9.12.1997   

EN

Official Journal of the European Communities

C 372/5

1.

The purpose of this notice is to provide guidance as to how the Commission applies the concept of relevant product and geographic market in its ongoing enforcement of Community competition law, in particular the application of Council Regulation No 17 and (EEC) No 4064/89, their equivalents in other sectoral applications such as transport, coal and steel, and agriculture, and the relevant provisions of the EEA Agreement (1). Throughout this notice, references to Articles 85 and 86 of the Treaty and to merger control are to be understood as referring to the equivalent provisions in the EEA Agreement and the ECSC Treaty.

2.

Market definition is a tool to identify and define the boundaries of competition between firms. It serves to establish the framework within which competition policy is applied by the Commission. The main purpose of market definition is to identify in a systematic way the competitive constraints that the undertakings involved (2) face. The objective of defining a market in both its product and geographic dimension is to identify those actual competitors of the undertakings involved that are capable of constraining those undertakings' behaviour and of preventing them from behaving independently of effective competitive pressure. It is from this perspective that the market definition makes it possible inter alia to calculate market shares that would convey meaningful information regarding market power for the purposes of assessing dominance or for the purposes of applying Article 85.

3.

It follows from point 2 that the concept of ‘relevant market’ is different from other definitions of market often used in other contexts. For instance, companies often use the term ‘market’ to refer to the area where it sells its products or to refer broadly to the industry or sector where it belongs.

4.

The definition of the relevant market in both its product and its geographic dimensions often has a decisive influence on the assessment of a competition case. By rendering public the procedures which the Commission follows when considering market definition and by indicating the criteria and evidence on which it relies to reach a decision, the Commission expects to increase the transparency of its policy and decision-making in the area of competition policy.

5.

Increased transparency will also result in companies and their advisers being able to better anticipate the possibility that the Commission may raise competition concerns in an individual case. Companies could, therefore, take such a possibility into account in their own internal decision-making when contemplating, for instance, acquisitions, the creation of joint ventures, or the establishment of certain agreements. It is also intended that companies should be in a better position to understand what sort of information the Commission considers relevant for the purposes of market definition.

6.

The Commission's interpretation of ‘relevant market’ is without prejudice to the interpretation which may be given by the Court of Justice or the Court of First Instance of the European Communities.

7.

The Regulations based on Article 85 and 86 of the Treaty, in particular in section 6 of Form A/B with respect to Regulation No 17, as well as in section 6 of Form CO with respect to Regulation (EEC) No 4064/89 on the control of concentrations having a Community dimension have laid down the following definitions, ‘Relevant product markets’ are defined as follows:

‘A relevant product market comprises all those products and/or services which are regarded as interchangeable or substitutable by the consumer, by reason of the products' characteristics, their prices and their intended use’.

8.

‘Relevant geographic markets’ are defined as follows:

‘The relevant geographic market comprises the area in which the undertakings concerned are involved in the supply and demand of products or services, in which the conditions of competition are sufficiently homogeneous and which can be distinguished from neighbouring areas because the conditions of competition are appreciably different in those area’.

9.

The relevant market within which to assess a given competition issue is therefore established by the combination of the product and geographic markets. The Commission interprets the definitions in paragraphs 7 an 8 (which reflect the case-law of the Court of Justice and the Court of First Instance as well as its own decision-making practice) according to the orientations defined in this notice.

10.

The concept of relevant market is closely related to the objectives pursued under Community competition policy. For example, under the Community's merger control, the objective in controlling structural changes in the supply of a product/service is to prevent the creation or reinforcement of a dominant position as a result of which effective competition would be significantly impeded in a substantial part of the common market. Under the Community's competition rules, a dominant position is such that a firm or group of firms would be in a position to behave to an appreciable extent independently of its competitors, customers and ultimately of its consumers (3). Such a position would usually arise when a firm or group of firms accounted for a large share of the supply in any given market, provided that other factors analysed in the assessment (such as entry barriers, customers' capacity to react, etc.) point in the same direction.

11.

The same approach is followed by the Commission in its application of Article 86 of the Treaty to firms that enjoy a single or collective dominant position. Within the meaning of Regulation No 17, the Commission has the power to investigate and bring to an end abuses of such a dominant position, which must also be defined by reference to the relevant market. Markets may also need to be defined in the application of Article 85 of the Treaty, in particular, in determining whether an appreciable restriction of competition exists or in establishing if the condition pursuant to Article 85 (3) (b) for an exemption from the application of Article 85 (1) is met.

12.

The criteria for defining the relevant market are applied generally for the analysis of certain types of behaviour in the market and for the analysis of structural changes in the supply of products. This methodology, though, might lead to different results depending on the nature of the competition issue being examined. For instance, the scope of the geographic market might be different when analysing a concentration, where the analysis is essentially prospective, from an analysis of past behaviour. The different time horizon considered in each case might lead to the result that different geographic markets are defined for the same products depending on whether the Commission is examining a change in the structure of supply, such as a concentration or a cooperative joint venture, or examining issues relating to certain past behaviour.

13.

Firms are subject to three main sources or competitive constraints: demand substitutability, supply substitutability and potential competition. From an economic point of view, for the definition of the relevant market, demand substitution constitutes the most immediate and effective disciplinary force on the suppliers of a given product, in particular in relation to their pricing decisions. A firm or a group of firms cannot have a significant impact on the prevailing conditions of sale, such as prices, if its customers are in a position to switch easily to available substitute products or to suppliers located elsewhere. Basically, the exercise of market definition consists in identifying the effective alternative sources of supply for the customers of the undertakings involved, in terms both of products/services and of geographic location of suppliers.

14.

The competitive constraints arising from supply side substitutability other then those described in paragraphs 20 to 23 and from potential competition are in general less immediate and in any case require an analysis of additional factors. As a result such constraints are taken into account at the assessment stage of competition analysis.

15.

The assessment of demand substitution entails a determination of the range of products which are viewed as substitutes by the consumer. One way of making this determination can be viewed as a speculative experiment, postulating a hypothetical small, lasting change in relative prices and evaluating the likely reactions of customers to that increase. The exercise of market definition focuses on prices for operational and practical purposes, and more precisely on demand substitution arising from small, permanent changes in relative prices. This concept can provide clear indications as to the evidence that is relevant in defining markets.

16.

Conceptually, this approach means that, starting from the type of products that the undertakings involved sell and the area in which they sell them, additional products and areas will be included in, or excluded from, the market definition depending on whether competition from these other products and areas affect or restrain sufficiently the pricing of the parties' products in the short term.

17.

The question to be answered is whether the parties' customers would switch to readily available substitutes or to suppliers located elsewhere in response to a hypothetical small (in the range 5 % to 10 %) but permanent relative price increase in the products and areas being considered. If substitution were enough to make the price increase unprofitable because of the resulting loss of sales, additional substitutes and areas are included in the relevant market. This would be done until the set of products and geographical areas is such that small, permanent increases in relative prices would be profitable. The equivalent analysis is applicable in cases concerning the concentraiton of buying power, where the starting point would then be the supplier and the price test serves to identify the alternative distribution channels or outlets for the supplier's products. In the application of these principles, careful account should be taken of certain particular situations as described within paragraphs 56 and 58.

18.

A practical example of this test can be provided by its application to a merger of, for instance, soft-drink bottlers. An issue to examine in such a case would be to decide whether different flavours of soft drinks belong to the same market. In practice, the question to address would be whether consumers of flavour A would switch to other flavours when confronted with a permanent price increase of 5 % to 10 % for flavour A. If a sufficient number of consumers would switch to, say, flavour B, to such an extent that the price increase for flavour A would not be profitable owing to the resulting loss of sales, then the market would comprise at least flavours A and B. The process would have to be extended in addition to other available flavours until a set of products is identified for which a price rise would not induce a sufficient substitution in demand.

19.

Generally, and in particular for the analysis of merger cases, the price to take into account will be the prevailing market price. This may not be the case where the prevailing price has been determined in the absence of sufficient competition. In particular for the investigation of abuses of dominant positions, the fact that the prevailing price might already have been substantially increased will be taken into account.

20.

Supply-side substitutability may also be taken into account when defining markets in those situaitons in which its effects are equivalent to those of demand substitution in terms of effectiveness and immediacy. This means that suppliers are able to switch production to the relevant products and market them in the short term (4) without incurring significant additional costs or risks in response to small and permanent changes in relative prices. When these conditions are met, the additional production that is put on the market will have a disciplinary effect on the competitive behaviour of the companies involved. Such an impact in terms of effectiveness and immediacy is equivalent to the demand substitution effect.

21.

These situations typically arise when companies market a wide range of qualities or grades of one product; even if, for a given final customer or group of consumers, the different qualities are not substitutable, the different qualities will be grouped into one product market, provided that most of the suppliers are able to offer and sell the various qualities immediately and without the significant increases in costs described above. In such cases, the relevant product market will encompass all products that are substitutable in demand and supply, and the current sales of those products will be aggregated so as to give the total value or volume of the market. The same reasoning may lead to group different geographic areas.

22.

A practical example of the approach to supply-side substitutability when defining product markets is to be found in the case of paper. Paer is usually supplied in a range of different qualities, from standard writing paper to high quality papers to be used, for instance, to publish art books. From a demand point of view, different qualities of paper cannot be used for any given use, i.e. an art book or a high quality publication cannot be based on lower quality papers. However, paper plants are prepared to manufacture the different qualities, and production can be adjusted with negligible costs and in a short time-frame. In the absence of particular difficulties in distribution, paper manufacturers are able therefore, to compete for orders of the various qualities, in particular if orders are placed with sufficient lead time to allow for modification of production plans. Under such circumstances, the Commission would not define a separate market for each quality of paper and its respective use. The various qualities of paper are included in the relevant market, and their sales added up to estimate total market galue and volume.

23.

When supply-side substitutability would entail the need to adjust significantly existing tangible and intangible assets, additional investments, strategic decisions or time delays, it will not be considered at the stage of market definition. Examples where supply-side substitution did not induce the Commission to enlarge the market are offered in the area of consumer products, in particular for branded beverages. Although bottling plants may in principle bottle different beverages, there are costs and lead times involved (in terms of advertising, product testing and distribution) before the products can actually be sold. In these cases, the effects of supply-side substitutability and other forms of potential competition would then be examined at a later stage.

24.

The third source of competitive constraint, potential competition, is not taken into account when defining markets, since the conditions under which potential competition will actually represent an effective competitive constraint depend on the analysis of specific factors and circumstances related to the conditions of entry. If required, this analysis is only carried out at a subsequent stage, in general once the position of the companies involved in the relevant market has already been ascertained, and when such position gives rise to concerns from a competition point of view.

25.

There is a range of evidence permitting an assessment of the extent to which substitution would take place. In individual cases, certain types of evidence will be determinant, depending very much on the characteristics and specificity of the industry and products or services that are being examined. The same type of evidence may be of no importance in other cases. In most cases, a decision will have to be based on the consideration of a number of criteria and different items of evidence. The Commission follows an open approach to empirical evidence, aimed at making an effective use of all available information which may be relevant in individual cases. The Commission does not follow a rigid hierarchy of different sources of information or types of evidence.

26.

The process of defining relevant markets may be summarized as follows: on the basis of the preliminary information available or information submitted by the undertakings involved, the Commission will usually be in a position to broadly establish the possible relevant markets within which, for instance, a concentration or a restriction of competition has to be assessed. In general, and for all practical purposes when handling individual cases, the question will usually be to decide on a few alternative possible relevant markets. For instance, with respect to the product market, the issue will often be to establish whether product A and product B belong or do not belong to the same product market. it is often the case that the inclusion of product B would be enough to remove any competition concerns.

27.

In such situations it is not necessary to consider whether the market includes additional products, or to reach a definitive conclusion on the precise product market. If under the conceivable alternative market definitions the operation in question does not raise competition concerns, the question of market definition will be left open, reducing thereby the burden on companies to supply information.

28.

The Commission's approach to geographic market definition might be summarized as follows: it will take a preliminary view of the scope of the geographic market on the basis of broad indications as to the distribution of market shares between the parties and their competitors, as well as a preliminary analysis of pricing and price differences at national and Community or EEA level. This initial view is used basically as a working hypothesis to focus the Commission's enquiries for the purposes of arriving at a precise geographic market definition.

29.

The reasons behind any particular configuration of prices and market shares need to be explored. Companies might enjoy high market shares in their domestic markets just because of the weight of the past, and conversely, a homogeneous presence of companies throughout the EEA might be consistent with national or regional geographic markets. The initial working hypothesis will therefore be checked against an analysis of demand characteristics (importance of national or local preferences, current patterns of purchases of customers, product differentiation/brands, other) in order to establish whether companies in different areas do indeed constitute a real alternative source of supply for consumers. The theoretical experiment is again based on substitution arising from changes in relative prices, and the question to answer is again whether the customers of the parties would switch their orders to companies located elsewhere in the short term and at a negligible cost.

30.

If necessary, a further check on supply factors will be carried out to ensure that those companies located in differing areas do not face impediments in developing their sales on competitive terms throughout the whole geographic market. This analysis will include an examination of requirements for a local presence in order to sell in that area the conditions of access to distribution channels, costs associated with setting up a distribution network, and the presence or absence of regulatory barriers arising from public procurement, price regulations, quotas and tariffs limiting trade or production, technical standards, monopolies, freedom of establishment, requirements for administrative authorizations, packaging regulations, etc. In short, the Commission will identify possible obstacles and barriers isolating companies located in a given area from the competitive pressure of companies located outside that area, so as to determine the precise degree of market interpenetration at national, European or global level.

31.

The actual pattern and evolution of trade flows offers useful supplementary indications as to the economic importance of each demand or supply factor mentioned above, and the extent to which they may or may not constitute actual barriers creating different geographic markets. The analysis of trade flows will generally address the question of transport costs and the extent to which these may hinder trade between different areas, having regard to plant location, costs of production and relative price levels.

32.

Finally, the Commission also takes into account the continuing process of market integration, in particular in the Community, when defining geographic markets, especially in the area of concentrations and structural joint ventures. The measures adopted and implemented in the internal market programme to remove barriers to trade and further integrate the Community markets cannot be ignored when assessing the effects on competition of a concentration or a structural joint venture. A situation where national markets have been artifically isolated from each other because of the existence of legislative barriers that have now been removed will generally lead to a cautious assessment of past evidence regarding prices, market shares or trade patterns. A process of market integration that would, in the short term, lead to wider geographic markets may therefore be taken into consideration when defining the geographic market for the purposes of assessing concentrations and joint ventures.

33.

When a precise market definition is deemed necessary, the Commission will often contact the main customers and the main companies in the industry to enquire into their views about the boudaries of product and geographic markets and to obtain the necessary factual evidence to reach a conclusion. The Commission might also contact the relevant professional associations, and companies active in upstream markets, so as to be able to define, in so far as necessary, separate product and geographic markets, for different levels of production or distribution of the products/services in question. It might also request additional information to the undertakings involved.

34.

Where appropriate, the Commission will address written requests for information to the market players mentioned above. These requests will usually include questions relating to the perceptions of companies about reactions to hypothetical price increases and their views of the boundaries of the relevant market. They will also ask for provision of the factual information the Commission deems necessary to reach a conclusion on the extent of the relevant market. The Commission might also discuss with marketing directors or other officers of those companies to gain a better understanding on how negotiations between suppliers and customers take place and better understand issues relating to the definition of the relevant market. Where appropriate, they might also carry out visits or inspections to the premises of the parties, their customers and/or their competitors, in order to better understand how products are manufactured and sold.

35.

The type of evidence relevant to reach a conclusion as to the product market can be categorized as follows:

36.

An analysis of the product characteristics and its intended use allows the Commission, as a first step, to limit the field of investigation of possible substitutes. However, product characteristics and intended use are insufficient to show whether two products are demand substitutes. Functional inter-changeability or similarity in characteristics may not, in themselves, provide sufficient criteria, because the responsiveness of customers to relative price changes may be determinded by other considerations as well. For example, there may be different competitive contraints in the original equipment market for car components and in spare parts, thereby leading to a separate delineation of two relevant markets. Conversely, differences in product characteristics are not in themselves sufficient to exclude demand substitutability, since this will depend to a large extent on how customers value different characteristics.

37.

The type of evidence the Commission considers relevant to assess whether two products are demand substitutes can be categorized as follows:

38.

Evidence of substitution in the recent past. In certain cases, it is possible to analyse evidence relating to recent past events or shocks in the market that offer actual examples of substituion between two products. When available, this sort of information will normally be fundamental for market definition. If there have been changes in relative prices in the past (all else being equal), the reactions in terms of quantities demanded will be determinant in establishing substitutability. Launches of new products in the past can also offer useful information, when it is possible to precisely analyse which products have lost sales to the new product.

39.

There are a number of quantitative tests that have specifically been designed for the purpose of delineating markets. These tests consist of various econometric and statistical approaches estimates of elasticities and cross-price elasticities (5) for the demand of a product, tests based on similarity of price movements over time, the analysis of causality between price series and similarity of price levels and/or their convergence. The Commission takes into account the available quantitative evidence capable of withstanding rigorous scrutiny for the purposes of establishing patterns of substitution in the past.

40.

Views of customers and competitors. The Commission often contacts the main customers and competitors of the companies involved in its enquiries, to gather their views on the boundaries of the product market as well as most of the factual information it requires to reach a conclusion on the scope of the market. Reasoned answers of customers and competitors as to what would happen if relative prices for the candidate products were to increase in the candidate geographic area by a small amount (for instance of 5 % to 10 %) are taken into account when they are sufficiently backed by factual evidence.

41.

Consumer preferences. In the case of consumer goods, it may be difficult for the Commission to gather the direct views of end consumers about substitute products. Marketing studies that companies have commissioned in the past and that are used by companies in their own decision-making as to pricing of their products and/or marketing actions may provide useful information for the Commission's delineation of the relevant market. Consumer surveys on usage patterns and attitudes, data from consumer's purchasing patterns, the views expressed by retailers and more generally, market research studies submitted by the parties and their competitors are taken into account to establish whether an economically significant proportion of consumers consider two products as substitutable, also taking into account the importance of brands for the products in question. The methodology followed in consumer surveys carried out ad hoc by the undertakings involved or their competitors for the purposes of a merger procedure or a procedure pursuant to Regulation No 17 will usually be scrutinized with utmost care. Unlike pre-existing studies, they have not been prepared in the normal course of business for the adoption of business decisions.

42.

Barriers and costs associated with switching demand to potential substitutes. There are a number of barriers and costs that might prevent the Commission from considering two prima facie demand substitutes as belonging to one single product market. It is not possible to provide an exhaustive list of all the possible barriers to substitution and of switching costs. These barriers or obstacles might have a wide range of origins, and in its decisions, the Commission has been confronted with regulatory barriers or other forms of State intervention, constraints arising in downstream markets, need to incur specific capital investment or loss in current output in order to switch to alternative inputs, the location of customers, specific investment in production process, learning and human capital investment, retooling costs or other investments, uncertainty about quality and reputation of unknown suppliers, and others.

43.

Different categories of customers and price discrimination. The extent of the product market might be narrowed in the presence of distinct groups of customers. A distinct group of customers for the relevant product may constitute a narrower, distinct market when such ha group could be subject to price discrimination. This will usually be the case when two conditions are met: (a) it is possible to identify clearly which group an individual customer belongs to at the moment of selling the relevant products to him, and (b) trade among customers or arbitrage by third parties should not be feasible.

44.

The type of evidence the Commission considers relevant to reach a conclusion as to the geographic market can be categorized as follows:

45.

Past evidence of diversion of orders to other areas. In certain cases, evidence on changes in prices between different areas and consequent reactions by customers might be available. Generally, the same quantitative tests used for product market definition might as well be used in geographic market definition, bearing in mind that international comparisons of prices might be more complex due to a number of factors such as exchange rate movements, taxation and product differentiation.

46.

Basic demand characteristics. The nature of demand for the relevant product may in itself determine the scope of the geographical market. Factors such as national preferences or preferences for national brands, language, culture and life style, and the need for a local presence have a strong potential to limit the geographic scope of competition.

47.

Views of customers and competitors. Where appropriate, the Commission will contact the main customers and competitors of the parties in its enquiries, to gather their views on the boundaries of the geographic market as well as most of the factual information it requires to reach a conclusion on the scope of the market when they are sufficiently backed by factual evidence.

48.

Current geographic pattern of purchases. An examination of the customers' current geographic pattern of purchases provides useful evidence as to the possible scope of the geographic market. When customers purchase from companies located anywhere in the Community or the EEA on similar terms, or they procure their supplies through effective tendering procedures in which companies from anywhere in the Community or the EEA submit bids, usually the geographic market will be considered to be Community-wide.

49.

Trade flows/pattern of shipments. When the number of customers is so large that it is not possible to obtain through them a clear picture of geographic purchasing patterns, information on trade flows might be used alternatively, provided that the trade statistics are available with a sufficient degree of detail for the relevant products. Trade flows, and above all, the rationale behind trade flows provide useful insights and information for the purpose of establishing the scope of the geographic market but are not in themselves conclusive.

50.

Barriers and switching costs associated to divert orders to companies located in other areas. The absence of trans-border purchases or trade flows, for instance, does not necessarily mean that the market is at most national in scope. Still, barriers isolating the national market have to identified before it is concluded that the relevant geographic market in such a case is national. Perhaps the clearest obstacle for a customer to divert its orders to other areas is the impact of transport costs and transport restrictions arising from legislation or from the nature of the relevant products. The impact of transport costs will usually limit the scope of the geographic market for bulky, low-value products, bearing in mind that a transport disadvantage might also be compensated by a comparative advantage in other costs (labour costs or raw materials). Access to distribution in a given area, regulatory barriers still existing in certain sectors, quotas and custom tariffs might also constitute barriers isolating a geographic area from the competitive pressure of companies located outside that area. Significant switching costs in procuring supplies from companies located in other countries constitute additional sources of such barriers.

51.

On the basis of the evidence gathered, the Commission will then define a geographic market that could range from a local dimension to a global one, and there are examples of both local and global markets in past decisions of the Commission.

52.

The paragraphs above describe the different factors which might be relevant to define markets. This does not imply that in each individual case it will be necessary to obtain evidence and assess each of these factors. Often in practice the evidence provided by a susbset of these factors will be sufficient to reach a conclusion, as shown in the past decisional practice of the Commission.

53.

The definition of the relevant market in both its product and geograhic dimensions allows the identification the suppliers and the customers/consumers active on that market. On that basis, a total market size and market shares for each supplier can be calculated on the basis of their sales of the relevant products in the relevant area. In practice, the total market size and market shares are often available from market sources, i.e. companies' estimates, studies commissioned from industry consultants and/or trade associations. When this is not the case, or when available estimates are not reliable, the Commission will usually ask each supplier in the relevant market to provide its own sales in order to calculate total market size and market shares.

54.

If sales are usually the reference to calculate market shares, there are nevertheless other indications that, depending on the specific products or industry in question, can offer useful information such as, in particular, capacity, the number of players in bidding markets, units of fleet as in aerospace, or the reserves held in the case of sectors such as mining.

55.

As a rule of thumb, both volume sales and value sales provide useful information. In cases of differentiated products, sales in value and their associated market share will usually be considered to better reflect the relative position and strength of each supplier.

56.

There are certain areas where the application of the principles above has to be undertaken with care. This is the case when considering primary and secondary markets, in particular, when the behaviour of undertakings at a point in time has to be analysed pursuant to Article 86. The method of defining markets in these cases is the same, i.e. assessing the responses of customers based on their purchasing decisions to relative price changes, but taking into account as well, constraints on substitution imposed by conditions in the connected markets. A narrow definition of market for secondary products, for instance, spare parts, may result when compatibility with the primary product is important. Problems of finding compatible secondary products together with the existence of high prices and a long lifetime of the primary products may render relative price increases of secondary products profitable. A different market definition may result if significant substitution between secondary products is possible or if the characteristics of the primary products make quick and direct consumer responses to relative price increases of the secondary products feasible.

57.

In certain cases, the existence of chains of substitution might lead to the definition of a relevant market where products or areas at the extreme of the market are not directly substitutable. An example might be provided by the geographic dimension of a product with significant transport costs. In such cases, deliveries from a given plant are limited to a certain area around each plant by the impact of transport costs. In principle, such an area could constitute the relevant geographic market. However, if the distribution of plants is such that there are considerable overlaps between the areas around different plants, it is possible that the pricing of those products will be constrained by a chain substitution effect, and lead to the definition of a broader geographic market. The same reasoning may apply if product B is a demand substitute for products A and C. Even if products A and C are not direct demand substitutes, they might be found to be in the same relevant product market since their respective pricing might be constrained by substitution to B.

58.

From a practical perspective, the concept of chains of substitution has to be corroborated by actual evidence, for instance related to price interdependence at the extremes of the chains of substitution, in order to lead to an extension of the relevant market in an individual case. Price levels at the extremes of the chains would have to be of the same magnitude as well.