A Survey on Competition in Vertically-Related Markets Marc Bourreau∗ Jerome Pouyet† Nicolas Schutz‡ Thomas Tregouet§

Abstract This document reviews the economic theory relevant to the analysis of verticallyrelated industries.

∗

ENST and CREST-LEI. Address: ENST, Department of Economics and Social Sciences, 46 rue Barrault, 75634 Paris Cedex 13, France. E-mail: [email protected]. † Ecole Polytechnique and CEPR. Address: Department of Economics, Ecole Polytechnique, 91128 Palaiseau Cedex, France. E-mail: [email protected] ‡ Paris School of Economics (PSE). Address: Paris School of Economics, 48 Boulevard Jourdan, 75014, Paris, France. E-mail: [email protected]. § Ecole Polytechnique. Address: Department of Economics, Ecole Polytechnique, 91128 Palaiseau Cedex, France. E-mail: [email protected]

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Contents 1 Introduction

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I Successive vertical oligopolies without pure upstream competitors 6 2 The impact on consumer welfare of service-based competition when facilitybased competition is in place

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2.1

A simplified version of H¨offler and Schmidt (2007) . . . . . . . . . . . . . . .

7

2.2

The impact of service-based entry on downstream prices and consumers surplus

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2.3

The impact of wholesale regulation . . . . . . . . . . . . . . . . . . . . . . .

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2.4

Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3 Complete foreclosure: Does an integrated firm want to supply a potential competitor?

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3.1

Complete foreclosure with a monopolized wholesale market . . . . . . . . . .

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3.2

Complete foreclosure with an oligopolistic wholesale market . . . . . . . . .

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4 Partial foreclosure

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4.1

The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4.2

The softening effect and its impact on the incentives to undercut . . . . . . .

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4.3

Policy implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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II Successive vertical oligopolies with pure upstream competitors 24 5 Market analysis in successive vertical oligopolies

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5.1

The two-stage Cournot oligopolies model . . . . . . . . . . . . . . . . . . . .

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5.2

Upstream and downstream competition without vertically integrated firms .

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5.3

Upstream and downstream competition with one integrated firm and captive sales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.4

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Upstream and downstream competition when the integrated firm participates in the wholesale market

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

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6 Consumer foreclosure

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7 Dynamic framework: Does vertical integration facilitates upstream collusion?

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7.1

Single-market tacit collusion . . . . . . . . . . . . . . . . . . . . . . . . . . .

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7.2

Upstream collusion in successive vertical oligopolies . . . . . . . . . . . . . .

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1

Introduction

This paper surveys recent work in the literature on competition between vertically related markets. In that framework, the upstream firms produce an input, which is used by the downstream firms to produce a final good. The analysis of the functioning of these market depends on a number of factors among which (i) the presence of vertically-integrated firms, that is, firms which are present both on the upstream and the downstream markets, (ii) the presence of pure upstream or pure downstream firms, that is, firms which are active on only one of the markets. The first part of the analysis considers models of competition between at least one integrated firm and one pure downstream firm. There are no pure upstream competitor. The first question we ask is the following. Starting from the situation in which there is only one integrated firm, when does the presence of a pure downstream firm increase welfare? This analysis is performed under the assumption that the vertically-integrated firm is willing to be the upstream provider of the pure downstream firm. The second question we ask is precisely: When does an integrated firm prefer providing the upstream good to a pure downstream firm rather than completely foreclosing that downstream competitor? The analysis is then extended to the case in which several integrated firms compete potentially to be the upstream provider of pure downstream firms. The first part concludes with some considerations about the possibility of partial foreclosure, that is, the emergence of situations in which the potential for competition on the upstream market between integrated firms does not realize and pure downstream firms obtain the upstream good but at a price strictly above the marginal cost. The second part of the analysis considers situations in which there are at least one pure upstream firms. The analysis draws on several papers inspired by antitrust concerns rather than regulatory ones. We start with the so-called two-stage Cournot oligopolies model, in which the transactions between the producers of the upstream good and the buyers of that good take place through a merchant market. The analysis provides some insights on how one should analyze the functioning of these markets, and on the impact of integrated firms in that context. The analysis continues with the issue of ‘consumer foreclosure’, that is, of foreclosure of

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some upstream producers by other upstream producers through the use of exclusive contracts with the buyers of the upstream good. Finally, the analysis concludes with the question of tacit collusion in vertically-linked industries. There, we ask the following question: Does the presence of one or more verticallyintegrated firms facilitate tacit collusion in the industry?

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Part I

Successive vertical oligopolies without pure upstream competitors 2

The impact on consumer welfare of service-based competition when facility-based competition is in place

It is often argued that, when facility-based competition is in place, the introduction of servicebased firms should enhance the competitive pressure on the downstream market. These service-based firms can have a positive impact on the consumers’ surplus, first, by further differentiating the product, and second, by increasing the competitive pressure on the final market. For instance, Bourreau and Do˘gan (2006) show that consumers’ surplus increases when the unbundling tariff decreases, namely, consumers benefit from an increase in servicebased competition. As a result, refusals to deal with service-based firms are often considered as anti-competitive behaviors. More precisely, refusals to supply at the facility level are viewed as an instrument for vertical foreclosure. Though the direct effect of introducing service-based firms seems to be clearly understood, there may also be indirect effects. First, if the wholesale good is priced above marginal cost, then the service-based firms are high-cost competitors on the downstream market, which may have an adverse impact on downstream competitive conditions.1 Second, the mere presence of these firms may change the downstream behavior of their suppliers in a non-trivial way. Given that there are, at least, three effects (a direct effect and two indirect effects) at work, it is useful to set up a model to disentangle them. The following analysis relies on a simplified version of H¨offler and Schmidt (2007).

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Integrated firm 1

Upstream Market

Upstream good

Integrated firm 2

w1

Upstream good Firm d

Downstream good

Downstream good

Downstream good

Downstream Market p1

pd

p2

End-Users

Figure 1: A simplified version of H¨offler and Schmidt (2007).

2.1

A simplified version of H¨ offler and Schmidt (2007)

The structure of the model is depicted in Figure 1. There are two facility-based firms, 1 and 2 and a service-based firm, d. For simplicity, we assume that only firm 1 can supply firm d on the wholesale market at some price w1 .2 All costs are normalized to zero for simplicity. This is without loss of generality in a linear demand framework, as long as marginal costs are constant. Firms compete in prices on the downstream market. The representative consumer maximizes the following quadratic utility function: " # 2 (q + q + q ) 1 n 1 2 d U = q1 + q2 + qd − (q1 + q2 + qd )2 − q 2 + q22 + qd2 − . 2 2(1 + γ) 1 3

(1)

Parameter γ is a substitutability index. When γ = 0, the final goods are totally unrelated, and firms are local monopolies. On the other hand, when γ = ∞, the downstream good is homogenous, and firms compete `a la Bertrand. Assume first that service-based firm d is not active on the final market. Solving the 1

In a regulated environment, assuming that the regulator is able to implement marginal cost access pricing, this effect is limited. However, as we show later on, access regulation can have various impacts, depending on the way it is implemented (e.g., wholesale price cap vs. retail minus X regulation). 2 This assumption is discussed extensively in the subsequent sections.

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representative consumer’s optimization problem, we obtain the following downstream demand functions: 1+γ Di = 3 + 2γ

  pi − pj 1 − pi − γ , i 6= j ∈ {1, 2}. 3

(2)

The solution for the consumer’s program when firm d supplies a positive quantity on the final market can be written as: 1 Di = 3

   p1 + p2 + pd 1 − pi − γ pi − , i ∈ {1, 2, d}. 3

(3)

Notice that in both cases, the demand faced by a firm is decreasing in its own price and increasing in its rivals’ prices. Clearly, this linear specification of the demand functions entails a loss of generality. In particular, it implies that a firm loses the same number of customers when it increases its price, whatever the initial level of its price, and whatever the prices of its rivals. Nevertheless, these demand functions enable us to shed some light on the different effects at work. They also allow us to derive interesting comparative statics results on the impact of downstream differentiation. The sequence of decision-making is as follows: Stage 1: Integrated firm 1 sets its upstream price w1 . Stage 2: Firms 1, 2 and d set their downstream prices simultaneously.

2.2

The impact of service-based entry on downstream prices and consumers surplus

We want to compare the downstream prices in the situation in which only integrated firms are active on the downstream market, to a situation in which the three firms supply a positive quantity on the final market. In the first situation, the profit of firm i ∈ {1, 2} is given by πi = pi Di . In the second case, the three firms earn: π1 = p1 D1 + w1 Dd

(4)

π 2 = p2 D 2

(5)

πd = (pd − w1 )Dd

(6)

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Two things are worth noticing here. First, integrated firm 1 earns some positive upstream profits, which should affect its pricing incentives on the downstream market. Second, the marginal cost of firm d is affected by the upstream price set by firm 1. The two-firm game has a unique Nash equilibrium given by: p1 = p2 =

3 . 6+γ

(7)

As intuition suggests, these equilibrium prices are decreasing in γ, the substitutability parameter. After some algebra, one shows easily that the equilibrium of the three-firm game can be written as:3 9(4 + 3γ)(18 + 21γ + 5γ 2 ) , 2 (648 + 1296γ + 909γ 2 + 249γ 3 + 20γ 4 ) 3 (216 + 378γ + 213γ 2 + 35γ 3 ) = , 2 (648 + 1296γ + 909γ 2 + 249γ 3 + 20γ 4 ) 3(3 + γ)(108 + 150γ + 55γ 2 ) = . 2 (648 + 1296γ + 909γ 2 + 249γ 3 + 20γ 4 )

p1 =

(8)

p2

(9)

p3

(10)

Comparing prices in the two situations, we obtain three results of interest. First, the downstream price of firm 2 always decreases following firm d’s entry. Second, the downstream price of firm 1, the wholesale supplier, is always larger when the pure downstream firm is active. Last, provided that parameter γ is sufficiently small, the trade-weighted average downstream price increases when firm d enters into the industry. In other words, in this standard linear-demand model, the conventional wisdom is sometimes proven wrong: the entry of a service-based firm can raise prices. To see why, it is worth decomposing the impact of service-based entry into three effects:4 • A direct pro-competitive effect. The service-based operator threatens the demand of 3

We omit the equilibrium value of w1 . These are the so-called first round effects. Actually, there are also second, third, ..., nth round effects, due to the strategic complementarity between downstream prices. To see this, notice that, in this linear-demand framework with constant marginal costs, prices are always strategic complements: when a firm increases its downstream price, this induces its rivals to increase their prices as well. Heuristically, when a service-based firm enters into the downstream market, the best-responses of the two integrated firms are affected, which leads them to change their prices: these are the first-round effects, which are described in the next paragraph. Following this, the integrated firms are led to further price changes, since downstream prices are strategic complements: these are the second, third, ... nth round effects. This process of price adjustments carries on until a new equilibrium is reached. 4

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the facility-based operators, which react by lowering their prices. • A ‘raise your rival’s cost’ effect. The pure downstream firm does not compete on a level playing field on the downstream market, since the wholesale product is priced above the marginal cost. • A softening effect. When integrated firm 1 increases its downstream price, some of the customers it loses will purchase from pure downstream firm d, which raises the upstream demand. Put differently, integrated firm 1 internalizes the fact that any customer lost on the downstream market can be recovered on the upstream market. Therefore it is induced to charge higher downstream prices when the service-based firm enters. This effect will play an important role in section 4. It turns out that the raise your rival’s cost and the softening effects dominate the procompetitive effect when γ is small enough. When this is the case, the downstream price index increases after pure downstream firm d has entered. In other words, the entry of a service-based competitor can be used by integrated firms as a tool to soften competition on the downstream market. The benefits from service-based competition should not be taken for granted. It is worth noticing that this result is by no means standard, as it comes directly from the softening effect. In a single-market model of price competition with differentiated products, the entry of a new competitor always decreases the price level.5 A caveat is in order here. With our linear demand specification, it turns out that, for the upstream supplier, the softening effect and the raise your rival’s cost effect always dominate the pro-competitive effect, implying that integrated firm 1’s price is always larger when firm d is active. A priori, there is no reason why this result should still hold with other demand specifications. First, it may well be that the pro-competitive effect dominates the softening effect and the raise your rival’s cost effect. Second, if the degree of strategic complementarity between downstream prices is sufficiently large, namely, if a firm reacts strongly when one of its rivals changes its price, one may obtain the following mechanism. Following firm d’s entry, firm 1 increases its price, while firm 2 decreases its price due to the pro-competitive effect. Since downstream prices are strategic complements, firm 1 best-responds by decreasing its price. If downstream prices are sufficiently strategic complements, the industry may attain a 5

Provided that the downstream Nash equilibrium is stable and downstream prices are strategic complements, which is standard.

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new equilibrium, in which the upstream supplier’s downstream price is lower than previously. So far, we have focused on the impact of service-based entry on downstream prices. We have seen that the price index may well increase following firm d’s entry, which should affect consumers surplus negatively. However, the entry of a service-based competitor also brings about some gains to the consumers, in terms of differentiation. To evaluate this trade-off between higher downstream prices and higher downstream variety, it is natural to use the utility function of the representative consumer, as defined in equation (1). It turns out that, in this linear demand framework, the variety effect always dominates the anti-competitive effect.6 Let us now focus on the industry profit. The integrated firm which supplies the wholesale market benefits from service-based entry as long as the substitutability parameter is not too large (i.e., γ ≤ 26.772). We restrict now the analysis to such a range of values for γ otherwise, there would never be any entry of a service-based firm. The profit of the servicebased entrant obviously increases. The impact on the profit of the facility-based firm which does not supply the wholesale market is ambiguous a priori: On the one hand, it benefits from the softening effect; on the other hand, it suffers from the pro-competitive effect. In this linear demand framework, the latter effect always dominates the former. Overall, it turns out that, in this linear demand framework, the entry of a retailer always increases the industry profit. Overall, welfare always increases following the entry of the service-based firm.

2.3

The impact of wholesale regulation

H¨offler and Schmidt provide also an interesting result on the impact of so-called retail minus X regulations. These regulations require that the wholesale supplier charges an upstream price which does not exceed its downstream price minus the retail cost. In the terms of our model, such a constraint translates into w1 ≤ p1 , since downstream costs are normalized to zero. H¨offler and Schmidt show that the upstream supplier may be tempted to use them as a commitment to charge a high downstream price, which would have strongly anti-competitive effects. Put differently, an integrated firm may prefer to increase its downstream price, rather 6

Therefore, consumers are always better off after service-based entry. This result is not general, though. Using a spatial competition model ` a la Salop (1979), H¨offler and Schmidt (2007) show that consumers can lose from service-based entry if transport costs are large enough.

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than decreasing its upstream price in order to satisfy the retail minus X regulation. H¨offler and Schmidt show that, provided that the substitutability parameter is large enough, the introduction of a retail minus X regulation increases the prices of the integrated firms. By contrast, if the regulator mandates marginal cost pricing on the wholesale market, then, the softening effect and the raise your rival’s cost effect vanish. With this type of regulation, the entry of a service-based competitor always benefits consumers through lower prices.

2.4

Limitations

Two caveats are in order here. First, the above analysis is not valid if firms compete a` la Cournot on the retail market. Under Cournot competition, the strategic variable of a firm is the quantity it supplies on the downstream market, not the price it charges. Each firm dumps a quantity in the market, and the final price is determined by an inverse demand function, P (Q), where Q denotes the sum of the three firms’ quantities. It can be shown that there is no softening effect under Cournot competition: an integrated firm can no longer impact the pure downstream firm’s quantity through its downstream action (since quantities are chosen simultaneously). When firms compete in quantities, the entry of a service-based competitor always decreases downstream prices, provided that the inverse demand function is concave. Second, the market structure is completely exogenous: neither the wholesale prices, nor the identities of the wholesale suppliers are endogenously determined. This leads us to ask two related questions. First, assume that a new service-based competitor shows up; do facility-based firms want to supply it on the wholesale market, or do they prefer foreclosing it completely? Second, assuming that somebody actually wants to supply this competitor, will tough competition drive upstream prices to the marginal cost? These issues are dealt with in the next two sections.

3

Complete foreclosure: Does an integrated firm want to supply a potential competitor?

This section aims at answering the following question. Consider an industry with some facility-based firms and some service-based firms. Assume that a potential service-based

12

entrant shows up. Does one of the integrated firms actually want to supply this entrant on the wholesale market? If the answer is no, we will say that the service-based competitor is completely foreclosed from the downstream market. Before starting the formal analysis, it is worth emphasizing the conceptual difficulties involved when dealing with complete foreclosure. To know whether or not the entrant will be completely foreclosed, one has to know how the demand functions are modified when an additional downstream firm is added. A lot of things may change: the total demand may increase, the price elasticities of the demand functions may be affected, the entrant may threaten more one of the integrated firms, . . . To assess the potential for complete foreclosure in a market, all these facts have to be known. To begin with, we analyze a simple market structure, in which the upstream market is monopolized by a vertically integrated incumbent. This will allow us to get some insights on the role of the mode of competition (Bertrand or Cournot). We then turn to the more complicated situation, in which the wholesale market is populated by several vertically integrated firms.

3.1

Complete foreclosure with a monopolized wholesale market

The market structure we are considering is depicted in Figure 2. There are two firms: a facility-based incumbent 1, and a service-based entrant d. The incumbent can decide to supply firm d on the wholesale market at price w1 . Alternatively, it can decide to foreclose the entrant completely. Once again, for simplicity, we normalize all costs to zero. The timing is the same as in the H¨offler and Schmidt (2007) model: first, the incumbent makes its upstream offer, second, both firms compete in the final market. Assume first that firms compete in prices with differentiated products on the final market, with downstream prices p1 and pd . Denote by Di (p1 , pd ) the demand which addresses to firm i ∈ {1, d} when both firms are active in the final market. Denote by Dm (p1 ) the incumbent’s downstream demand when it forecloses the entrant completely, and define pm the incumbent’s downstream monopoly price. We show that, in this price competition framework, the incumbent prefers to supply the entrant. Assume that the incumbent sets an upstream price w1 = pm and a downstream price equal to pm , namely, the incumbent charges its downstream monopoly price on both markets. The entrant best responds by setting some

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Incumbent 1

Upstream good

Upstream Market

w1

Downstream firm d

Downstream good

Downstream good

Downstream Market p1

pd End-Users

Figure 2: Complete foreclosure with a monopolized wholesale market.

downstream price pd ≥ pm . Then, the incumbent’s profit is given by: π1 = pm D1 (pm , pd ) + pm Dd (pm , pd ) = pm (D1 (pm , pd ) + Dd (pm , pd )) .

(11)

Assuming that the entrant brings new consumers into the market, it must be that D1 (pm , pd )+ Dd (pm , pd ) > Dm (pm ). Therefore, the incumbent can make more profits if it supplies the entrant. The intuition is clear: by imposing a high enough upstream price, the incumbent can prevent the entrant from being a tough competitor. Therefore, its price-cost margins are not eroded. Besides, it extracts some additional profits from the consumers which are brought into the market by firm d.7,8 Unfortunately, this encouraging result is not robust to changes in the mode of competition. 7

Actually, even in a mature market, it is not clear that the incumbent wants to exclude the entrant from the downstream market when firms compete in prices. With a simple model of price competition in the Hotelling segment, in which the market is fully covered in the sense that all consumers buy the good at equilibrium, assuming that the retail market is covered, it can be shown that complete foreclosure does not arise in equilibrium, provided that transport costs and utility derived from the final good are not too high. 8 The impact of firm d’s entry on final prices can be analyzed as in section 2: prices decrease if the pro-competitive effect dominates the raise your rival’s cost effect and the softening effect.

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Consider for instance that firms compete a` la Cournot on the retail market. Assume that the inverse demand function is given by P = 1 − Q, where Q = q1 + qd denotes the total quantity supplied on the retail market and P denotes the downstream price. The incumbent’s and the entrant’s profits are given by P q1 + w1 qd and (P − w1 )qd respectively. Solving for the Nash equilibrium on the downstream market, we get: q1 = (1 + w)/3 and qE = (1 − 2w)/3. Substituting these expressions into firm 1’s profit, we obtain π1 = (1 + 5w(1 − w)) /9. Maximizing this expression subject to qd ≥ 0, we get w = 1/2, an upstream price which leads the entrant to produce exactly 0 in equilibrium. In other words, the incumbent sets a wholesale price such that the entrant serves no customers. Actually, it can be shown, as in Foros (2004), that the incumbent chooses to exclude the entrant from the retail market whenever the latter firm is less efficient. Put differently, under quantity competition, if a service-based firm wants to enter, it has to provide higher-quality products on the retail market, or, almost equivalently, its cost function has to be lower than the incumbent’s. The results of this section can be summarized as follows. When the wholesale market is monopolized, if a service-based firm wants to enter, it has to add some value to the wholesale good. This may be done by bringing new customers into the market (see equation (11)), by further differentiating the wholesale product (as in footnote 7), by producing a high quality good, or by being more efficient than the incumbent (as in Foros (2004)). From the viewpoint of welfare, assuming linear demands in the case of price competition with differentiated products, the industry profit increases, as well as the surplus of consumers (this may not be always true with other specifications of the demand system.

3.2

Complete foreclosure with an oligopolistic wholesale market

We have just seen that the theoretical literature provides mixed results on complete foreclosure in the simple two-firm case. We now show that things get even more complicated when several facility-based firms are present, as in Figure 3. In particular, we will see that, even under price competition with differentiated products, a complete foreclosure equilibrium can exist. One may be tempted to apply the reasoning we made before, to deal with complete foreclosure under price competition. When an integrated firm starts supplying the upstream market, it can charge a large enough upstream price, in order to soften the downstream competition, and capture most of the profits earned by the pure downstream firm. However this reasoning misses an important point: when the service-based firm enters the 15

downstream market, it threatens the integrated firm which does not supply the upstream market. This latter firm is therefore induced to lower its downstream price, which affects the profit of the upstream supplier negatively. At the end of the day, the upstream supplier obtains some positive upstream profits, but on the other hand, downstream competition may become tougher. This example shows how important it is to understand how the demand patterns are modified when a new firm enters the retail market. Ordover and Shaffer (2006) tackle this issue.9 The remaining of this section summarizes the main insights of their paper. The market structure is depicted in Figure 3. There are two integrated firms, 1 and 2, and a pure downstream firm d. Again, we assume price competition with differentiated products on the retail market. Integrated firms compete in linear prices on the wholesale market.10 Some asymmetry is assumed between facility-based firms, namely, one of these firms has a larger pre-entry consumer base than the other. The novelty of this paper is that the entry of a service-based entrant can affect the demand patterns in two different ways. When the pure downstream firm enters the market, it steals customers from both integrated firms. To go further, it is necessary to make assumptions on which of the two integrated firms suffers more from this cannibalization effect. Under proportional cannibalization, the sales of the entrant’s product cannibalize the sales of the incumbents’ products in proportion to the incumbents’ pre-entry market shares. By contrast, under own-supplier cannibalization, the entrant’s sales cannibalize only the sales of its upstream supplier. To clarify, consider the following numerical example. Assume that, before entry, and if retail prices were the same, the product of firm 1 would be chosen by 70% of the consumers, while the product of firm 2 would be chosen by 30% of the consumers. Assume further that, after entry, the entrant would capture 10% of the market if all downstream prices were the same. Then, under proportional cannibalization, if all downstream prices were the same, the market share of firm 1 would decrease from 70% to 63%, while the market share of firm 2 would decrease from 30% to 27%. By contrast, under own-supplier cannibalization, if the entrant were supplied by firm 1, the market share of firm 1 would decrease from 70% to 60%, while the market share of firm 2 would remain unchanged.11 9

See also Brito and Pereira (2006) for similar insights. As explained later on, there may be some product differentiation on the upstream market. More precisely, the identity of the upstream supplier may have an impact on the entrant’s positioning on the downstream market. 11 Ordover and Shaffer (2006) do not consider the scenario, in which the entrant cannibalizes only the 10

16

Integrated firm 1

Upstream Market

Upstream good

Integrated firm 2

w1

w2

Upstream good

Firm d

Downstream good

Downstream good

Downstream good

Downstream Market p1

pd

p2

End-Users

Figure 3: Complete foreclosure with two facility-based firms.

The interpretation for these two polar assumptions is the following. Assume that the upstream good is differentiated, and assume further that this differentiation translates into the downstream market. Then, if the entrant purchases from firm 1, its product will be closer to firm 1’s product: this is own-supplier cannibalization. On the other hand, if the upstream good is homogenous, then, there is no reason why the entrant should be closer to one of the two firms: this is proportional cannibalization. Ordover and Shaffer (2006) obtain a first result under proportional cannibalization: there is no complete foreclosure equilibrium. Intuitively, starting from a complete foreclosure situation, the smaller facility-based firm has incentives to deviate and supply the entrant, which will steal more consumers from the bigger firm. Some of the profits made on these cannibalized consumers will then be passed through to the upstream supplier. There is also an adverse price effect: the integrated firm which does not supply the wholesale market decreases its downstream price. However, this latter effect is always dominated. As we have just seen, complete foreclosure never arises in equilibrium, since the smaller integrated firm has a strictly profitable deviation. It can then be shown that, under proportional cannibalization, the only equilibrium is the competitive outcome on the wholesale demand of the integrated firm which does not supply the upstream market.

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market. Intuitively, once the smaller firm starts supplying the wholesale market, the integrated firms keep undercutting12 each other until the marginal cost is attained, just as in a standard single-market Bertrand competition model.13 In other words, firms play a prisoner’s dilemma: they would like to commit not to supply the entrant ex ante, in order to avoid tough upstream competition. At the end of the day, they end up with zero upstream profit, and a more competitive retail market. The results under own-supplier cannibalization are less encouraging: there exists a complete foreclosure equilibrium. When a facility-based firm starts supplying the service-based entrant, it obviously secures some upstream profits. On the other hand, it loses many customers and its downstream profits shrink. Besides, there is also a negative price effect: the other facility-based firm will lower its downstream price. At the end of the day, the two negative effects dominate the positive one, and an integrated firm is worse off when it supplies the service-based entrant. For the same reasons, there is no equilibrium in which the entrant is supplied. Basically, the upstream supplier prefers to deviate and exit the upstream market, rather than losing downstream market shares. Let us summarize the results we get in this linear demand framework. Under proportional cannibalization, wholesale competition leads to the perfectly competitive outcome on the upstream market. By contrast, under own-supplier cannibalization, at the only upstream equilibrium, the service-based entrant is excluded from the retail market. Obviously, the choice of linear demands entails a loss of generality here: there exists probably a set of demand functions such that the service-based firm is excluded even if it enters under proportional cannibalization. Similarly, there exists probably another set of demand functions such that the entrant manages to get access to the upstream good under own-supplier cannibalization. Broadly speaking, with more general demands, the above results could be rephrased as follows: the entrant is more likely to obtain wholesale access if it cannibalizes the integrated firms proportionally. Therefore, to assess whether or not the pure downstream firm will be completely foreclosed, it is crucial to predict whether it will enter under proportional or own-supplier cannibalization. As a last step, Ordover and Shaffer (2006) endogenize the entrant’s product positioning. 12 13

By undercutting, we mean setting a slightly lower price. The next section challenges that view.

18

This allows them to derive interesting policy implications. The modelling strategy is the following. The wholesale products are slightly differentiated, and this upstream differentiation translates into the downstream market. If the entrant does not make any effort, the good it produces remains a close substitute to the good produced by its wholesale supplier. In the terminology we used before, if no effort is made, the service-based firm enters under ownsupplier cannibalization. The entrant can also make an effort, or equivalently, pay a fixed cost, which allows it to further differentiate its retail product. If it does so, the service-based firm enters under proportional cannibalization. Clearly, if the entrant can commit ex ante to its positioning, it makes the effort and chooses proportional cannibalization. Therefore, it is supplied in equilibrium.14 On the other hand, if it cannot commit to further differentiate its product, both integrated firms anticipate that they will suffer from own-supplier cannibalization if they start supplying the entrant. As a result, the service-based firm is completely foreclosed in equilibrium.15 This result has strong policy implications. It may be welfare-improving to allow wholesale contracts, which would seem anti-competitive a priori. In particular, the regulator may want to allow the servicebased firm to sign a non-compete agreement with its wholesale supplier. In such a contract, the entrant would commit no to target the downstream customers of its upstream supplier. This would prevent facility-based firms from foreclosing the entrant completely. Finally, in this paper, if there is no complete foreclosure equilibrium, then the only possible outcome is the perfect competition outcome. In other words, partial foreclosure never arises: the entrant is either foreclosed completely, or supplied at marginal cost. The next section challenges the generality of this result. The welfare analysis under proportional cannibalization is quite straightforward. There is no complete foreclosure and the service-based firm is served at the wholesale marginal cost. The number of varieties available increases and there is a downward pressure on final prices: consumers are better off following the entry of the service-based firm. Integrated firms, by contrast, suffer from this entry. Under own-supplier cannibalization, the welfare analysis is also straightforward since there is complete foreclosure of the service-based entrant. Therefore, under standard regularity assumptions, total welfare always increases following 14

Provided that the fixed differentiation cost is not too high. Again, some assumptions on the fixed differentiation cost and the level of downstream substitutability are needed. 15

19

the entry of a pure retailer.

4

Partial foreclosure

In an environment with several facility-based firms, the conventional wisdom is the following. If an integrated firm supplies the upstream market at a price above the marginal cost, then other facility-based firms have incentives to set a slightly lower price in order to capture the wholesale profit. In other words, provided that somebody is already supplying the wholesale market, this market can be analyzed as an isolated market. It follows that the Bertrand result applies: firms should keep undercutting each other until the marginal cost is attained. This section shows that this reasoning misses an important point. Broadly speaking, competition between two vertically integrated structures on the upstream market is fundamentally different from competition between pure upstream firms, or from competition between an integrated firm and a pure upstream firm. To understand the incentives of integrated firms to undercut each other on the upstream market, it is crucial to study the related retail market: a standard single market analysis can be misleading.

4.1

The model

This section relies on Bourreau, Hombert, Pouyet, and Schutz (2007). The market structure is the same as in Ordover and Shaffer (2006) (see Figure 3). There are two integrated firms, 1 and 2, and a pure downstream firm d. In the first stage, facility-based firms compete in linear tariffs, w1 and w2 , on the wholesale market. For expositional purposes, we assume that complete foreclosure equilibria do not exist: at least one integrated firm wants to make an upstream offer. This seems to be a sensible assumption with price competition and product differentiation, as shown in section 3. [This assumption could also be justified on the ground that there exists a regulated wholesale offer that firm d can always use to secure its demand for the upstream good at the regulated price.] In the second stage of the game, firms compete in prices with differentiated products on the downstream market. Contrary to Ordover and Shaffer (2006), we rule out any asymmetry between firms on the downstream market. This implies that, if downstream prices were the same, each firm’s market share would be equal to one third. Again, all costs are normalized to zero for simplicity. The notations are the same as in section 2. The firms’ downstream prices are denoted by 20

p1 , p2 and pd . Their downstream demands are D1 , D2 and Dd .16 To fix ideas, assume that firm 1 supplies the upstream market at price w1 > 0. Then, the profits are given by:

4.2

π1 = p1 D1 + w1 Dd

(12)

π 2 = p2 D 2

(13)

πd = (pd − w1 )Dd .

(14)

The softening effect and its impact on the incentives to undercut

The key effect in this model can be isolated by inspecting the first order conditions on the downstream market: ∂π1 ∂D1 ∂Dd = D1 + p1 + w1 = 0, ∂p1 ∂p1 ∂p1 ∂π2 ∂D2 = D2 + p2 + 0 = 0. ∂p2 ∂p2

(15)

Comparing these two expressions, we see that there is an additional term in firm 1’s first order condition. This term is strictly positive, which implies that firm 1 has more incentives to raise its downstream price than its integrated rival. This is the softening effect, which we already mentioned in section 2. When an integrated firm supplies the upstream market, it internalizes the fact that any customers lost on the retail market can be recovered on the wholesale market. This implies that, for any given upstream price w1 > 0, at the downstream market equilibrium, the wholesale supplier 1 charges a larger downstream price than its integrated rival 2. Integrated firm 2, which does not supply the wholesale market, benefits from the softening effect. Intuitively, firm 2 is better off when its rivals charge high downstream prices, as competition on the downstream market is thus relaxed. This implies that, for any given value of w1 , firm 2 earns strictly larger downstream profits than firm 1. With this in mind, the comparison between the total profits of the two facility-based firms becomes ambiguous. On the one hand, firm 1 earns strictly positive upstream profits. On the other hand, firm 2 benefits from the softening effect, and earns large downstream profits. It may well be the case 16

Contrary to section 2, we do not need to specify these demand functions.

21

that the latter effect dominates the former, implying that, surprisingly, the integrated firm which supplies the upstream market earns lower total profits than its integrated rival which is inactive on the upstream market. Besides, since we have ruled out complete foreclosure by assumption, the upstream supplier does not want to exit the wholesale market. This result has clear implications in terms of incentives to undercut on the upstream market. Assume that integrated firm 1 supplies the upstream market at w1 , and denote by π1 the profit it earns in this case. The question is whether firm 2 wants to set w1 − , with  small enough, to capture the wholesale market. Put differently, the question is whether integrated firm 2 wants to replace firm 1. If it does so, it earns (almost) π1 . To answer this question, we need to compare the profit of firm 2 before undercutting, π2 , with the profit of firm 2 after undercutting, π1 . And we have just seen that this comparison is ambiguous. Intuitively, when firm 2 undercuts the wholesale market, it captures the upstream profits at the cost of losing the softening effect. There is a tradeoff between stealing the upstream profits and making the integrated rival more aggressive on the downstream market. If the softening effect is strong enough, then, firm 2 does not want to undercut: a clear departure from the standard single-market Bertrand competition. Due to this tradeoff, we may obtain equilibria on the upstream market which are strikingly non-competitive. For instance, define wm as the upstream price that an integrated firm would charge if its integrated rival made no upstream offer.17 wm is the monopoly upstream price. If the softening effect is strong enough, then, there exists an equilibrium in which an integrated firm sets its monopoly price wm , while the other integrated firm makes no upstream offer. In other words, the monopoly outcome may persist even under the threat of competition. It becomes clear that a simple single-market analysis of the wholesale market can be misleading. Taken on a stand-alone basis, our upstream market has all the characteristics which traditionally lead to the perfect competition outcome. Yet, to assess its competitiveness, one has to analyze the factors which determine the softening effect. The intensity of downstream competition is one such factor. Assume that the downstream demand functions are given by the following expression: 

p1 + p2 + p d Di = 1 − pi − γ pi − 3 17

Since we have ruled out complete foreclosure, wm exists.

22

 ,

(16)

as in section 2. Again, γ is positively related to the degree of downstream substitutability. A simple comparative statics exercise shows that there exists a threshold γ 0 , such that noncompetitive equilibria exist if, and only if, γ ≥ γ 0 . Downstream competition has to be sufficiently intense for non-competitive equilibria to exist. Intuitively, if downstream products are almost unrelated (γ low), then, the softening effect vanishes: an increase in firm 1’s downstream price has basically no impact on firm d’s demand, hence, no impact on the upstream demand. In this case, integrated firms have strong incentives to undercut the upstream market, which ends up being competitive. Interestingly, this implies that there is a tension between downstream and upstream competitiveness. When downstream competition is soft, upstream competition should be intense, and vice versa. Therefore, potential servicebased entrants have additional incentives to offer large downstream differentiation, in order to avoid being partially foreclosed. Let us briefly consider the welfare analysis in this case of partial foreclosure. Consumers’ surplus (respectively, the industry’s profit) is larger (respectively, smaller) in the competitive equilibrium than in the non-competitive equilibrium. As another extension, let us assume now that the service-based firm is perfectly competitive, i.e., it always price its downstream product at its marginal cost. Then, we obtain that a non-competitive equilibrium never exists. A conclusion might be that when the pressure exerted by the service-based firms is strong, the risk of the emergence of a non-competitive equilibrium becomes negligible.

4.3

Policy implications

This model has three regulatory implications. First, a sufficiently low price cap on the wholesale market, can restore head-to-head upstream competition. At the only equilibrium, the price cap is not binding, and the wholesale good is priced at marginal cost. The intuition goes as follows. The higher the upstream price, the stronger the softening effect: when the upstream supplier raises its downstream price, it increases its upstream profits a lot if the upstream margin is large. If the regulator imposes a wholesale price cap, it decreases the intensity of the softening effect, which strengthens the incentives to undercut. Provided that the price cap is sufficiently low, the best response of the integrated firm which does not supply the upstream market is to undercut the upstream supplier. Stated differently, by putting a lid on the wholesale offer, the regulator can limit the intensity of the softening effect, thereby 23

restoring the incentives to undercut. The following heuristical reasoning is useful to grasp the intuition. Initially, the entrant is excluded from the downstream market. One of the two integrated firms starts supplying it by setting a price equal to the price cap. Assuming that the price cap is sufficiently low, the softening effect is weak, and the rival integrated firm chooses to undercut. This process carries on until the marginal cost is attained. The price cap does have an impact on the upstream outcome, although it is not binding in equilibrium. Possibilities of bypassing the upstream market can also act as an upstream price cap. For instance, if the cost of building a network or the price of a spectrum license decrease, firm d may be able to threaten firm 1 and 2 to enter as a facility-based competitor if the wholesale price is too high. Again, this would put a lid on the wholesale offer, which may restore the competitiveness of the wholesale market. Last, vertical separation of one of the integrated firms, or, alternatively, the entry of a pure upstream competitor, can make the upstream market competitive by breaking down the interactions between the two markets.18 Two criticisms can be made. First, the main result of the paper, namely, the existence of non-competitive upstream equilibria, is not robust to changes in the mode of competition. More precisely, the softening effect vanishes when firms compete `a la Cournot, since the upstream supplier can no longer influence firm d’s downstream quantity through its downstream action. Second, Bourreau, Hombert, Pouyet, and Schutz (2007) provide no results on the role of the market structure. Several questions remain unanswered. What is the impact of having more downstream firms? More facility-based firms? Relatedly, given the effects described above, one may wonder which market structure will emerge. In particular, one may wonder whether service-based firms are more likely to enter than facility-based firms.

18

This result can be proven, provided that downstream prices are strategic complements.

24

Part II

Successive vertical oligopolies with pure upstream competitors 5

Market analysis in successive vertical oligopolies

In the previous sections, the wholesale market was always assumed to have a strongly competitive market structure. In particular, firms competed in prices with homogenous products on the upstream market. One may wonder how our insights are modified when imperfect competition is added on the upstream market. In this section, we review the two-stage Cournot oligopolies model, which was initially proposed by Salinger (1988).

5.1

The two-stage Cournot oligopolies model

There are M (M ≥ 2) independent upstream firms that produce a homogenous good and compete in quantities. Each upstream firm has constant marginal cost cu . There are N (N ≥ 2) downstream firms that serve the final consumers. Downstream firms use the upstream good to produce the final product. Downstream firms produce a homogenous good at constant marginal cost cd and compete in quantities. Downstream demand is characterized by the inverse demand function P (Q), where Q is the total production of downstream good. Denote by w and p the wholesale price and the retail price, respectively. The fact that upstream firms are not active on the downstream market should be understood in a loose sense. A pure upstream firm may produce a final good in another industry. Hence, the analysis would still be relevant if the other downstream markets in which pure upstream firms are vertically integrated and the downstream market of the industry described in the model are sufficiently ‘independent’. We sketch the main result of this model when there is no facility-based firm. The profit of a downstream firm n is given by: πd,n = (P (Q) − w − cd )qn ,

25

where qn denotes the chosen quantity, P (Q) the retail price, and w + c the total marginal cost, comprising both own marginal product cost c and the wholesale price w. The optimal quantity satisfies the first-order condition: P (Q) − w − c + qn P 0 (Q)(1 + λd ) = 0,

(17)

where λd denotes the conjectural variation parameter for the downstream market. The conjectural variation parameter λd parameterizes the mode of competition at stake in the downstream market. Lower values of λd correspond to more intense downstream competition. Note that λd = 0 yields the Cournot competition and λd = −1 the Bertrand competition. Keeping everything else constant, we have that the equilibrium retail price p will be increasing in λd ∈ [−1, 0]. Rewriting equation (17) yields the standard Lerner formula: Ld =

1 1 p − (w + c) (1 + λd ), = p N εd

(18)

where εd = −p/QP 0 (Q) is the elasticity of the downstream demand. In equilibrium, the quantity sold on the retail market must equal the quantity sold on the wholesale market. Writing w as a function of this quantity and aggregating over the first-order conditions, we obtain the upstream demand derived from the downstream market: w(Q) = P (Q) − cd +

Q 0 P (Q)(1 + λd ). N

(19)

Note that when N goes to infinity, or when λd = −1 (Bertand competition), the upstream demand is given by w(Q) = P (Q) − cd , i.e. the final demand adjusted the for downstream marginal cost. The analysis of the upstream market is analogous, once the upstream demand is obtained. The upstream Lerner formula writes as: Lu =

1 1 (1 + λu ), u Mε

(20)

w dQ where εu = − Q is the elasticity of the upstream demand. After some algebra, we obtain: dw

εu = εd δτ, 26

(21)

w , the ratio between the wholesale price and the retail price, is the dilution factor, p dp is the pass-through rate. The pass-through measures the extent to which an dw

where δ = and τ =

increase in the wholesale price w will be passed to the retail price p. Inderst and Valletti (2007) uses the two-stage Cournot oligopolies model to illustrate the interplay between upstream and downstream competition for the determination of the wholesale price. They show that standard views on market power effects may be misleading in successive oligopoly markets. Three market structures are studied in the paper: (1) there are only pure downstream and upstream firms; (2) there is one facility-based firm that does not participate in the wholesale market and pure downstream and upstream firms; (3) there is one facility-based firm that participate in the wholesale market and pure downstream and upstream firms. The reader should keep in mind that no general insights can be drawn in each settings. Many effects are at work and there is no reason to believe that some effects should always dominate the others.

5.2

Upstream and downstream competition without vertically integrated firms

This setting is a benchmark for the subsequent analysis. There are essentially two insights that can be drawn from Inderst and Valletti’s analysis: 1. In the two-stage Cournot oligopoly model without vertically integrated firms, the mode and the intensity of downstream competition have little effect on the wholesale price. 2. Second, one should not expect a robust pattern of correlations between the elasticity of downstream demand, the elasticity of upstream demand, the dilution factor and the pass-through rate. The first insight is merely technical. It stems for the fact that in two-stage Cournot oligopoly model without vertically integrated firms, the upstream and downstream markets are only indirectly linked through the wholesale price which raises equally each downstream firm’s marginal cost (see equation (18)). Yet, whether there is Bertrand or Cournot competition and/or goods are homogenous or not, roughly speaking, marginal costs affect equilibrium prices and quantities in a similar fashion. Hence, the outcome of upstream competition should not depend closely on the mode and the intensity of downstream competition. 27

We borrow an example developed by Inderst and Valletti to illustrate the second insight. Remember that the elasticity of demand on the upstream and downstream market are linked through the following equation: εu = εd δτ,

(22)

and that the upstream firms’ markup is given by the Lerner’s formula: Lu =

1 1 1 (1 + λu ), M εd δτ

(23)

where M is the number of upstream firms. Should we deduce from these equations that an exogenous increase in εd will result in a decrease in Lu through an increase in εu ? The answer is ambiguous as the exogenous shift in εd may also affect the equilibrium values of δ and τ . It is easy to exhibit a downstream demand function such that an exogenous shift in the parameters that increases εd also decreases both δ and τ . Hence, by equation (20), upstream firms’ markup may increase or decrease following an exogenous increase in εd . More allegorically, an increase in the intensity of downstream competition may not translate systematically into a fiercer upstream competition.

5.3

Upstream and downstream competition with one integrated firm and captive sales

In this setting, there is one vertically integrated firm that does not participate in the wholesale market. There are also M − 1 pure upstream suppliers and N − 1 pure downstream firms. The structure of the model is depicted in figure 4. The participation of one integrated firm introduces two effects: 1. The number of upstream suppliers decreases (from M to M − 1) so that competition is less intense on the wholesale market 2. The facility-based firm operates on the retail market at marginal cost cu + cd < w + cd , i.e. the integrated firm is more efficient than the nonintegrated downstream firms. Pure downstream firms have lower market shares than integrated firms. This tends to make the upstream demand more elastic. The elasticity of the upstream good demand can be linked unambiguously to the intensity of downstream competition. As the intensity of downstream competition increases, the market 28

U1

...

U2

UM

Wholesale market

D1

...

D2

DN

Retail market Figure 4: Successive oligopolies with one facility-based firm

share of pure downstream firms decreases (since the integrated firm is more efficient) which in turn tends to make wholesale demand more elastic. Wholesale price under vertical integration. Remember that the wholesale price is given by the Lerner formula: Lu =

1 1 (1 + λu ), u M −1ε

(24)

which can be compared to the wholesale price in the absence of vertical integration (see equation (20)). Vertical integration has two effects on the wholesale price through the number of upstream firms and the upstream good demand elasticity. First, the reduction in the number of upstream firms (from M to M − 1) that compete in the wholesale market tends to increase w. Second, vertical integration makes the upstream good demand more elastic (εu raises) which in turn decreases the upstream firms’ margin. As we have seen above, the second effect is stronger, the more intense the downstream competition and/or the less differentiated the downstream goods. Thus, when the integrated firm does not participate in the wholesale market, vertical integration tends to reduce the wholesale price if downstream competition is sufficiently intense. 29

Market power and market shares under vertical integration. Intuitively the downstream market share of the integrated firm could be an indicator of the upstream firms’ market power. The larger the integrated firm’s downstream market share, the more constrained the pure upstream firms are. One should then expect an inverse relationship between the integrated firm’s market share and the wholesale price. Yet, the analysis reveals that a high market share of the integrated firm is an indicator of: • strong downstream competition. The integrated firm is more efficient than the nonintegrated downstream firms (cu + cd < w + cd ). This means that the integrated firm has a higher (downstream) market share. Under fierce downstream competition, this cost advantage is crucial since the vertically integrated firm can (almost) serve the whole demand by undercutting its downstream rivals.19 • weak upstream competition. A less competitive wholesale market results in higher wholesale price, which strengthens the pure downstream firms’ cost disadvantage (cu + cd < w + cd ). Since pure downstream firms are less competitive, the vertically integrated firm’s downstream market share is large. This last point shows that the integrated firm’s market share and the wholesale price can increase jointly if upstream competition is weak. Our first intuition may thus be misleading.

5.4

Upstream and downstream competition when the integrated firm participates in the wholesale market

The decision of the integrated firm to participate in the wholesale market depends on a trade-off between two effects. On the one hand, participating in this market allows to earn some upstream profits. On the other hand, the upstream price decreases, which makes the downstream market more competitive. Incentives of the integrated firm to participate in the wholesale market. A first obvious observation is in order: an increase in the number of pure upstream firms makes 19

For instance, under Bertrand competition, the vertically integrated firm sets its retail price just below w + cd . The integrated firm serves the whole retail demand and pure downstream firms have zero market share.

30

participation less attractive. Intuitively, an increase in the number of pure upstream firms decreases both the wholesale and the retail prices. Inderst and Valletti informally argue that the incentives of an integrated firm to participate in the wholesale market also depends on the intensity of upstream competition. Under weak upstream competition, the integrated firm prefers not to participate in the wholesale market to protect a high margin in the retail market. Under fierce upstream competition, it becomes more profitable to participate in the wholesale market. The impact of conditions on the retail market is, in general, ambiguous. The two measures of competition on the upstream market (mode of competition and number of firms) have opposite comparative statics on the integrated firm’ incentives to participate in the wholesale market. On the one hand, if downstream competition is fierce, the reduction in the wholesale price following the entry of the integrated firm has a large negative effect on its cost advantage (cu +cd < w +cd ). This makes participation less profitable. On the other hand, if the number of pure downstream firms increases, the integrated firm’s retail market share decreases so that it may find it profitable to recoup market share through participation in the wholesale market. Wholesale price under vertical integration once participation is taken into account. Once participation is taken into account, the various effects that impact the wholesale price are difficult to disentangle. Hence, the impact of vertical integration on the wholesale price is not clear. Nevertheless, with a linear demands specification, Inderst and Valletti show unambiguously that the wholesale price is lower under vertical integration. Horizontal merger between upstream firms. The impact of a horizontal merger between pure upstream firms is also ambiguous. If a horizontal merger occurs in the wholesale market, there is fewer pure upstream suppliers. On the other hand, as was pointed above, a decrease in the number of upstream firms makes it more likely that the integrated firm enters the upstream market. As a result, a standard single-market analysis may overestimate the impact of the merger, as it would not take into account the potential entry of the integrated firm.

31

6

Consumer foreclosure

So far, we have only dealt with the issue of input foreclosure, i.e., the situation in which a pure downstream firm cannot get proper access to the upstream good. The following section analyzes consumer foreclosure, i.e. the situation in which a pure upstream firm cannot sell its good to downstream firms.20 The literature on consumer foreclosure studies models in which an incumbent upstream firm and two downstream firms can agree on contracts to deter entry of an efficient pure upstream firm. Upstream entry deterrence is motivated by the fact that the industry profit under monopoly (i.e., if there is only one upstream firm) is generally greater than under competition. Therefore, downstream firms will often be willing to sign exclusive contracts with the incumbent to limit competition and share the industry profit. Rasmusen, Ramseyer, and Wiley (1991) and Segal and Whinston (2000) analyze this effect in a model where downstream firms are independent, i.e. they do not compete for consumers. Following these papers, Fumagalli and Motta (2006) and Abito and Wright (2007) then showed how this effect can be related to the intensity of downstream competition. We first present a simplified version of Segal and Whinston (2000)’s model (which is itself based on Rasmusen, Ramseyer, and Wiley (1991)). There is an incumbent firm I and a potential entrant E in the upstream market. The incumbent and the entrant produce the upstream good at marginal cost cI and cE respectively. The entrant is more efficient than the incumbent in producing the upstream good, but faces a fixed cost of entry f . Two downstream firms D1 and D2 value the upstream good v and have a unit demand. We consider a three-stage model. In the first stage, the incumbent offers exclusive contracts to downstream firms. These contracts involve the incumbent offering some fixed compensation x to downstream firms in return of them agreeing to purchase exclusively the input from the incumbent. The downstream firms either accept or reject the offers. Let si ∈ 0, 1 denote the acceptance decision of Di and S = s1 + s2 the number of downstream firms that sign the contract (S ∈ {0, 1, 2}). In the second stage, the efficient entrant observes the downstream firms’ acceptance decision and makes its own entry decision. In the third stage, the upstream firm(s) set their wholesale prices wI and wE . The upstream firms can discriminate between downstream firms that signed the exclusive contract in stage 1 and 20

“Consumer foreclosure” is best-known in the literature as “naked exclusion”.

32

those which have not. Three different specifications are analyzed: the incumbent can make (1) simultaneous and non-discriminatory exclusive offers, (2) simultaneous and discriminatory offers and (3) sequential offers. In what follows, we assume that the fixed cost of entry is sufficiently high so that the entrant requires both downstream firms to profitably enter.21 Therefore, by signing an exclusive contract, a downstream firm makes it impossible for the entrant to achieve its minimum viable scale, thereby imposing a negative externality on the other downstream firm. In stage 3, if E has entered the upstream market, it sets its wholesale price wE slightly below cI so that both downstream firms purchase the intermediate good from E. On the other hand, if E has not, I sets its monopoly price wI = v. Its profit is then equal to πI = 2(v − cI ) − Sx. The game played by D1 and D2 in stage 1 when I makes simultaneous and non-discriminatory offers is depicted in table 1. (The upper left entry in each box is D1 ’s payoff for the corresponding strategy; the lower right is D2 ’s payoff) D2 \D1

s1 = 1 x

s1 = 0 ?

0

s2 = 1 x v − cI

x

x ?

s2 = 0 v − cI

0

Table 1: Simultaneous and non-discriminatory offers: two Nash equilibria (? symbol)

There is both an exclusion equilibrium (s1 = s2 = 1) and an entry equilibrium (s1 = s2 = 0) in this game. A coordination problem arises since E needs serving both downstream firms to enter profitably: if one downstream firm signs, E will not enter, so that it is always an equilibrium for both downstream firms to sign. There is also an entry equilibrium because I cannot set a sufficiently high compensation x. Since I cannot make discriminatory offers, it must offer the same compensation x to both downstream firms. The maximal compensation it can offer is given by πI = 2(v − cI − x) = 0, i.e. x = v − cI . This is not enough to make a downstream firm sign an exclusive contract if it anticipates that the other firm will not sign. There is no obvious reason to presume that downstream firms will coordinate either on the 21

A sufficient condition is cI < f .

33

exclusion equilibrium or on the entry equilibrium.22 Coordination failure is no longer an issue when the incumbent makes simultaneous and discriminatory offers or sequential offers. When I offers x1 and x2 to D1 and D2 respectively, the two downstream firms play the game depicted in table 2 in stage 1. D2 \D1

s1 = 1 x1

s1 = 0 ?

0

s2 = 1 x2

x2 v − cI

x1 s2 = 0 0

v − cI

Table 2: Simultaneous and discriminatory offers: one Nash equilibrium (? symbol)

There is a unique exclusion equilibrium if either x1 or x2 is greater than v − cI . Suppose for instance that x1 is slightly above v − cI and x2 is (slightly above) zero. Then, D1 is always willing to sign the exclusive contract since it maximizes its profits whatever D2 ’s strategy is.23 Since D2 observes both x1 and x2 , it should rationally anticipate that D1 will sign an exclusive contract with I and thus that entry will be deterred. D2 then accepts any offers made by the incumbent. This ‘divide and conquer’ strategy yields I a positive profit πI = 2(v − cI ) − x1 − x2 = v − cI > 0. Once sequential contracts are allowed, there is a unique exclusion equilibrium and the incumbent can exclude without any compensation. Even it receives no compensation, the first downstream firm anticipates that if it rejects the offer, the incumbent will still exclude by giving the second downstream firm a sufficient compensation. Given this, the first downstream firm will sign without compensation, and so will the second. Therefore, once sequential contracts are allowed, the incumbent gets its monopoly profit πI = 2(v − cI ). Fumagalli and Motta (2006) (thereafter FM) and Abito and Wright (2007) (thereafter AW) discusses these results when downstream firms are downstream competitors. They show how the existence of entry and exclusion equilibria can be related to the intensity of downstream competition. When downstream firms compete, their profits not only depend 22

According to Segal and Whinston (2000), the entry equilibrium is more plausible than the exclusion equilibrium. They argue that the exclusion needs strong lack of coordination among downstream firms. 23 In other words, it is a dominant strategy for D1 to sign the exclusive contract.

34

on their own wholesale price but also on the price paid by their rival. This additional externality affects the scope for entry deterrence. We focus here on the simultaneous and non-discriminatory offers’ case. Both FM and AW add to Segal and Whinston (2000)’s model a final stage in which downstream firms order the input and compete in the retail market. The key difference between the two papers is that in FM, downstream firms must pay a small but positive fixed cost ε > 0 at the end of stage 3 if they want to be active in the retail market. Under weak downstream competition, Segal and Whinston (2000)’s conclusions should still be valid: there is both an exclusion equilibrium and an entry equilibrium. Indeed, in the limit case of independent downstream monopolies, there is no additional externality. Under strong downstream competition, FM and AW derive opposite conclusions: according to FM, there is a unique entry equilibrium; while AW claim that there is a unique exclusion equilibrium. In the remainder of this section, we show that the FM’s logic applies when ε is high with respect to some measure of downstream market differentiation while the AW’s logic applies in the reverse case. In the final stage, downstream firm i (i = 1, 2) compete for consumers by setting a price pi . If both downstream firms are active in the final market, Di makes a profit equal to πi = (pi − wi )Qi (pi , pj ). Firms are symmetric. Let w = (w1 , w2 ) and denote by Pi (w) the equilibrium retail prices in stage 4. In equilibrium, Di ’s profit is then given by πi (w) = (Pi (w) − wi )Q(Pi (w), Pj (w)). If there is only one active downstream firm, say Di , it makes its monopoly profit πim (wi ) = maxp (p − wi )Q(p) (for a wholesale price wi ). Suppose that at the end of stage 1, both downstream firms sign the exclusive contract. P Entry is deterred and in stage 3, the incumbent sets its monopoly price wIm = arg maxw (w− cI )Qi (Pi (w), Pj (w)). Downstream firms make profits πi (wIm ) + x − ε. Suppose now that none of the two downstream firms sign the exclusive contract in stage 1. The efficient upstream firm then enters the market and sets its wholesale price wE slightly below cI . Downstream firms make profits πi (cI , cI ) − ε. Things are more complicated when one downstream firm signs the exclusive contract (si = 1) while the other does not (sj = 0). Suppose that firm E enters the upstream market at stage 2. Then, at stage 3, the ‘free’ downstream firm (Dj ) purchases the intermediate good to E at price wj slightly below cI : wj = cI − η where η is small. Downstream firm i purchases the intermediate good to the incumbent at price cI . The two downstream firms then decide to be active or not in the retail market. The 35

free downstream firm always participates since it operates on the retail market at a lower marginal cost cI − η < cI . If Di is also active, it gets a profit πi (cI , cI − η) + x − ε, while if it stays out of the retail market, it gets only the compensation x. There are two cases. First, if ε > πi (cI , cI − η), downstream competition is strong enough so that the cost advantage of Dj drives firm i’s profit to zero if it participates. Di thus prefers to stay out the retail market to save on ε. This in turn implies that Dj monopolizes the retail market and gets its monopoly profits πjm (cI ). Second, if ε < πi (cI , cI − η), Di and Dj are sufficiently differentiated so that Di is better-off being active in the retail market. Fumagalli and Motta (2006) assume that ε > πi (cI , cI − η). At the end of stage 1, the downstream firms thus play the game depicted in figure 3. D2 \D1

s1 = 1 m π1 (wI , wIm ) +

s1 = m π1 (cI )

x−ε

0 −ε

s2 = 1 π2 (wIm , wIm ) + x − ε

x π1 (cI , cI ) − ε

x s2 = 0 π2m (cI ) − ε

π2 (cI , cI ) − ε

Table 3: Fumagalli and Motta (2006): ε > πi (cI , cI − η), i = 1, 2

Exclusion is an equilibrium if I can offer a compensation x > πim (cI ) − πi (wIm , wIm ) ' πim (cI ). With symmetric marginal cost wIm , downstream firms get almost zero profits since downstream competition is fierce, i.e. πi (wIm , wIm ) ' 0. When entry is deterred, the inP cumbent’s profit is (wIm − cI ) Qi (Pi (wIm ), Pj (wIm )) − 2x. Therefore, an upper bound for x is (wIm − cI )Di (wIm ), wIm ) = maxw (w − cI )Qi (w, w). Yet, under standard assumptions on demand functions, it is lower than maxp (p − cI )Q(p) = πjm (cI ), the profit Dj would get if it does not sign the exclusive contract. In other words, exclusion cannot be an equilibrium. Anticipating this, I offers compensation x = 0 because it makes zero profit when E enters the upstream market. There is thus a unique entry equilibrium in which the incumbent offers zero compensation for signing exclusive contract. Abito and Wright (2007) implicitly assume that ε < πi (cI , cI − η). At the end of stage 1, the downstream firms play the game depicted in figure 4. (ε is omitted since downstream firms are always active) When downstream competition is fierce, downstream firms get almost zero profits, i.e. 36

D2 \D1

s1 = 1 π1 (wIm , wIm ) + x

s1 = 0 π1 (cI − η, cI )

s2 = 1 π2 (wIm , wIm ) + x

π2 (cI , cI − η) + x

π1 (cI , cI − η) + x

π1 (cI , cI )

s2 = 0 π2 (cI − η, cI )

π2 (cI , cI )

Table 4: Abito and Wright (2007): ε < πi (cI , cI − η), i = 1, 2

πi (wIm , wIm ) ' πi (cI − η, cI ) ' πi (cI , cI ) ' 0. Thus, omitting downstream firms’s profits in table 4, D1 and D2 play the game depicted in figure 5. It has a unique exclusion equilibrium as long as x is positive. Downstream firms benefit little from buying the upstream good at the competitive level since they would be left with almost no profits in equilibrium anyway. They can each do better by signing an exclusive contract with the incumbent and sharing the monopoly profit. Therefore, in AW’s setting, when downstream competition is fierce, there exists a unique exclusion equilibrium in which the incumbent offers a positive but small compensation for signing exclusive contract. D2 \D1

s1 = 1

s1 = 0

x

0

s2 = 1 x x

x 0

s2 = 0 0

0

Table 5: Abito and Wright (2007): ε < πi (cI , cI − η), i = 1, 2

Fumagalli and Motta (2006) and Abito and Wright (2007)’s views can be summarize as follow: • When downstream competition is fierce and the fixed cost to be active in the retail market is small but significant, entry should occur in equilibrium. • When downstream competition is fierce and the fixed cost to be active in the retail market is not significant, exclusion should occur in equilibrium.

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• When downstream competition is weak, there is both an exclusion equilibrium and an entry equilibrium. If downstream firms lack of coordination, exclusion should occur, and reciprocally.

7

Dynamic framework: Does vertical integration facilitates upstream collusion?

It is often argued that vertical integration facilitates tacit collusion on the upstream market. If this point is taken seriously, telecommunications industries should be particularly subject to tacit collusion, since all upstream firms are vertically integrated. To investigate whether this argument is correct, we start by reviewing the canonical model of tacit collusion. Then we present Nocke and White (2007)’s paper, which analyzes the impact of vertical integration in a dynamic framework.

7.1

Single-market tacit collusion

We now present an oversimplified model of single-market tacit collusion. Two firms,1 and 2, compete a` la Bertrand with homogenous products and zero marginal cost. Denoting by p the price of the cheapest firm, the demand function is given by D(p). We denote by pm (resp. πm ) the monopoly price (resp. profit) in the one-period game. Firms are assumed to play this price competition game in an infinite number of periods. Firm i ∈ {1, 2} maximizes the present discounted value of its profits: +∞ X

δ t πti ,

(25)

t=0

where πti denotes the profit earned by firm i at date t. δ is the discount factor: the larger δ, the more firms care about their future. Consider the following strategies. First, both firms play pm in stage 0. Second, at date t > 0, a firm plays pm if both firms have charged pm in all preceding periods. Otherwise, it sets a price equal to zero. These strategies are referred to as trigger strategies. If a firm undercuts the monopoly price, then its rival punishes it in all subsequent periods. Assume that both firms play the trigger strategy described above. Then both firms set the 38

monopoly price at each period, and earn half of the monopoly profit. The present discounted P t value of profits of each firm is equal to +∞ t=0 δ πm /2 = πm / (2(1 − δ)). Consider a deviation from firm 1 at date 0. If firm 1 undercuts the monopoly price, it gains immediately a payoff equal to πm . On the other hand it will be punished in all subsequent periods. Therefore, the present discounted value of its profits is equal to πm . This deviation is profitable if πm > πm /2(1 − δ), i.e., if δ < 1/2. If δ ≥ 1/2, there exists an equilibrium, sustained with trigger strategies, in which both firms charge the monopoly price at each period.24 In other words, if firms are patient enough, they are able to collude tacitely, and secure the monopoly profit of the industry. In this simple model, 1/2 is the value of the critical discount factor : this is the value of the discount factor above which firms may manage to collude tacitely. This concept is useful to understand the model of Nocke and White (2007).

7.2

Upstream collusion in successive vertical oligopolies

We now investigate whether collusive outcomes are more likely to arise in a vertically integrated industry. Nocke and White (2007) consider an industry with M upstream firms and N downstream firms. There are no integrated firms initially. Upstream firms compete in twopart tariffs with homogenous products on the upstream market. Downstream firms compete in prices or in quantities. There may be some downstream differentiation. These interactions are repeated infinitely. In this framework, a vertical integration is said to facilitate upstream collusion if it decreases the critical discount factor. A vertical integration has essentially two effects on the critical discount factor. First, following a vertical merger, pure upstream firms obtain a smaller deviation payoff. Indeed, the downstream unit of the vertically integrated firm no longer purchases its input on the upstream market. This reduces the monopoly profit on the upstream market. This effect is referred to as the outlets effect. Second, following a vertical merger, it becomes more difficult to punish a vertically integrated firm when it deviates. When a pure upstream firm deviates, it is severely punished, and it obtains zero profit in all subsequent periods, since there are no rents on the upstream market. On the other hand, when an integrated firm deviates, it still loses the upstream collusive profits in subsequent periods, but it earns positive rents on the downstream market. 24

More precisely, this is a subgame perfect equilibrium.

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Hence, the punishment is less severe for integrated firms. This is the punishment effect. Obviously, these two effects go in opposite directions. The outlets effect pushes the industry towards more collusion, while the punishment effect induces less collusion. Nocke and White (2007) show that, when the industry is initially completely unintegrated, a vertical merger reduces the critical discount factor. In other words, in an unintegrated industry, when a vertical merger takes place, the outlets effect dominates the punishment effect, and collusion becomes more likely. This seems to confirm the conventional wisdom, which states that collusion becomes more easily implementable when an industry becomes more integrated. However, Nocke and White (2007) also show that things become more complicated when a vertical merger occurs in an industry which was already partially integrated. Assume that there are initially K − 1 integrated firms in this industry, and consider the impact of a K th vertical integration. The intensity of the punishment effect is the same as before: it becomes harder to punish the newly integrated firm, since it can earn positive downstream profits anyway. For the K − 1 integrated firms, and for all pure upstream firms, the intensity of the outlets effect is not affected either: they have less incentives to cheat, since the downstream division of the newly integrated firm will never purchase the intermediate input on the upstream market. By contrast, the deviation payoff of the K th integrated firm increases, since this firm can now coordinate its upstream deviation with a downstream price cut. At the end of the day, it may well be that, in a partially integrated industry, an additional vertical integration makes collusion more difficult to implement. In order to disentangle these effects, Nocke and White (2007) propose a comparative statics exercise with linear demands (see equation (3)). They obtain the following results. When the degree of retail differentiation is sufficiently large (i.e., γ sufficiently low), the critical discount factor is minimized when all upstream firms are vertically integrated. In other words, when downstream products are weak substitutes, it is easier to collude in a fully integrated industry. By contrast, when downstream products are weakly differentiated (γ sufficiently high), the number of vertical integrations which minimize the critical discount factor is interior, namely, collusion is easier to sustain in a partially integrated industry than in a fully integrated industry. Intuitively, the degree of retail differentiation modifies essentially the incentives to deviate of the K th integrated firm. When downstream products are poor substitutes, the ability of firm K to coordinate its upstream deviation with a downstream price cut affects its deviation payoff only marginally. Therefore, the impact of the K th vertical

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integration can still be analyzed in terms of the outlets effect and the punishment effect. Since the latter effect dominates the former, this implies that the K th vertical integration facilitates collusion. To summarize, it seems that the conventional wisdom is confirmed, provided that downstream products are sufficiently differentiated.

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Salop, S. C. (1979): “Monopolistic Competition with Outside Goods,” Bell Journal of Economics, 10(1), 141–156. Segal, I. R., and M. D. Whinston (2000): “Naked Exclusion: Comment,” American Economic Review, 90(1), 296–309.

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