Concentration Indexes – Four-Firm Concentration Ratios, Herfindahl-Hershman Indexes (HHI), Rothschild Index, Learner Index, Mergers

MBA651 - Economic Analysis for Managers
Bo Kurtovic

Concentration refers to the extent to which a small number of firms or enterprises account for a large proportion of economic activity such as total sales, assets or employment. In the usual content, it is a function of the number of firms and their respective shares of the total production in a market.
The best industries, from an investing perspective, are near monopolies, that is, highly concentrated industries. Leading firms in concentrated industries, those with only two or three major competitors, typically report higher profit margins than companies in fragmented markets. These firms give a higher priority to increasing profit margins than to gaining market share through price-cutting. Oil refiners are examples of concentrated industries.
On the other hand, fragmented markets with many participants competing for position are usually price competitive, resulting in lower profit margins. For instance, the apparel industry with dozens of companies battling for market share generates net profit margins around 6 percent, compared to the 11 percent average margin for all companies making up the S&P 500 Index.

Four-Firm Concentration Ratio
One of the most commonly used concentration ratio is the four-firm concentration ratio, or C4, which consists of the market share, as a percentage, of the four largest firms in the industry. In general, the four-firm concentration ratio is the percentage of market output generated by the four largest firms in the industry.
Four-firm concentration ratio provides a very crude measure of the size structure of an industry. Four-firm concentration ratios that are close to zero indicate markets in which there are many sellers, encouraging competition among producers for the right to sell to consumers. Industries with four-firm concentration ratios close to one indicate markets in which there is little competition among producers for sales to consumers.

The four-firm concentration ratio is given by: C4 = (S1 + S2 + S3 + S4) / ST where
S1, S2, S3 and S4 denote the sales of four largest firms in the industry and ST denote the total sales of all firms in the industry.
It can also be calculated as C4 = w1 + w2 + w3 + w4 where w1-4 denote the market shares of top four firms.

Following chart represents the market segmentation for software industry. The top four firms by market share are Microsoft, IBM, Oracle and Computer Associates.


Given the above data, four-firm concentration ratio for software industry can be calculated as:
C4 = w1 + w2 + w3 + w4 = 0.228 + 0.105 + 0.059 + 0.023 = 0.415

Herfindahl-Hershman Index (HHI) HHI is a commonly accepted 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 number can range from close to zero to 10,000. By squaring the market shares before adding them up, the index weighs firms with high market shares more heavily. The HHI is expressed as:
HHI = 10,000 (w1^2 + w2^2 + w3^2 + w4^2 + … wn^2) where w denote the market shares of a given firm.
The HHI takes into account the relative size and distribution of the firms in a market and approaches zero when a market consists of a large number of firms of relatively equal size. The HHI increases both as the number of firms in the market decreases and as the disparity in size between those firms increases.
Markets in which the HHI is between 1000 and 1800 points are considered to be moderately concentrated, and those in which the HHI is in excess of 1800 points are considered to be concentrated.

Example Assume that the market for the widgets is equally shared by 10 widget makers. Their premerger HHI would be:
10,000 (0.1^2 + 0.1^2 + 0.1^2 + 0.1^2 + 0.1^2 + 0.1^2 + 0.1^2 + 0.1^2 + 0.1^2 + 0.1^2) = 1,000
The highest possible HHI is 10,000 (a monopoly = 100 percent). On the low end, HHI can be extremely small because the index declines with each added player and there is no limit to the number that can be added.
Now suppose a merger occurred between two of them, doubling the market share of one company, and shrinking the total market to nine companies.
10,000 (0.2^2 + 0.1^2 + 0.1^2 + 0.1^2 + 0.1^2 + 0.1^2 + 0.1^2 + 0.1^2 + 0.1^2) = 1,200

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 Learner 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
Statistical 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. This 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 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 closed substitutes (have large, positive cross-price elasticity) are considered to belong to a given industry class.

According to the U.S. Department of Justice’s merger guidelines, an industry is considered “concentrated” if the HHI exceeds 1,800; it is “un-concentrated” if the HHI is below 1,000. Consolidating production in the hands of fewer firms through mergers and acquisitions is the most direct route to industrial concentration. Given that, federal government created agencies and legislature to oversee transactions that, by eliminating one or more competitors, would lead to undue increases in concentration and the possible exercise of market power by the remaining firms.
Two important factors that antitrust authorities consider in deciding whether to allow a proposed merger to proceed are the level of market concentration if the merger is consummated and the change in market concentration from its premerger level. The guidelines state that proposed mergers are unlikely to be challenged if the post merger market is un-concentrated (HHI remains below 1,000). However, mergers generally will not be approved if, following consummation, market concentration falls within the 1,000–1,800 range and the HHI increases by more than 100 points or, if the post merger HHI is 1,800 or more, concentration increases by more than 50 points. Exceptions are provided when the merging firms can demonstrate significant cost savings, when barriers to entry are low, or when one of the merger’s partners would fail otherwise.

· Michael R. Baye, “Managerial Economics and Business Strategy”, 6e, The McGraw-Hill Companies, Inc.
· "The Concept of Monopoly and the Measurement of Monopoly Power" The Review of Economic Studies, Vol. 1, No. 3, pp. 157-175
· Warren-Boulton, Frederick R, “Implications of U.S. Experience with Horizontal Mergers and Takeovers for Canadian Competition Policy”.
· Matthew Shapiro, “Measuring Market Power in U.S Industry”, National Bureau of Economic Research
· Miller, Edwin L., “Mergers and acquisitions : a step-by-step legal and practical guide”, 2008
· Hannah, Leslie, Concentration in modern industry : theory, measurement, and the U.K. experience”, 1977

1. There are five banks competing in a local market. Each of the five banks has a 20 percent market share. What is the four-firm concentration ratio for the local banking industry?
a. 1.0
b. 0.8
c. 0.6
d. 0.45

The correct answer is b (0.8).
C4 = w1 + w2 + w3 + w4 = 0.2 + 0.2 + 0.2 + 0.2 = 0.8

2. There are six soft beverage manufacturers competing in the market. Market shares are distributed as follows: Company 1 = 37%; Company 2 = 15%; Company 3 = 6%; Company 4 = 2%; Company 5 = 21%; Company 6 = 19%. What is the beverage industry HHI?

a. 5,675
b. 1,100
c. 7,547
d. 2,211

The correct answer is d (2,211).
10,000 (0.37^2 + 0.15^2 + 0.06^2 + 0.02^2 + 0.21^2 + 0.19^2) = 2,211

3. The industry elasticity of demand for video games is -3.0, and the elasticity of demand for a representative competitor, Gameworks, is -4.0. What is the Rothschild Index for this industry?

a. 0.75
b. 1.33
c. 0.25
d. -0.75

The correct answer is a (0.75).
R = ET / EF = - 3.0 / - 4.0 = 0.75

4. A firm in the carwash industry has a marginal cost of $5.00 and charges a price of $9.00. What are the Learner Index and the markup factor?
a. 0.78, 1.6
b. 0.15, 0.9
c. 0.44, 1.8
d. 0.98, 2.1

The correct answer is c (0.44, 1.8).
L = (P - MC) / P = (9.00 - 5.00) / 9.00 = 0.44
Markup Factor = 1 / (1 - L) = 1 / (1 - 0.44) = 1.8

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.
All of the above.

The correct answer is d (All of the above.).