herfindahl-Hirschman Index?
A common measure of market concentration. It is calculated by squaring the market share of each firm competing in a market, and then summing the resulting numbers. The HHI (Herfindahl-Hirschman Index) number can range from close to zero to 10,000. The HHI is expressed as:
HHI = s1^2 + s2^2 + s3^2 + ... + sn^2 (where sn is the market share of the ith firm).
The closer a market is to being a monopoly, the higher the market's concentration (and the lower its competition). If there was only one firm in an industry, that firm would have 100% market share, and the HHI would equal 10,000 (100^2), which is a monopoly. If there were thousands of firms competing (market share close to zero), the HHI would be close to zero, indicating nearly perfect competition.
The U.S. Department of Justice uses the HHI for evaluating mergers. The U.S. Department of Justice considers a market with a result of less than 1,000 to be a competitive marketplace; a result of 1,000-1,800 to be a moderately concentrated marketplace; and a result of 1,800 or greater to be a highly concentrated marketplace. As a general rule, mergers that increase the HHI by more than 100 points in concentrated markets raise antitrust concerns.
Rothschild Index
The Rothschild Index provides a measure of the sensitivity to price of the demand for the product group as a whole relative to the sensitivity of the quantity demanded of a single firm to a change in its price. The Rothschild Index is given as:
R = ET / EF
Where ET is the elasticity of demand for the total market and EF is the elasticity of demand for the product of an individual firm.
The Rothschild Index can take on a value between 0 and 1. When the index is 1, the individual firm faces a demand curve that has the same sensitivity to price as the market demand curve. In contrast, when the elasticity of demand for an individual firm’s product is much greater, then the Rothschild Index is close to 0.
Lerner Index
The Lerner Index, named after the economist Abba Lerner, describes a firm's market power. It is defined as:
L = (P - MC) / P
where P is the market price set by the firm and MC is the firm's marginal cost. The index ranges from a high of 1 to a low of 0, with higher numbers implying greater market power. For a perfectly competitive firm where P = MC, Learner Index equals to 0 and such a firm has no market power.When a firm charges a price that is higher than marginal cost, the Learner Index takes on a value greater than 0. Therefore, the Learner Index provides a measure of how much firms in an industry mark-up their prices over marginal cost. The higher the Learner Index, the greater the firm’s markup.
The Lerner Index is related to the markup charged by a firm. By re-arranging the Lerner Index formula in the following way
P = (1 / (1 - L)) MC
we can derive that 1 / (1 - L) is the markup factor. It defines the factor by which marginal cost is multiplied to obtain the price of the good.
Limitations of the Concentration Indexes
Statistics and all other data should always be interpreted with caution and the concentration indexes are no exception. There are three potential limitations to interpretation of concentration indexes:
1.Concentration indexes are based on domestic market and exclude foreign imports, which tends to overstate the true level of concentration in industries with significant number of foreign producers.
2.Concentration indexes are based on national market. In many industries, the relevant markets are local and might be composed of only a few firms which tend to understate the actual level of concentration in the local markets.
3.Definition of product classes and aggregation across product classes can affect the concentration ratios. As a general rule, products that are close substitutes are considered to belong to a given industry class.
Multiple Choice Questions
1. As a general rule of thumb, the U.S. Department of Justice may scrutinize a proposed merger if the Herfindahl-Hirschman index is:
A. Above 1000
B. Below 1000
C. Above 1800
D. Below 1800
Answer: C. Above 1800
2. A firm has a marginal cost of $22 and charges a price of $35. The Lerner index for this firm is:
A. .37
B. .63
C. .59
D. .26
Answer: A. .37 (P-MC)/P = (35-22)/35 = .37
3. The concentration and Herfindahl-Hirschman indices computed by the U.S. Bureau of Census must be interpreted with caution because:
A. they may understate the actual level of concentration in markets served by foreign firms.
B. national data tends to overstate the degree of concentration when the relevant markets are local.
C. the definition of product classes used to define an industry affects the results.
D. All of the Above
Answer: C. the definition of product classes used to define an industry affects the results.
4. The index that measures the potential for a change in social welfare by examining the effect of small changes in industry output is the:
A. Concentration Ratio
B. Lerner Index
C. Rothschild Index
D. Herfindahl Index
Answer: C. Rothschild Index
5. Which of the following statements could be considered limitations to concentration indexes?
A.Industry’s market includes foreign contributors.
B.Relevant markets are local.
C.Product class includes products that are NOT close substitutes.
D.All of the above.
Answer: D. All of the Above
References