Silviase/jgov_v1.4_full_ann huggingface dataset:
## A price increase is profitable if $ p - (p - c) \eta > 0 $

Thus, if one knows the premerger price, the marginal cost, and the own-price elasticity of demand for the candidate group of products in question, one can perform this calculation to determine whether that group of products (i.e., the products controlled by a hypothetical monopolist) constitutes its own relevant product market.

Note that, in the case where $ \eta = 1 $ , the calculation simplifies even further to

$$ A\ price\ increase\ is\ profitable\ if\ c>0 $$

Consequently, when c>0 (which will be true in most circumstances) and the own-price elasticity for a group is less than or equal to one in absolute value, the group is automatically a separate relevant market, i.e., we do not need to perform the full calculation.

### 2. Case Study: Bumble Bee/Connor Brands Acquisition

An application of the own-price elasticity of demand concept is found in the recent merger of two sardine companies. In 2004, Bumble Bee Seafoods, LLC (Bumble Bee), a manufacturer of canned seafood, announced its intention to acquire the sardines business of Connor Bros. Income Fund, Inc. (Connor Brands). Prior to the acquisition, Bumble Bee sold sardines under its own Bumble Bee brand name. Bumble Bee also distributed in the U.S. a second sardines brand called King Oscar that was manufactured in Norway by a Norwegian company. Connor Brands manufactured and sold a number of sardine brands, the most important of which were Brunswick, Beach Cliff, and Port Clyde.

Sardine products in the U.S. fall into three segments: premium, mainstream, and "ethnic." The three segments differ in the species of fish used, the package type and size, and the supermarket aisle location where the products are stocked. In addition, the prices in the three segments differ substantially. Premium sardines sell at a retail price of around $0.50 per ounce, mainstream sardines sell at $0.20 per ounce, and ethnic sardines have a price of $0.08 per ounce.

Bumble Bee's branded product and the three major Connor Brands products were all in the mainstream segment. Bumble Bee's share of the mainstream segment was 13 percent, while Connor Brands' share of the mainstream segment was 63 percent. Thus, the combined share of the merging parties in the mainstream segment was over 75 percent. The Herfindahl-Hirschman Index (HHI) in this segment, which
already exceeded 3500, would increase by over 1600 post-merger. $ ^{134} $ King Oscar, the brand distributed by Bumble Bee, was in the premium segment. Connor Brands did not sell a premium product. Thus, the merger would have no effect on shares or HHIs in the premium segment. Neither company sold any significant products in the ethnic segment.

The U.S. DOJ reviewed the proposed acquisition. The parties had a strong financial incentive to close the transaction by April 30, 2004, but the DOJ was unable to complete its regulatory review in that time frame. Thus, in a somewhat unusual arrangement, the parties and the DOJ agreed that the transaction would close on April 30, 2004. The DOJ, however, retained the right to require that particular remedies be subsequently carried out if its analyses indicated that such remedies would be needed to maintain competition.

Given the parties' shares in the various segments, relevant market definition was the key question. If the mainstream and premium segments constituted two separate relevant markets, any competitive concerns would arise only in the mainstream segment since Connor Brands did not have a premium brand. If, on the other hand, the two segments constituted a single relevant market, competitive concerns might extend to the premium King Oscar brand. Thus, whether the remedy required by the DOJ would involve a divestiture of King Oscar depended on the answer to the relevant market question. For example, if the mainstream and premium segments were separate relevant markets, any divestiture required by the DOJ would necessarily involve only the merging parties' mainstream brands, rather than King Oscar.

To analyze the question of whether the mainstream and premium segments constituted separate relevant markets, the own-price elasticities of demand for each segment were estimated by the economists retained by the parties as well as by the DOJ economists. $ ^{135} $ The data used for the estimation provided information on weekly price and the quantity sales in a number of U.S. cities. $ ^{136} $ The data covered a time
period of approximately two years. A demand equation for the premium segment of the following form was estimated:

$$ \log Q_{i t}^{P}=\alpha_{_{i}}+\delta_{_{t}}+\theta\log P_{i t}^{P}+\gamma\log P_{i t}^{M}+X_{_{i t}}\beta $$

where $ Q_{it}^{P} $ is the quantity sold in the premium segment in city i and week t, $ \alpha_{i} $ is a fixed effect for city i, $ \delta_{t} $ is a fixed effect for week t, $ P_{it}^{P} $ is a price index for the premium segment in city i and week t, $ P_{it}^{M} $ is a price index for the mainstream segment in city i and week t, and $ X_{it} $ is a vector of other variables that might affect demand for premium products (e.g., personal disposable income). $ ^{137} $ A similar equation was estimated for the mainstream segment.

The coefficient of interest for market definition is $ \theta $ , which is the own-price elasticity of demand. For both the premium segment and the mainstream segment, the estimates of $ \theta $ were approximately -1. For both segments, a statistical test did not reject the hypothesis that the own-price elasticity of demand was equal to -1.

As discussed above, the finding of an own-price elasticity of demand equal to or less than one (in absolute value) indicates that the group of products in question is a separate relevant market. Thus, the premium segment and the mainstream segment were found to be separate relevant product markets. These econometric findings were also consistent with business documents and the views of industry analysts.

Because premium sardines were found to be a separate relevant market, and there was no product overlap in the premium segment, the DOJ did not require a divestiture of Bumble Bee's King Oscar distribution arrangement. On the other hand, because mainstream sardines were found to be a separate relevant market, and because the merger would have led to a substantial increase in concentration in an already concentrated market, the DOJ required that the parties divest the Port Clyde brand, along with several other of Connor Brands' smaller brands and some production assets.

processed data and analytic services to the manufacturers of the products that are sold in the supermarket, drug, and mass merchandiser channels. The manufacturers use the data for their own market research purposes. Thus, many manufacturers involved in mergers will have ready access to retail scanner data. These data are described below in more detail in our discussion of the estimation of own- and cross-price elasticities.
### B. Price Correlation and Cointegration Analyses

### 1. Methodology

George Stigler and Robert Sherwin introduced price correlation analyses in the early 1980s as a method for delineating the boundaries of the relevant market. $ ^{138} $ In its most basic form, this type of analysis involves the computation of the correlation between the price series of two potentially competing products. A high positive correlation would suggest that the products are likely to be substitutes and therefore in the same relevant market.

Analyses of the relationships among prices of potentially competing products are appealing for its simplicity, as well as its roots in classic economic theory. For example, if two products A and B are substitutes, then arbitrage should lead to similar or uniform prices (after accounting for shipping costs and differences in product features or characteristics). $ ^{139} $ That is because a reduction in the price of product A would induce customers to switch from product B to product A, thereby causing the sellers of product B to lower their price, as well. Not only would this confirm the “law of one price,” but it also would generate a positive correlation in the prices of products A and B. Similarly, price correlations also have been applied to assess geographic market definition. As noted by Stigler and Sherwin, price correlations are useful because they capture the identity and location of the buyers and sellers who, through their transactions, establish the market price. $ ^{140} $

However, correlation analyses have been criticized for their relevance and applicability. $ ^{[141]} $ For example, economists have noted that the prices of two products can be highly correlated even if they are not substitutes. This could be the case if the prices of the two products are subject to common market factors, such as changes in the business cycle or changes in the price of an input that is used to make both products (e.g., electricity or a common raw material). In addition, the correlation may
even be spurious. The price correlation approach also is based on a market concept that may not be consistent with the market definition analysis described in the U.S. Merger Guidelines. $ ^{142} $ Finally, because a price correlation analysis is necessarily a pairwise comparison (e.g., a comparison between two products only), the result may or may not be consistent with the construct described in the U.S. Merger Guidelines, which describes a methodology that begins with the principal product at issue and incorporates as many additional products as necessary until a relevant market is defined.

To address the shortcomings of price correlation analyses, economists have turned to econometric techniques. Among the more sophisticated of these methods is multivariate cointegration analysis, which has been used in a number of applications to test the degree to which different products are substitutes. $ ^{143} $ Cointegration analysis extends the price correlation concept by focusing on the long-term equilibrium relationships between the prices of competing products. The price series of potentially competing products are said to be cointegrated if unexpected changes in prices in the short-term do not persist, but rather are “corrected” so that the long-run equilibrium relationships between the two prices are restored. In other words, if deviations from equilibrium are corrected—a consequence of arbitrage and the willingness of consumers to respond to short-term changes in price—then the products are likely to be substitutes and therefore in the same relevant market. These techniques have been used and applied by antitrust economists to assess market definition.

###### 2. Case Study: U.S. v. Continental Can

For an example of how the cointegration approach can be applied to assess market definition, we turn to a historical analysis of the market definition controversy in U.S. v. Continental Can Co., which is one of the U.S. Supreme Court's most widely
debated and discussed opinions in the area of antitrust law. $ ^{144} $ To this day, it is referred to as the textbook case on interindustry competition, market definition, and the relevance of long-run competition. In 1963, the U.S. DOJ challenged the 1956 acquisition of Hazel-Atlas Glass Company (Hazel-Atlas), a manufacturer of glass containers, by Continental Can Company (Continental Can), a manufacturer of metal can containers. $ ^{145} $ The Government challenged the merger on the grounds that the acquisition violated Section 7 of the Clayton Act. $ ^{146} $

The metal and glass container industries were considered highly concentrated at the time. In 1955, Continental Can was the second largest producer of metal containers in the U.S. with a share of 33 percent. The largest producer of metal cans was the American Can Company, whose share was around 38 percent. The third largest producer had a five percent share, and the rest of the market was divided among 75 to 90 firms. Hazel-Atlas was the third largest producer of glass containers with a share of almost 10 percent. The two larger producers of glass containers were Owens-Illinois Glass Company with a share of 34 percent and Anchor-Hocking Glass Company, whose share was 12 percent. The rest of the market was divided among at least 39 other firms. Although both companies were among the largest in their respective industries, Continental Can did not produce glass containers, and Hazel-Atlas did not produce metal cans. The critical issue was therefore product market definition, or specifically whether metal cans and glass containers were in the same market.

A U.S. District Court dismissed the Government’s complaint after it found there was only one product line (containers for the beer industry) in which the interindustry competition between metal and glass containers was significant enough to include both industries in the same market. $ ^{147} $ The Supreme Court, however, reversed the District Court’s decision after it found the relevant product market to include both glass and metal containers for all end uses. This ultimately led to the divestiture of Hazel-Atlas to another glass company.
In a recent study of the issue, Wu and Wu examined whether the Supreme Court was correct in reversing the District Court's decision by constructing an econometric model of the long-run equilibrium relationships that describe the competitive interaction between the glass and metal container industries. $ ^{148} $ In developing their model, Wu and Wu also accounted for the fact that glass and metal containers are sold into many of the same downstream industries that use both can and glass containers to package their products. To simplify the analysis, they focused on the beer industry, which was probably the most important downstream industry for these types of containers at the time.

The study found that a high degree of competition between manufacturers of metal and glass container industries in that it did not appear to take long for a change in the price difference between the two products to be arbitraged away. For example, an unexpected shock to the price of metal containers was found to be short-lived: 72 percent of the shock had disappeared one year after the shock and 93 percent of the shock was gone two years after the shock. Put differently, Wu and Wu's results suggest that had firms in the metal can industry raised prices by five percent in 1956, assuming everything else held constant, the price differential would have been arbitraged away to 1.4 percent by 1957, 0.35 percent in 1958, and 0.25 percent by 1966. In light of the one or two year time horizons suggested by the U.S. Merger Guidelines, the speed of arbitrage suggested by these numbers would indicate significant interindustry competition. Thus, these findings support the Supreme Court's opinion in U.S. v. Continental Can Co. that competition between the metal and glass container industries has been “...insistent, continuous, effective and quantitywise very substantial....” $ ^{149} $

### C. Elzinga-Hogarty Tests for Geographic Market Definition

### 1. Methodology

For many products and services, the principal market definition inquiry focuses on the geographic dimension, rather than the product dimension. For example, geographic market definition tends to be hotly contested in cases where locational considerations, shipping costs, or transportation costs may limit the competitiveness of
non-local suppliers. The analysis that is undertaken is similar in concept to the approach taken to identify the products that are in the relevant market in that the geographic scope of the market can be evaluated based on the following test: could a small but significant and non-transitory price increase in one location be accomplished by a hypothetical monopolist who controlled all of the production assets in that location? Or would “imports” from outside locations defeat the attempted price increase? If the answer to the latter question is “yes,” then both locations would be considered part of the same relevant geographic market.

One empirical approach to geographic market definition is to apply a method that was proposed by Kenneth Elzinga and Thomas Hogarty in the late 1970s. $ ^{150} $ The so-called “Elzinga-Hogarty test” analyzes data on shipments of product into and out of a candidate geographic area. The underlying premise behind the test is that a candidate geographic area is more likely to be a relevant geographic market if it is more “self contained.” To assess this, Elzinga and Hogarty proposed an analysis based on two statistics: the “Little In From Outside” (LIFO) statistic and the “Little Out From Inside” (LOFI) statistic.

The LIFO statistic measures the extent to which there are significant imports of product into a candidate area by sellers located outside the candidate area. It is the percentage of shipments purchased by buyers in the candidate area that are made by sellers outside the area. The LOFI statistic measures the extent to which there are significant exports of product by sellers in the candidate area to buyers located outside the candidate area. In other words, it is the percentage of sales made by sellers located in the candidate area to buyers outside the area. Both statistics matter, and under the Elzinga-Hogarty test, if both statistics are less than 25 percent (or in a stronger form of the test, less than 10 percent), then the candidate area is likely to be a relevant geographic market.

In general, Elzinga-Hogarty tests can be useful if the degree to which prices to all customers may be tempered by the ability of (1) some subset of customers to purchase products from sellers outside a candidate geographic market or travel to sellers outside a given area, and (2) the competitive importance of a subset of sellers within a candidate area to sell to customers located outside the area. That is because switching by the marginal consumers may protect the inframarginal consumers. However, this is not always the case (e.g., when price discrimination is possible). In
addition, inferences regarding market definition should not be based on shipment data alone. A variety of market factors also must be considered. For example, historical shipment patterns may not reveal much about future shipment patterns if current sellers are operating at full capacity and if entry and expansion are not likely to occur. Government regulations also can affect the import and export of products across countries, as well. Thus, analyses of shipment data must be conducted with a clear understanding of the relevant government regulations, quotas, or other restrictions that may affect the pattern of shipments from one region to another.

### 2. Case Study: Market Definition in Hospital Merger Analyses

In the 1990s, hospital mergers were contested on numerous occasions by the U.S. DOJ and FTC. $ ^{151} $ In all of these cases, the scope of the geographic market was hotly contested, and Elzinga-Hogarty analyses were applied to help the courts assess the issue. Although most of the references to the Elzinga-Hogarty test in the U.S. courts involve cases in the health care field, the Elzinga-Hogarty test also has been applied to assess market definition in other industries. $ ^{152} $

In the case of hospital services—which does not involve the import or export of a physical product—the Elzinga-Hogarty statistics are computed slightly differently. The LIFO statistic is computed by finding the percentage of all patients from a given area who went to a hospital outside the area. In other words, it measures the extent to which patients residing in a given area used hospitals located outside that area (i.e., the patient outflow from the area). The LOFI statistic is computed by finding the percentage of all patients treated by the area hospitals who do not reside in that area.
This statistic therefore measures the extent to which the hospitals in a given area served patients who did not live in that area (i.e., the patient inflow into the area).

Although Elzinga-Hogarty tests have been frequently used to assess hospital market definition, they also have been criticized as being overly simplistic. $ ^{153} $ For example, one criticism is that while patient travel can indicate that geographically distant hospitals are alternatives for consumers, the lack of travel does not imply that the hospitals are in separate markets. Indeed, competitive pricing could well lead consumers to simply choose the closest hospital. Patient travel patterns also may reflect travel to major medical centers, and if information about differences in quality of care or the health of the patient is not available, it may be difficult to draw conclusions about hospital choice from patient travel patterns.

Despite these shortcomings, patient travel data are often the only available data. Yet even so, the application of the test requires a careful analysis of the market factors that can affect observed patterns of patient choice and travel.

### I II. Empirical Approaches to Quantifying the Degree of Substitution Among Firms, Brands, or Products

### A. Diversion Ratios

### 1. Methodology

The diversion ratio is a statistic that was first proposed as a way of assessing unilateral competitive effects. $ ^{154} $ The diversion ratio for a product A with respect to a product B is defined as the percentage of A's lost sales (after an increase in the price of product A) that would be captured by the seller of product B. It is therefore related to the own- and cross-elasticities of demand, which are discussed further below. Diversion ratios also can be used to perform a simplified merger simulation, as discussed below.

In the specific case where (1) each merging firm has a single product and (2) the
two products are symmetric in terms of their shares and profit margins, the merger would be expected to increase price by a percentage equal to $ \frac{mD}{1-m-D} $ where m is the products' profit margin and D is the products' diversion ratio with respect to each other. $ ^{155} $

Diversion ratios also can be calculated from information about the own- and cross-price elasticities of demand, customer switching data, customer survey results, or company market shares (under certain strong assumptions). For example, the formula for the diversion ratio from product A to product B is:

$$ D=\frac{\eta_{_{BA}}}{\eta_{_{AA}}}\frac{Q_{_{B}}}{Q_{_{A}}} $$

where $ \eta_{_{BA}} $ is the cross-price elasticity of B with respect to the price of A, $ \eta_{_{AA}} $ is the own-price elasticity of A, and $ Q_{_{A}} $ and $ Q_{_{B}} $ are the quantities sold of products A and B, respectively.

Alternatively, if it is appropriate to assume that the diversion ratios are proportional to market shares and that the elasticity of demand for the whole market is zero, the diversion ratio from product A to product B can be computed using the following formula:

$$ D=\frac{s_{_{B}}}{1-s_{_{A}}} $$

where $ s_{A} $ and $ s_{B} $ are the market shares of products A and B, respectively.

### 2. Case Study: Vail Ski’s Acquisition of Ski Resorts in Colorado

In 1996, Vail Ski Resorts, Inc. (Vail Ski) proposed to acquire three Colorado ski resorts (Keystone, Breckenridge, and Arapahoe Basin) owned by Ralston Resorts, Inc. (Ralston). Prior to the merger, Vail Ski owned two resorts in the area (Vail and Beaver Creek Resort). All five resorts involved in the transaction were located less than a 90 minute drive from Denver, Colorado. Although one might think that ski resorts compete for skiers who could easily choose to ski at mountains elsewhere in the