Market Delineation and Product Differentiation

Transcription

1 PRELIMINARY DRAFT March 27, 2000 Market Delineation and Product Differentiation Jonas Häckner * Department of Economics, Stockholm University S Stockholm, Sweden Phone: Fax: jonas.hackner@ne.su.se Abstract The purpose of this study is to analyse theoretically the implications of applying the procedure for market delineation used by competition authorities in the EU and in the U.S. Specifically, we investigate the circumstances under which the procedure will lead to a positive relation between actual market power and the assessed degree of market dominance. Another objective is to test whether the procedure is neutral in the sense that it does not discriminate among different sources of market power. In order to address these issues, we develop an oligopoly model that allows for an arbitrary number of firms as well as for vertical and horizontal product differentiation. It is found that the correlation between actual market power and assessed market dominance is likely to be weak in industries where the marginal cost of production is low and that the procedure discriminates strongly among different sources of market power. JEL lassification: K40, L13, L40 Keywords: Market Delineation, ompetition Policy, Product Differentiation * I am grateful to Sten Nyberg and to seminar participants at the Stockholm School of Economics and at ION (International ompetition Network, Stockholm) for helpful comments.

2 1. Introduction In the EU, the E Merger Regulation gives the European ommission the authority to challenge mergers that lead to dominant market positions and, under Article 86 of the Treaty of Rome, many anti-competitive activities are considered legal unless the firm in question has a dominant market position. In the United States, mergers that substantially reduce competition are considered illegal under Section 7 of the layton Act. onsequently, competition authorities are often in a position where they have to determine whether or not a specific firm is dominant. This, in turn, calls for some relatively simple operationalization of the dominance concept. According to a common definition, market dominance is present when a firm is in a position to behave to an appreciable extent independently of its competitors, its customers and ultimately of the 1 consumers. Market dominance, market concentration and monopoly power are therefore largely equivalent concepts. 2 Both European and American competition authorities use market shares as a proxy for 3 dominance. This practice is based on results from oligopoly theory that predict a strong relationship between market shares and the degree of monopolistic pricing (i.e., price-cost margins) in ournot markets. Obviously, market shares cannot be computed without having defined a relevant market. This issue is often as complex as it is important, in the sense that a narrow market definition more or less automatically leads to an assessment of a large market share and vice versa. Hence, from a practical point of view, the issue of market dominance has to a large extent already been determined when the market is defined. The procedures that are used to determine the relevant product market are more or less 4 identical in European and American practice. The point of departure is a firm accused of anticompetitive behaviour or a group of firms with the ambition to merge. For simplicity, let us

3 call this entity the defendant firm. The ultimate goal is to assess the market share of the defendant. For this purpose, the competition authority will define a so called antitrust market. 5 Let the term candidate market denote a set of product varieties that are reasonably close substitutes to the product(s) produced by the defendant. A candidate market is considered to be an antitrust market if a hypothetical monopolist, controlling the entire set of products, is likely to find it profitable to raise prices significantly. The significance threshold in legal practice is an increase in price by five to ten percent. If there are alternative candidate markets that satisfy the test, the competition authority will generally go for the narrowest market definition. The procedure can be viewed of as a series of hypothetical experiments. First, suppose that the defendant imposes a small but significant and nontransitory increase in price. If this price 6 change is likely to be profitable, then the relevant market will consist of the defendant alone. If the price increase is unprofitable, due to the fact that consumers reallocate demand to competitors, the firm(s) producing the next-best substitute will be added to the provisional market definition. The hypothetical price question is then asked under the presumption that all firms belonging to the expanded market definition act collectively. Again, the market definition is broadened further only if the price increase is likely to be unprofitable. This iterative process continues until the number of product varieties included in the market definition is large enough 7 to make the collective price increase profitable. The economic reasoning behind the price test is straightforward. First, the relevant product market is defined as a set of product varieties that are relatively close substitutes. Second, a significant price increase is likely to be unprofitable as long as there are close substitutes available outside the provisional market definition. Hence, the market definition is expanded until all close substitutes are included, which seems intuitively appealing from an economic point of view. On the other hand, the welfare implications of applying the procedure are likely to depend

4 8 on the context in which it is used. A strict welfare analysis is beyond the scope of this study. Instead, we attempt to answer two specific questions. First, we want to investigate the circumstances under which the test will generate a positive relation between actual market dominance (defined in terms of the price-cost margin) and assessed market dominance (measured in terms of the market share). Second, we want to study whether the test is neutral in the sense that it does not discriminate among different sources of market power. There are several mechanisms that can generate market power. For example, competitive pressure is likely to be weak: when there is a small number of firms interacting strategically with the defendant, when the degree of substitutability between products is small (i.e. when there is a large amount of horizontal product differentiation) and when the defendant has a large quality advantage (i.e. when there is a large amount of vertical product differentiation). Hence, given a certain price-cost margin we want to examine if the procedure will define the relevant market differently depending on whether market power is based on entry barriers, horizontal product differentiation or vertical product differentiation. To incorporate these mechanisms, the Dixit (1979) model is extended to allow for an arbitrary number of firms. In contrast to previous studies, we analyse the properties of the market delineation procedure within a standard oligopolistic framework where it is possible to separate the effects of actual market structure, vertical product differentiation and horizontal product differentiation. 9 There is a vast legal and economic literature on antitrust market delineation. An important aspect of the debate focuses on determining the correct point of reference when estimating critical

5 price elasticities in a merger context. One standpoint is that this point is the competitive price level (Shaerr (1985)). But it has also been argued that the competition authority should only take into account the marginal effect of a merger and that the most relevant point of reference is the actual pre-merger equilibrium price (Posner (1976), Baxter (1983), Werden (1993)). This view seems to be reflected in both the European ommission (1997) and in U.S. Department of Justice and Federal Trade ommission (1998). However, when investigating the abuse of dominant positions, the European ommission (1997, p. 7) argues that it should be taken into account that the prevailing price may...already have been substantially increased.... Although some attention has 10 been given to the welfare effects of mergers when products are differentiated, relatively few studies discuss the actual properties of the market delineation procedure under product differentiation. It has been acknowledged that market shares may not be good predictors of market power in the presence of product differentiation (see e.g. Hay & Werden (1993) and Schmalensee (1982)) but on the other hand Willig (1991) argues that market shares are in fact 11 informative under the assumption of Bertrand competition and a logit demand structure. As an alternative to the price test Werden and Froeb (1994) show that the direct welfare effects of a merger can be forecasted by the use of simulation techniques given the assumption of logit demand. Sometimes, firms are in a position to change their product mix in response to changes in relative prices. Such potential supply-side substitution can be considered to be evidence in support of a broad market definition since it may limit the profitability of an increase in price. This study, however, focuses on demand-side substitution. Furthermore, we limit the analysis to the definition of a relevant product market, although in practice the geographical aspect is obviously of equal 12 importance. Finally, we assume that marginal production costs are constant and equal across firms, i.e we assume that product quality depends primarily on fixed investments, for example in

6 advertising and R&D. This assumption is made in order to keep the analysis reasonably tractable and to ensure a positive relation between price-cost margins and product quality. Hence, given that there is a positive relation between market power and product quality we want to investigate the circumstances under which high quality will translate into a narrow market definition. The assumption has two important implications. First, it introduces a potential link between the degree of vertical product differentiation and market structure. However, it is difficult to say anything in general about the properties of this relation. If a firm invests heavily in a quality enhancing technology it will experience high fixed costs on the one hand and high profit-margins on the other. The exact relation between product quality and market structure is therefore largely indeterminate and will not be taken into account in the analysis. Second, it introduces a potential link between the degree of horizontal product differentiation and market structure. When products are close substitutes in a horizontal sense profit margins are small. Thus, entrant firms will find it difficult to cover their fixed costs and we would expect a small number of firms in a free entry equilibrium. This relation is not explicitly modelled but the implications of it are discussed in section 4. The main results of this study are the following. Actual market power, measured in terms of the price-cost margin, is positively related to product quality and to horizontal product differentiation. It is negatively related to the number of firms interacting strategically with the defendant. When the marginal cost is low the price test is unable to discriminate between highquality firms and low-quality firms. Moreover, the assessed degree of market dominance will be negatively related to the degree of horizontal product differentiation. This indicates a negative relation between actual market power and assessed market dominance. For higher marginal costs, there is a positive relation between product quality and assessed market dominance. There is a non-monotone relation between market power stemming from horizontal differentiation and the

7 assessed degree of market dominance. Finally, the price test discriminates strongly among different sources of market power. Given a common price-cost margin, firms whose market power is based primarily on horizontal differentiation will be assessed a broader market definition compared to firms producing high quality goods and firms with few actual competitors. The test will favor firms whose market power is based on vertical differentiation as compared to firms with few actual competitors. The paper is organized as follows. First, the model is introduced. Then, we examine how the antitrust market definition relates to market power stemming from vertical and horizontal product differentiation and from market concentration. Next, we investigate whether the price test is neutral in the sense that it does not discriminate among different sources of market power. The results are summarized and discussed in section A Model of the Product Market There are n price-setting firms producing one product variety each. Aggregate demand-side preferences are represented by the following utility function: 13 U(q, I) ' j n i'1 q i a i & 1 n 2 ( j q 2 i %2( j q i q j ) % I. i'1 i j Hence, utility is quadratic in the consumption of q-goods and linear in the consumption of other goods, I. The parameter (0[0, 1] measures the substitutability between the products (i.e., the degree of horizontal product differentiation). If ( = 0, then the products satisfy entirely different consumer needs and each firm has monopolistic market power, while if ( = 1, the products are

8 perfect substitutes. Finally, a measures quality in a vertical sense. Other things equal, an increase i in a increases the marginal utility of consuming good i. Throughout the analysis, the term quality i will refer to vertical product differentiation while substitutability will refer to horizontal product differentiation. onsumers maximize utility subject to the budget constraint 3piq i + I # m, where m denotes income and the price of the composite good is normalized to one. The first-order condition determining the optimal consumption of good k is MU Mq k ' a k & q k & ( jj k q j & p k ' 0. (1) Summing over all firms, noting that 3q = q + 3q and 3a = a + 3a, yields firm k s demand i k j i k j function: q k (p k, p &k ) ' (a k &p k )[((n&2)%1]&( jj k (a j &p j ) (1&()[((n&1)%1]. (2) Profit maximization then implies the following reaction function p k (p &k ) ' a k %c k 2 & ( jj k (a j &p j ) 2[((n&2)%1] (3) where c is firm k s marginal cost of production. Summing over all firms we arrive at the k equilibrium prices and quantities for firm k:

9 p( k ' q( k ' a k [( 2 (n 2 &5n%5)%3((n&2)%2]&(((n&2)%1)[( jj k (a j &c j )&c k (((n&2)%2)] [((n&3)%2][((2n&3)%2] (a k &c k )[( 2 (n 2 &5n%5)%3((n&2)%2]&(((n&2)%1)( jj k (a j &c j ) [((n&2)%1] (1&()[((n&3)%2][((n&1)%1][((2n&3)%2] Thus, firm k s equilibrium price and quantity depend on the average quality of its competitors but are independent of the exact distribution of qualities across firms. The model turns out to have reasonable properties given the assumption of a uniform marginal cost, c k = c j = c, œj: Proposition 1: The actual degree of market power, measured in terms of the price-cost margin, i) decreases in the number of firms that interact strategically, ii) increases in own quality level, decreases in the average quality level of the competitors, and iii) increases in the degree of horizontal differentiation. Proof: Follows from differentiation. The Nash equilibrium price increases in a and decreases in k (, 3a j and n. The relation Mp* k / Mn is calculated under the assumption that the average quality - - level, a, remains constant among the competitors. Hence, 3a j = (n - 1)a. We have also used the condition j j k (a j &c) # (a k &c)[(2 (n 2 &5n%5)%3((n&2)%2] ((((n&2)%1) which is equivalent to q* $ 0. ~ k

10 Figure 1 illustrates how the equilibrium prices are affected by vertical and horizontal product differentiation. Figure 1 about here We model product heterogeneity in the simplest possible way by assuming that there are two quality segments in the market, "a and a. Differences in quality are assumed not to translate into differences in marginal cost. The parameter " measures the degree of vertical differentiation. If " < 1 (" > 1) a firm of type a produces a quality above (below) average, while products are vertically undifferentiated if " = 1. Let n and n be the number of firms producing qualities a and a "a "a, respectively. onsequently, n = n + n. To economize on notation we also let n and n a "a a "a denote the sets of firms belonging to each category. Note that products belonging to the same category are not identical. As long as ( < 1 there is an element of horizontal product differentiation, i.e. the products satisfy partly different consumer needs. Finally, we let p * denote z the Nash equilibrium price for a firm of type z0{a, "a}. 3. The Price Test The U.S. Department of Justice and Federal Trade ommission (1998) state that:...the Agency will begin with each product (narrowly defined) produced or sold by each merging firm and ask what would happen if a hypothetical monopolist of that product imposed at least a small but significant and nontransitory increase in price, but the terms of sale of all other products remained constant. If, in response to the price increase, the reduction in sales of the product would be large enough that a hypothetical monopolist would not find it profitable to impose such an increase in price, then the Agency will add to the product group the product that is the next-best substitute for the merging firm s

11 product... (p. 6-7). and according to the European ommission (1998): 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...but permanent relative price increase...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. (p. 7). To model this procedure explicitly, suppose that a subset of firms of type a form a coalition. Instead of charging the Nash equilibrium price, the firms in the coalition charge the price 8p *, a where 8 $ 1. Assume also, in accordance with the guidelines, that the firms outside the coalition stick to the Nash equilibrium prices that were optimal before the coalition was formed. The coalition produces a high quality (relative to the average competitor) if " < 1 and vice versa. The price test is based on some threshold value 8*. Given a certain coalition, the competition authority will investigate whether or not it would be profit maximizing for the colluding firms to raise their prices by 100(8* - 1) percent (as compared to the pre-collusive level). If not, an additional firm of the same type (i.e., quality segment) will be included in the 14 hypothetical coalition. This iterative process continues until the 100(8* - 1) percent price increase is considered to be consistent with profit maximizing behavior. Let n a be the smallest set of firms (i.e. product varieties) for which a hypothetical profit- maximizing monopolist of type a would actually charge a price above 8*p a*. Moreover, let pa be the coalition s best response to the equilibrium prices of non-colluding firms (p * and p *). a "a The threshold n, which is the solution to p / p * = 8*, will generally be a function of actual a a a market structure, n, the degree of horizontal product differentiation, (, the degree of vertical 15 product differentiation, ", and the critical value 8*. Although n a (n, (, ", 8*) is a complex function (See Appendix) it is possible to draw a number of conclusions.

12 One important question is how n a is related to market power stemming from actual market concentration, n, horizontal product differentiation, (, and vertical product differentiation, ". First, let us consider the case where the marginal cost of production is low. For c = 0, n a reduces to the following expression: n a ' ([2n(8( &1)&28 ( %3]%2(8 ( &1) ((28 ( &1). (4) The greater the number of firms interacting strategically, n, the broader is the market definition. This is intuitive since an increase in competitive pressure reduces the profitability of an increase in price. Note also that n a is independent of the level and the distribution of product quality. Hence, in this case the price test is unable to discriminate between high-quality firms and lowquality firms. In other words, the assessed market shares will be determined solely by the degree of horizontal differentiation and the total number of firms. The correlation between market dominance (measured in terms of market shares) and quality related market power (measured in terms of price-cost margins) can therefore be expected to be zero. At first glance, this result might seem surprising. However, quality differences are reflected in Nash equilibrium prices. Therefore, the point of departure for the price test will differ between high-quality coalitions and low-quality coalitions, and there is no reason why the effect of a percentage change in price should differ significantly between the two types. Finally, we can note that n a is decreasing in (. A typical relation between n a and ( is illustrated in Figure 2. Basically, the more horizontally differentiated the products are, the broader will be the market definition. In the extreme case where firms have monopolistic market power (( = 0) there are no gains at all from coordinating prices. Hence, the price test would indicate that all n firms belong to the same market. The correlation between market dominance (measured in terms of market shares) and market power (based on horizontal

13 differentiation) can therefore be expected to be negative. It might seem surprising that firms producing close substitutes find it relatively more profitable to increase prices significantly. However, if the degree of horizontal differentiation is low competition will drive prices towards the level of marginal cost, which is zero in expression (4). Hence, the collusive markup can be 16 significant in percentage terms while it is insignificant in absolute terms. Figure 2 about here To summarize, when the marginal cost is low we would expect the price test to have the following properties: Proposition 2: For a zero marginal cost (c = 0) the assessed degree of market dominance is i) positively correlated with market concentration ii) iii) uncorrelated with the degree of vertical differentiation, and negatively correlated with the degree of horizontal differentiation. For intermediate levels of marginal cost the relation between actual and assessed market dominance is more complex. To isolate the effects of horizontal product differentiation, (, and competitive pressure, n, on the antitrust market definition, let us first abstract from the issue of vertical product differentiation, i.e. let us assume that " = 1. Then, the following claim is true. Proposition 3: When the marginal cost is moderate (0 < c < a/(28* - 1)) and products are vertically undifferentiated (" = 1) the assessed degree of market dominance is positively correlated with market concentration. The relation between horizontal differentiation and assessed market

14 dominance is u-shaped. When the marginal cost is high (( > a/(28* - 1)) all n firms belong to the antitrust market. Proof: Note that when " = 1 there is no need to distinguish between firm types and the production volumes are positive for all (s. The relation Mn a /Mn is increasing in 8* and strictly positive for 8* = 1 which proves the first statement. Next, we will show that n a is u-shaped and continuous on the interval 80(0, 1]. The denominator of n a has two roots, ( = 0 and ( ' a(28 ( &1)%c(28 ( &3) a(28 ( &1)&c(2n(8 ( &1)&48 ( %5). The latter increases in c and equals one for c = 0 which proves continuity. Note that Mn a / M( = -4 and n a = +4 for ( = 0. Moreover, Mn a / M( = [a - c(28* - 1)]/[2c(8*-1)] and n a = n for ( = 1. Note also that n a (() has two stationary points. Hence, for c < a/(28* - 1) only one of the roots ~ (which we denote by () can belong to the interval (0(0, 1]. The relationship between n a and ( must therefore be u-shaped. Finally, we will show that n a = n for c > a/(28* - 1). In this case n a is decreasing in ( both at ( = 0 and at ( = 1. onsequently, it must be the case that the function n a (() has either two or zero stationary points on the interval (0(0, 1]. However, it is ~ straightforward to show that the condition c > a/(28* - 1) is equivalent to ( > 1. Thus, for c > a/(28* - 1) there must be a monotone and negative relation between n a and (. Finally, as n a = n for ( = 1 all n firms must belong to the antitrust market. ~ When the marginal cost is positive and products are perfect substitutes no deviation from marginal cost pricing can be profitable unless all firms are included in the hypothetical coalition. Hence, n a = n for ( = 1. When products are remote substitutes the gains from price coordination are

15 small. This too indicates a broad antitrust market definition. As a consequence, the market is most narrowly defined when the degree of horizontal product differentiation is moderate. Although, n a (() is u-shaped for c > 0 and monotone for c = 0 the function will approximate expression (4) for small but positive marginal costs. This is illustrated in Figure 3 which depicts n a (() for different levels of c. Figure 3 about here Finally, let us examine the effect of product quality on the antitrust market definition when the marginal cost is significant. Proposition 2 states that n a is approximately unaffected by the presence of vertical product differentiation when the marginal cost of production is low. However, for higher cost levels n a decreases in the defendant s level of quality (i.e. it increases in "). This is illustrated in Figure 4 where n a (() is drawn for different levels of ". Basically, the u-shaped relation between n a and ( shifts downwards as product quality improves. The greater the proportion of high-quality firms the broader is the market definition of a high-quality defendant. On the other hand, the greater the proportion of low-quality firms the narrower will be the market definition of a low-quality defendant. Figure 4 about here Proposition 4: The higher the quality of the defendant s product (i.e. the lower ") the narrower is the market definition. An increase in the proportion of high-quality firms will broaden the market definition if the defendant produces a high quality (" < 1). An increase in the proportion of lowquality firms will narrow the market definition if the defendant produces a low quality (" > 1).

16 Proof: Follows from differentiation. ~ Our second main objective is to examine if the price test is neutral. In other words, given a certain price-cost margin, will the procedure define the relevant market differently depending on whether market power is based on entry barriers, horizontal product differentiation or vertical product differentiation? In order to answer this question we first derive a parameter relation such that the defendant s price-cost margin remains constant. Second, we study how changes in the parameters along this isoprice relation will affect the antitrust market definition. It turns out that firms whose market power is based primarily on horizontal differentiation will be assessed a broader market definition compared to firms producing high quality goods and firms with few actual competitors. Moreover, the test will favor firms whose market power is based on vertical differentiation as compared to firms with few actual competitors. Proposition 5: Given a certain price-cost margin, p * - c, and a certain degree of actual market a concentration, n, the price test will define the market more narrowly if market power is based on vertical product differentiation, ", as compared to horizontal product differentiation, (. For a given amount of horizontal differentiation, (, the price test will define the market more broadly if market power is based on vertical product differentiation, ", as compared to actual market concentration, n. Finally, as long as there is no vertical product differentiation, " = 1, the price test will define the market more broadly if market power is based on horizontal product differentiation, (, as compared to actual market concentration, n. - - Proof: Let the price-cost margin be fixed at the level m a so that p a* - c = m a. The set of parameters that generate a price-cost margin equal to m is then: - a

17 " ' 1 a(n "a (c(n&2)%1) a[( 2 (n(n "a &2)&2n "a %3)%((2n%n "a &5)%2] % % c[( 2 (2n&3)%((5&2n)&2]& m a [((n&3)%2][((2n&3)%2]. Note that the relation between " on the one hand and ( and n on the other, must be negative in order to keep the price-cost margin constant. This follows trivially from Proposition 1. In analogy, for a given level of ", the relation between ( and n must also be negative. Inserting the above relation into the expression for n a (See Appendix) we arrive at n a ' 2(8(&1)[((c(n&1)%n m a )%c% m a ]%( m a (28(&3) ([ m a (28(&1)%2c(8(&1)] which is increasing in n and decreasing in (. This proves the first two statements. Solving for a similar isoprice relation between ( and n given a certain degree of vertical product differentiation is more complex and we confine the analysis to the case where products are vertically undifferentiated, " = 1. The set of parameters that yield a constant price-cost margin then equals n ' m a (3(&2)%(1&()(a&c) ( m a while the corresponding isoprice market definition is n a ' 1 ( m a [2c(8(&1)% m a (28(&1)] 2a(1&()(8(&1)(c% m a )%2c 2 (8(&1)(1&()% m a [2c(8(&1)(2(&2)% m a (((48(&3)&2(8(&1))] which is decreasing in (. This proves the third and final statement.~

18 Suppose that two firms, A and B, belong to different product markets but enjoy the same amount of market power in terms of price-cost margins. Let firm A produce a low quality product in a market where products are remote substitutes in a horizontal sense while the opposite is true for firm B. Then Proposition 5 implies that firm A will be given a broader antitrust market definition. Alternatively, let firm A belong to a market with few actual competitors, while firm B bases its market power on horizontal or vertical product differentiation. Then Proposition 5 implies that firm B will be given the broadest market definition. Intuitively, when the degree of horizontal differentiation is significant, there is little to gain from price coordination. Hence, a hypothetical coalition will not find it profitable to raise prices significantly unless a large number of firms are included. Figure 5 illustrates how the antitrust market, n a, is defined (panels 5.d, 5.e and 5.f) given that the parameters belong to the isoprice relations "(n), "(() and n(() (panels 5.a, 5.b and 5.c). It is evident from this example that firms possessing the same degree of market power may be assessed very different degrees of market dominance. In other words, the price test discriminates strongly among different sources of market power. Figure 5 about here 4. Policy Discussion We are now in a position to draw some conclusions about the likely properties of the market delineation procedure. First, when the marginal cost is low the relation between actual market power and assessed market dominance is likely to be negative. Moreover, profit margins are

19 smaller the lower the degree of horizontal differentiation. Hence, if there are fixed costs of production the total number of firms, n, is likely to be smaller in markets where products are close substitutes. As n a is positively related to n this may in fact reinforce the tendency to assess a narrow market definition when the degree of horizontal differentiation is low. Second, for higher marginal costs, there is a positive relation between the quality of the defendant s product and the assessed degree of market dominance. Furthermore, as long as products are relatively close substitutes in a horizontal sense the relation between assessed market dominance and the degree of horizontal differentiation is positive. Hence, in this case the price test is more likely to generate a positive relation between actual market power and assessed market dominance. To gain a better understanding of the overall properties of the procedure let us study a 17 simple example. Specifically, we want to highlight how actual price-cost margins and assessed market shares are related to vertical and horizontal product differentiation and to the marginal cost of production. The results are summarized in Table 1 where the shaded parts refer to parameter configurations such that low-quality firms exit the market in equilibrium.

20 Table 1 1.a " = 9/10 " = 1 " = 11/10 c = 1/4 s = 33% s = 33% s = 33% m = 43 m = 40 m = 37 a a a c = 2/4 s = 50% s = 50% s = 50% m = 22 m = 18 m = 15 a a a c = 3/4 s = 50% s = 50% s = 50% 1.b 1.c m = 11 m = 7 m = 3 a a a " = 9/10 " = 1 " = 11/10 c = 1/4 s = 33% s = 33% s = 33% m = 41 m = 38 m = 35 a a a c = 2/4 s = 33% s = 33% s = 33% m = 21 m = 17 m = 14 a a a c =3/4 s = 33% s = 20% m a = 7 m a = 3 " = 9/10 " = 1 " = 11/10 c = 1/4 s = 33% s = 33% s = 33% m = 39 m = 36 m = 33 a a a c = 2/4 s = 33% s = 25% m a = 16 m a = 13 c = 3/4 s = 25% s = 17% m a = 6 m a = 2 Assessed market shares (s) and actual price-cost margins (m ) for a a defendant firm of type a given various degrees of horizontal (() and vertical (") product differentiation. The marginal cost of production (c) is assumed to be 0, 10 and 20 in panels 1.a, 1.b and 1.c respectively.

21 As expected, price-cost margins increase in product quality and in the degree of horizontal differentiation. On the other hand, the assessed market shares seem to show a slightly different pattern, especially when the marginal cost is low. The procedure may generate both type I and type II errors. For example, in panel 1.a the firm type that charges the highest price will be assessed to have the smallest degree of market dominance while many low-price firm types are considered to benefit from duopolistic market power. Table 2 contains the correlation coefficients, r, between the assessed market shares and the price-cost margins shown in Table 1. The coefficients within brackets are computed under the restriction that products are vertically undifferentiated (" = 1), i.e the case which is closest in line with the assumption of a uniform marginal cost. As predicted, the price test seems to perform better the higher the marginal cost of production, c. Table 2 c = 0 c = 10 c = 20 r = r = 0.53 r = 0.84 (r = -0.94) (r = 0.0) (r = 0.75) The correlation between assessed market shares and price-cost margins for different marginal costs. To sum up, the price test is likely to react to differences in actual market concentration and vertical product differentiation in a way that is consistent with the legal framework where market power and market dominance are largely equivalent concepts. On the other hand, there is a nonmonotone relation between market power, stemming from horizontal differentiation, and assessed

22 market dominance. This problem becomes more severe the lower the marginal cost of production. onsequently, the price test is likely to perform poorly when applied to industries where the costs of production are primarily fixed. Assessed market shares should hence be interpreted with great care in such industries. Finally, given the objectives of the legal framework, the price test seems to have an undesirable property in that it discriminates strongly among different sources of market power. From this perspective, it might be preferable to base the dominance criterion on assessed price-cost margins (instead of market shares) in markets where products are differentiated.

23 References Anderson, S. and A. De Palma, 1992, The Logit as a Model of Product Differentiation, Oxford Economic Papers 44, Baxter, W., 1984, Responding to the Reaction: The Draftsman s View, in Fox, E.M. and J.T Halverson (eds.), Antitrust Policy in Transition: The onvergence of Law and Economics, hicago: American Bar Association, Section of Antitrust Law, Dixit, A., 1979, A Model of Duopoly Suggesting a Theory of Entry Barriers, Bell Journal of Economics 10, European ommission, 1989, ouncil Regulation (EE) No. 4064/89 OJ L 395/1 30 (The E Merger Regulation), November European ommission, 1997, ommission Notice on the Definition of Relevant Market for the Purposes of ommunity ompetition Law, Official Journal of the European ommunities (97/ 372) Geroski, P.A., 1998, Thinking reatively about Markets, International Journal of Industrial Organization 16, Häckner, J., 2000, A Note on Price and Quantity ompetition in Differentiated Oligopolies, Journal of Economic Theory, (forthcoming). Hay, G. and G. Werden, 1993, Horizontal Mergers: Law, Policy, and Economics, American Economic Review 83, McAfee, R.P, Simons, J. and M. Williams, 1992, Horizontal Mergers in Spatially Differentiated Noncooperative Markets, Journal of Industrial Economics 40, Posner, R., 1976, Antitrust Law: An Economic Perspective, hicago: University of hicago Press.

24 Schaerr, G.., 1985, The ellophane Fallacy and the Justice Department s Guidelines for Horizontal Mergers, Yale Law Journal, 94(3), Schmalensee, R., 1982, Another Look at Market Power, Harvard Law Review, 95, U.S. Department of Justice and Federal Trade ommission, 1998, 1992 Horizontal Merger Guidelines, Washington D. Werden, G., 1993, Market Delineation under the Merger Guidelines: A Tenth Anniversary Retrospective, Antitrust Bulletin 38, Werden, G. and L. Froeb, 1994, The Effects of Mergers in Differentiated Products Industries: Logit Demand and Merger Policy, Journal of Law, Economics and Organization 10, Willig, R., 1991, Merger Analysis, Industrial Organization Theory, and Merger Guidelines, Brookings Papers on Economic Activity, Microeconomics, ourt Decisions Hoffmann-La Roche & o. AG v. E ommission, ase 85/76 Judgement of 13 February 1979 ER 461.

25 Appendix The antitrust market definition for c > 0: n a ' ca%ab ((c%ad) where A / (((2n&3)%2)[( 2 (2n 2 (8 ( &1)&6n(8 ( &1)%48 ( &3)%((4n(8 ( &1)&68 ( %5)%2(8 ( &1)] B / [((2n(8 ( &1)&28 ( %3)%2(8 ( &1)][( 2 ((1&")n "a (n&2)&2n%3)%(((1&")n "a %2n&5)%2] / ( 2 (2n(8 ( &1)&48 ( %5)(2n&3)%((2n(48 ( &5)&148 ( %19)%2(28 ( &3) D / (28 ( &1)[( 2 ((1&")n "a (n&2)&2n%3)%(((1&")n "a %2n&5)%2]

26 Endnotes 1.See the Hoffman-la Roche case (1979). 2.The term market dominance is more commonly used in European practice while the American counterpart is market concentration. Here, these concepts are regarded as synonyms. Under U.S. law the relevant issue is whether or not a merger is likely to create significant market power. In the EU the question is typically whether or not a firm already possesses market power. 3.In the U.S., market dominance, or market concentration, is measured in terms of the Herfindahl- Hirschman Index while the European ommission uses actual market shares. 4.See, for example, the European ommission (1997) and U.S. Department of Justice and Federal Trade ommission (1998, Section 1.1) for definitions of relevant product markets. 5.A comparative discussion of alternative market definitions can be found in Geroski (1998). 6.In order to forecast the likely effects of a hypothetical price change, the competition authorities often collect evidence from expert witnesses (e.g. competitors). 7.The European ommission (1997) and the U.S. Department of Justice and Federal Trade ommission (1998) focus on products rather than firms. In the theoretical part of this study it is assumed that each firm produces a unique product variety. Hence, in this context, firm and product variety can be regarded as synonyms.

27 8.For example, a full-fledged welfare analysis of a merger is a complex issue that would include effects on fixed and marginal costs of production, post-merger market prices and the consumers valuation of product variety. 9.See e.g. Werden (1993) for an overview. 10.See e.g. Werden & Froeb (1994) and McAfee et al (1992). 11.See e.g. Anderson & De Palma (1992) for a discussion on oligopolistic competition with a logit demand structure. 12.Horizontal differentiation can be interpreted in terms of geographical distance. Hence, the discussion has some bearing on geographical market delineation as well. 13.This extension of the Dixit (1979) model was developed in Häckner (2000). 14.This seems to be the most obvious way to interpret the term next-best substitute in this framework. 15.It may of course be the case that a significant increase in price is unprofitable even for n = n. The next step would then be to include firms of type "a in the hypothetical coalition. However, allowing for vertical product differentiation within the coalition makes the problem intractable. a a

28 16.When products are vertically differentiated and products are close substitutes in a horizontal sense n a is not defined since low-quality firms have a zero market share in equilibrium. However, when n is defined, i.e. for small enough cs, the relation between n and c is negative. a a 17.In Table 1 it is assumed that a = 200, n = 6, n a "a = 4 and 8* = 1.05 The threshold 8* is consistent with the practice in the U.S. and in the EU.