January 24, 2001 Vertical Integration and ompetition Policy Jonas Häckner + Department of Economics, Stockholm University S-106 91 Stockholm, Sweden + Phone: +46-8-163049 Fax: +46-8-159482 E-mail: jonas.hackner@ne.su.se Abstract Recently, the European ommission has decided to implement a simplified procedure in the context of vertical integration. If the combined market shares of the merging firms are less than 25 percent, upstream and downstream, the ommission will consider the merger harmless. The purpose of this study is to examine the welfare aspects of vertical integration in a simple model and investigate the accuracy of the proposed rule of thumb. The welfare implications of vertical integration turn out to depend on relative market shares and the degree of product differentiation. Basically, a merger is harmless from a social point of view when the upstream market is relatively concentrated compared to the downstream market and/or if products are sufficiently close substitutes. We therefore suggest an alternative screening rule: If the upstream market is significantly less concentrated than the downstream market, or if products obviously are close substitutes, mergers may be approved at an early stage of the screening process. Otherwise the merger may be detrimental to welfare and the competition authority should evaluate it more carefully. JEL lassification: L42, L13 Keywords: Vertical Integration, Merger, ompetition Policy
1 1. Introduction Market foreclosure has for a long time been the prime policy concern in the context of vertical 1 integration. The idea is that the integrated firm may have an incentive to exit the upstream market. Withdrawing from the upstream market might for example lead to a strategic gain in the 2 sense that it increases the costs of downstream competitors. An integrated firm may also want to save fixed costs by concentrating marketing and advertising expenses to the downstream market. In any case, there is a risk that market foreclosure will harm competitors as well as consumers. Upstream competitors will have fewer outlets, downstream competitors may experience an increase in cost and final consumers may suffer from increases in price. Recently, the European ommission has decided to implement a simplified procedure 3 when dealing with merger applications in the case of vertical integration. Basically, if the combined market shares of the merging firms are less than 25 percent, upstream and downstream, the ommission will consider the merger harmless. A merger that fails the test could still be approved but only after a thorough evaluation. From a welfare perspective it is far from clear-cut whether or not vertical integration is 4 efficient. On the one hand, it can lead to an increase in market concentration or facilitate for a dominant firms to exercise market power in a related market. On the other hand, it may mitigate the problem of double marginalization. 1 This view was for example stated by the U.S. Supreme ourt in the Brown Shoe case (Brown Shoe o., Inc. v U.S.). 2 See e.g. Riordan (1998). 3 The European ommission (2000). 4 See e.g. Riordan (1998) and Salinger (1988).
2 The purpose of this study is to examine the welfare aspects of vertical integration and foreclosure in a simple model and investigate if the proposed rule of thumb is efficient. We apply a worst case scenario in the sense that it is assumed that the integrated firm exits the upstream market (as seller and buyer) either to increase profits or to reduce fixed costs. We then ask under what circumstances such foreclosure is likely to be detrimental to welfare. This makes it possible set up a number of conditions under which competition authorities would want to evaluate the merger more carefully. We then compare this set of conditions to the proposed rule of thumb and suggest an alternative screening rule. In order to calculate market shares it obviously necessary to assess the relevant market definition, the so called antitrust market. This is done by applying to the model the market delineation procedure proposed by the European ommission. 5 There is a vast literature on vertical integration. losest in spirit to this study is perhaps Salinger (1988) where firms compete in quantities using constant returns to scale technologies. Timing is sequential and downstream firms act as price takers in relation to upstream firms. Finally, input and output are both assumed to be undifferentiated. There is no explicit welfare analysis, but it is concluded that the merging firms will increase output in the downstream market at the expense of unintegrated firms whose input demand will diminish. It will always be in the merging firms interest to withdraw from the upstream market which leads to an increase in the price of inputs. The price of final goods will sometimes increase as well. In contrast to Salinger (1988), Riordan (1998) assumes that the merging downstream firm has access to a superior technology which makes it dominant also before the merger occurs. It faces competition from a competitive fringe of firms who act non-strategically. In this model, vertical integration always leads to an increase in input and output prices. The welfare loss from higher prices may however 5 The European ommission (1997).
3 sometimes be offset by a more intense exploitation of the cost advantage held by the dominant firm. Hart & Tirole (1990) and Ordover, Saloner & Salop (1990) discuss vertical integration in a contract theoretical framework that explicitly takes into account firms incentives to bid on other firms or to remain unintegrated. As mentioned above, our model resembles that of Salinger (1988) with an oligopolistic market structure (upstream and downstream) but in contrast to most earlier studies we will explicitly introduce an element of product differentiation. The decision to integrate is assumed to be exogenous. omplete models, like Hart & Tirole (1990) and Ordover, Saloner & Salop (1990), are developed for 2x2 firms. Hence, they cannot be used to address the questions raised in this study. The main findings are the following. The welfare implications of vertical integration turn out to depend on relative market shares (upstream and downstream) rather than absolute market shares. A merger is harmless from a social point of view when the upstream market is relatively concentrated compared to the downstream market and/or when downstream products are relatively close substitutes. The rule of thumb proposed by the European ommission is based on absolute market shares and tends to favor mergers where both markets are competitive in the sense that a lot of firms interact strategically. Moreover, it will tend to favor mergers in markets where downstream products are relatively differentiated. Taking into account that market shares that are based the antitrust market definition are affected by the degree of upstream concentration as well as product differentiation we suggest an alternative screening rule: If the upstream market is significantly less concentrated than the downstream market and/or if it is obvious that products are close substitutes mergers may be
4 6 approved at an early stage of the screening process. If these conditions are not satisfied the merger may be detrimental to welfare and the competition authority should evaluate it more carefully. The paper is organized as follows. First, the model is introduced. Then we examine the pre-merger equilbrium and derive an expression for aggregate welfare. Next, the post-merger equilibrium is examined in a similar fashion. The following section contains a welfare comparison which leads to a set of conditions under which vertical integration is beneficial from a social point of view. Then the antitrust market is defined. The final section discusses the accuracy of the proposed rule of thumb. We also suggest an alternative rule that is based on the results from the welfare comparison. 2. The Model Let us first consider the pre-merger situation. There are m upstream firms producing a homogenous input at a constant marginal cost k. The input is then sold to n downstream firms producing differentiated goods to final consumers. The downstream firms are assumed to produce one product variety each. All firms compete à la ournot. The timing is as follows: First, the upstream firms choose quantities which results in a market clearing input price, c. Second, the 7 downstream firms choose quantities taking the input price as given. The downstream production technology is the simplest possible. One unit of input corresponds to one unit of output. For 6 It could be argued that the degree of product differentiation is, to a large extent, unobservable by the competition authority. 7 The same timing assumption was made in Salinger (1988). For a discussion of alternative timing structures, see Salinger (1989).
5 simplicity, it is assumed that downstream firms face a zero marginal cost of transforming the input into a differentiated good. This means that c can be interpreted as the downstream marginal cost of production. Product differentiation may be the result of fixed investments, for example in advertising, or may be due to some geographical distance between outlets. To solve for the subgame perfect equilibrium we first derive the demand for inputs. The upstream equilibrium is then solved for given this input demand function. Aggregate demand-side preferences of the final consumers are represented by the following utility function. 8 U(q, I) a M n i1 q i 1 2 ( M n i1 q 2 i 2 M igj q i q j ) I. (1) Hence, utility is quadratic in the consumption of q-goods and linear in the consumption of other goods, I. The parameter [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 perfect substitutes. Finally, a measures quality in a vertical sense. Other things equal, an increase in a increases the marginal utility of consuming good i. onsumers maximize utility subject to the budget constraint pq i i+ I S where S denotes income and the price of the composite good is normalized to one. The first-order condition determining the optimal consumption of good z is 0U 0q z a q z M jgz q j p z 0. 8 This extension of the Dixit (1979) model was developed in Häckner (2000).
6 Hence, firm z s inverse demand function is p z (q z, q z ) a q z M jgz q j. (2) 2.1 The Pre-Merger Equilibrium Profit maximization given a common marginal cost c implies the following reaction function q z (q z ) a c M jgz q j 2 (3) which, in turn, means that the symmetric downstream equilibrium quantity is: q a c (n 1) 2. (4) Now, let us turn to the upstream market. Let Q denote total factor demand, i.e, Q = nq*. Then the inverse demand for inputs is given by c(q) an Q((n 1) 2) n. Upstream firm x maximizes profits, % = (c(q) - k)q, with respect to own output Q taking into x x x account that Q = Q + Q where Q is the total output of other upstream firms. Let a double x ygx ygx star indicate the subgame perfect equilibrium. Noting that Q ygx = (m-1)q x in a symmetric equilibrium we can solve for the aggregate subgame perfect equilibrium output,
7 and the corresponding equilibrium input price, Q mn(a k) (m1)((n 1) 2) c a km m 1. The latter turns out to be independent of the downstream market structure. Given this upstream equilibrium price, the downstream subgame perfect equilibrium price and quantity equal: p q m(a k) (m1)((n 1) 2) a[(n 1) m 2] km[(n 1) 1)] (m1)((n 1) 2). Disregarding fixed costs, welfare, measured in terms of the sum of consumers and producers surplus, is given by: W = U(q**, I**) + n(p** - c**)q** + (c** - k)q**. Inserting the subgame perfect equilibrium prices and quantities we end up with the following welfare measure: 9 W S mn(a k)2 [(m2)(n 1) 3m 4] 2(m1) 2 ((n 1) 2) 2. 9 2 Note that the qq component of the utility function equals qn(n-1)/2 in the symmetric case. i j
8 2.2 The Post-Merger Equilibrium Vertical integration is modeled in the simplest possible way. The merging upstream firm simply 10 exits the external input market. Instead it supplies the input internally at marginal cost, k. Hence, a merger has three effects. The upstream market becomes more concentrated. On the other hand, fewer firms demand the input produced in the upstream market. Finally, the merging downstream firm will be more aggressive as it is operating at a lower marginal cost. The net welfare effect will depend on the original market structure and the degree of horizontal product differentiation. Assume that the marginal cost of downstream production is k for one firm and c for the other n - 1 firms, where k c. Then equation (3) implies the following equilibrium quantities: q k k[(n 2) 2] a(2 ) c(n 1) 2 (n 1) 2(n 2) 4 (5) q c 2c a(2 ) k 2 (n 1) 2(n 2) 4 (6) where subscripts k and c refer to marginal production costs. Since firm k produces its input internally the external factor demand equals Q = (n-1)q *. The inverse factor demand then equals c c(q) (n 1)[a(2 ) k] Q[4 2(n 2) 2 (n 1)] 2(n 1) Again, upstream firm x maximizes profits, % = (c(q) - k)q, with respect to own output Q taking x x x into account that Q = Q + Q where Q is the total output of other upstream firms. Let a x ygx ygx double star indicate the subgame perfect equilibrium. Noting that Q ygx = (m-2)q x in a symmetric equilibrium (since firm k no longer produces for the upstream market) we can solve for the aggregate subgame perfect equilibrium output, 10 It is conceivable that the upstream part of the merged firm may sometimes have an incentive to sell to outsiders. However, this incentive is likely to be weak as it internalizes the effect of lower input prices on downstream profits. In any case the output supplied in the external input market is always reduced as a consequence of the merger. It might also be cost saving to exit the external input market as sales efforts and marketing can then be concentrated to the downstream market.
9 Q (m 1)(n 1)(a k) m((n 1) 2) (7) and the corresponding equilibrium input price, c a(2 ) k( 2(m 1)) 2m (8) which, again, is independent of the downstream market structure. Given this upstream equilibrium price, the downstream subgame perfect equilibrium prices and quantities equal: q k ((n 1) 2m)(a k) 2m((n 1) 2) q c (m 1)(a k) m((n 1) 2) p k a[(n 1) 2m] k[(n 1)(2m 1) 2m] 2m((n 1) 2) p c a[2(n 2) 2 (n 1)2(m1)] k[2(m(n 1) n2) 2 (n 1)2(m 1)] 2m((n 1)2) Disregarding fixed costs, welfare, measured in terms of the sum of consumers and producers surplus, is now given by: W = U(q**, I**) + (n - 1)(p ** - c**)q ** + (p ** - k)q ** + (c** - k)q**. Inserting the subgame c c k k perfect equilibrium prices and quantities we end up with the following welfare measure: 11 11 2 In this case the qq component of the utility function equals (n-1)q q + q (n-1)(n-2)/2. i j k c c
10 W S (a k)2 [3 2 (n 1) 2 4(n 1)(m 2 nm n2)4(3m 2 n(2m1)(1 n))] 8m 2 ((n 1)2) 2 3. A Welfare omparison In order to investigate the welfare aspects of the EU policy towards vertical integration we need first to analyze the conditions under which such integration is likely to be beneficial from a social point of view. It turns out that vertical integration is harmful to society when the following two conditions hold. First, products must be relatively differentiated. Second, the number of downstream firms, n, has to be strictly larger than the number of upstream firms, m. Proposition 1: Vertical integration increases welfare if the number of downstream firms, n, is smaller or equal to the number of upstream firms, m. On the other hand, if n > m, there exists a ^ unique threshold level of product differentiation,, such that vertical integration reduces welfare ^ ^ if <. increases in n and decreases in m. Proof: The sign of the difference between post-merger welfare and pre-merger welfare (disregarding fixed cost savings) is determined by the function 1(m, n, ) 4m 3 [(n 1)2] m 2 [3 2 (n 1) 2 16(n 1) 4(2n 5)] 2m(n 1)[3 2 (n 1) 2(2n 5) 8] (n 1)[3 2 (n 1) 4(n 2) 4] which is continuos and strictly convex in. Since 1 is quadratic in it has either two or zero ^ roots. Let the larger root (in case the roots exist) be denoted by (See Appendix). It is ^ straightforward to show that > 0 if and only if
11 n > ñ 2m 3 5m 2 4m1 2m 2 4m1. ^ ~ ~ and that = 0 for n = n. The right-hand side of the expression for n is strictly increasing in m and ~ approximately linear with a slope equal to unity. It is easy to check that n < n for n = m and that ~ n > n for n m + 1. Hence, if n m vertical integration is always beneficial from a welfare ~ perspective. This proves the first statement in the proposition. If n > m, i.e., if n > n, then 1(m, n, 0) < 0 so we may conclude that both roots exist and that the smaller root is negative. ~ ^ onsequently, for n > n there exist a unique threshold > 0 such that vertical integration reduces ^ welfare for [0, ]. This proves the second statement in the proposition. Finally, it can be shown ^ ^ ^ that 0/0n > 0. alculating 0/0m is quite complex but it has been checked numerically that 0/0m < 0 for n{2, 20}. This proves the third statement in the proposition.a A merger has two main counteracting effects. First, it reduces the number of upstream firms which 12 leads to higher factor- and consumer prices and lower welfare. Let this be denoted the market structure effect. Second, it makes the merging firm more aggressive in the downstream market which is likely to have a positive effect on welfare since it mitigates the problem of double marginalization that is inherent in this kind of vertical structure. Let this be denoted the cost effect. When products are differentiated, changes in the marginal cost of one firm will have a relatively small impact on the pricing decisions of other firms in the downstream market. Hence, the market structure effect dominates. When the number of upstream firms is large to begin with the market structure effect is likely to be weak. Thus, a merger is more likely to be beneficial. Finally, when the number of downstream firms is large the pre-merger competitive pressure is significant. Hence, non-integrated firms are not able to reduce prices much in response to a more aggressive integrated competitor. onsequently, the cost effect is weak and a merger is more likely to be harmful. 12 Of course there is an additional counteracting effect in the sense that fewer firms demand the input in the upstream market. This effect is likely to be weaker than the strategic effect however.
4. The Antitrust Market Definition 12 Since the input is undifferentiated the antitrust market definition in the upstream market seems unproblematic. The pre-merger market share is simply one divided by the total number of upstream firms, m. In the downstream market however it is not obvious how many product varieties to include in the antitrust market definition. We therefor apply the market delineation procedure proposed by the European ommission (1997): 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 form a coalition. Instead of charging the Nash equilibrium price, the firms in the coalition charge the price p**, where 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 price test is based on some threshold value *. 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(* - 1) percent (as compared to the pre-collusive 13 level). If not, an additional firm will be included in the hypothetical coalition. This iterative process continues until the 100(* - 1) percent price increase is considered to be consistent with profit maximizing behavior. The procedure certainly has the flavor of Bertrand competition although firms compete à la ournot in the model. Instead of asking if colluding firms would increase prices significantly the relevant question to ask in this context is if colluding firms are likely to withdraw supply 13 In legal practice the threshold is an increase in price by five to ten percent.
13 14 sufficiently to raise prices significantly. Let n be the smallest set of firms (i.e. product varieties) for which a hypothetical profit- maximizing monopolist would actually withdraw demand to such an extent that prices reaches the level *p**. Moreover, let p be the price that corresponds to the coalition s best response to the equilibrium quantities of non-colluding firms. Finally let p** be the pre-collusive equilibrium price. The threshold n, which is the solution to p / p** = *, will generally be a function of the number of firms interacting strategically, n, the degree of horizontal product differentiation, and the critical value *. The objective of the hypothetical coalition is to choose the collusive output level, q, so to maximize the profit earned by a representative member: % = (p - c)q where p = a - [(n -. 15 1)q + (n-n )q**] - q by equation (2). This implies the following collusive output and price: q m(a k)((n 1) 2) 2(m1)((n 1) 2)((n 1) 1) p a[(m(n 1) 2(n 1)) 2(m2)] km[(2n n 1) 2] 2(m1)((n 1) 2). Solving for n from the condition determining the antitrust market definition, p / p** = *, we arrive at: n 2( 1)[a((n 1)m2) km(n1)] m(a k(2 1)) m(a k). This function increases in * which is intuitive since only a large coalition would find it profit maximizing to act as to increase prices to a large extent. More surprising is that there is a negative relation between the size of the antitrust market and the degree of horizontal product 14 It seems a bit unclear what type of competition is actually referred to in European and U.S. merger guidelines. ournot competition seems very much to be the foundation of merger policy in some contexts. For example, the Herfindahl index that is used to screen merger applications in the U.S. is closely linked to the ournot model. 15 Note that the rule of thumb is applied to pre-merger market shares. Hence, q** is equivalent to the premerger equilibrium quantity of section 2.1.
14 16 differentiation,. In a sense, the more monopoly power downstream firms have, the broader will the market definition be. As products become more differentiated the gain from price coordination diminishes. This, in turn, means that a larger number of firms will have to be included in the market definition in order to make it worthwhile for them to increase prices significantly. As could be expected, the larger the number of downward firms interacting strategically, n, the broader is the antitrust market definition, n. Less obvious is perhaps that the antitrust market definition, n, becomes narrower as the number of upstream firms, m, increases. The intuition is the following. A competitive upstream market leads to a low input price which, in turn, results in a low equilibrium downstream price. This means that also a small downstream coalition will find it worthwhile to raise prices significantly in percentage terms. 5. Policy onsiderations In section 3 we found that vertical integration improves welfare if the number of downstream firms is smaller or equal to the number of upstream firms. If the number of downstream firms is larger than the number of upstream firms vertical integration is harmful if products are relatively differentiated. Hence, if we interpret the model literally and if market structure is observable upstream and downstream the competition authority would want to carefully evaluate vertical mergers in case products are differentiated and if 1/n < 1/m. Another way of putting it is of course that mergers should be considered harmless if products are relatively close substitutes and/or if 1/n > 1/m. This result is in sharp contrast to the rule of thumb proposed by the European ommission, namely that mergers should be considered harmless whenever 1/n and 1/m are smaller than 1/4. For simplicity, we assumed in the model that all downstream products were differentiated to the same extent. In practice, however, a large number of products can often be considered 16 It should be pointed out that the monotonic relation between n and is not robust to changes in the strategic variable. In the case of Bertrand competition the relation is u-shaped. See Häckner (2000).
15 substitutes to varying degrees, and the market boundary has to be determined in some way or another. Hence, market shares are not directly observable when products are differentiated. This, in turn, calls for some simple market delineation procedure such as the one applied by the European ommission. Given that the downstream market structure is not directly observable, an alternative rule of thumb could be to allow mergers if products are relatively close substitutes and/or if 1/n > 1/m. There are however three problems associated with this rule. First, we know that n is not independent of m. A small upstream market share increases the assessed downstream market share. This might lead to type II errors in the sense that potentially harmful mergers might be considered harmless at an early stage of the application process. The problem can be mitigated however by requiring that the downstream market should be significantly more concentrated than the upstream market for the merger to be considered harmless. Second, we know that n is not independent of. Specifically, the assessed downstream market share becomes smaller the larger the degree of product differentiation. This might lead to type I errors in the sense that some harmless mergers are evaluated more carefully than necessary. Hence, at worst, this will lead to a waste of administrative resources. Third, it could be argued that product differentiation is not really a fully observable variable. onsumers often perceive products as being differentiated even when product characteristics are similar. For example, this might be true for products that are heavily advertised. Hence, to a large extent, the degree of product differentiation lies in the eyes 17 of consumers. onsequently, it might be problematic to apply a rule of thumb that is contingent on product differentiation. To sum up. It seems as the welfare implication of vertical integration depends on relative market shares rather than absolute market shares. The screening rule proposed by the European ommission might therefore be improved on. One suggestion, which is in line with the findings in this study, would be to allow mergers (without a thorough evaluation) in case the upstream market is significantly less concentrated than the downstream market. If it is obvious that 17 The market delineation procedure could in fact be seen as a way to estimate the perceived degree of product differentiation.
16 downstream products are close substitutes, the merger should also be allowed. The policy conclusions are based on a stylized model and they should of course not be overemphasized. For example, if technology differs across firms, as in the Riordan (1998) study, the policy implications might change. The result that absolute market shares are poor welfare indicators (compared to relative market shares) is probably quite robust though.
References 17 Dixit, A., 1979, A Model of Duopoly Suggesting a Theory of Entry Barriers, Bell Journal of Economics 10, 20-32. European ommission, 2000, ommission Notice on a Simplified Procedure for Treatment of ertain oncentrations under ouncil Regulation (EE) No 4064/89, Official Journal of the European ommunities (2000/ 217). European ommission, 1997, ommission Notice on the Definition of Relevant Market for the Purpose of ommunity ompetition Law, Official Journal of the European ommunities (97/ 372). Häckner, J., 2000, A Note on Price and Quantity ompetition in Differentiated Oligopolies, Journal of Economic Theory 93, 233-239. Häckner, J., 2000, Market Delineation and Product Differentiation, mimeo, Department of Economics, Stockholm University. Hart, O. and Tirole, J., 1990, Vertical Integration and Market Foreclosure, Brookings Papers on Economic Activity, Special Issue, 205-276. Ordover, J. A., Saloner, G. and Salop, S.., 1990, Equilibrium Vertical Foreclosure, American Economic Review 80, 127-142. Riordan, M. H., 1998, Anticompetitive Vertical Integration by a Dominant Firm, American Economic Review 88, 1232-1248. Salinger, M. A., The Meaning of Upstream and Downstream and the Implication for Modeling Vertical Mergers, Journal of Industrial Economics 37, 373-387. Salinger, M. A., 1988, Vertical Mergers and Market Foreclosure, Quarterly Journal of Economics 103, 345-356.
18 Appendix ˆ m 6 2m 5 4m 4 (2n 1)2m 3 (3n 2)m 2 (4n 2 5n 1)2m(2n 2 1)n 2 n1 m 3 4m 2 m(2n 5)n 2 2 3(m 2 2m1)(n 1)