BEEZER, Circuit Judge:
Appellants William McGlinchy and Dan-de Products Corporation filed claims against various defendants for antitrust violations, breach of contract, and related torts. They appeal from the district [805]*805court’s (1) grant of summary judgment in favor of certain defendants; (2) denial of appellants’ motion to amend their complaint; (3) grant of judgment on the pleadings for failure to state an antitrust claim concerning the polybutylene market; (4) dismissal of the antitrust claims for lack of subject matter jurisdiction; and (5) dismissal of the claims against Shell International Chemical Company for lack of personal jurisdiction. We affirm.
I
In 1977 Shell Chemical Company purchased all the patents, rights, and commercial production facilities for polybutylene (PB) from Whetco Company. PB resin is used to manufacture various products, including piping designed to carry water.
In 1978 William McGlinchy entered into an oral agreement with Shell Chemical to promote the sale of PB pipe grade resin in Southeast Asia. On January 25,1979, Dan-de Products Corporation, owned and operated by McGlinchy, entered into a written contract with Shell Chemical for the same purpose. The written contract designated Dan-de as Shell Chemical’s representative for the promotion and solicitation of orders for PB pipe resin in designated countries throughout Southeast Asia. The contract expressly provided that it would remain in force for one year, ending December 81, 1979, with year-to-year renewal subject to termination at year-end upon 30 days prior notice. The written contract was extended in May 1979 to include Saudi Arabia.
On April 6, 1981 McGlinchy entered into a written contract with Shell Chemical to promote PB resin in South America. In June 1980 Dan-de and Shell International Chemical Company (SICC) entered into a similar written contract covering sale and promotion of PB resin in Africa and the Middle East.
On November 5, 1982 Shell Chemical notified McGlinchy and Dan-de in writing that the contract for promotion and sale of PB resin in Southeast Asia and Saudi Arabia would be terminated. The contract remained in force through December 31, 1982, and Shell Chemical continued to pay Dan-de commissions on actual sales through the end of 1983 as the contract required. The contract between Shell Chemical and McGlinchy covering PB resin sales and promotion in South America and the contract between SICC and Dan-de covering Middle Eastern and African PB resin sales were also terminated in 1982 by Shell Chemical and SICC, respectively, pursuant to the terms of those contracts.
In February 1984 McGlinchy and Dan-de (collectively, appellants) instituted this action against Shell Oil Company, Shell Chemical Co. and Pecten Chemicals, Inc. (collectively, Shell Oil defendants), SICC, and other Shell-related entities. The original complaint alleged federal and state antitrust violations, as well as breach of contract and related torts. Appellants filed a first amended complaint on May 29, 1984.
SICC subsequently moved to dismiss for lack of personal jurisdiction, failure to state a claim upon which relief can be granted, and lack of subject matter jurisdiction pursuant to 15 U.S.C. § 6a. Shell Oil defendants joined in the motion to dismiss for lack of subject matter jurisdiction. On November 30, 1984, the district court granted SICC’s motion to dismiss for lack of personal jurisdiction and further granted the motion to dismiss joined by Shell Oil defendants for lack of subject matter jurisdiction under section 6a.
Appellants next moved for leave to file a second amended complaint to add several manufacturers of PB pipe fittings as defendants and to add new antitrust claims relating to the promotion and sale of such fittings. On March 1, 1985 the district court denied appellants’ motion to file a second amended complaint but allowed them to add four causes of action against newly named PB pipe fitting defendants. Appellants then filed an amended first amended complaint (AFA complaint) against the Shell Oil defendants and the PB pipe fitting defendants.1
[806]*806Shell Oil defendants moved for judgment on the pleadings with respect to the federal and state antitrust claims relating to PB pipe fittings. The PB pipe fitting defendants joined in the motion, which the district court granted on June 7, 1985.
Subsequently the district court denied motions brought by Shell Oil defendants for summary judgment on appellants’ breach of contract claim and for judgment on the pleadings on the remaining claims.
In December 1985 appellants again attempted to amend their complaint to add claims for relief against Shell Oil defendants for fraud and negligent interference with contract. On February 7, 1986 the district court denied the motion and subsequently set the case for trial in May 1986.
After all the parties had taken the depositions of each side’s damages experts and discovery had closed, Shell Oil defendants moved the court to exclude the testimony of appellants’ damages experts and to enter judgment against appellants for failure to offer a competent theory proving the fact or amount of damages. The district court granted Shell Oil defendants’ motion on May 31, 1986, and entered judgment in their favor on June 5, 1986. Appellants’ motion for reconsideration was subsequently denied, and appellants timely appealed.
II
The final proceedings in the district court dealt with appellants’ only remaining claims: Shell Oil defendants’ breaches of contract (including promissory estoppel and quasi-contract) and Shell Oil defendants’ “tortious interference” with appellants’ contracts and business opportunities. Appellants contend that the district court erred in excluding damages studies prepared by appellants’ expert witnesses as well as the future testimony of those expert witnesses. Appellants also contend that the district court erred in granting summary judgment in favor of Shell Oil defendants for appellant’s failure to show a genuine issue about damages. We affirm both the exclusion of evidence and the grant of summary judgment.
A
We review a district court’s evidentiary decisions for an abuse of discretion. Taylor v. Burlington Northern R.R. Co., 787 F.2d 1309, 1315 (9th Cir.1986); United States v. Solomon, 753 F.2d 1522, 1524 (9th Cir.1985) (expert witnesses).
The district court did not abuse its discretion in granting the Shell Oil defendants’ motion to exclude the experts’ damages studies and future testimony. The studies did not meet the standard that, in the context of a motion for summary judgment, an expert must demonstrate his competence or back up his opinion with specific facts. Compare Bulthuis v. Rexall Corp., 789 F.2d 1315, 1318 (9th Cir.1985) (per curiam) (weighing Fed.R.Civ.P. 56(e) and Fed.R.Evid. 705) with United States v. Various Slot Machines on Guam, 658 F.2d 697, 700 (9th Cir.1981). Both the studies and testimony were properly excluded because any probative value was “substantially outweighed by the danger of unfair prejudice, confusion of the issues, or misleading the jury.” Fed.R.Evid. 403. See Solomon, 753 F.2d at 1525.
Appellants’ final list of witnesses designated Stephen Jizmagian as an expert witness on damages. As his deposition shows, appellants asked Jizmagian to forecast future lost profits to the McGlinchy companies after a change in relations between the McGlinchys and Shell. On the one hand, Jizmagian stated that he quantified in dollar terms the effect of the act or acts by Shell Oil Company, and that he attributed all of the future lost profits to acts of Shell Oil Company. On the other hand, Jizmagian acknowledged that he did not relate the loss to specific acts and, indeed, could not recall any specific acts by Shell Oil defendants. He added that the cause of the decline in sales theoretically could have been anything. Given this inconsistency, Jizmagian’s report and testimony would pose a great danger of confusing the fact and cause of damages with the amount of damages.
[807]*807Even as a “before and after” assessment of appellants’ damages from a hypothetical injury, Jizmagian’s study was hopelessly flawed. He did not confirm that relevant market conditions were the same before and after the time the injury was alleged to have occurred. See Pacific Coast Agric. Export Ass’n v. Sunkist Growers, Inc., 526 F.2d 1196, 1206-07 (9th Cir.1975), cert. denied, 425 U.S. 959, 96 S.Ct. 1741, 48 L.Ed.2d 204 (1976).
Worse, appellants’ causes of action specify that Shell Oil defendants breached obligations and tortiously interfered with appellants’ contracts and business opportunities involving particular product lines and in particular overseas countries and territories. Jizmagian, however, compiled his report and was prepared to testify on the basis of the appellants’ gross sales. He stated that he did not know which of appellants’ product lines had declined in sales, or in which geographic areas — even as between the United States and the rest of the world. Jizmagi-an’s report and testimony would pose a great danger of misleading a jury into believing that appellants’ losses associated with a decline in gross sales were the amount of damages to appellants from “lost profits” in particular product lines and territories.
Jizmagian’s speculation about the amount of appellants’ “lost profits” has no basis in the record. His study rests on unsupported assumptions and ignores distinctions crucial to arriving at a valid conclusion. See Various Slot Machines on Guam, 658 F.2d at 700 (quoting Merit Motors, Inc. v. Chrysler Corp., 569 F.2d 666, 672-73 (D.C.Cir.1977)). The district court did not abuse its discretion in excluding Jizmagian’s study and future testimony.
Appellants alternately named William McGlinchy as an expert witness and as a witness on damages, but never as an expert witness on damages. The parties, nevertheless, treated William McGlinchy as an expert witness on damages in Southeast Asia. The district court evaluated William McGlinchy as an expert witness on those damages.
In making his study William McGlinchy’s method was to forecast polybutylene resin sales, apply a given commission rate, and subtract out expenses to arrive at the net profits appellants would have earned but for the loss of their contract. The study’s value depends heavily on the accuracy of the sales forecast. To forecast sales through 1987, William McGlinchy said that he “took the 838,000 pounds for 1982 actual sales and applied the 41 percent [compound annual] growth figure.” He asserted that he based the 41 percent growth rate on local economic data, country by country in Southeast Asia, dating from the 1970’s.
Yet William McGlinchy later acknowledged that in fact he first divined a total sales figure for 1987, then plugged in a compound growth rate — 41 percent — that would work backward to the 1982 actual sales figure. Although the study stated that companies he had been associated with had enjoyed growth rates of 41 percent and 83 percent, the study gave no indication of how he estimated a total sales figure for 1987. Lacking any sound foundation, the study would mislead a jury into believing that damages had grown exponentially over the relevant period.
Other aspects of the study would have the same effect. For instance, the study assumed that expenses would stay at $60,-000 per year for nine years through 1991. When asked how he had arrived at the $60,000 per year figure, William McGlinchy replied, “I believe I arrived at it from experience plus inflation.” The flat figure, however, could reflect neither experience nor inflation. William McGlinchy did not otherwise document the figure.
Indeed, he documented little of the basis for his conclusions. His speculation about the amount of appellants’ damages has scant basis in the record. His study rests on unsupported assumptions and unsound extrapolation. See Various Slot Machines on Guam, 658 F.2d at 700 (quoting Merit Motors, Inc., 569 F.2d at 672-73). The district court did not abuse its discretion in excluding William McGlinchy’s study and future testimony.
[808]*808B
After excluding the experts’ studies and testimony, the district court granted Shell Oil defendants’ motion for summary judgment. A summary judgment “shall be rendered forthwith if the pleadings, depositions, answers to interrogatories, and admissions on file, together with the affidavits, if any, show that there is no genuine issue as to any material fact and that the moving party is entitled to a judgment as a matter of law.” Fed.R.Civ.P. 56(c). We review a grant of summary judgment de novo, viewing the evidence in a light most favorable to the non-moving party. Dolphin Tours v. Pacifico Creative Serv., 773 F.2d 1506, 1509 (9th Cir.1985).
The district court properly granted summary judgment in favor of Shell Oil defendants. In Celotex Corp. v. Catrett, 477 U.S. 317, 106 S.Ct. 2548, 91 L.Ed.2d 265 (1986), a majority consisting of five justices said, “In our view, the plain language of Rule 56(c) mandates the entry of summary judgment, after adequate time for discovery and upon motion, against a party who 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.” Id. 106 S.Ct. at 2552-53.
Before the district court granted summary judgment, appellants did not make a showing sufficient to establish the amount, causation, or fact of damages. The only evidence about amount of damages consisted in the studies of Jizmagian and William McGlinchy, previously excluded by the district court. The only other mention appellants made of damages was in listing William and Don McGlinchy as lay witnesses who would testify on damages. Appellants made no showing at all about causation or fact of damages.
After the district court granted summary judgment, Jizmagian, William McGlinchy, and Don McGlinchy made declarations about damages in connection with appellants’ motion for reconsideration of summary judgment. These declarations added nothing to the pleadings, depositions, and other papers that the appellants already had filed.
Appellants seek comfort from the concurring opinion in Celotex by Justice White, who also joined the majority opinion. They argue that naming a witness to support a claim defeats summary judgment unless the movant somehow shows that the named witness’s possible testimony raises no genuine issue of material fact. Cf id. at 2555-56 (White, J., concurring).
Even under this standard the district court properly granted summary judgment to Shell Oil defendants. The district court had excluded the damages studies by William McGlinchy and Jizmagian. Appellants named William McGlinchy and Don McGlinchy as lay witnesses on damages. In his deposition William McGlinchy, a plaintiff in this case, acknowledged that the damages studies by himself and Jizma-gian were the only ones prepared for the lawsuit; William McGlinchy specified that he generated his own study without contribution from Don McGlinchy.
Some sort of study estimating the amount of damages was essential to appellants’ case. As this court said in Dolphin Tours, the plaintiffs “must provide evidence such that the jury is not left to ‘speculation or guesswork’ in determining the amount of damages to award.” 773 F.2d at 1509-10. Summary judgment is appropriate where appellants have no expert witnesses or designated documents providing competent evidence from which a jury could fairly estimate damages. Rickards v. Canine Eye Registration Found., Inc., 704 F.2d 1449, 1452 (9th Cir.) (antitrust case), cert. denied, 464 U.S. 994, 104 S.Ct. 488, 78 L.Ed.2d 683 (1983).
In the absence of another study besides those that the district court had properly excluded, or the possibility that Don McGlinchy could rehabilitate William McGlinchy’s defective study, appellants could make no showing about the amount of damages. By eliminating these possibilities, Shell Oil defendants made their showing that the named witnesses’ possible testimony would raise no genuine issue of material fact about the amount of damages [809]*809appellants had sustained. Cf. Celotex, 106 S.Ct. at 2555-56 (White, J., concurring).
Once Shell Oil defendants made this showing, the burden was on appellants to come forward with specific facts showing there was a genuine issue for trial. Fed.R.Civ.P. 56(e); see Matsushita Elec. Indus. Co. v. Zenith Radio, 475 U.S. 574, 106 S.Ct. 1348, 89 L.Ed.2d 538 (1986). Appellants did not meet this burden; they produced no evidence at all to contradict Shell Oil defendants’ showing, or even to enable contradictory inferences. See British Airways Bd. v. Boeing Co., 585 F.2d 946, 951 (9th Cir.1978), cert. denied, 440 U.S. 981, 99 S.Ct. 1790, 60 L.Ed.2d 241 (1979). The declarations appellants submitted when seeking reconsideration of summary judgment merely restated the pleadings; as the Court pointed out in Celotex, 106 S.Ct. at 2554, Federal Rule 56(e) does not allow a party to oppose summary judgment on the pleadings themselves.
Unlike in Wool v. Tandem Computers Inc., 818 F.2d 1433, 1438 (9th Cir.1987), in this case appellants submitted no specific facts on which a finder of fact could reasonably conclude that appellants actually suffered damages, caused by Shell Oil defendants, in any quantifiable amount. The district court properly granted summary judgment in favor of Shell Oil defendants.
Ill
Appellants contend that the district court erred in denying appellants leave to amend their complaint to add causes of action for fraud and negligent misrepresentation. We affirm the district court’s denial of leave to amend.
Federal Rule of Civil Procedure 15(a) states that leave to amend “shall be freely given when justice so requires.” Bearing that standard in mind, we review a district court’s denial of a motion for leave to amend for an abuse of discretion. Unless we have a definite and firm conviction that the district court committed a clear error of judgment, we will not disturb the district court’s decision. California Arch. Bldg. Prod. v. Franciscan Ceramics, 818 F.2d 1466, 1472 (9th Cir.1987), cert. denied, — U.S. -, 108 S.Ct. 698, 98 L.Ed.2d 650 (1988).
“[U]ndue delay” is one valid reason for a district court to deny a party leave to amend. Id. at 1472 (citing Foman v. Davis, 371 U.S. 178, 182, 83 S.Ct. 227, 230, 9 L.Ed.2d 222 (1962)). Appellants claim that they only became aware of claims for fraud and negligent interference with contract after engaging in discovery in May 1985. Appellants should have been aware of a claim for negligent interference when they filed their original complaint, which included a claim for tortious interference. In any case, appellants did not give notice of their intention to amend their complaint until the middle of December, at least six months after they had become aware of the new claims. Discovery originally was scheduled to end on November 15, 1985, and a trial date was set for December 2, 1985. Appellants waited until the original trial date had been vacated to attempt to amend their complaint. This delay was undue.
“[Prejudice” is another valid reason for a district court to deny a party leave to amend. Id. at 1472 (citing Foman, 371 U.S. at 182, 83 S.Ct. at 230). Appellants contend that- Shell Oil defendants would have suffered no prejudice because discovery already had covered all the issues presented by the new claims for fraud and negligent interference with contract. As Shell Oil defendants point out, if appellants’ contention were true their delay in seeking leave to amend would be even more inexcusable. In fact the new claims, especially fraud, would have required additional discovery on a wide range of new issues; that discovery likely would have included new depositions by Shell Oil defendants’ employees. The new claims would have required additional research and rewriting of trial briefs. The resulting delay and expense would have prejudiced Shell Oil defendants, who were entitled to rely on a timely close of discovery and a near-term trial date.
Repeated failure to cure deficiencies by amendments previously allowed is [810]*810another valid reason for a district court to deny a party leave to amend. Foman, 371 U.S. at 182, 83 S.Ct. at 230. In February 1984 appellants filed their complaint. In May 1984 they filed a first amended complaint. In early 1985 they filed an amended first amended complaint. Appellants had ample opportunity to add new claims to their complaint.
The district court did not abuse its discretion in denying appellants leave to amend their complaint in February 1986; justice did not require otherwise.
IV
With respect to their antitrust claims concerning the PB market, the appellants appeal a judgment on the pleadings in favor of Shell Oil defendants and defendant U.S. Brass Corp., a manufacturer of insert pipe fittings. Because appellants’ complaint does not sufficiently state a claim upon which relief can be granted, we affirm the district court’s order.
We review de novo a dismissal by judgment on the pleadings under Rule 12(c). Gearhart v. Thorne, 768 F.2d 1072, 1073 (9th Cir.1985). All allegations of fact by the party opposing the motion are accepted as true. Doleman v. Meiji Mut. Life Ins. Co., 727 F.2d 1480, 1482 (9th Cir.1984). A dismissal on the pleadings for failure to state a claim is proper only if “the movant clearly establishes that no material issue of fact remains to be resolved and that he is entitled to judgment as a matter of law.” Id. (quoting 5 C. Wright & A. Miller, Federal Practice and Procedure: Civil § 1368, at 690 (1969)); see also General Cinema Corp. v. Buena Vista Distrib., 681 F.2d 594, 597 (9th Cir.1982).
In this case Rule 12(c) was used to raise the defense of failure to state a claim. See Aldabe v. Aldabe, 616 F.2d 1089, 1093 (9th Cir.1980). As a result, the motion for judgment on the pleadings faces the same test as a motion under Rule 12(b)(6): this court may affirm the district court’s dismissal “only if it is clear that no relief could be granted under any set of facts that could be proven consistent with the allegations.” Hishon v. King & Spalding, 467 U.S. 69, 73, 104 S.Ct. 2229, 2232, 81 L.Ed.2d 59 (1984); see also Conley v. Gibson, 355 U.S. 41, 45-46, 78 S.Ct. 99, 101-02, 2 L.Ed.2d 80 (1957); Newman v. Universal Pictures, 813 F.2d 1519, 1521-22 (9th Cir.1987). Not only must the court accept all material allegations in the complaint as true, but the complaint must be construed, and all doubts resolved, in the light most favorable to the plaintiff. NL Indus,, Inc. v. Kaplan, 792 F.2d 896, 898 (9th Cir.1986); Ernest W. Hahn, Inc. v. Codding, 615 F.2d 830, 834-35 (9th Cir.1980). Nonetheless, conclusory allegations without more are insufficient to defeat a motion to dismiss for failure to state a claim. McCarthy v. Mayo, 827 F.2d 1310, 1317 (9th Cir.1987).
B
In their AFA complaint appellants sued under sections 1 and 2 of the Sherman Act, 15 U.S.C. §§ 1 & 2,2 as well as under the California Business and Professional Code, §§ 16700-16760 (California Cartwright Act). Because the district court concluded that appellants had inadequately pleaded antitrust injury to maintain a claim under the Sherman and California Cartwright Acts, the district court granted the defendants’ motion for judgment on the pleadings for failure to state a claim.
Appellants contend that their complaint stated sufficient facts to preclude judgment on the pleadings on their federal and state antitrust claims relating to the PB pipe fitting market. Shell Oil defendants maintain that appellants have insufficiently [811]*811pleaded antitrust standing or antitrust injury. Defendant U.S. Brass Corp. also argues that the district court properly granted judgment on the pleadings because the complaint pleaded no antitrust injury and did not adequately allege the elements of an antitrust claim.
To establish a section 1 violation under the Sherman Act, a plaintiff must demonstrate three elements: (1) an agreement, conspiracy, or combination among two or more persons or distinct business entities; (2) which is intended to harm or unreasonably restrain competition; and (3) which actually causes injury to competition, beyond the impact on the claimant, within a field of commerce in which the claimant is engaged (i.e., “antitrust injury”). See Coastal Transfer Co. v. Toyota Motor Sales, U.S.A., 833 F.2d 208, 211 (9th Cir.1987); Aydin Corp. v. Loral Corp., 718 F.2d 897, 902 (9th Cir.1983); Rickards v. Canine Eye Registration Found., 783 F.2d 1329, 1332 (9th Cir.), cert. denied, — U.S. -, 107 S.Ct. 180, 92 L.Ed.2d 115 (1986); Cascade Cabinet Co. v. Western Cabinet & Millwork, 710 F.2d 1366, 1373 (9th Cir.1983).3
To establish a section 2 violation for an attempt to monopolize, a plaintiff must demonstrate four elements: (1) specific intent to control prices or destroy competition; (2) predatory or anti-competitive conduct directed toward accomplishing that purpose; (3) a dangerous probability of success; and (4) causal antitrust injury. Supermarket of Homes v. San Fernando Valley Bd., 786 F.2d 1400, 1405 (9th Cir.1986); Rickards, 783 F.2d at 1335.
A fair and liberal construction of the complaint demonstrates that appellants failed to allege the requisite antitrust injury to competition that is required under both sections 1 and 2 of the Sherman Act.4 The Sherman Act itself speaks of “restraint[s] of trade or commerce,” 15 U.S.C. § 1, and attempted monopolization of “trade or commerce,” 15 U.S.C. § 2, not individual competitors in a market. The alleged violation must cause injury to competition beyond the impact on the claimant under section 1, and must destroy competition and cause antitrust injury under section 2. To state an antitrust claim, therefore, appellants must allege “antitrust injury, which is to say injury of the type the antitrust laws were intended to prevent. ... The injury should reflect the anticompetitive effect either of the violation or of anticompetitive acts made possible by the violation.” Brunswick Corp. v. Pueblo Bowl-O-Mat, Inc., 429 U.S. 477, 489, 97 S.Ct. 690, 697, 50 L.Ed.2d 701 (1977) (emphasis in original). The antitrust laws [812]*812were enacted for “the protection of competition, not competitors.” Brown Shoe Co. v. United States, 370 U.S. 294, 320, 82 S.Ct. 1502, 1521, 8 L.Ed.2d 510 (1962) (emphasis in original).
In their AFA complaint appellants mechanically assert that the alleged violations of the antitrust laws “have had and continue to have a substantial effect on interstate and foreign trade and commerce.” Appellants later specifically identify the relevant market by alleging: “For the purposes of the antitrust claims alleged herein, PB is the relevant market for determining the anti-competitive effects of the defendant’s actions.” Nowhere in their AFA complaint, however, do appellants allege injury to the competitive market for PB. Instead, they allege that the actions between Shell Oil defendants and their overseas affiliates “were taken for the purpose of eliminating McGlinchy and Dan-de as representatives of Shell Chemical and as sellers of PB and PB-related products, and for the financial benefit of defendant Shell Chemical and the parties acting in concert with such defendant.” Thus appellants fail to state an antitrust claim based on defendants’ conduct with respect to PB and PB-related products. It is injury to the market or to competition in general, not merely injury to individuals or individual firms that is significant. Ralph C. Wilson Indus. v. Chronicle Broadcasting Co., 794 F.2d 1359, 1363 (9th Cir.1986); Fine v. Barry and Enright Prods., 731 F.2d 1394, 1399 (9th Cir.), cert. denied, 469 U.S. 881, 105 S.Ct. 248, 83 L.Ed.2d 186 (1984).
Appellants also allege that Shell Oil defendants and other defendant manufacturers of PB insert pipe fittings “engaged in a conspiracy and a systematic pattern and practice to eliminate flare fittings from the marketplace, particularly the flare fittings sold by plaintiffs.”5 Appellants allege that the “[c]o-conspirators and said defendants are in violation of the Sherman Act due to their attempt to monopolize the market for fittings for PB plumbing pipe and by wrongfully attempting to eliminate the flare fittings sold by plaintiffs.” Finally, appellants allege that Shell Oil defendants, in concert with defendants who compete with the appellants in the PB fittings market, “have engaged in a conspiracy to eliminate plaintiffs from the domestic fittings market, and also have seriously undermined plaintiffs' position in the foreign market, resulting in an unreasonable restraint of trade.”
These allegations focus on defendants’ conduct with respect to flare fittings. In their brief appellants argue that they alleged injury in the pipe fittings market, rather than the PB market. As appellants are forced to concede, however, the AFA complaint plainly alleges that “PB is the relevant market for determining the anti-competitive effect of defendant’s actions.”6
In addition, appellants’ allegations amount to an assertion that appellants’ own fittings business has been injured by the defendants’ conduct. Even if appellants claim a substantial loss to their flare fitting business within the broader PB market, “economic injury to a competitor does not equal injury to competition.” Cascade Cabinet Co., 710 F.2d at 1373. The elimination of a single competitor, without more, does not prove anticompetitive effect. Kaplan v. Burroughs Corp., 611 F.2d 286, 291 (9th Cir.1979), cert. denied, 447 U.S. 924, 100 S.Ct. 3016, 65 L.Ed.2d 1116 (1980). As we have stated:
Proof that the defendant’s activities had an impact upon competition in a relevant market is an absolutely essential element of the rule of reason case. It is the impact upon competitive conditions in a [813]*813definable market which distinguishes the antitrust violation from the ordinary business tort.
Id. Appellants’ failure to allege injury to competition is a proper ground for dismissal by judgment on the pleadings. See Seattle Totems Hockey Club v. National Hockey League, 783 F.2d 1347, 1350 (9th Cir.), cert. denied, — U.S.-, 107 S.Ct. 405, 93 L.Ed.2d 357 (1986).
Because appellants can prove no set of facts consistent with their complaint that would entitle them to relief under the antitrust laws, appellants have not sufficiently stated an antitrust claim relating to the PB market.
Y
Appellants appeal the district court’s dismissal of their Sherman Act claims — alleging concerted and unilateral refusal to deal in various foreign markets — against SICC and the Shell Oil defendants. Because appellants pleaded only injury to customers or potential customers located in Southeast Asia and to plaintiffs themselves, we affirm the district court’s holding that 15 U.S.C. § 6a precluded subject matter jurisdiction.7
The existence of subject matter, jurisdiction presents a question of law reviewable de novo. See Peter Starr Prod. Co. v. Twin Continental Films, Inc., 783 F.2d 1440, 1442 (9th Cir.1986).
Appellants argue that their antitrust claims do not relate exclusively to foreign commerce and that their allegations meet the requirements of section 6a. Moreover, they contend that their complaint has alleged injury to competition in the United States in the relevant market.
SICC responds that appellants have not met the requirements of subsections 1(A) and 1(B) by showing that any effect on United States commerce was “direct, substantial, and reasonably foreseeable.” 15 U.S.C. § 6a. In addition, SICC maintains that appellants have not sufficiently alleged an antitrust violation as required by subsection 2 of section 6(a). Shell Oil defendants argue that because all of the purportedly illegal conduct by defendants lacks the requisite domestic effect, the district court properly dismissed the antitrust claims alleging concerted and unilateral refusal to deal in various foreign markets for lack of subject matter jurisdiction under section 6a.
Section 6a was added by the Foreign Trade Antitrust Improvements Act of 1982, Pub.L. No. 97-290, 96 Stat. 1246. It provides:
Sections 1 to 7 of this title shall not apply to conduct involving trade or commerce (other than import trade or import commerce) with foreign nations unless—
(1) such conduct has a direct, substantial, and reasonably foreseeable effect—
(A) on trade or commerce which is not trade or commerce with foreign nations, or on import trade or import commerce with foreign nations; or
(B) on export trade or export commerce with foreign nations, of a person engaged in such trade or commerce in the United States; and
(2) such effect gives rise to a claim under the provisions of sections 1 to 7 of this title, other than this section.
If sections 1 to 7 of this title apply to such conduct only because of the operation of paragraph (1)(B), then sections 1 to 7 of this title shall apply to such conduct only for injury to export business in the United States.
15 U.S.C. § 6a.8 There is little case law interpreting this section. In Eurim-[814]*814Pharm GmbH v. Pfizer, Inc., 593 F.Supp. 1102 (S.D.N.Y.1984), the district court granted defendants’ motion to dismiss for lack of subject matter jurisdiction because the plaintiff had failed to establish that defendants’ alleged conduct resulted in an anticompetitive effect on United States domestic or import commerce. Id. at 1107. The court reasoned that section 6a "was intended to exempt from United States antitrust law conduct that lacks the requisite domestic effect, even where such conduct originates in the United States or involves American-owned entities operating abroad.” Id. at 1106.
In Liamuiga Tours v. Travel Impressions, Ltd., 617 F.Supp. 920 (E.D.N.Y.1985), the district court dismissed a plaintiff’s antitrust claim under section 6a because there was “no jurisdictional nexus” for the court to decide the claim under the Sherman Act. Id. at 925. The court reasoned that section 6a’s legislative history demonstrated that “the effect required for jurisdictional nexus must be an anticompet-itive effect in the domestic market.” Id. at 924.
In The ‘In’ Porters, S.A. v. Hanes Printables, Inc., 663 F.Supp. 494 (M.D.N.C.1987), the district court dismissed an antitrust claim because the foreign company plaintiff failed to meet the jurisdictional requirements of section 6a. Id. at 501. The court reasoned that section 6a “establishes three requirements that an antitrust plaintiff, other than a domestic importer, must prove to establish subject matter jurisdiction: (1) the defendant’s conduct must have a direct, substantial, and reasonably foreseeable effect on (2) plaintiffs continuing ability to export (3) from the United States." Id. at 500 (emphasis in original; footnote omitted). The court concluded that the foreign company plaintiff failed to establish that it was within the class of injured United States exporters. Id.
In McElderry v. Cathay Pacific Airways, 1988 U.S.Dist. LEXIS 660, 1988-1 Trade. Cas. (CCH) 1167,878, at 57,387, 678 F.Supp. 1071, 1077. (S.D.N.Y. Feb. 3, 1988), the district court dismissed plaintiff's antitrust claims "for failure to meet the requirements of [section 6a].” Id. at 57,388, 678 F.Supp. at 1077. The court reasoned that under section 6a federal courts do not have jurisdiction under the Sherman Act unless there is a direct, substantial, and reasonably foreseeable anti-competitive effect on United States commerce, regardless of whether there was anticompetitive conduct in the United States. Id. at 57,388-89, 678 F.Supp. at 1077.
[815]*815In their first amended complaint appellants alleged that their agreement with Shell Chemical involved “the promotion and solicitation of orders for PB resin in Hong Kong, India, Indonesia, Malaysia, the Philippines, Singapore, Taiwan, and Thailand,” including attempts “to locate, develop and to promote local manufacturers or extrud-ers of PB pipe in South East Asia.” Because appellants challenge conduct in their antitrust claim that involves trade or commerce (other than import trade or import commerce) with foreign nations, they must satisfy either subsection (1)(A) or (1)(B), and subsection 2 of section 6a.
Appellants draw our attention to their allegations that “Dan-de was and is now engaged in the domestic and overseas business of selling and promoting pipe,” and that the defendants’ conspiracy resulted “in the termination of plaintiffs’ agreement with Shell Chemical to be its exclusive representative in the sale, promotion, and distribution of PB resin and products in South East Asia and other areas.”
As to subsection (1)(A), appellants have failed to allege that the defendants’ conduct has a “direct, substantial, and reasonably foreseeable effect” on domestic commerce or import trade. 15 U.S.C. § 6a(l)(A). As to subsection (1)(B), appellants have not sufficiently alleged a direct, substantial, and reasonably foreseeable effect on export trade or commerce. 15 U.S. C. § 6a(l)(B). Indeed, in their first amended complaint appellants never maintained that they were exporters.
Finally, appellants have failed to allege an antitrust claim under subsection 2 of section 6a. Appellants must allege antitrust injury to the market or to competition in general, not merely injury to individuals or individual firms. See Ralph C. Wilson Indus., 794 F.2d at 1363; Fine, 731 F.2d at 1399. Appellants’ first amended complaint only alleges injury to themselves, rather than to the relevant market.
After a careful review of the first amended complaint, we conclude that appellants’ claims relate only to foreign commerce without the requisite domestic anti-competitive effect. The district court properly dismissed the antitrust claims concerning refusal to deal in foreign trade and commerce on the ground that the court lacked subject matter jurisdiction.
VI
Appellants argue that the district court improperly dismissed contract and tort claims against SICC for lack of personal jurisdiction. The district court found that it did not have personal jurisdiction over SICC, a nonresident, London-based firm, because appellants failed to demonstrate either “pervasive activities” by SICC in California or “minimum contacts” linking SICC to California. We affirm the district court’s dismissal of the AFA complaint against SICC for lack of personal jurisdiction.
Appellants also argue that the district court erred in denying them leave to amend defects in the AFA complaint. The district court found that appellants’ proposed Second Amended Complaint failed to cure defects in the AFA complaint. We affirm the district court’s denial of leave to amend the AFA by the proposed Second Amended Complaint.
We review dismissal of the complaint against SICC de novo. Fields v. Sedgwick Associated Risks, Ltd., 796 F.2d 299, 301 (9th Cir.1986).
Appellants argue that SICC conducted “pervasive activities” in California, thereby subjecting SICC to personal jurisdiction in that state. The district court found that SICC’s activities were not sufficiently pervasive to subject it to personal jurisdiction under the “pervasive activities” test. As set out in Data Disc, Inc. v. Systems Tech. Assoc., Inc., 557 F.2d 1280, 1287 (9th Cir.1977), this test requires an allegation that “the nonresident[’s] ... activities within the [forum] state are ‘substantial’ or ‘continuous and systematic.’ ”
At no point have appellants alleged facts which would support a prima facie case for personal jurisdiction based on “substantial” or “continuous and systematic” activities in [816]*816California. SICC has never maintained offices, qualified to do business, or regularly solicited business in California. SICC has never assigned agents or employees to work regularly in California, has never owned, used, or possessed real property in California, and has never contracted to supply goods or services in California.
SICC has never conducted any “substantial” or “continuous and systematic” activities in California. Thus SICC has not conducted “pervasive activities” in California.
Alternatively, appellants argue that they alleged sufficient “minimum contacts” in the AFA complaint to establish personal jurisdiction over SICC. We apply three criteria to determine whether sufficient “minimum contacts” exist to establish personal jurisdiction: “(1) the nonresident defendant must perform some act by which he purposefully avails himself of the benefits and protections of the forum's laws; (2) the plaintiff's claim must arise out of or result from the defendant’s forum-related activities; and (3) the exercise of jurisdiction must be reasonable.” Raffaele v. Compagnie Generale Maritime, 707 F.2d 395, 397 (9th Cir.1983); see also Data Disc, 557 F.2d at 1287.
Appellants allege that because the contract between SICC and appellants was signed by appellants in California, SICC “purposely availed” itself of the benefits and protections of California laws. The district court considered this allegation insufficient to constitute an SICC “act” of “purposefully availing.” We agree.
Four reasons explain why appellants’ execution of the contract in California is insufficient to meet the “purposefully availing” part of the “minimum contacts” test.
First, the contract was negotiated in England. Because “the substance of the relationship was formed” in England, the formality of signing the contract in California cannot establish jurisdiction. R.E. Sanders & Co. v. Lincoln-Richardson Enters., Inc., 108 Cal.App.3d 71, 80, 166 Cal. Rptr. 269, 273-74 (1980) (quoting Lakeside Ridge & Steel Co. v. Mountain State Constr. Co., 597 F.2d 596, 604 (7th Cir.1979), cert. denied, 445 U.S. 907, 100 S.Ct. 1087, 63 L.Ed.2d 325 (1980).
Second, the contract makes no reference to California or to the United States, either as appellants’ place of residence or as a forum for dispute settlement.
Third, no authorized agents of SICC were alleged to have performed or executed any portion of the contract in California. The parties conducted contract execution and termination by international mail. Such contacts are insufficient to constitute an act purposefully availing SICC of California laws. See Interdyne Co. v. SYS Computer Corp., 31 Cal.App.3d 508, 107 Cal.Rptr. 499, 501 (1973).
Fourth, even paired with appellants’ alleged acts of inviting SICC to use and to observe California facilities and expertise, appellants’ allegations fail to state a prima facie case. It is well settled that “[t]he unilateral activity of those who claim some relationship with a nonresident defendant cannot satisfy the requirement of contact with the forum State.” Hanson v. Denckla, 357 U.S. 235, 253, 78 S.Ct. 1228, 1239, 2 L.Ed.2d 1283 (1958).9
Appellants’ invitation to SICC to avail itself of appellants’ California facilities constitutes unilateral activity. In the absence of contractual obligations by SICC, such as sale of goods or services to California residents or a deliberate presence in California, such activity is insufficient to satisfy part one of the “minimum contacts” test. Similarly, apppellants’ statement that they “performed 90% of [their] activities in the Bay Area,” even if accurate, describes only unilateral activity. Again, such activity fails to create personal jurisdiction over SICC.
Thus appellants’ complaint fails to state that SICC “purposefully availed” itself of California’s laws. As we stated in Republic Int’l Corp. v. Amco Eng’rs, Inc., 516 F.2d 161 (9th Cir.1975), “ ‘[a plaintiff’s] per[817]*817formance in California cannot give jurisdiction over ... [a nonresident defendant]; it is [a defendant’s] activity that must provide the basis for jurisdiction.’ ” Id. at 167 (citation omitted). See also Hanson, 357 U.S. at 253, 78 S.Ct. at 1289. Here the complete absence of activity by SICC in California bars personal jurisdiction over SICC.
Appellants suggest that a different result is compelled by our recent holding in Haisten v. Grass Valley Medical Reimbursement Fund, Ltd., 784 F.2d 1392 (9th Cir.1986). In Haisten, we stated:
[R]ecent Supreme Court cases indicate that modification of our three-prong test is appropriate. In particular, within, the rubric of ‘purposeful availment’ the Court has allowed the exercise of jurisdiction over a defendant whose only ‘contact’ with the forum state is the ‘purposeful direction’ of a foreign act having effect in the forum state.
Id. at 1397 (emphasis in original) (quoting Calder v. Jones, 465 U.S. 783, 104 S.Ct. 1482, 79 L.Ed.2d 804 (1984)).
SICC’s contractual obligations were to be carried out expressly in countries other than the United States. The contract makes no reference to California, to appellants’ residence in California, or to any reliance on appellants’ facilities in California. Appellants nevertheless allege that SICC’s contractual obligations constitute a “foreign act purposefully directed]” to have an “effect” in California.
This argument is specious. While the contract was indeed a “foreign act,” it was not “purposefully directed]” to have any “effect” in California. In Haisten, the insurance agreement “explicitly concerned the indemnification of California physicians against liability solely under California malpractice law. Thus, the effect in California was not only foreseeable, it was contemplated and bargained for.” Id. In Calder, which we cited in Haisten, the Supreme Court considered a libel claim by a plaintiff who defendant knew to reside in California. The Calder court noted that defendants “knew that the brunt of that injury would be felt by [the plaintiff] in the State in which’ the National Enquirer [owned by defendant] has its largest circulation.” More specifically, the Calder court pointed to the fact that the defendant’s “intentional, and allegedly tortious, actions were expressly aimed at California.” Calder, 465 U.S. at 789, 104 S.Ct. at 1487 (emphasis added).
The facts of this case are significantly different. The relevant contract does not name California, expressly or by implication. The contract does not name the United States. It does name twenty-one other countries. There are no terms in the contract which would indicate that SICC contemplated an effect in California, much less that any such effect should be considered a material term of agreement. The contract was “purposefully directed” at activities in nations other than the United States; appellants concede this when they recite their “willingness and ability” to “travel anywhere, anytime and any place ... to expand the market for [SICC’s product].”
Finally, unlike in Calder or Haisten, in this case personal jurisdiction is sought on a contract claim, not on a tort claim. Appellants have failed to allege sufficient facts, including a tortious act or effect, to establish personal jurisdiction over their tort claims.
Appellants do not allege an “act ... purposefully availing” SICC of the forum’s laws, or a “foreign act ... purposefully directed ...” at an “effect” in California; hence appellants fail to satisfy part one of the “minimum contacts” test. Having established that appellants did not allege sufficient facts to support personal jurisdiction under either the “pervasive activities” test or under part one of the “minimum contacts” test, we need not consider whether appellants have satisfied parts two and three of the “minimum contacts” test.10 [818]*818The district court properly dismissed appellants’ complaint against SICC for lack of personal jurisdiction.
We review denial of leave to amend a complaint for abuse of discretion. Halet v. Wend Inv. Co., 672 F.2d 1305, 1310 (9th Cir.1982). The deficiencies in the AFA complaint are not cured by new facts or allegations presented by appellants in the proposed Second Amended Complaint. Accordingly, the district court did not abuse its discretion in denying leave to amend by means of the Second Amended Complaint. Id.
VII
The district court did not abuse its discretion in excluding the expert witnesses’ studies and testimony and properly granted summary judgment in favor of Shell Oil defendants on appellants’ contract theory and tortious interference claims. The district court did not abuse its discretion in denying appellants leave to amend their complaint to include claims for fraud and negligent interference with contract.
Because appellants failed to state sufficiently an antitrust claim upon which relief can be granted, the district court properly granted judgment on the pleadings in favor of Shell Oil and PB pipe fitting defendants. The district court also properly dismissed appellants’ Sherman Act claims against SICC and Shell Oil defendants relating to various foreign markets. Appellants’ complaint does not satisfy the requirements of 15 U.S.C. § 6a, thereby depriving the district court of subject matter jurisdiction.
The district court properly dismissed appellants’ AFA complaint against SICC for lack of personal jurisdiction and did not abuse its discretion in denying appellants leave to amend.
AFFIRMED.