
    VIRGIN ATLANTIC AIRWAYS LIMITED, Plaintiff-Appellant, v. BRITISH AIRWAYS PLC, Defendant-Appellee.
    Docket No. 99-9402.
    United States Court of Appeals, Second Circuit.
    Argued Sept. 22, 2000.
    Decided July 24, 2001.
    
      Charles E. Koob, New York, NY (Joseph F. Wayland, David E. Vann, Jr., Ann Rappleye, Karen Cestari, Simpson Thacher & Bartlett, New York, NY, of counsel), for Plaintiff-Appellant.
    John L. Warden, New York, NY (John W. Dickey, Joseph E. Neuhaus, Christine C. Monterosso, Kevin R. Puvalowski, Sullivan & Cromwell, New York, NY; E. Mar-cellus Williamson, Latham & Watkins, Washington, DC, of counsel), for Defen-danb-Appellee.
    Before: CARDAMONE, MINER, and POOLER, Circuit Judges.
   CARDAMONE, Circuit Judge:

This appeal from a grant of summary judgment requires us to examine concepts underlying antitrust law. Foremost among them is the notion that competition fosters consumer welfare. Since competition, which is the very essence of business, results in lower prices for consumers, it is a positive aspect of the marketplace. Thus, what the antitrust laws are designed to protect is competitive conduct, not individual competitors. This concept is the framework upon which we decide this appeal.

Plaintiff Virgin Atlantic Airways Limited (Virgin) brings antitrust causes of action under §§ 1 and 2 of the Sherman Act, 15 U.S.C. §§ 1, 2 (1994), against defendant British Airways Pic (British Airways). It alleges that defendant, while marketing its global network of airline services, engaged in predatory business practices, pointing specifically to British Airways’ use of incentive agreements with corporate clients and travel agencies. Virgin theorizes that these agreements offered below-cost pricing and thus attracted passengers to British Airways’ transatlantic flights. Losses from pricing tickets below cost, Virgin continues, were recouped by coupling these flights with other routes on which British Airways exercised monopoly power and could charge higher fares. The net effect, according to Virgin, was to impede Virgin’s efforts to expand service from London’s Heathrow Airport to five markets in the United States: New York (John F. Kennedy airport); Los Angeles; Chicago; San Francisco; and Washington, D.C. Virgin further claims British Airways offset its losses from the incentive agreements by charging higher fares on these five transatlantic routes, until Virgin emerged as a competitor.

The United States District Court for the Southern District of New York (Cedarb-aum, J.) granted summary judgment to British Airways finding that Virgin’s claims lacked factual support. See Virgin Atl. Airways Ltd. v. British Airways PLC, 69 F.Supp.2d 571, 581, 582 (S.D.N.Y.1999). On appeal, Virgin contends the district court misunderstood the economic analysis of its key expert witness and failed to apply the correct legal standards.

After reviewing the voluminous exhibits filed under seal in this case, as well as Virgin’s letter of July 2, 2001 filed pursuant to Rule 28(j) of the Federal Rules of Appellate Procedure, we affirm the district court’s grant of summary judgment, not only agreeing that Virgin submitted insufficient proof to permit a factfinder to render a verdict in its favor, but also concluding that Virgin failed to show how British Airways’ competition harmed consumers.

BACKGROUND

History of Virgin and British Airways and the Desirability of Heathrow Flights

The British government founded British Airways as a state-owned airline in 1939, a status it maintained until its privatization in 1987. British Airways is now incorporated under English law. Virgin is also incorporated under English law, but is a newer company, having been founded by its present chairman Richard C.N. Bran-son in 1984. When it began operations, Virgin offered only a single daily flight between London’s Gatwick Airport (Gatwick) and Newark Airport in New Jersey. The United Kingdom’s Traffic Distribution Rules then in effect limited Virgin to operating flights out of Gatwiek, because only carriers operating out of Heathrow as of the rules’ 1977 effective date could continue to do so. British Airways was one such carrier. The restrictions were imposed because Heathrow was congested and the British government wished to promote the development of other London airports, such as Gatwiek.

Heathrow is considered superior to Gatwick because it has two runways and a large terminal, while Gatwick has one runway and more limited gate .facilities. Heathrow is also located near a number of major corporate offices that generate demand for international travel, while fewer corporate offices surround Gatwiek and local ground transportation is less developed. Further, since Heathrow is perceived as the premier airport in Europe, it is preferred by national flag carriers of other countries, resulting in more connecting traffic to the benefit of local hub carriers. Gatwiek, on the other hand, serves a large proportion of charter flights, which provide fewer connecting passengers.

By 1991, seven years after its founding, Virgin had added five new routes out of Gatwiek. Since Virgin wanted to operate from Heathrow, it lobbied for access and ultimately the Traffic Distribution Rules were abolished, freeing up a limited number of slots at Heathrow. Virgin promptly transferred three routes from Gatwiek: New York (JFK); Tokyo; and Los Ange-les. In making this change, it gave up peak operating times at Gatwiek for less attractive times at Heathrow. Even though it has gained access to the desired airport, Richard Branson acknowledges Virgin can never replicate British Airways’ network due to Heathrow’s limited space and the method used for assigning slots.

Allocation of Slots at Heathrow

Significant aspects of this appeal are tied to the assignment of slots, so we take a moment to describe the allocation process. A “slot” is a time period allotted to an airline at a particular airport for taking off or landing. An airline requires both a departure and an arrival slot to operate a single flight. In 1992 an independent coordinator was hired to administer the slot allocation process at Heathrow. Every six months airlines desiring slots must submit an application to the coordinator. The application is used to designate new slots desired, and to identify which old slots should be retained and which should be relinquished for reallocation.

Any airline that has operated a slot at least 80 percent of the time in the prior six months has a grandfathered right to reclaim it for the upcoming six months. If not operated sufficiently often, the airline loses its right to the slot. More than 90 percent of the slots at Heathrow are allocated based upon the exercise of grandfathered rights. The remaining slots are known as “pool slots” and generally consist of commercially undesirable times — often early in the morning or late at night — or inconsistent times that make it difficult to sustain a regular frequency (ie., round-trip flight). Most of these slots go unclaimed even though priority over pool slots is given to new entrants to the airport.

Once a slot is allocated, an airline may use the slot for any destination, operate it for any commercial purpose, lease it to other carriers, share it with partners, or swap it for another slot held by a different carrier. An airline may also engage in “secondary trading,” that is, it may swap a desirable slot for another airline’s undesirable slot plus monetary compensation. Given the capacity restraints at Heathrow, such trading is rare. The airport declared in 1997 that, because it has almost no room to expand, the number of available slots would grow, if at all, by only three percent over the next several years.

Presence of Virgin and British Airways at Heathrow

At the close of discovery in July 1997, British Airways held the largest number of Heathrow slots for the 1996-97 operating year — 161,100—amounting to 39 percent of those available and totaling nearly three times as many slots as the second-largest holder, British Midland, with 56,500. British Airways operated 19 monopoly routes out of Heathrow, 45 duopoly routes, competed with two other airlines on 19 routes, and competed with three or more airlines on its remaining 11 routes. Although British Airways added 8,450 flights to its schedule between 1991 and 1997, it maintained a relatively constant 39 percent share of total Heathrow departures in the ten years between July 1987 and 1997. About 45 percent of Heathrow passengers fly British Airways. Meanwhile, passenger operations at Heathrow increased overall by 24 percent. The number of passengers between United States and United Kingdom airports grew from 7,636,319 to 12,759,560.

British Airways considers its United States United Kingdom routes the most profitable and views Virgin as a “cherry-picker” seeking to take business from those routes. Richard Branson has in fact said that “Virgin Atlantic flies only on intensely competitive routes.” By July 1997 Virgin held 6,300 slots at Heathrow— about two percent of those available — from which it operated six transatlantic routes, while it flew another three transatlantic routes from Gatwick.

Virgin is economically successful. In the New York market it carried more passengers flight for flight in 1995 than its competitors, including British Airways. It is the third largest carrier across the Atlantic, and reputedly largely because of its entry into the market, the market share of United Kingdom carriers in United Kingdom United States traffic grew from 38 percent in 1983 to 59 percent in 1995.

British Airways’ Incentive Agreements

Part of the way in which British Airways competes in the airline industry is through the use of incentive agreements entered into with travel agencies and corporate customers. Such practice is allegedly common, with at least three different United States-based carriers purportedly using similar incentives. As British Airways describes its own agreements, commissions or discounts are awarded when specified thresholds of sales are reached, but the agreements contain no set mandatory minimum. As a general rule, the incentive agreements are based exclusively on measures such as sectors flown or revenue earned. In some agreements, travel anywhere on British Airways will count toward the thresholds, while in other agreements certain routes are specified. “Back-to-dollar-one” provisions allow the discount or rebate to apply retroactively to all sales under the agreement once a performance target is met.

Graphs prepared by British Airways show that in 1995-96 corporate deals accounted for 1.96 percent of United Kingdom bookings on routes between the United Kingdom and the United States. No figures are provided for corporate deals involving United States sales. Travel agencies that booked 80 percent or more of their bookings between the United States and the United Kingdom on British Airways accounted for 3.01 percent of tickets sold in the United States and .33 percent of tickets sold in the United Kingdom.

With respect to the individual routes for which Virgin claims it was delayed entry, British Airways’ corporate deals accounted for the following percentages of United Kingdom bookings in 1995-96: 2.42 between Heathrow and New York; .71 between London and Los Angeles; 3.22 between London and Chicago; 1.7 between London and San Francisco; and 3.79 between London and Washington, D.C. For United Kingdom sales through travel agencies in the same time frame, those agencies that booked 80 percent or more on a particular route through British Airways accounted for the following percentages: .25 between Heathrow and New York; .34 between London and Los Angeles; 1.05 between London and Chicago; 1.8 between London and San Francisco; and 3.11 between London and Washington, D.C.

For United States sales, travel agencies that booked 80 percent or more of their bookings through British Airways accounted for the following percentages of bookings from London: 1.12 to New York; 1.82 to Los Angeles; 2.65 to Chicago; 1.85 to San Francisco; and 2.53 to Washington, D.C.

PROCEEDINGS

Virgin filed the instant complaint alleging antitrust causes of action on October 21, 1993 in the Southern District of New York. A motion to dismiss by British Airways was granted in part and denied in part on January 3, 1995. Discovery on Virgin’s remaining claims under §§ 1 and 2 of the Sherman Act was completed in July 1997, after which British Airways moved for summary judgment.

British Airways argued that insufficient evidence existed to show predatory or anti-competitive conduct. Virgin responded by submitting extensive exhibits and affidavits, with the heart of its argument set forth in the November 25, 1997 affidavit of B. Douglas Bernheim, Ph.D., which we analyze in our discussion. Dr. Bernheim explains Virgin’s theory of predatory foreclosure and the bundling of ticket sales, and predicts that had British Airways not engaged in these practices, Virgin would have (1) initiated service to San Francisco in 1992 instead of 1994, (2) initiated service to Washington, D.C. in 1995 instead of 1996, (3) initiated service to Chicago in 1996, (4) added a second flight to Los Angeles in 1996, and (5) added a third flight to New York (JFK) in 1997.

The district court granted summary judgment to British Airways principally on the ground that Virgin failed to support its expert’s theories of anticompetitive practices with factual evidence pertaining to the five routes for which Virgin claims injury. See Virgin Atl. Airways Ltd., 69 F.Supp.2d at 581, 582. Virgin filed this timely appeal.

DISCUSSION

I Standard of Review

Summary judgment is appropriate only if British Airways can show the absence of genuine issues of material fact and its entitlement to judgment as a matter of law. Fed.R.Civ.P. 56(c); Celotex Corp. v. Catrett, 477 U.S. 317, 323, 106 S.Ct. 2548, 91 L.Ed.2d 265 (1986). No special burden is imposed on a plaintiff opposing summary judgment in an antitrust case, Eastman Kodak Co. v. Image Technical Servs., Inc., 504 U.S. 451, 468, 112 S.Ct. 2072, 119 L.Ed.2d 265 (1992), and Virgin as plaintiff can defeat the motion by coming forward with “specific facts” to show a “genuine” issue exists requiring a trial, Matsushita Elec. Indus. Co. v. Zenith Radio Corp., 475 U.S. 574, 585-87, 106 S.Ct. 1348, 89 L.Ed.2d 538 (1986). The trial court should not weigh the evidence or determine the truth of any matter, Anderson v. Liberty Lobby, Inc., 477 U.S. 242, 249, 106 S.Ct. 2505, 91 L.Ed.2d 202 (1986), but should instead draw all inferences from the facts in the light most favorable to Virgin, Matsushita, 475 U.S. at 587, 106 S.Ct. 1348.

A grant of summary judgment is reviewed de novo. Capital Imaging Assocs., P.C. v. Mohawk Valley Med. Assocs., Inc., 996 F.2d 537, 542 (2d Cir.1993). Although such relief may be difficult to obtain due to the factual complexities of antitrust cases, the motion can serve as a tool by which “to isolate and dispose of factually unsupported claims.” Celotex Corp., 477 U.S. at 323-24, 106 S.Ct. 2548. Wasteful trials and prolonged litigation that “may have a chilling effect on procompetitive market forces” should be avoided. Tops Mkts., Inc., v. Quality Mkts., Inc., 142 F.3d 90, 95 (2d Cir.1998).

II Restraint of Trade Claim Under § 1 of Sherman Act

Turning now to the merits, Virgin alleges that British Airways’ incentive agreements constitute an unreasonable restraint of trade in violation of § 1 of the Sherman Act. That provision makes illegal “[e]very contract, combination in the form of trust or otherwise, or conspiracy, in restraint of trade or commerce among the several States, or with foreign nations.” 15 U.S.C. § 1. To establish a § 1 claim Virgin must show: “(1) a combination or some form of concerted action between at least two legally distinct economic entities; and (2) such combination or conduct constituted an unreasonable restraint of trade either per se or under the rule of reason.” Tops Mkts., Inc., 142 F.3d at 95-96.

The district court disposed of Virgin’s § 1 claim on the second prong. See Virgin Atl. Airways, Ltd., 69 F.Supp.2d at 582. Before discussing the second prong, we address for a moment whether Virgin can satisfy the first prong by showing concerted action. See McNally Wellman Co. v. N.Y. State Elec. & Gas Corp., 63 F.3d 1188, 1194 (2d Cir.1995) (“We need not affirm for the reasons expressed by the district court but may affirm on any ground supported by the record.”).

A. Concerted Action

Independent actions taken by an entity fall outside the purview of § 1. See Monsanto Co. v. Spray-Rite Serv. Corp., 465 U.S. 752, 761, 104 S.Ct. 1464, 79 L.Ed.2d 775 (1984) (explaining that in the context of § 1 of the Sherman Act, “[i]ndependent action is not proscribed”); Capital Imaging Assocs., 996 F.2d at 542 (“Unilateral conduct on the part of a single person or enterprise falls outside the purview of this provision [§ 1] in the antitrust law.”). Accordingly, to prevail on its claim, Virgin must produce direct or circumstantial evidence reasonably tending to prove that British Airways and other parties to the incentive agreements were consciously committed “to a common scheme designed to achieve an unlawful objective.” Monsanto Co., 465 U.S. at 768, 104 S.Ct. 1464; see also id. at 764 & n. 9, 104 S.Ct. 1464; Capital Imaging Assocs., 996 F.2d at 545 (“The plaintiffs evidence must prove the actors had an intent to adhere to an agreement that was designed to achieve an unlawful objective.”).

Virgin acknowledges in its appellate brief that “[t]his case turns on [British Airways’] unilateral conduct, not on any alleged conspiracy.” This admission is supported by the fact that there is no allegation that British Airways’ incentive arrangement partners agreed to do anything in exchange for the benefits British Airways awarded to high-volume ticket buyers. For example, no mandatory minimum purchases are required under British Airways’ incentive arrangements, and purchasers are free to choose whatever flight package best suits them or to purchase tickets on competing airlines. In the absence of anything other than unilateral conduct on the part of British Airways, Virgin’s § 1 claim must fail.

B. Unreasonable Restraint of Trade

Even if Virgin could establish concerted action, it still must show the contracts unreasonably restrained trade either per se or under the rule of reason. See Capital Imaging Assocs., 996 F.2d at 542. As Virgin has conceded throughout this litigation, see Virgin Atl. Airways Ltd., 69 F.Supp.2d at 582, the agreements challenged here do not fall within one of the classes of agreements that the Supreme Court has declared illegal, per se. Accordingly, our analysis proceeds under the rule of reason.

Under the rule of reason, Virgin is first required to show the incentive agreements had “an actual adverse effect on competition as a whole in the relevant market.” Id. at 543; accord Tops Mkts., 142 F.3d at 96. The fact that the defendant’s actions prevent a plaintiff from competing in a market is not enough, standing alone, to satisfy this initial burden of proof. See Tops Mkts., 142 F.3d at 96. If Virgin surmounts its first hurdle, the burden shifts to British Airways to establish the procompetitive value of its incentive agreements. Clorox Co. v. Sterling Winthrop, Inc., 117 F.3d 50, 56 (2d Cir.1997). If defendant carries that burden, the burden of proof then shifts back to Virgin to show the same procompetitive effect could be achieved through alternative means that are less restrictive of competition. Id. In other words, Virgin can recover only if it were ultimately to show that British Airways’ actions had a “competition-reducing” effect, harming consumers. Atl. Richfield Co. v. USA Petroleum Co., 495 U.S. 328, 344, 110 S.Ct. 1884, 109 L.Ed.2d 333 (1990).

1. Actual Adverse Effect. The district court dismissed Virgin’s § 1 cause of action for failure to show that British Airways’ incentive agreements had an actual adverse effect on the relevant market. See Virgin Atl. Airways Ltd., 69 F.Supp.2d at 582. In making this ruling, the trial court relied on its analysis of Virgin’s § 2 claims, under which it concluded that Virgin had not furnished a factual basis to support its theories of anti-competitive conduct. See id. at 581.

Regardless of whether a § 2 analysis may be neatly imported into a relevant § 1 analysis, our precedents suggest that whether an actual adverse effect has occurred is determined by examining factors like reduced output, increased prices and decreased quality. See Tops Mkts., 142 F.3d at 96; Capital Imaging Assocs., 996 F.2d at 546. With respect to price, Virgin does not submit any data comparing the cost of a British Airways’ ticket on any of the five routes in question before and after Virgin’s entry or expansion in these markets. Although Dr. Bernheim, Virgin’s expert economist, calculated that “fares are approximately 14% lower, on average, when Virgin is present on a route,” Virgin does not provide the hard data upon which he relied.

Moreover, the charts and graphs the expert attached as exhibits incorporate data only through 1996-preceding the years when Virgin added its flight to Chicago, its second flight to Los Angeles and its third flight to New York (JFK). Although Dr. Bernheim’s affidavit purports to be useful in interpreting market facts affecting this litigation, expert testimony rooted in hypothetical assumptions cannot substitute for actual market data. See Brooke Group Ltd. v. Brown & Williamson Tobacco Corp., 509 U.S. 209, 242, 113 S.Ct. 2578, 125 L.Ed.2d 168 (1993).

With respect to whether consumers experienced a decrease in quality due to Virgin’s delayed entry, Dr. Bernheim cites Richard Branson’s affidavit and other uncontested documentary evidence showing Virgin offered higher quality services than British Airways. Virgin met its burden on this point, as the evidence suggests that consumers had fewer services available until Virgin entered or expanded flights in the five markets. Regarding output, Dr. Bernheim calculated that when Virgin competes on a new route, passenger traffic on that route increases at a greater rate than average passenger growth on other routes where Virgin is not present.

Virgin also could meet its initial burden of showing adverse impact on competition in the relevant market by demonstrating that British Airways “had sufficient market power to cause an adverse effect on competition.” Tops Mkts., 142 F.3d at 96. Market power is defined as “the ability of a single seller to raise pricefs] and restrict output.” Eastman Kodak Co., 504 U.S. at 464, 112 S.Ct. 2072. Rather than determine whether Virgin could establish that British Airways possessed market power when it entered into the incentive agreements — an analysis complicated by the particular facts surrounding the allocation of slots at Heathrow — we by-pass this question because the claim must be dismissed for Virgin’s failure to meet its ultimate burden of proof, that is, harm to consumers from British Airways’ agreements.

2. Procompetitive Justification. The efficiency argument in favor of incentive agreements like those used by British Airways is obvious, yet quite important. Dr. Bernheim acknowledged that “the use of corporate deals and [travel agent commission overrides] can be a natural and desirable consequence of competition among airlines for corporate and travel agent business.” These kinds of agreements allow firms to reward their most loyal customers. Rewarding customer loyalty promotes competition on the merits. Since the incentive agreements serve a procom-petitive purpose, Virgin must show the same purpose could be achieved without restricting competition.

3. Alternative Means. We find nothing in the record in which Virgin suggests an alternative program that would achieve the same procompetitive effect as the incentive agreements. Since the ultimate goal of our § 1 analysis is to determine whether restrictions in an agreement among competitors have a potential to harm consumers, Clorox Co., 117 F.3d at 56, Virgin’s failure to address this point leaves intact the evidence that British Airways’ incentive agreements are good for competition.

While Virgin believes it was disadvantaged by such agreements, injury to a competitor cannot be said to be the sine qua non of a § 1 violation. The Sherman Act and other antitrust laws are designed to protect competition, not individual competitors. Atl. Richfield Co., 495 U.S. at 338, 110 S.Ct. 1884. Accordingly, Virgin’s cause of action under § 1 of the Sherman Act was properly dismissed.

Ill Attempted Monopolization Claim Under § 2 of Sherman Act

We next address the claim of attempted monopolization under § 2 of the Sherman Act. Section 2 makes it a crime to “monopolize, or attempt to monopolize, or combine or conspire with any other person or persons, to monopolize any part of the trade or commerce among the several States, or with foreign nations.” 15 U.S.C. § 2. Virgin charges British Airways with engaging in predatory foreclosure and the bundling of ticket sales in an attempt to foreclose transatlantic competition by diverting passengers from Virgin and other airlines to itself. Virgin Atl. Airways Ltd., 69 F.Supp.2d at 579-81. Virgin’s arguments to support this theory of attempted monopolization are set out in detail in Dr. Bernheim’s 84 page affidavit. We include his views, where pertinent, in the discussion that follows.

To prove that British Airways’ practices constituted an attempted monopolization, Virgin must establish “(1) that [British Airways] has engaged in predatory or anticompetitive conduct with (2) a specific intent to monopolize and (3) a dangerous probability of achieving monopoly power.” Spectrum Sports, Inc. v. McQuillan, 506 U.S. 447, 456, 113 S.Ct. 884, 122 L.Ed.2d 247 (1993). The relevant markets for Virgin’s § 2 claims are the five U.S. cities, serviced from London’s Heathrow, which are the subject of this litigation: New York, Chicago, Los Angeles, San Francisco and Washington.

Dr. Bernheim defines his attempted monopolization theory of “predatory foreclosure” as pricing a good or service below cost with the object of deterring and/or delaying the entry or expansion of a competitor. Losses on sales priced below cost are, under Dr. Bernheim’s theory, immediately recouped by setting prices substantially above costs on other sales. His theory of predatory foreclosure is derived from the theory of predatory pricing. Predatory pricing is a means by which “a single firm, having a dominant share of the relevant market, cuts its prices in order to force competitors out of the market, or perhaps to deter potential entrants from coming in.” Matsushita, 475 U.S. at 584 n. 8, 106 S.Ct. 1348. The purpose is to “gain and exercise control over prices in the relevant market.” Brooke Group, 509 U.S. at 222, 113 S.Ct. 2578.

To succeed on a predatory pricing claim, a plaintiff must prove two elements: (1) “that the prices complained of are below an appropriate measure of its rival’s costs,” id., and (2) that the predatory rival has a “dangerous probability” of recouping its investment through a below cost pricing scheme, id. at 224, 113 S.Ct. 2578. To show how market foreclosure through predation works, Dr. Bernheim uses hypothetical examples based on assumptions said to reflect actual conditions involving British Airways and Heathrow-based travel.

A. Below Cost Pricing

Virgin’s expert alleges that British Airways has monopoly power over routes originating at Heathrow because of the large number of slots it owns and the limitation on total supply brought about by space constraints. His theory of predatory foreclosure derives from British Airways’ monopoly control over the limited slots. We summarize in a moment how his theory applies in this case. But, we must note first that even with monopoly power, a business entity is not guilty of predatory conduct through excluding its competitors from the market when it is simply exploiting competitive advantages legitimately available to it. Advanced Health-Care Servs., Inc. v. Radford Cmty. Hosp., 910 F.2d 139, 147 n. 14 (4th Cir.1990). Moreover, the Supreme Court has expressed deep skepticism regarding the viability of proving a predatory pricing scheme. See Matsushita, 475 U.S. at 589, 106 S.Ct. 1348 (“[P]redatory pricing schemes are rarely tried, and even more rarely successful.”); accord Brooke Group, 509 U.S. at 226, 113 S.Ct. 2578. Success under such a scheme is rare because a predatory competitor must not only sustain short-term losses to drive out competition, but also maintain monopoly power long enough to recoup those losses and derive additional gain. Matsushita, 475 U.S. at 588-89, 106 S.Ct. 1348.

1. Costs of Added Flights. Passing to Dr. Bernheim’s theory, he concludes that British Airways induced corporate customers and travel agents to shift in its favor as much airline traffic as possible, and that its incentive schemes became “noncompen-satory on the margin.” That is to say, Dr. Bernheim believes that the incentive agreements resulted in incremental passengers — ie., those who would not have traveled on British Airways but for the agreements — being charged below cost. Dr. Bernheim calculated British Airways’ cost by positing that the airline offered additional frequencies and thereby incurred additional costs to carry the customers it attracted through the incentive agreements. He relied on a June 1997 paper prepared by the Antitrust Division of the Department of Justice (Antitrust Division), which instructed that (1) “individual flights or groupings of flights on a city-pair” are the relevant increments for calculating costs, (2) more costs are incremental the longer a strategy is in place and (3) aircraft costs are incremental within a relatively short to medium time frame.

Dr. Bernheim reasons that since British Airways’ incentive agreements are meant to be long-term deterrents to competition, “nearly all of [the airline’s] costs of flying an additional frequency should be counted as relevant incremental costs,” defined as the cost of incremental incentive payments plus the variable costs incurred in adding an additional frequency. To determine whether British Airways’ additional frequencies are noncompensatory on the margin, Dr. Bernheim measured the ratio of the incremental incentive payments to incremental revenue, as well as the ratio of the other variable costs to incremental revenue. If the sum of those ratios exceeded one, the competitive frequency was deemed noncompensatory.

Based on information retrieved from a British Airways’ database, he estimated that the incremental cost of adding a frequency from London to the United States is approximately 90 percent of incremental revenue, without accounting for incremental incentive payments to travel agents and corporate clients. He then calculated the ratio of incremental incentive payments to incremental revenue for each of British Airways’ incentive agreements with corporations and travel agencies. Using two methods of calculation, he found the incremental incentive payments quite large, usually greater than 10 percent. Because the incremental cost is 90 percent of incremental revenue, Dr. Bernheim concluded that the incremental frequencies added to accommodate passengers gained through incentive agreements were noncompensa-tory on the margin.

The expert reasoned from this conclusion that competition was foreclosed because another airline could attract customers away from British Airways’ incentive agreements only by offering flights below both its own and British Airways’ costs. With regard to the deterrent effect of British Airways’ practices upon Virgin specifically, Dr. Bernheim explains that an airline will not add a flight to its schedule unless it can maintain a load factor, ie., the percentage of occupied seats, of between 65-75 percent. With British Airways’ incentive agreements diverting passengers who would otherwise be available to the competition, another airline needs more time to attract sufficient customers to make a new route economically feasible. Hence, Dr. Bernheim concludes that but for these agreements, Virgin would have earlier expanded service to New York and Los An-geles and initiated service to Chicago, San Francisco and Washington, D.C.

2. Virgin Has Failed to Prove Underpricing Due to the Incentive Agreements. Considering that Dr. Bernheim relied on the June 1997 paper prepared by the Antitrust Division in formulating his theory, we find it important to note that the paper also explained that the Antitrust Division determines whether an airline is pricing tickets below cost by “identifying] and measuring] only those costs that [the incumbent airline] could have avoided had it not embarked on the pricing/capacity strategy under scrutiny.” (emphasis added). British Airways submitted an affidavit from Robert S. Pindyck, Ph.D., also an expert economist, who notes that because Dr. Bernheim compared incremental costs only against incremental revenue from in-centivized passengers, his results necessarily relied on the assumption that only in-centivized passengers were ultimately funding additional frequencies. The district court, with which we agree on this point, criticized Dr. Bernheim for making that assumption. See Virgin Atl. Airways Ltd., 69 F.Supp.2d at 579-80.

Virgin attempts to substantiate its theory of underpricing using the following evidence: (1) British Airways over time has maintained a constant average load factor of about 70 percent; and (2) two British Airways executives testified at depositions that the use of incentive agreements enabled the airline to offer more flight services. Regarding the load factor, Virgin argues that because that factor has remained constant even as British Airways flew more passengers, British Airways necessarily must have added flights to accommodate incentivized passengers. We know that the airline added 8,450 flights to its schedule between 1991 and 1997. The question is whether these flights would have been added absent the incentive agreements. If they would have been, then Dr. Bernheim incorrectly charges their entire cost against incremental revenue.

According to charts submitted by British Airways, in total just over five percent of its bookings on United States United Kingdom routes derive from corporate deals and travel agencies that book 80 percent or more of their flights on British Airways. These figures are roughly consistent with Dr. Bernheim’s estimate that between three and 14 percent of passengers on United States United Kingdom routes are incremental. Considering these relatively small percentages, along with the fact that since 1991 the number of passengers flown between the United States and the United Kingdom has increased by more than five million people, Virgin has not shown that the additional flights to British Airways’ schedule were entirely attributable to the use of incentive agreements. Without such a showing, a factfinder can only speculate whether the costs of those additional flights were incurred solely because of the agreements. See Brooke Group, 509 U.S. at 242, 113 S.Ct. 2578 (“When an expert opinion is not supported by sufficient facts to validate it in the eyes of the law, or when indisputable record facts contradict or otherwise render the opinion unreasonable, it cannot support a jury’s verdict.”).

The deposition testimony of British Airways’ chief executive, which provides that without incentive agreements the number of flights the airline operates “would go down,” is not a sufficient substitute for market data to support a finding that British Airways added flights on its New York, Los Angeles, Chicago, San Francisco or Washington, D.C. routes because of incentivized passengers. The same is true of the testimony given by British Airways’ director of passenger and cargo business, who stated broadly that “selling the network” offers the potential to mount more services. Without more, a factfinder cannot make a reasoned determination whether Virgin was delayed in entering or expanding services in the five subject markets because of alleged below cost pricing.

Virgin contends it has no obligation to produce particularized market data so long as it can show sufficient profits were diverted from the five routes to prevent its entry or expansion. But Virgin fails to prove even that much. Dr. Bernheim determined that if Virgin had received its share of profits that were otherwise diverted by British Airways’ incentive agreements, it would have added flights to each of the five markets at issue. The share of diverted revenues however, is calculated based on assumptions involving all of British Airways’ United States-United Kingdom routes.

Finally, nothing in the record suggests British Airways stopped using or restructured its incentive agreements following Virgin’s entry or expansion. Since Virgin now represents a competitive threat in the five markets, a factfinder would be left to conclude the agreements are rational for British Airways independent of any alleged improper motive. See IIIA Phillip E. Areeda & Herbert Hovenkamp, Antitrust Law ¶ 807f (1996) (stating that business practices presumptively should not be viewed as an attempt to monopolize when “the practices have been ongoing for several years and rivals have managed to profit, new entry has occurred, and their aggregate market shares are stable”).

Moreover, insofar as Dr. Bernheim relied upon the calculation methods set forth by the Antitrust Division, he fails to account for another principle noted in the discussion, that is, that “[a] pricing strategy by a suspected predator harms consumers when the strategy is rational only if the victim exits the market.” The fact that Virgin has accumulated a large share in the New York, Los Angeles and San Francisco markets, which rivals British Airways’ share, undercuts the applicability of the principle in this case.

Virgin has therefore failed in its burden to show below cost pricing. With the evidence suggesting only that British Airways added profitable flights to its schedule simply to accommodate a general increase in traffic, a factfinder would necessarily conclude that the decision to offer incentives was nothing more than an attempt to generate increased business on the whole by limiting profitability on selected sales. We must be mindful that low prices are a positive aspect of a competitive marketplace and are encouraged by the antitrust laws. See Eastman Kodak, 504 U.S. at 478, 112 S.Ct. 2072 (“Because cutting prices to increase business is ‘the very essence of competition,’ ... mistaken inferences would be ‘especially costly’ and would ‘chill the very conduct the antitrust laws are designed to protect.’”) (quoting Matsushita, 475 U.S. at 594, 106 S.Ct. 1348); accord Brooke Group, 509 U.S. at 226, 113 S.Ct. 2578. As long as low prices remain above predatory levels, they neither threaten competition nor give rise to an antitrust injury. Atl. Richfield Co., 495 U.S. at 340, 110 S.Ct. 1884. Virgin has not shown otherwise with respect to British Airways’ flights on the transatlantic routes in question.

B. Recoupment of Losses by the Bundling of Ticket Sales

Virgin’s theory of predatory foreclosure has a second prong for purposes of showing attempted monopolization, namely that British Airways immediately recouped losses on a below cost ticket by overpricing a “bundled” ticket sold at the same time on a monopoly route. Dr. Bernheim defines “bundling” as “the business practice of selling two or more distinct goods only as a ‘bundle,’ or a package, with a single price charged for the entire bundle.” British Airways allegedly bundled the sale of tickets on its flights by offering discounted fares to corporate customers and increased commissions to travel agencies who entered into the incentive agreements. Dr. Bernheim opines that to induce these entities to “unbundle” individual routes and consider purchasing tickets on another airline for one route of a multi-route trip, Virgin would have to match the monetary value of British Airways’ incentive agreements, which in turn would cause Virgin to sell its services below cost. Since this option is not commercially viable, and Virgin cannot replicate the network British Airways offers, Virgin claims it could not compete fairly for passengers who wished to fly the transatlantic leg of their journey on an airline other than British Airways.

Virgin’s claim that British Airways recouped its losses from underpricing by “bundling” its sales is distinct from claims based on the “tying” of sales. An invalid tying arrangement conditions the purchase of one product to the purchase of a second product that the buyer either does not want or would have preferred to purchase elsewhere. Jefferson Parish Hosp. Dist No. 2 v. Hyde, 466 U.S. 2, 12, 104 S.Ct. 1551, 80 L.Ed.2d 2 (1984). In contrast, a bundling arrangement offers discounted prices or rebates for the purchase of multiple products, although the buyer is under no obligation to purchase more than one item. See SmithKline Corp. v. Eli Lilly & Co., 575 F.2d 1056, 1065 (3d Cir.1978) (affirming judgment for plaintiff on Sherman Act § 2 cause of action, where defendant bundled products by offering bonus rebate on sale of three pharmaceutical drugs); Ortho Diagnostic Sys., Inc. v. Abbott Labs., Inc., 920 F.Supp. 455, 467-69 (S.D.N.Y.1996) (recognizing a potential Sherman Act § 2 claim based on bundling where defendant priced products lower if purchased in combination).

But unlike SmithKline Corp., 575 F.2d at 1065, where the court pointed to expert testimony demonstrating the anticompetitive effects of a bundling arrangement, or Lepage’s Inc. v. 3M, No. CIV. A. 97-3983, 1999 WL 346223, at *6 (E.D.Pa. May 14, 1999), where the plaintiff introduced exhibits showing that specific customers felt compelled to purchase products under the defendant’s bundling program because the plaintiff could not match the discounts, no evidence in the instant case is offered to show that British Airways’ incentive agreements were coercive in relation to the transatlantic routes identified by Virgin. Such evidence would be particularly relevant, since some of the agreements were limited to bookings on specific routes. Whether those routes included New York, Los Angeles, Chicago, San Francisco or Washington, D.C., is vital to an understanding of the effect of the agreements on competition for those flights. Cf. Atl. Richfield Co., 495 U.S. at 334, 110 S.Ct. 1884 (“[I]njury, although causally related to an antitrust violation, nevertheless will not qualify as ‘antitrust injury’ unless it is attributable to an anti-competitive aspect of the practice under scrutiny.”).

Virgin did submit an affidavit from Kevin Mitchell, president of a business travel purchasing and agency group, who testified that British Airways’ incentive agreements make it “economically irrational” to purchase tickets from a lower-priced competitor. Nonetheless, as the district court pointed out, Mitchell never refers to any specific agreement, nor did he say that he reviewed any existing agreement to understand how it applied to any one particular party. See Virgin Atl. Airways Ltd., 69 F.Supp.2d at 581. With respect to the documentary evidence showing that two travel agencies strongly encouraged its employees to sell British Airways’ flights for purposes of meeting performance targets, Virgin does not link these documents to the applicable incentive agreements or actual sales data. As such, a factfinder cannot know whether these agents promoted flights on the five routes for which Virgin claims injury.

Nor did Virgin submit any figures indicating what percentage of bundled sales actually included one of the five routes at issue. If relatively few such routes were included, then Virgin could have competed for a larger share of the market without being influenced by the incentive agreements. For example, although British Airways was the sole carrier on 19 routes from Heathrow in July 1997, only three of those routes were to cities in the United States. It makes no sense for British Airways to have bundled tickets on those three routes with tickets on the five United States-United Kingdom routes at issue. With respect to the remaining 16 routes, six involved destinations to smaller cities within the United Kingdom, and the other 10 destinations included Alexandria (Egypt), Bologna (Italy), Dhahran (Saudi Arabia), Gibraltar, Leibzig (Germany), Madras (India), Nagoya (Japan), Orly (France), Tbilisi (Georgia) and Venice (Italy). No evidence is submitted to show which of these flights were bundled with more competitive transatlantic routes, what prices were paid on the bundled flights, what costs were incurred, and whether British Airways realized sufficient profits to cover the alleged losses on the transatlantic flights.

Nor does Virgin define on which routes beyond the 19 on which the airline was the sole carrier, British Airways allegedly exercised monopoly power, a term associated as noted with the ability to control prices or exclude competition. See Eastman Kodak, 504 U.S. at 481, 112 S.Ct. 2072; United States v. Grinnell Corp., 384 U.S. 563, 571, 86 S.Ct. 1698, 16 L.Ed.2d 778 (1966). British Airways points out that only 17.4 percent of its total available seat kilometers, and only 17.1 percent of its sold capacity is allocated to routes for which it holds a 60 percent or higher market share. Again, Virgin fails not only to define whether these particular routes are included within its definition of British Airways’ alleged monopoly power, but also to proffer evidence showing how this small percentage of British Airways’ business was sufficient to cover losses sustained on un-derpriced tickets for bundled flights to New York, Los Angeles, Chicago, San Francisco or Washington, D.C.

Even if this percentage were sufficient to constitute monopoly power, nothing in the proof indicates how far above its costs British Airways priced its monopoly fares. A monopolist presumably always charges the highest available price to maximize its profits without attracting competitors to enter the market. See Phillip Areeda & Donald F. Turner, Predatory Pricing and Related Practices Under Section 2 of the Sherman Act, 88 Harv. L.Rev. 697, 704-05 (1975) (explaining that a monopolist will charge lower than a profit-maximizing price only when necessary to preserve market share by deterring rivals). Thus, an antitrust plaintiff asserting that a monopolist defendant engaged in a predatory scheme faces a significant hurdle in showing the defendant raised prices in one market to compensate for losses elsewhere. See Robert H. Bork, The Antitrust Paradox: A Policy at War with Itself 145 (1978) (“The predator would already be maximizing profits in all markets and so would have no way of increasing profits elsewhere to finance predation.”).

In addition to arguing that prices were raised on monopoly routes, Virgin contends that British Airways covered losses by charging 14 percent more for airfares on the five challenged routes prior to Virgin’s entry and expansion. Yet, as discussed with respect to the § 1 claim, Virgin proffers no data comparing ticket prices, and Dr. Bernheim relies upon data that pre-dates Virgin’s activity in several markets. Nor has Virgin shown whether a 14 percent higher fare would balance out the losses on below-cost tickets. Absent proof of recoupment, a factfinder could conclude only that British Airways reduced fares under its incentive agreements, but not that the antitrust laws were violated. See Brooke Group, 509 U.S. at 224, 113 S.Ct. 2578. Without proof of re-coupment, predatory pricing produces lower aggregate prices benefitting consumers. See id. (stating that recoupment is the ultimate object of an unlawful predatory pricing scheme).

IV Monopoly Leveraging Claim Under § 2 of Sherman Act

Within the context of § 2 claims, the Supreme Court has recognized the impropriety of monopoly leveraging, ie., the use of monopoly power in one market to strengthen a monopoly share in another market. See Eastman Kodak, 504 U.S. at 483, 112 S.Ct. 2072; United States v. Griffith, 334 U.S. 100, 107, 68 S.Ct. 941, 92 L.Ed. 1236 (1948), disapproved of on other grounds, Copperweld Corp. v. Independence Tube Corp., 467 U.S. 752, 104 S.Ct. 2731, 81 L.Ed.2d 628 (1984). In Berkey Photo, Inc. v. Eastman Kodak Co., 603 F.2d 263, 275 (2d Cir.1979), we stated it would also be a violation of § 2 to use monopoly power in one market to gain a competitive advantage in another, even without an attempt to monopolize the second market.

Since Berkey Photo, we have questioned this proposition. In Twin Laboratories, Inc. v. Weider Health & Fitness, 900 F.2d 566, 570-71 (2d Cir.1990), we characterized as dictum the statements in Berkey Photo that a monopolist acts improperly in refusing to sell monopolized goods needed by a rival to compete in a second market. We further distinguished the precedent on the basis that it involved a tying arrangement, and indicated that Berkey Photo “requires tangible harm to competition.” Id. at 571. More recently, we noted that uncertainty exists as to the continued scope of a monopoly leveraging claim as an independent cause of action in light of the Supreme Court’s opinion in Spectrum Sports, 506 U.S. at 459, 113 S.Ct. 884. AD/SAT v. Associated Press, 181 F.3d 216, 230 (2d Cir.1999) (per curiam). In Spectrum Sports, the Supreme Court stated that § 2 of the Sherman Act “makes the conduct of a single firm unlawful only when it actually monopolizes or dangerously threatens to do so.” 506 U.S. at 459, 113 S.Ct. 884 (emphasis added). Such a requirement goes beyond “gaining] a competitive advantage” as set out in Berkey Photo, 603 F.2d at 275.

Were we to allow pursuit of a monopoly leveraging claim, Virgin would need to submit proof that British Airways: (1) possessed monopoly power in one market; (2) used that power to gain a competitive advantage over Virgin in another distinct market; and (3) caused injury by such anticompetitive conduct. AD/SAT, 181 F.3d at 230. In other words, Virgin would have to demonstrate that British Airways’ use of alleged monopoly power via its incentive agreements “ ‘threaten[ed] the [second] market with the higher prices or reduced output or quality associated with the kind of monopoly that is ordinarily accompanied by a large market share.’” Id. (second alteration in original) (quoting III Phillip E. Areeda et al., Antitrust Law ¶ 652).

It is unnecessary for us to decide, as a matter of law, the viability of a claim for monopoly leveraging as described in Ber-key Photo, since Virgin lacks the requisite proof. We refer to the evidentiary weaknesses discussed in the foregoing sections, insofar as they pertain to whether Virgin could prove British Airways used monopoly power to foreclose competition. See Ortho Diagnostic Sys., 920 F.Supp. at 465 (indicating that a claim for monopoly leveraging requires a showing of predatory or anticompetitive conduct). In addition, Virgin again failed to define in which markets British Airways supposedly exercised monopoly power.

As AD/SAT makes clear, to support a monopoly leveraging claim a plaintiff must show a defendant possesses monopoly power in one market and uses it to gain a competitive advantage in a different distinct market. See 181 F.3d at 230. In paragraph 123 of its complaint, Virgin alleged that British Airways “possesses monopoly power in certain airport markets and in certain markets for airline passenger service” and used that power in an unlawful leveraging scheme. But in its appellate briefs, Virgin refers only to British Airways’ monopoly power at Heathrow and maintains that it need simply show British Airways engaged in anticompeti-tive conduct affecting its entire network, without providing any specific facts to support its allegations. Under these circumstances, summary judgment is appropriate. See Celotex Corp., 477 U.S. at 322, 106 S.Ct. 2548 (explaining that summary judgment must be granted where a party “fails to make a showing sufficient to establish the existence of an element essential to that party’s case, and on which that party will bear the burden of proof at trial”).

CONCLUSION

Having conducted a thorough review of the record and arguments before us, we find no basis for reversing the district court. Summary judgment was properly granted, for where “deficiencies in proof would bar a reasonable jury from finding that the scheme alleged would likely result in sustained supracompetitive pricing, the plaintiffs case has faded.” Brooke Group, 509 U.S. at 226, 113 S.Ct. 2578. The judgment in favor of defendant British Airways is affirmed.  