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ConcurrencesRevue des droits de la concurrence
enCompetitions
Remarks on the calculation of local market shares
Droit & économie l Concurrences N° 1-2011 – pp. 37-41
Antoine Chapsal [email protected]
l Economist
Laurent [email protected]
l Economist
Concurrences N° 1-2011 I Droit & économie I A. Chapsal, L. Eymard, Remarks on the calculation of local market shares 37
Droit & économie
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n.Antoine Chapsal [email protected]
Economist
Laurent [email protected]
Economist
AbstractThe method usually applied to compute local market shares
is severely flawed. Once the relevant geographic market has been defined, it consists in computing the ratio between the
total value of sales by all plants or stores of the firm located in the relevant market over the total value of sales operated
by all plants and stores within the area. This method, which exclusively focuses on the competitive situation that would be faced by a hypothetical customer located precisely in the
centre of the relevant market, is biased since it considers that (i) some suppliers whose catchment areas do intersect with
the relevant market do not exert any competitive pressure in the relevant market, and (ii) the competitive pressure exerted
by the suppliers that are taken into account in the market share calculation is the same whatever their location. This
paper presents two alternative methods, which significantly reduce this bias, with no need for additional data.
Le mode de calcul des parts de marché locales généralement utilisé est considérablement biaisé. Il consiste à calculer la part de marché d’une entreprise en divisant ses ventes
effectuées sur le marché géographique pertinent, par le total des ventes effectuées par toutes les entreprises implantées
dans cette zone. Cette méthode, qui se focalise exclusivement sur la situation d’un unique consommateur localisé au
centre de la zone étudiée, ne tient pas compte de la pression concurrentielle exercée par les entreprises implantées juste
à l’extérieur du marché pertinent et donc susceptibles de vendre à l’intérieur de cette zone. De même, aucune
distinction n’est effectuée entre les entreprises implantées à l’intérieur du marché géographique pertinent en fonction
de leur localisation. Cet article présente deux méthodes qui permettent, sans que des données supplémentaires ne soient nécessaires, de réduire considérablement ce biais.
Remarks on the calculation of local market shares
1. Despite their well-known limitations, market shares play a big role in the assessment of competition cases. In merger control, they are used as a screening test in order to determine whether a market is likely to be “affected” by the contemplated merger, and to identify market segments or geographical areas where the merger is expected to have a significant impact. In antitrust cases, they are widely considered as a crude but meaningful measure of the market power of various firms, and they are used when evaluating whether a firm (or set of firms) is likely to enjoy a single (or collective) dominant position.
2. Whether market shares accurately reflect market power is an issue widely debated, and the limits of market share figures in markets characterised by low entry barriers, tenders, and product differentiation are now well understood.1 In contrast, the method commonly applied to calculate market shares is generally taken for granted. However, especially in the case of markets where competition is local, the usual calculation method relies on assumptions making little economic sense and is thus severely flawed.
3. In many markets, competition takes place locally. This is the case for ponderous raw material producers like cement plants, as well as for retailers, which operate in local catchment areas. Local market delineation is generally driven by the relative importance of transportation costs compared to the value of the product sold. In such cases, market power is therefore to be analysed locally, taking into account the distance between customers and firms’ plants or points of sale.
4. The method usually applied to compute a firm’s market share on a given local market only takes into account the suppliers located within the relevant catchment area, without making any distinction between them. For all its simplicity, such a method is nevertheless based on implicit assumptions that make little sense. It yields market share figures that cannot be considered an even remotely acceptable indicator of market structure.
5. The remainder of this article is structured as follows. We first present the method usually applied to compute market shares when firms compete geographically, discuss its underlying assumptions and show how biased this methodology can be (Part I.). We then present two alternative methods to compute local market shares and their specific merits. These methods significantly reduce of the abovementioned bias (Part II.).
I The method usually applied to compute local market share is severely flawed
1.How are local market shares usually computed?6. The local market share of a given firm is usually computed according to the following methodology (hereafter, the “usual method”). For the sake of simplicity, this firm is labelled “F”, and “F1”, “F2”, “F3”, etc. refer to F plants or stores. It faces a competitor, labelled “C”, which owns several plants or stores (“C1”, “C2”, “C3”, etc.).
1 For instance, monopolies (100% market share) do not necessarily hold significant market power when barriers to entry are low (see Baumol, Panzar and Willig, Contestable markets and the theory of industry structure, 1982).
Concurrences N° 1-2011 I Droit & économie I A. Chapsal, L. Eymard, Remarks on the calculation of local market shares 38
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n.flawed because it relies on implicit assumptions making little economic sense, yielding market share figures that bear little relationship to the actual functioning of markets.
2. This method relies on implicit assumptions that make little economic sense9. As explained above, the usual method only takes into account the suppliers that are located within the relevant market and it disregards all other suppliers. In doing so, it fails to reflect the competitive situation faced by most customers in the relevant market. In Figure 2 below, customer t1 could be supplied either by F1 or C2. By excluding C2 from the market share calculation, the usual method fails to account for the actual set of possible suppliers from the point of view of t1, or all other customers in the relevant market that could be supplied by C2.
10. This implies the usual method exclusively focuses on the competitive situation that would be faced by a hypothetical customer that would be located precisely in the centre of the relevant market. If it exists, this is indeed the unique customer that could only be supplied by any supplier located in the relevant market.
Figure 2
11. In other words, the usual method adopts the viewpoint of a single hypothetical customer located in the centre of the relevant geographical market, that is, at the same location as F1. This makes little sense and this may significantly bias market share calculation.
12. On top of excluding suppliers that could be active within the relevant market, the usual method does not distinguish between the various suppliers located inside the relevant market. In Figure 3, both C1 and C2 are located within the relevant market, defined as F1’s catchment area. These two plants are thus taken into account in the market share calculation, and according to the usual methodology they are treated identically, even though the distance between F1 and C2 is much smaller than that between F1 and C1. Yet, it would make more sense to take into account the likely fact that, ceteris paribus, C2 exerts a stronger competitive pressure on F1 than C1 does, since C2 competes with F1 for many more of its potential customers than C1.
– The first step consists in delineating the relevant geographic market on which market shares are to be calculated. Local markets are generally defined as the catchment area of a given supplier.2 In the remainder of this article, we assume that market shares are to be calculated on a local market defined as F1’s catchment area. This area is represented by a circle of radius l around F1.
3 This radius depends on market-specific facts, such as transportation costs relative to product value, or customer preferences regarding how travel time is valued.
– The second step consists in computing the ratio between the total value4 of sales by all F plants or stores (F1, F2, F3…) located in the reference catchment area over the total value of sales operated by all plants and stores within the area.
7. The following simple shows how local market shares are usually calculated. In Figure 1, F1’s catchment area, which defines the relevant market, is represented by the grey surface. F1, whose value of sales is 100, faces two rivals within its catchment area, labelled C1 and C2, with sales value of 150 and 75 respectively. Another plant belonging to firm F (F2) is also present in the reference catchment area, with sales amounting to 50. The rival plant C3 is not located in the catchment area, and therefore not accounted for when computing F’s market share.
Figure 1
In this example, F’s sales value in the relevant geographic market amounts to 150 (100 for F1 and 50 for F2), and the total sales value operated in the reference catchment area equals 375 (150 for F and 150 + 75 for C plants). According to the usual method, F’s market share thus equals 40% (i.e., 150/375).
8. This method seems appealing because of its simplicity and it is, if not the only one, at least the one most commonly used by competition authorities. It is, however, severely
2 See for instance Promodes c/ BRMC (case COMP/M.242), Leroy Merlin c/ Brico (COMP/M.2898), Kinfisher v./Castorama (case COMP/M.1333), Cement (cases COMP/33.126 and 33.322).
3 The definition of the reference catchment can vary from one decision to another. In particular, the distance l around each supplier can either be calculated as the crow flies or as a road distance. This does not affect our reasoning. Note also that the definition of the catchment area can be either identical for all supplier or specific to each one of them depending on their respective size, production cost, etc. For the sake of simplicity, we present in this paper the general case where the size of the catchment area is the same for all suppliers. Using an alternative assumption would not affect our reasoning either.
4 It also can be the volume of sales or, when F is a retailer, the surface of a store.
Concurrences N° 1-2011 I Droit & économie I A. Chapsal, L. Eymard, Remarks on the calculation of local market shares 39
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n.15. It is worth mentioning that the usual method does not bias market shares in a systematic way. It may either overestimate or underestimate the actual market position of the alleged dominant firms or parties to the contemplated merger. Similarly, the magnitude of the mistake may vary a lot from a case to another, depending on the specific location of suppliers outside the reference catchment area. However, what matters is that the usual method relies on inaccurate implicit assumptions, so that the market share figures it yields lack relevance.
16. The above criticisms echo the more general skepticism that is sometimes expressed regarding the meaning of market share data in differentiated product markets, since the partition of the set of product into those that belong to the relevant market and those that do not fails to account for the varying degrees of competitive proximity between products. However, in the case of geographic differentiation, this problem can be solved relatively easily. The next section presents two alternative solutions, i.e., calculation methods that avoid the severe flaws of the usual method.
II. Two alternative methods
1. The distance-based method17. The first alternative method is based on the idea that the competitive pressure exerted by a plant on another one is greater when both plants are close than when they are distant. In other words, this first method reflects the fact that the competitive pressure exerted by a plant on the relevant market normally decreases as the distance between that plant and the centre of the reference catchment area increases.
18. According to the distance-based method, market shares are computed following two steps. Once the relevant market has been defined (as F1’s catchment area), all plants whose catchment areas intersect with F1’s are identified. This includes plants that are located outside the relevant market but that have potential customers inside it. Each one of these plants is then attributed a weight that is smaller, the greater its distance to the centre of the relevant market. The weight attributed to a particular supplier equals the surface of the intersection between its catchment area and the relevant market over the total surface of its catchment area. This implies that, assuming that customers are evenly located, the competitive pressure exerted by a particular plant is commensurate to the proportion of its potential customers located within the relevant market.
Figure 3
13. The usual method is therefore based on both assumptions that (i) some suppliers whose catchment areas do intersect with the relevant market do not exert any competitive pressure in the relevant market, and (ii) the competitive pressure exerted by the suppliers that are taken into account in the market share calculation is the same whatever their location. These assumptions are at odds with basic economic reasoning, and the usual method is not only irrelevant from a theoretical perspective but also inadequate to assess firm’s market power in practice. The bias introduced by the erroneous assumptions described above can indeed be very significant. The usual method thus should not be relied upon in competition analysis.
14. The usual method is therefore biased and it is likely to yield severely flawed market shares. The significance of the bias can be illustrated by the fact that a slight change in the radius of the reference catchment area could induce a significant variation in market shares. The situation described in Figure 4 illustrates this phenomenon.
Figure 4
F’s market share with the original radius (circle drawn with a continuous line) equals 50% (150/300). If the radius is slightly reduced, F’s market share falls to 25% (50/200), and it is 33% (150/450) if the chosen radius is a bit greater than l. In this example, market shares therefore vary a lot when one makes a small change in the radius of the relevant market. In practice, this lack of robustness constitutes a major drawback of this method since the size of catchment areas cannot in general be estimated very precisely.
Concurrences N° 1-2011 I Droit & économie I A. Chapsal, L. Eymard, Remarks on the calculation of local market shares 40
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n.market.6 In order to account for the geographic distribution of customers, another method is available. While this second method could appear slightly more complicated that the distance-based method, it can be entirely parameterised and its implementation need not be difficult.
2.The demand-based method22. As explained above, the usual method adopts the viewpoint of one single hypothetical customer, which would be located exactly in the centre of the relevant geographic market. Yet, there is no reason why all other potential customers on the market should be disregarded. A second alternative method is based on the view that there is not only one single potential customer but a large number of customers disseminated across the relevant local market.
23. This method consists in taking into account all customers and to compute, for each of them, F’s market share as follow: all suppliers than could supply one particular customer are identified, and F’s market share from the point of view of this customer is defined as the sales of all F plants among them over the total sales of these plants.7 An average market share is then calculated, by averaging market share figures over all customers in the relevant market. A simple example, illustrated in Figure 6, illustrates this method. In this example, there are two customers (t1 and t2) and F1 faces two competitors C1, located within its catchment area, and C2, located outside. As shown in Figure 6, all producers (F1, C1, and C2) can supply t1, but t2 can only be supplied by F1 or C2 (since t2 is not located in C1’s catchment area).
Figure 6
6 A direct implication of this assumption is that demand is more important in area where the catchment areas of several suppliers intersect. This means that suppliers are located where the demand is high. This is consistent with economic reasoning when each supplier can choose its location (i.e., the location is endogenous). The second alternative methodology would be more relevant than the “distance-based” method when the location of suppliers is constrained by exogenous factors such as administrative authorisations or access to natural resources.
7 Considering a hypothetical customer that would be located at the centre of the relevant market, this market share definition is equivalent to the usual method.
Figure 5
19. In the example displayed in Figure 5, F1 and C1’s catchment areas intersect. This means that both producers compete for the customers located within the intersection of their respective catchment areas. It is therefore relevant to consider that C1 can sell a fraction of its production within this area. According to this first alternative method, this fraction can be estimated as the ratio of the surface A over the surface of C1’s catchment area. Assume for instance that the radius of the catchment area is of length 1, and that the distance between F1 and C1, which is necessarily greater than 1 since C1 is not located in F1’s catchment area, is 1.1. According to the distance-based method, 33%5 of C1’s production is sold in F1’s catchment area, which amounts to 16.5 (50 x 33%). Overall sales in the relevant market therefore equal 66.5, i.e., F1’s total sales (50) plus the sales of C1 in A (16.5). According to this method, F’s market share is therefore is slightly greater than 75% (50/(50+16.5)), instead of 100% with the usual method.
20. This method does not suffer from the flaws of the usual method since (i) it takes into account all suppliers that are likely to sell even a small fraction of their production within the reference catchment area, and (ii) it accounts for the fact that the competitive pressure exerted by a supplier in the relevant market is lower when it is located far away from the centre of the relevant market. More precisely, if the competitor is far away from F1 (which means that it does not exert a significant competitive pressure on this plant), the region defined by the intersection of catchment areas is small, and thus, the fraction of the competitor’s sales accounted for when computing F’s market share is also limited. This method therefore weighs C1’s sales by a factor that directly depends on how far it is from F1. As is explained above, this is perfectly relevant from an economic viewpoint.
21. This first alternative method is based on the assumption that each supplier’s sales are evenly distributed across its own catchment area. While this assumption is in most cases better founded than the two assumptions implicitly underlying the usual method, it does not necessarily reflect the actual geographical location of the customers in the relevant
5 This figure is obtained using standard trigonometric formulas.
Concurrences N° 1-2011 I Droit & économie I A. Chapsal, L. Eymard, Remarks on the calculation of local market shares 41
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n.a lot of attention in recent economic literature.8 While our methods for market share calculation relate to situations where firms are active on geographically differentiated market and UPPs to situations where the differentiation is along the product dimension, these two kinds of measures weigh the competitive pressure exerted by two firms on each other by the “distance” between them – whether geographic distance between two plants or distance in terms of product characteristics, assessed through diversion ratios. Along with UPPs, our methods for market shares calculation should therefore replace in competition cases the usual method as screening tests to identify situations that require an in-depth competitive analysis. n
8 Joseph Farrell & Carl Shapiro, “Antitrust Evaluation of Horizontal Mergers: An Economic Alternative to Market Definition” (Nov. 25, 2008), available at http://faculty.haas.berkeley.edu/Shapiro/.
Since all producers compete for t1, F’s market share from t1’s viewpoint is 30% (150/(150+150+200)). F’s market share from t2’s viewpoint is 43% (150/350). Assuming that t1 and t2 are equally important, F’s market share according to the demand-based method equals 36.5% ((30+43)/2), whereas it equals 50% (150/300) according to the usual method.
24. This alternative method is extremely flexible. In particular, it does not require a perfect knowledge of the exact location of each customer. If customer location is unobserved, one may randomly draw a large number of potential customers within the reference catchment area. The way that each potential customer location is randomly drawn can be parameterised, according to the available information regarding the geographic distribution of customers (for instance, population density data in the case of consumer products) Also, each customer can be given a different weight, depending on its demand or location.
25. It can be shown the usual and distance-based methods are in fact variants of this demand-based method.
– The usual method is equivalent to the demand-based method where only one hypothetical customer, located at the centre of the relevant market, is taken into account. This is undoubtedly the poorest variant of the demand-based method.
– The distance-based method is also a variant of the demand-based method, where it is assumed that each supplier’s sales are evenly distributed across its own catchment area.
26. The demand-based method is highly flexible and yields much more relevant estimates of market shares than any other method, once the characteristics of the local market (geographical distribution of customers, etc.) have been taken into account.
27. In any event, both alternative methods are based on reasonable assumptions. The market shares computed using these methods are much more likely to allow one to draw a correct conclusion on the effective position of firms within a given catchment area.
III. Conclusion28. The usual method to compute local market shares relies on unreasonable assumptions and is very likely to yield market share figures lacking economic relevance. The two alternative methods described above rely on far more reasonable assumptions regarding geographic competition, and the market share figures they yield are more likely to correctly reflect firms’ effective market power.
29. The methods presented above are simple ways to compute market shares when products are spatially differentiated. Interestingly, these methods could be related to the measure of Upward Pricing Pressure indices (UPPs) that attracted
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