CONTENTS LIST OF CONTRIBUTORS vii PREFACE ix CONSUMERS, ECONOMICS, AND ANTITRUST John B Kirkwood TITAN AGONISTES: THE WEALTH EFFECTS OF THE STANDARD OIL (N J.) CASE Michael Reksulak, William F Shughart II, Robert D Tollison and Atin Basuchoudhary 63 SUCCESSFUL MONOPOLIZATION THROUGH PREDATION: THE NATIONAL CASH REGISTER COMPANY Kenneth Brevoort and Howard P Marvel 85 THE MORTON AND INTERNATIONAL SALT CASES: DISCOUNTS ON SALES OF TABLE SALT John L Peterman 127 INJUNCTIVE RELIEF IN SHERMAN ACT MONOPOLIZATION CASES Robert W Crandall and Kenneth G Elzinga 277 UNITED SHOE MACHINERY REVISITED Roger D Blair and Jill Boylston Herndon 345 AN ECONOMIC JUSTIFICATION FOR A PRICE STANDARD IN MERGER POLICY: THE MERGER OF SUPERIOR PROPANE AND ICG PROPANE Richard O Zerbe Jr and Sunny Knott 409 v vi VERTICAL MERGERS AND MARKET FORECLOSURE William S Comanor and Patrick Rey 445 THE COMPETITIVE-NEIGHBORS APPROACH TO ANALYZING DIFFERENTIATED PRODUCT MERGERS Paul A Johnson, James Levinsohn and Richard S Higgins 459 SETTLING THE CONTROVERSY OVER PATENT SETTLEMENTS: PAYMENTS BY THE PATENT HOLDER SHOULD BE PER SE ILLEGAL Cristofer Leffler and Keith Leffler 475 PREFACE As readers have noticed, the last several volumes of Research in Law and Economics have consisted of special issue volumes This will continue This volume is one of the best Jack Kirkwood put this volume together with modest assistance from me I believe this is an outstanding volume and expect to meet the high standard set here in future volumes Richard O Zerbe, Jr Editor ix CONSUMERS, ECONOMICS, AND ANTITRUST John B Kirkwood ABSTRACT This is the first paper in a volume devoted exclusively to antitrust law and economics It summarizes the other papers and addresses two issues First, after showing that the federal courts generally view consumer welfare as the ultimate goal of antitrust law, it asks what they mean by that term It concludes that recent decisions appear more likely to equate consumer welfare with the well-being of consumers in the relevant market than with economic efficiency Second, it asks whether a buyer must possess monopsony power to induce a price discrimination that is not cost justified It concludes that a buyer can often obtain an unjustified concession simply by wielding bargaining power, but the resulting concession may frequently – though not always – improve consumer welfare INTRODUCTION Antitrust is finding its bearings After decades of debate about its aims and methods, antitrust law has largely adopted a single goal and a single methodology Today, most courts and commentators agree that the ultimate purpose of the antitrust statutes is not to protect rivals but to benefit consumers.1 It is also widely accepted that the most useful tool for determining whether consumers have been helped or harmed is economic analysis.2 Antitrust Law and Economics Research in Law and Economics, Volume 21, 1–62 Copyright © 2004 by Elsevier Ltd All rights of reproduction in any form reserved ISSN: 0193-5895/doi:10.1016/S0193-5895(04)21001-6 JOHN B KIRKWOOD Within this consensus, however, disagreements remain While there is little doubt that the overarching goal of antitrust is consumer welfare, there is a significant split over the definition of the term.3 One view holds that consumer welfare should mean economic efficiency Under this view, the ultimate goal of antitrust law is not simply, or even primarily, to protect consumers, but to enhance the efficiency of the economy – that is, to increase the total economic value that society derives from its limited resources Since total value includes value realized by producers as well as value obtained by consumers, under this definition it is possible for “consumer welfare” to increase even though consumers are harmed The goal of efficiency analysis is to maximize the total “wealth” of society, regardless of how it is distributed The principal alternative view holds that consumer welfare should refer exclusively to the welfare of consumers – those who purchase the products or services sold in the relevant market.4 Under this view, the ultimate purpose of antitrust is to protect consumers from exploitation More precisely, antitrust should prevent firms from using practices that increase their market power – their power to charge prices above the competitive level – unless such conduct would, on balance, benefit consumers in the relevant market More simply, the goal of antitrust is to ensure, whenever possible, that consumers pay competitive prices for the products and services they purchase.5 This view of consumer welfare is also limited: it takes no account of resource savings or other efficiencies that benefit the overall economy but not improve the well-being of consumers in the relevant market The second element of the antitrust consensus – the role of economics – also generates disagreements While few would question the importance of economics in contemporary antitrust analysis, there are frequent debates about the economic impact of specific practices As Carlton and Perloff observe (2000, p 605): Even if one accepts the proposition that the goal of the antitrust laws is to promote efficiency, economists often have difficulty determining which practices result in inefficient behavior The application of economics to antitrust law is, in short, a work in progress This volume provides a forum for the economic research needed to continue that progress It contains ten papers devoted exclusively to antitrust law and economics In Part I of this paper, I describe the nine other papers in this volume, summarizing their approaches, their conclusions, and their significance for the development of antitrust In Part II, I address the debate over the meaning of consumer welfare, an issue that potentially affects all areas of antitrust but has particular impact on merger analysis In Part III, I examine an issue that is raised but not resolved by one of the papers; namely, whether a buyer needs to have monopsony power in order to induce a price discrimination that is not cost justified – the core of a Robinson-Patman violation After answering that question, I assess whether Consumers, Economics, and Antitrust non-cost-justified discrimination induced by a large buyer is likely to hurt or improve consumer welfare Part I – The Economic Research Papers Written by some of the most distinguished scholars in antitrust today, the nine economic research papers in this volume reflect the consensus described above They uniformly assume that the goal of antitrust is consumer welfare and that economic analysis is a vital tool in achieving that goal In addition, they help to resolve debates that surround each element Several papers shed light on the meaning of consumer welfare One paper advances the debate by exploring a new measure of efficiency that assigns a value to preventing consumer exploitation Another focuses almost entirely on consumer prices, rather than technical efficiency, in assessing the welfare implications of 10 monopolization orders All nine papers evaluate the economic impact of specific practices In doing so, the papers look to the past as well as the future Five of the articles evaluate older antitrust cases to determine whether the decisions reached, the relief ordered, or both, enhanced consumer welfare The verdicts are striking After extensive reviews of the evidence, the authors conclude that hardly any case helped consumers or economic efficiency, and some hurt both Out of the 14 antitrust cases examined, only one seems to have had a positive impact In that case, Brevoort and Marvel conclude that a dominant firm built and maintained its position through non-price predation, and the order entered against the firm most likely promoted new entry These papers provide strong evidence for the proposition that many older antitrust cases did not produce a discernible improvement in consumer welfare and some may have actually harmed consumers Significantly, the 13 cases reviewed in this volume were all decided before 1965 In that period, consumer welfare was not the generally accepted goal of antitrust law and economic analysis had neither the importance nor the sophistication it has today It was not until 1977 that the Sylvania Court elevated the importance of economic analysis by insisting that per se condemnation of a category of practices must rest on “demonstrable economic effect.”6 Two years later, the Court declared – for the first time – that the Sherman Act was a “consumer welfare prescription.”7 Academic commentary also shifted in the late 1970s From 1976 to 1978, Posner, Bork and Areeda each published seminal treatises arguing that antitrust law should be dominated by a single goal (consumer welfare) and a single methodology (economic analysis).8 Given these developments, it is not surprising that Kwoka and White (1989) contend that an “antitrust revolution” began in the mid-1970s JOHN B KIRKWOOD By chronicling the shortcomings of earlier decisions, the historical papers provide further support for the antitrust revolution Moreover, the findings and insights in these papers should make it easier for future antitrust courts to reach decisions that improve consumer welfare For example, Crandall and Elzinga’s paper on relief in monopolization cases identifies numerous obstacles to effective antitrust relief, serving as a caution to modern-day enforcement The Peterman paper similarly identifies ways in which Robinson-Patman enforcement may harm consumers In Part III, I suggest several ways in which enforcement may promote consumer welfare The four remaining papers in this volume apply economic analysis to contemporary issues The first paper analyzes a recent Canadian merger that was approved by the Canadian Competition Tribunal largely because it would increase economic efficiency Applying the traditional measure of efficiency, the Tribunal calculated that the merger’s cost savings would outweigh its adverse impact on prices Zerbe and Knott critique this measure because it gives no weight to consumer exploitation – to the transfer of wealth from consumers to producers To correct for this, the authors utilize a new measure of efficiency that takes wealth transfers into account so long as people would be willing to pay to avoid them Using this measure, the authors conclude that the merger may have reduced efficiency The final three papers apply economic analysis to several perennial antitrust issues: the impact of vertical foreclosure, mergers of differentiated products, and misuse of patents The first paper explains a new way in which vertical foreclosure can enhance the market power of an upstream supplier The second refines an innovative technique for identifying substitutes among a set of differentiated products and explains how the technique can improve merger analysis The final paper confronts an especially contentious policy issue – the treatment of patent settlements in which the patent holder pays the challenger to exit the market Relying on both economic analysis and basic principles of patent law, Leffler and Leffler argue that such settlements should be per se illegal These nine papers suggest that antitrust is on the right track – that a consumer oriented, economically driven approach to antitrust law is appropriate They also underscore the importance of economic research in implementing this approach Part II – The Meaning of Consumer Welfare While most economists and courts agree that the ultimate goal of antitrust is consumer welfare, there is less agreement on the meaning of the term Though the issue underlies most of antitrust law and is critical to the efficiency defense in merger cases, the courts rarely address it explicitly Consumers, Economics, and Antitrust Robert Bork is the chief proponent of the view that consumer welfare should mean economic efficiency In a classic paper (1966) and a popular book (1978), Bork argued that the “whole task of antitrust can be summed up as the effort to improve allocative efficiency without impairing productive efficiency so greatly as to produce either no gain or a net loss in consumer welfare” (1978, p 91) He added: “These two types of efficiency make up the overall efficiency that determines the level of our society’s wealth, or consumer welfare” (ibid emphasis added) Bork’s definition of consumer welfare adopts the traditional measure of economic efficiency.9 Under this standard, a practice that reduces costs will increase consumer welfare even if it raises prices so long as the gains to producers (from the lower costs and higher prices) exceed the losses to consumers (from the higher prices).10 This definition of consumer welfare, in short, focuses on the economy as a whole rather than on consumers.11 Bork’s principal opponent is Professor Robert Lande In 1978, when Bork’s book began to create a stir, Lande was a staff attorney in the policy office of the Bureau of Competition of the Federal Trade Commission (FTC) As head of that office, I asked him to prepare an independent analysis of the goals of the antitrust laws, based on a fresh reading of the legislative histories His findings and supporting analysis were so acute – and revolutionary – that the Hastings Law Journal published a revised version of his paper (Lande, 1982), and it became one of the most cited pieces ever published by that periodical.12 Lande concluded that in passing the antitrust laws, Congress was interested, as Bork contended, in furthering economic efficiency It was also concerned with various social and political goals But its dominant objective was neither economic efficiency nor any social or political value Instead, according to Lande, Congress wanted above all to prevent firms from exploiting consumers To put it more precisely, Congress’s overarching goal was to stop firms from using unfair tactics to acquire or preserve market power and thereby force consumers to pay higher prices As Lande wrote recently, the “overriding concern was that consumers should not have to pay prices above the competitive level” (1999, pp 961–962).13 In concept, Lande’s interpretation of consumer welfare contrasts sharply with Bork’s While Bork focuses on economic efficiency, Lande focuses primarily on prices in the relevant market Lande illustrates the difference by describing how his approach would alter “the fundamental question asked in merger analysis.” Lande states (1999, p 962): Instead of asking, “is the merger likely to be efficient,” [my approach would ask], “is the merger likely to lead to higher consumer prices?”14 Lande’s interpretation of congressional intent has been highly influential in certain arenas His original article has been cited in at least 285 other law JOHN B KIRKWOOD review articles15 and has garnered considerable support among law professors Even Judge and former professor Frank Easterbrook, closely associated with the economically oriented Chicago School, appears to have taken Lande’s side in this dispute (1986, pp 1702–1703): The choice [Congress] saw was between leaving consumers at the mercy of trusts and authorizing the judges to protect consumers However you slice the legislative history, the dominant theme is the protection of consumers from overcharges.16 According to Lande’s recent paper (1999, pp 963–966), 25 antitrust professors, virtually all lawyers and many leading figures in the field (e.g Philip Areeda), have endorsed his construction The United State Department of Justice and the FTC have also adopted Lande’s view in their important Horizontal Merger Guidelines (1992, revised 1997), almost without reservation In the latest revisions, the Guidelines state that efficiencies cannot save an otherwise anticompetitive merger unless the efficiencies are sufficient to prevent an adverse impact on consumers.17 Thus, if the government can show that a merger would cause a significant price increase in the absence of any cost savings, the merging parties cannot justify the transaction by demonstrating cost savings unless they can show that these cost reductions would alter the merged firm’s pricing calculus and cause it to refrain from a price increase By making the impact on consumers in the relevant market the litmus test of a likely merger challenge – and virtually ignoring impact on producer costs and economic efficiency as independent values – the federal agencies have essentially embraced Lande’s and rejected Bork’s definition of consumer welfare.18 Although Lande’s interpretation of Congressional intent has swayed many law professors as well as the federal enforcement agencies, it has made less headway among courts and economists As of 1999, Lande could cite only three federal court decisions that referenced his revolutionary article, none more recently than 1988 Similarly, his list of professorial endorsements included only three economists.19 Why so little support in the courts and economics departments? Has Bork’s view conquered where it counts – among the judiciary? Part II examines recent federal decisions and concludes that they have not picked Bork over Lande To the contrary, while the courts have not settled on a definition of consumer welfare, they seem more concerned with preventing consumer exploitation than promoting economic efficiency Indeed, in the one area where the two scholars’ views plainly conflict – the efficiencies defense in merger cases – the courts have, without citing Lande’s analysis, overwhelmingly adopted it In contrast, the economics papers in this volume, to the extent they define welfare, almost always equate it with economic efficiency Several papers, however, display a heightened sensitivity to the impact of a practice or order on Consumers, Economics, and Antitrust consumers in the relevant market In two of these papers, this added attention does not alter the ultimate result: whether the authors focus on economic efficiency or consumer exploitation, their conclusions are the same In the third paper, though, the authors apply a new measure of efficiency – a measure that assigns a value to preventing consumer exploitation – and conclude that it could change the welfare evaluation of a recent merger Part III – Buyer Power, Consumer Welfare and the Robinson-Patman Act The antitrust law that is least likely to promote consumer welfare, whether viewed as economic efficiency or the absence of consumer exploitation, is the RobinsonPatman Act This Depression-era statute prohibits sellers, in certain instances, from favoring some of their customers with price or promotional concessions that they not extend to competing customers Of all the antitrust laws, the RobinsonPatman Act is the most unabashed in its favoritism of small business In Morton Salt – one of the earliest and most important cases decided under the Act – the Supreme Court declared that the statute’s goal was to prevent large buyers from gaining an advantage over their smaller rivals: The legislative history of the Robinson-Patman Act makes it abundantly clear that Congress considered it to be an evil that a large buyer could secure a competitive advantage over a small buyer solely because of the large buyer’s quantity purchasing ability.20 This concern for “competitive advantage,” rather than consumer impact or economic efficiency, led the Court to adopt what is called the “Morton Salt inference,” which essentially allows judges to infer competitive injury from a substantial and sustained price differential More recently, as the purpose and approach of antitrust law has shifted, both the Morton Salt inference and the Act itself have been heavily criticized as protectionist of small business, anticompetitive and ultimately harmful to consumers As a result, federal and state antitrust authorities have largely stopped enforcing the Act, though private enforcement continues In his landmark analysis of Morton Salt, published in this volume, John Peterman concludes, based on the evidence in the record, that the inference of competitive injury was unjustified in that case His findings indicate that the salt manufacturers’ discounts were procompetitive and enhanced consumer welfare Like so many other critiques of the Act, his paper raises the question whether Robinson-Patman enforcement can ever benefit consumers In Part III, I examine that issue by focusing on the core elements of a secondary-line Robinson-Patman violation.21 Despite its shortcomings (both real 490 CRISTOFER LEFFLER AND KEITH LEFFLER preliminary injunction criteria of the Federal Rules.47 The payment permits the patent holder to increase the value of his patent rights – through the exclusion of competitors – beyond the substantive and procedural rights granted to him by Congress Such agreements to exchange cash for additional exclusion are, therefore, anticompetitive and satisfy the conditions for per se illegality Commentators rejecting the per se approach based on “institutional failure” point to Congress’s rules regarding preliminary injunctions as a prime example of such failure.48 Under those procedural rules, a patent holder may not satisfy the criteria to obtain a preliminary injunction but may ultimately prevail in the litigation Thus, the challenger will have been permitted to make infringing sales during the pendency of the patent litigation despite the fact that the patent is ultimately held to be valid and infringed Some commentators consider this a clear example of an institutional breakdown that the patent holder can “remedy” by paying the challenger not to market the product pending the resolution of the patent litigation A procedural rule granting patent holders a right to pre-trial exclusion without meeting the standard preliminary injunction rules would, however, provide a greater reward to patent holders than Congress in fact granted.49 The reward granted to innovators by Congress may or may not be optimal in certain cases It is, however, the reward that the patent holders are entitled to.50 Recognizing that payment by the patent holder to the alleged infringer in connection with an “interim settlement” is anticompetitive, some litigants have attempted to convince the enforcement agencies and courts that the cash transferred to the challenger was not a “payment,” but merely analogous to a bond that secured the parties’ stipulated preliminary injunction For antitrust purposes, however, there is all the difference in the world between a payment by the patent holder to the challenger and the mere posting of a bond to secure a preliminary injunction The latter does not supersede the challenger’s unilateral calculus as to whether to enter the market; the former clearly does.51 CONCLUSION Congress is the appropriate entity to determine the optimal balance between dynamic and static efficiency as it relates to the reward to be given to inventors Congress is specifically designated by the Constitution as the body responsible for making that determination Moreover, the courts and enforcement agencies lack the institutional competence to second-guess Congress’s determination even if they had the authority to so Consequently, the proper role for antitrust enforcement authorities is to determine whether the patent holder’s exclusion of a potential rival has resulted Settling the Controversy Over Patent Settlements 491 solely from the bundle of procedural and substantive rights granted to the patent holder by Congress as a reward for innovation Where the challenger makes a unilateral determination that the potential rewards of patent litigation, discounted by the probability of success, not warrant (or no longer warrant) the cost of litigation, the parties are permitted to agree that the challenger will confess the validity and infringement of the patent Such agreements are required to obviate or end patent litigation that is not efficient However, it should be per se unlawful for the patent holder to pay the challenger to drop his challenge to the patent and confess validity and infringement In this instance, the patent holder procures the challenger’s exit other than through use of the bundle of rights granted by Congress Moreover, Congress has designed the patent litigation system in such a way that consumers will benefit from the probability that the patent is invalid if either: a) the litigation continues and the patent is invalidated, or b) the risk of invalidity induces the patent holder to grant to the challenger a license reflecting that probability Allowing the patent holder to eliminate that probability (and the attendant consumer benefits) by paying the challenger to recognize validity is to allow private purchase of additional protections to patent holders not granted by Congress Allowing such agreements can only be based on the proposition that Congress should have given a greater reward to inventors – that Congress got the balance between dynamic and static efficiency wrong There is, however, no theory, data, or analysis supporting this proposition And, even if such theory, data or analysis were forthcoming, Congress, rather than the courts or enforcement agencies, has the institutional authority to strike the optimal balance Our analysis takes as a given the efficiency balancing that Congress has in fact struck Under the patent litigation system created by Congress, a patent enjoys only a rebuttable, not a conclusive presumption of validity This probability of invalidity has an economic value Under the system as created by Congress, the challenger has an incentive to capture that value and that incentive creates consumer benefit In contrast, a payment by the patent holder to the challenger captures the value of the probability of patent invalidity The agreement between the patent holder and the challenger divides the profits from agreed validity and thereby eliminates any consumer benefit Through an agreement not to compete, the patent holder changes the congressionally mandated rebuttable presumption of validity into a conclusive presumption When a patent holder thus enlarges the reward granted to him by Congress, in the form of paying a potential rival to confess validity, he and his co-conspirator reduce efficiency and consumer welfare and therefore commit a per se violation of the antitrust laws In contrast, a license granted by the patent holder to the challenger in exchange for the latter’s recognition of the validity and infringement of the patent cannot be condemned as per se unlawful on its face precisely because it may represent the lawful exercise by the patent holder of the rights granted to him by Congress 492 CRISTOFER LEFFLER AND KEITH LEFFLER Absent a payment by the patent holder to the challenger, such a license will include a royalty payment that will reflect each litigant’s view of the probability of a finding of invalidity and the value of such a finding to each In stark contrast to the result when the patent holder pays the challenger to exit the market, the partial exclusion effected by the license results in increased efficiency and consumer welfare NOTES See, e.g Aro Corp v Allied Witan Co., 531 F.2d 1368, 1372 (6th Cir 1976) (“Public policy strongly favors settlement of disputes without litigation Settlement is of particular value in patent litigation.”); Joy Manufacturing Co v National Mine Service Co, Inc., 810 F.2d 1127, 1131 (Fed Cir 1987) (Newman, J concurring) Some courts and commentators have concluded that a patent settlement in which the patent holder pays the infringer to stay off the market is per se illegal See, e.g In re Terazosin Hydrochloride Antitrust Litigation, 164 F Supp 2d 1340 (S D Fla 2000); Eon Labs Manufacturing, Inc v Watson Pharmaceuticals, Inc., 164 F Supp 2d 350 (S D N Y 2001) Others appear to favor that conclusion but not state it expressly See, e.g Andrx Pharmaceuticals, Inc v Biovail Corp., 256 F 3d 799 (D.C Cir 2001); Anthony (2000); and Balto (2000) Other commentators urge application of the rule of reason See, e.g Leary (2001); Gilbert and Tom (2001); Addanki (2001); Chin and Krattenmaker (2001); and McDonald (2002) While we use the phrase “cash payments,” we include all lump sum payments; that is, all payments or benefits from the patent holder to the challenger that not vary depending on the output of the disputed patented good There may be circumstances in which it is not clear from the parties’ written agreement whether the payment was in exchange for the challenger’s exit from the market or, rather, was in exchange for the transfer of some legitimate goods or services For example, in the K-Dur matter before the FTC and in private litigation, K-Dur Antitrust Litigation, MDL 1419 (D.N.J.) (private cases), the brand-name and generic manufacturers assert that the payments were not in exchange for an agreement not to enter, but in exchange for intellectual property rights transferred by the generic manufacturers to the brand-name manufacturer Such factual disputes not alter the economic and legal analysis presented here There is simply a preliminary factual dispute, as there is in many (most) antitrust cases, as to what the true terms of the agreement are If the fact finder in such a case concludes that the payment was made in exchange for the challenger’s exit from the market, the agreement should be per se unlawful If, however, the payments are found to be unrelated to the agreement not to enter, as was found to be the case by the ALJ in the K-Dur matter, then our analysis is not applicable In this case the costs and benefits of the litigation are borne by the parties Their decisions as to their own welfare should be dispositive It is possible that others not part of the lawsuit have an interest in establishing (or preventing) a precedent However, such external beneficiaries can attempt to influence the settlement decisions by, for example, bearing some of the costs of litigation Patent disputes can arise from complementary or product extension patents In these cases, private and social wealth is created by use of the patent Settlements are presumably Settling the Controversy Over Patent Settlements 493 efficient since the litigants not affect competition between themselves by their litigation vs settlement decision The value of K is of no consequence except as it relates to the cost of litigation More complex demand, costs and intertemporal conditions not add to the points illustrated herein The exact duopoly solution is not important to the analysis or propositions, though the results depend upon there being some competition between the incumbent and the entrant; that is, that the resulting price be less than the monopoly price The industry output will be (Q = − 1) and each firm’s output equal to 1.5, which, with a price of 1, yields profit of 1.5 More generally, the total duopoly profit is given by P e × Q e = (1/2 × P m ) × (K − 1/2P m ) = (1/4 × K) × (K − 1/4 × K) = 3/16 × K 10 The social gain is given by consumer value of the increased output which equals the increased area under the demand curve We assume technical conditions are satisfied to make such a calculation independent of income Hence the social gain equals the change in output, Q = [Q e − Q m ] (i.e [{K − 1/4 × K} − {1/2 × K}] = 1/4 × K), times the average price, (P e + P m )/2 (= [1/4 × K + 1/2 × K]/2 = 3/8 × K) In the case considered of K = 4, this equals (3 − 2) × (2 + 1)/2 = 1.5 11 We consider below the case where the parties have different expectations about the likelihood that the patent is invalid 12 The expected profit from litigation is given by the Probability of invalidity times the entrant’s profit if invalid less the cost of litigation In this case this [PROB × 1/2 × ␲e − CL] equals 0.25 [0.5 × 1.5 − 0.5] 13 The expected profit from litigation is (1 − PROB) × (P m × Q m ) + PROB × 1/2 × P e × Q e − CL Allowing entry gives a profit of 1/2 × P e × Q e Therefore litigation has positive expected profit if (1 − PROB) × (P m × Q m − 1/2 × P e × Q e ) − CL > For the case considered, this equals (1 − 0.5) × (2 × − 1/2 × × 3) − 0.5 = 0.75 14 The increase in surplus from entry, calculated above, is 1.5 Since there is a 50% chance of patent invalidity and entry, the expected increase in surplus is 50% of the increase if entry occurs 15 The monopolist’s expected profits are (1 − PROB) × (P m × m) + PROB × 1/2 × P e × Q e − CL The entrant’s expected profits are PROB × 1/2 × P e × Q e − CL Summing gives the expression in the text 16 This is true since P e × Q e is less than P m × Q m and CL is positive 17 The expected loss in profit to the monopolist from litigation is given by P m × Q m − [{1 − PROB} × P m × Q m + PROB × 1/2 × P e × Q e − CL] This simplifies to PROB × P m × Q m − PROB × 1/2 × P e × Q e + CL The entrant’s expected profitability is PROB × 1/2 × P e × Q e − CL Subtracting the entrant’s expected profit from the monopolist’s loss from litigation gives (PROB) × (P m × Q m − P e × Q e + × CL This is greater than zero since P m × Q m is greater than P e × Q e 18 For all licensing fees below the monopoly price, the combined profits of the parties will fall since at such a fee the entrant will compete and price will fall below the monopoly level The case of a licensing fee equal to the monopoly price is uninteresting Henceforth in referring to a licensing fee we limit ourselves to cases in which the entrant has an incentive to produce positive levels of output 19 A licensing fee lower than Lmin cannot occur with a payment from the monopolist to the entrant A more efficient fee below Lmin , with a payment from the entrant to the monopolist, is mathematically possible but of no economic relevance since such a fee 494 CRISTOFER LEFFLER AND KEITH LEFFLER reduces the combined profits of the entities below that available at Lmin ; that is, the contracting parties have no incentive to reach such a deal 20 Using the same formulas as above, the patent holder’s expected profit from litigation is [1 − PROB] × P m × Q m + PROB × P e × Q e or, for the example case, [1−PROB] × [1/2×K] × [K − 1/2 × K] + PROB × [1/4 × K] × [K − 1/4 × K] − CL, which for K = and CL = 0.5 equals 3.25 The entrant’s expected profit from litigation is PROB × P e × Q e − CL = PROB × [1/4 × K] × [K − 1/4 × K] − CL which for K = and CL = 0.5 equals 0.85 21 The minimum fee that would yield a profit of 3.0 to the patent holder is 0.90284 The maximum fee that would yield profit of 0.7 to the challenger is 0.90161 22 In this situation, we can solve for an efficiency-maximizing settlement which finds the lowest possible licensing fee which in combination with a lump sum payment can lead to settlement For the example this occurs at a license fee of 0.90456 with a lump sum payment of 0.002284 23 We know of no research, nor can we envision any such research, that evaluates the number of instances in which the PTO issues invalid patents While a large percentage of litigated patents are found to be invalid, those cases that go to litigation are not likely representative of all patents This uncertainly as to the appropriate distribution of invalidity is, however, of no consequence to our conclusions We have simulated a host of other distributions of invalidity In the appendix, we report an extreme case of patent validity in which the mean actual validity is 90% with a quasi-normal distribution around that mean In this extreme case, about 86% of cases that can be settled can be settled with a license fee Of those cases requiring a lump sum payment to settle, less than a quarter of such settlements are efficient, and the surplus losses from inefficient lump sum settlements are over seven times any gains of efficient settlements Perhaps more importantly, the surplus gains from license fee settlements, which would be expected to be lost with lump sum settlements allowed, are over one hundred times larger than the gains from efficient settlements that can occur only with lump sum payments We have also investigated cases of quasi-normal (as explained below) distributions of the calculated probabilities The results are not different in substance from the case discussed here 24 The distributions used assume a standard deviation to the left of 1/4 of the distance from to the calculated probability and a standard deviation to the right of 1/4 the distance from the calculated probability to We also “pack” the distribution at the tails so that the total probability for to equals Finally, we evaluate the various cases at one-tenth probability intervals 25 The monopoly profit is given by 0.25 × K ∧ Hence we consider the cases CL = (0.003125 to 0.03125) × K∧ The Appendix shows the results for increments in CL equal to 1.25% of the monopoly profit The median total cost of patent litigation has been estimated to be $2.225 million in cases with monopoly profit estimated to range from 10 to $100 million See Miele (2000) This implies a median litigation cost of about 4% of the monopoly profit 26 If the appropriate welfare standard were consumer surplus rather than the sum of consumer surplus and profit, the inefficiency of allowing lump sum settlements is even stronger Considering only consumer welfare, efficient settlements require lump sum payments in less than 1/3 of 1% of the cases, and the surplus loss from inefficient settlements made because lump sum settlements are allowed is over 100 times the surplus gain from efficient settlements that would not occur absent lump sum settlements Settling the Controversy Over Patent Settlements 495 27 Professor Willig offered the Willig-Bigelow model in his testimony in the FTC K-Dur case though it did not play any role in the decision Willig-Bigelow also allow for risk aversion in their model We also allowed in the appendix for risk aversion by discounting the expected profits from litigation according to the variance of the probability of patent validity This implies a discount of 25% for the riskiest case of a 50/50 case of patent validity For a 90/10 chance the discount is about 1% Tables A4 and A5 summarizes the impact of including risk aversion As expected, risk aversion does reduce the likelihood that a patent dispute will not be settled However, it does this mainly by increasing the probability that one or the other party will not pursue litigation We find that efficient lump sum settlements are even rarer than in the absence of risk aversion 28 Ibid at 34 29 Ibid at 26 30 Ibid at 22 and 26 31 NCAA v Board of Regents of the University of Oklahoma, 468 U.S 85 (1984) (quoting Broadcast Music Inc v CBS, 441 U.S 1, 19–20, 1979) 32 This is exactly the approach advocated by Willig and Bigelow Even though they claim the per se rule unwarranted, they admit the framework to determine when lump sum settlements should be allowed “is a deep and complex question” (p 34) 33 See Fn 3, supra 34 U.S Const art I, § 8, cl 35 See Jones and Williams (1998) 36 Carlton and Perloff (1999) observe that “[t]oo little effort is put into R&D because information externalities prevent inventors from capturing the values of their discoveries in the absence of property rights” (pp 540–41) 37 See Tirole (1988): “The welfare analysis (of patents) is relatively complex, and more work is necessary before clear and applicable conclusions will be within reach,” and “[t]he current theories are much too rudimentary to be realistic” (p 399) 38 “[R]ules governing settlements affect what is truly meant by the patent grant itself In fact, in many fast-moving industries, the rules governing patent litigation and settlements are arguably far more important to patentees than the single variable on which economists have traditionally focused, namely patent length.” (Shapiro, 2001) 39 As stated by the Supreme Court, “[t]he heart of [the patent owner’s] legal monopoly is the right to invoke the State’s power to prevent others from utilizing his discovery without his consent.” Zenith Radio Corp v Hazeltine Research, Inc., 395 U.S 100, 135 (1969) 40 See 35 U.S C § 282 (“A patent is presumed valid.”); Magnivision, Inc v Bonneau Co., 115 F.3d 956, 960 (Fed Cir 1997) (“The validity of a patent is always subject to plenary challenge on its merits A court may invalidate a patent on any substantive ground, whether or not that ground was considered by the patent examiner.”); Roper Corp v Litton Systems, Inc., 737 F.2d 1266, 1270 (Fed Cir 1985) (“A patent is born valid It remains valid until a challenger proves it was stillborn or has birth defects, or it is no longer viable as an enforceable right.”); Bowser, Inc v United States, 388 F.2d 346, 349 (Ct Cl 1967) (“The strength of the presumption varies with the substance of the assertion, e.g if the asserting party relies on prior art that previously has been considered wither by the Patent Office or by another court then the presumption of validity is strong, or if the asserting party cites prior art that is more pertinent than that considered by the Patent Office or another court then the presumption of validity is considerably weakened.”) 496 CRISTOFER LEFFLER AND KEITH LEFFLER 41 The challenger’s agreement to recognize the validity and infringement of the patent may be integral to the settlement; without it the patent holder may be unwilling to dismiss the lawsuit 42 A patent holder’s payment to a challenger to stay out of the market is akin to other types of market allocation that are universally recognized as anticompetitive and per se illegal See, e.g XII Hovenkamp Antitrust Law para 2043, p 237 (an “agree[ment] not to engage in a certain type of research and development should ordinarily be regarded as a naked output restriction in the market for new innovations, and thus should be illegal per se”); Von Kalinowski, Antitrust Laws & Trade Regulation (2d ed.) § 73.02 (“Per se liability will flow from a horizontal agreement among competitors to suppress the use of patents for purposes of restraining trade”); Engine Specialties, Inc v Bombardier Ltd., 605 F.2d 1, 11 (1st Cir 1979) (agreement not to market product in development is per se unlawful); Discovision v Disc Mfg., Inc., 1997 U.S Dist LEXIS 7507 at ∗ 37–39 (D Del Apr 3, 1997) (agreement that “essentially eliminated the horizontal competitors’ incentive to innovate and design around [defendant’s] patents” is per se unlawful) 43 See Addanki (2001, p 5) (“In effect, there has been an institutional breakdown and a portion of the value of the patentee’s intellectual property has been appropriated”); Chin and Krattenmaker (2001, p 36) (a payment to the challenger to stay out of the market pending a determination of validity “might not have any anticompetitive effect beyond that contemplated by the patent law”); Gilbert and Tom (2001, p 31) (disallowing such payments by the patent holder “would force society to bear the risk that the patent would be ruled invalid when it is actually valid, and this can have disincentives for innovation”) Gilbert and Tom also argue that it is theoretically possible that the potential savings to consumers from a finding of invalidity, discounted by the probability of success of the lawsuit, are less than the litigation costs, and therefore, payment by the patent holder to the challenger avoids social waste Gilbert and Tom (2001, p 32) As we have shown, however, the instances in which such a theoretical possibility actually occurs are trivial Per se rules expressly take such theoretical possibilities into account and conclude that the benefits of permitting litigants to advance such possibilities are outweighed by the costs See Bork (1993) For example, we not permit the dominant retailer in New York to pay a would-be entrant to stay out of the state even if it could be established that the potential consumer benefits from entry, discounted by the likelihood of a successful entry, were less than the cost-of-entry efforts 44 See, e.g McDonald (2002, p 12) McDonald argues that a payment from the patent holder to the challenger should be unlawful only if the antitrust plaintiff first proves that the patent is invalid The rationale for this proposed rule appears to be the assertion that such a payment causes no harm to consumers if the patent is valid, and therefore the payment should be deemed lawful unless the antitrust plaintiffs first demonstrate that the patent is invalid This argument rests on two fundamental fallacies First, the argument assumes away the real-world setting in which the patent holder makes the payment to the challenger The McDonald argument rests on a false, Manichaean worldview in which patents are either valid or invalid The reality is that there exists a third category – patents whose validity is subject to challenge – and it is precisely that category with which the antitrust analysis is concerned Asserting that payments to recognize the validity of valid patents are not anticompetitive tells us nothing about whether payments to recognize the validity of patents as to which there is some probability of invalidity are anticompetitive At one point, the McDonald article itself seems to acknowledge this, asserting that “how to evaluate competitive effects when you are not sure, or cannot know, whether the patent is valid” is “a Settling the Controversy Over Patent Settlements 497 worthy topic for another day” (McDonald, 2002, p 13) Second, this argument overlooks the economic relevance of the ability of the patent holder to grant permission to the challenger to enter the market The patent challenger is not in the position of an ordinary potential market entrant who needs governmental approval to enter Even if the patent challenger were in that position, one could make a compelling argument that it is per se unlawful for the incumbent manufacturer to pay the challenger to withdraw his request for government approval 45 In the famous dictum of Justice Jackson, “We are not final because we are infallible, but we are infallible only because we are final.” Brown v Allen, 344 U.S 443, 540 (1953) (Jackson, J., concurring) 46 Variations on this erroneous “institutional failure” argument abound For example, McDonald (2002) notes that the Hatch-Waxman Amendments permit a generic drug manufacturer to challenge a pharmaceutical patent without first actually entering the market and thereby becoming potentially liable to the patent holder for damages (p 8) Thus, for the generic manufacturer, the only risk in the patent litigation “is further legal expense,” while for the patent holder “the downside risk is enormous – the loss of its patent” (p 9) The implicit argument is that these “errors” in the current system fail to provide adequate protection to the patent holder – Congress “should have” created a greater incentive to innovate More precisely, the argument is that the private patent litigants should be permitted to remedy that Congressional error by means of a payment in exchange for market exclusion 47 See Fed R Civ P 65 48 See, e.g Addanki (2001, p 51) (failure of a patent holder to obtain a preliminary injunction to prevent pre-trial infringing sales represents “an institutional breakdown and a case where the value of the patentee’s intellectual property has been expropriated”); Gilbert and Tom (2001, p 31) (failure of a patent holder to obtain a preliminary injunction to prevent pre-trial infringing sales could “expose the patentee to the risk of enormous losses that might not be compensated in damages from a thinly capitalized generic firm.”) The implicit argument offered by Gilbert and Tom is that the patent holder should be permitted to remedy this “defect” in the patent system by paying the challenger not to enter pre-trial (p 33) 49 Payments from the patent holder to a challenger not to enter the market are particularly anticompetitive in the pharmaceutical industry Not only does the patent holder begin with a 30-month protection against invalidity as mandated by the Hatch-Waxman Amendments, but an agreement with the first entrant can preclude entry by other challengers See Federal Food, Drug, and Cosmetic Act, 21 U.S C § 301 et seq (1994); In re Ciprofloxacin Hydrochloride Antitrust Litigation, 166 F.Supp.2d 740 (E D N Y 2001); In re Cardizem CD Antitrust Litigation, 105 F.Supp.2d 682, 685 (E D Mich 2000); In re Terazosin Hydrochloride Antitrust Litigation, 164 F.Supp.2d 1340 (MDL 2000); Engelberg (1999, pp 403–406) 50 Absent the payment by the patent holder to the challenger, the parties to patent litigation should be permitted to settle a threatened motion for preliminary injunction to the extent and for the reasons that they should be permitted to settle the entire case Under the preliminary injunction procedures, consumers have some protection since the court is required to find that the injunction is in the public interest See Aoude v Mobil Oil Corp., 862 F.2d 890, 892 (1st Cir 1988) (“The criteria for preliminary injunctive relief can be summarized as follows: (1) The likelihood of merits’ success; (2) The potentiality for irreparable injury; (3) A balancing of the relevant equities (most importantly, the hardship to the nonmovant if the restrainer issues as contrasted with the hardship to the nonmovant if the interim relief is withheld); and (4) The effect on the public interest of a grant or denial of the restrainer.”) 498 CRISTOFER LEFFLER AND KEITH LEFFLER 51 In Antitrust Law Journal, summer 2003, Langenfeld and Li argue that partial settlement agreements, or what we call “interim settlements,” should not be treated as per se illegal (p 810) They argue that “[i]n general, such agreements can have a plausible proconsumer and procompetitive motivation” and that “a per se treatment of such agreements can reduce consumer welfare under plausible circumstances” (pp 805, 810) They conclude that “[t]he courts and agencies should evaluate these partial settlement agreements on a case-by-case basis to determine the validity of the long-run procompetitive motivation, and perform a full rule-of-reason analysis when the procompetitive motivation appears to be valid” (p 810) As we have shown, however, regardless of some “plausible procompetitive motivation,” on the part of the settling parties, lump sum payments are anticompetitive in virtually all cases Per se treatment is, therefore, appropriate The potential welfare losses from the unlikely error of preventing an efficient interim settlement will be far outweighed by the gains from preventing inefficient interim settlements that perpetuate monopoly and by the costs of implementing a rule of reason in these difficult circumstances REFERENCES Publications Addanki, S (2001) Using economics to analyze the competitive implications of IP strategies: An illustrative example Committee Materials (Vol 1, p 53), ABA May Anthony, S F (2000) Riddles and lessons from the prescription drug wars: Antitrust implications of certain types of agreements involving intellectual property Available at http://www.ftc.gov/ speeches/anthony/stip000601.htm Balto, D A (2000) Pharmaceutical patent settlements: The antitrust risks Food & Drug Law Journal, 55, 321 Bork, R (1993) The antitrust paradox Free Press Carlton, D., & Perloff, J (1999) Modern industrial organization Chin, Y W., & Krattenmaker, T G (2001) Antitrust update, Vol 2, Mergers & Acquisitions No 8, p 38 Engelberg, A B (1999) Special patent provisions for pharmaceuticals: Have they outlived their usefulness? IDEA: The Journal of Law and Technology, 39, 389 Gilbert, R J., & Tom, W K (2001) Is innovation king at the antitrust agencies? Committee Materials (Vol 1, p 33), ABA March XII Hovenkamp, Antitrust Law Para 2043, p 237 Jones, C., & Williams, J (1998) Measuring the social return to R&D Quarterly Journal of Economics, 113 Langenfeld, J., & Li, W (2003) Intellectual property and agreements to settle patent disputes: The case of settlement agreements with payments from branded to generic drug manufacturers Antitrust Law Journal, 70, 777 Leary, T B (2001) Antitrust issues in the settlement of pharmaceutical patent disputes, Part II Available at http://www.ftc.gov/speeches/leary/learypharmaceuticalsettlement.htm McDonald, K (2002) Patent settlements and payments that flow the ‘wrong’ way: The early history of a bad idea Healthcare Chronicle, 15(4), Miele, A (2000) Patent strategy: The manager’s guide to profiting from patent portfolios Shapiro, C (2001) Antitrust limits to patent settlements Working Paper (May 1) Tirole (1988) The theory of industrial organization Settling the Controversy Over Patent Settlements 499 Von Kalinowski (n.d.) Antitrust laws & trade regulation (2nd ed.) § 73.02 Willig, R., & Bigelow, J (2002) Antitrust policy towards agreement that settle patent litigation Draft (October) Legal Cases Andrx Pharmaceuticals, Inc v Biovail Corp., 256 F 3d 799 (D.C Cir 2001) Aoude v Mobil Oil Corp., 862 F.2d 890, 892 (1st Cir 1988) Aro Corp v Allied Witan Co., 531 F.2d 1368, 1372 (6th Cir 1976) Bowser, Inc v United States, 388 F.2d 346, 349 (Ct Cl 1967) Broadcast Music Inc v CBS, 441 U.S 1, 19–20 (1979) Brown v Allen, 344 U.S 443, 540 (1953) (Jackson, J., concurring) Discovision v Disc Mfg., Inc., 1997 U.S Dist LEXIS 7507 at ∗ 37–39 (D Del Apr 3, 1997) Engine Specialties, Inc v Bombardier Ltd., 605 F.2d 1, 11 (1st Cir 1979) Eon Labs Manufacturing, Inc v Watson Pharmaceuticals, Inc., 164 F Supp 2d 350 (S D N Y 2001) In re Cardizem CD Antitrust Litigation, 105 F.Supp 2d 682, 685 (E D Mich 2000) In re Ciprofloxacin Hydrochloride Antitrust Litigation, 166 F.Supp.2d 740 (E D N Y 2001) In re Terazosin Hydrochloride Antitrust Litigation, 164 F Supp 2d 1340 (S D Fla 2000) Joy Manufacturing Co v National Mine Service Co., Inc., 810 F.2d 1127, 1131 (Fed Cir 1987) (Newman, J concurring) K-Dur Antitrust Litigation, MDL 1419 (D.N.J.) Magnivision, Inc v Bonneau Co., 115 F.3d 956, 960 (Fed Cir 1997) NCAA v Board of Regents of the University of Oklahoma, 468 U.S 85 (1984) Roper Corp v Litton Systems, Inc., 737 F.2d 1266, 1270 (Fed Cir 1985) Zenith Radio Corp v Hazeltine Research, Inc., 395 U.S 100, 135 (1969) Statutes 35 U.S.C § 282 Federal Food, Drug, and Cosmetic Act, 21 U.S.C § 301 et seq (1994) Federal Rule Civil Procedure 65 U.S Const art I, § 8, cl APPENDIX A Proposition If the disputing parties have equal beliefs about the patent invalidity, there will exist a licensing fee settlement Proof: (A) Find the minimum license fee, Lmin , the patent holder will accept rather than litigate 500 CRISTOFER LEFFLER AND KEITH LEFFLER Define the patent holder’s profit from litigating, L Let I be the probability of invalidity, C the cost of litigation, Pe the price with entry, Qe the quantity with entry, Pm the price with monopoly, and Qm the quantity with monopoly L = 1/2 × I × P e × Q e + (1 − I) × P m × Q m − C For the linear demand case considered, L = 1/2 × I × 1/4 × K × 3/4 × K + (1 − I) × 1/2 × K × 1/2 × K − C = 1/4 × K − 5/32 × K × I − C Define the patent holder’s profit from settling, S, with a licensing fee of L Let Ps be the price with settlement, Qs the quantity with settlement S = 1/2 × P s × Q s + L × 1/2 × Q s For the linear demand case considered, S = 1/2 × (1/2 × 1/2 × K + 1/2 × L) × (K − 1/4 × K − 1/2 × L) + 1/2 × L × (K − 1/4 × K − 1/2 × L) = −3/8 × L + 1/2 × K × L + 3/32 × K Lmin will be defined by the solution of S− S− L = L = −3/8 × L + 1/2 × K × L + [3/32 × K − (1/4 × K − 5/32 × K × I − C)] = Using the quadratic equation to solve for L L = [−1/2 × K + (1/4 × K + 3/2 × {−5/32 × K + 5/32 × K × I + C})1/2 ] (−3/4) (B) Find the maximum fee, Lmax , that the challenger will accept rather than litigate Define the challenger’s profit from litigation L = 1/2 × I × P e × Q e − C For the linear demand case considered, L= 1/2 × I × 1/4 × K × 3/4 × K − C 3/32 × K2 × I − C Settling the Controversy Over Patent Settlements Define the challenger’s profit from settling, 501 S, with a licensing fee of L S = 1/2 × P s × Q s − L × 1/2 × Q s For the linear demand case considered, S = 1/2 × (1/4 × K + 1/2 × L) × (3/4 × K − 1/2 × L) − 1/2 × L × (3/4 × K − 1/2 × L) = 1/8 × L − 1/4 × K × L + 3/32 × K Lmax will be defined by the solution of S− S− L = L = 1/8 × L − 1/4 × K × L + [3/32 × K − (3/32 × K × I − C)] = Using the quadratic equation to solve for L L max = [1/4 × K − (1/16 × K − 1/2 × {3/32 × K − 3/32 × K × I + C})1/2 ] 1/4 (C) A licensing fee settlement will exist as long as Lmax exceeds Lmin L max − L = [1/4 × K − (1/16 × K − 1/2 × {3/32 × K − 3/32 × K × I + C})1/2 ] 1/4 − [−1/2 × K + (1/4 × K + 3/2 × {−5/32 × K + 5/32 × K × I + C})1/2 ] −3/4 = K − × (1/64 × K ∧ + 3/64 × K ∧ × I − 1/2 × C)1/2 − 2/3 × K + 4/3 × (1/64 × K ∧ + 15/64 × K ∧ × I + 3/2 × C) Note that this expression is increasing in both I and C Therefore, the expression will be at its minimum at I = and C = Evaluating at I and C = L max − L = 1/3 × K − × (1/8 × K) + 4/3 × (1/8 × K) = Therefore L max − L will be positive for all values of I and C > APPENDIX B Proposition There exists an efficient licensing fee settlement with equal beliefs as to patent invalidity 502 CRISTOFER LEFFLER AND KEITH LEFFLER Proof: (A) Define the price with litigation, Plit P lit = (1 − I) × P m + I × P e For the linear demand case considered, P lit = 1/2 × K − 1/4 × K × I (B) Define the price at the minimum licensing fee of Lmin , Plmin P lmin = 1/2 × (P m + L ) For the linear demand case considered, P lmin = 7/12 × K − 2/3 × (1/64 × K ∧ + 15/64 × K ∧ × I + 3/2 × C)1/2 (C) An efficient licensing settlement will exist if Plit exceeds Plmin P lit − P lmin = 1/2 × K − 1/4 × K × I − 7/12 × K + 2/3 × (1/64 × K ∧ + 15/64 × K ∧ × I + 3/2 × C)1/2 − 1/12 × K − 1/4 × K × I + 2/3 × (1/64 × K ∧ + 15/64 × K ∧ × I + 3/2 × C)1/2 Note that this expression is increasing in C Therefore, it will be minimized for C = Evaluating at C = 0, we have P lit − P lmin = −1/12 × K − 1/4 × K × I + 2/3 × ([1/64 × K ∧ 2] + [15/64 × K ∧ × I])1/2 − 1/12 × K − 1/4 × K × I + 1/12 × K × (1 + 15 × I)1/2 Since this expression is positive for all values < I > 1, an efficient licensing settlement exists Settling the Controversy Over Patent Settlements 503 APPENDIX C Details of Simulations Assumptions for Base-Case Simulation # Cases The intrinsic probability of invalidity ranges from 0.1 to 0.9 in 0.1 increments The challenger’s expectations as to invalidity have a mean probability with a distribution such that for each 1/4 of the interval between the intrinsic probability and the bounds of and 1, there is a probability density equal to the area under a normal curve for the appropriate number of standard deviations from the mean These expectations are evaluated at the mean and at the mid point of each of three standard deviations to the left and the right of the intrinsic probability The remaining probability is split between the left and right tails The challenger’s expectations are evaluated at the mean of each standard deviation interval The patent holder’s expectations are distributed just like the challenger’s The distributions are independent The costs of litigation are varied from 1.25% of the monopoly profit to 12.5% of the monopoly profit in 1.25% intervals Total cases × × × 10 (equal to the intrinsic) 10 7,290 504 CRISTOFER LEFFLER AND KEITH LEFFLER APPENDIX D Table A4 Probability of Various Settlement Possibilities.a Number of Cases Considered = 7,290 Litigation not expected Expected entry profit negative Conceding entry profit > litigation Both 1.a and 1.b No settlement expected Settlement expected Fee settlement possible Only lump sum settlement possible Positive surplus from settlement Negative surplus from settlement Expectation of Result (%) Probability for Settling Cases (%) Expected Surplus Gain 44.29 38.96 5.29 0.04 4.99 54.47 46.98 3.74 0.90 2.85 92.62 0.33507 1.77 5.61 0.00299 −0.02161 Note: Intrinsic Prob of Invalidity, Quasi Normal, Mean = 0.1 Settlement of licensing fee at midpoint of Lmin and Lmax a The cases are probability weighted for the likelihood of the beliefs as to invalidity APPENDIX E Table A5 Probability of Various Settlement Possibilities.a Number of Cases = 7,290 No risk aversionb Litigation not expected No settlement expected Settlement expected Fee settlement possible Only lump sum settlement +Surplus from settlement − Surplus from settlement With risk aversionc Litigation not expected No settlement expected Settlement expected Fee settlement possible Only lump sum settlement +Surplus from settlement − Surplus from settlement a The Expectation of Result (%) Probability for Settling Cases (%) Expected Surplus Gain 92.89 7.11 0.59 6.51 0.00120 −0.03449 99.49 0.51 0.11 0.40 0.00016 −0.00172 19.03 2.46 78.51 30.83 0.10 68.73 cases are probability weighted for the likelihood of the beliefs as to invalidity