By this appeal Dolphin Tours, Inc. (Dolphin) challenges the district court’s grant of summary judgment in favor of various tour operators which conducted Japanese language tours of northern California. We reverse the grant of summary judgment and remand to the district court for further proceedings.

BACKGROUND

Dolphin brought this action for alleged violations of sections 1 and 2 of the Sherman Act, 15 U.S.C. §§ 1 and 2. Dolphin seeks treble damages under section 4 of the Clayton Act, 15 U.S.C. § 15 , and injunc-tive relief under § 16 of the Clayton Act, 15 U.S.C. § 26 . Dolphin claims that the defendants formed a cartel to keep the price of Japanese language tours artificially high, formulated a plan by which various gift shops which were made part of the defendants’ tours paid kickbacks to the defendants, and conspired to eliminate Dolphin from the Japanese language tour market (the “market”).

In order to establish its damages Dolphin engaged the services of a tourism expert and economist, Dr. James Mak, a survey research firm, SMS Research Corporation (SMS), and an accountant, Dr. David Weiner. A survey was prepared by Dr. Mak and SMS, and administered by SMS. The results of this survey were then used as the basis of Dr. Mak’s report (the “Report”) on the market share Dolphin could have attained in the market and as base figures by Dr. Weiner to project the net profit Dolphin could have made at the projected market shares.

The survey was designed to test whether Japanese tourists preferred tours given by Japanese tour operators or American tour operators, and whether their choice would be affected by price differences. The survey approach was roughly as follows. Two samples of Japanese tourists were interviewed in Hawaii. Only the responses of Japanese tourists traveling on pre-paid package tours were considered. The tourists interviewed were given a choice between two tour companies, A or B. A was given characteristics associated with a Japanese tour operator, including ease of access and greater certainty in booking. B was given characteristics associated with an American tour operator, including use of native American tour guides who spoke Japanese. The tourist was asked which tour operator he would choose if the tour prices were the same. He was then asked whether his choice would be the same if the tour he did not choose was five, ten, or fifteen dollars cheaper. Tourists were also asked questions on their age, sex, and occupation so that the samples could be weighted according to the characteristics of the total population of Japanese visitors to San Francisco. Some Japanese tourists preferred the American tour operator even when the prices were the same, and a substantial number of tourists which preferred the Japanese tour operator changed their preference as the price differential increased in favor of the American tour operator.

Dr. Mak reached the following conclusions based on his evaluation of the survey results:

The report also indicates that roughly twenty to twenty-four percent of Japanese tourists would prefer the American tour company even if the American tour and the Japanese tour were offered at the same price.

Dr. Mak also addressed other market concerns relevant to antitrust damages in his report. Starting from evidence provided by Dolphin that defendants had: (1) acted as a cartel in setting prices; (2) successfully co-opted San Francisco Bay Tours (SFBT), another American tour operator offering Japanese language tours, into its pricing scheme; and (3) attempted to co-opt Dolphin into its pricing scheme, Dr. Mak concluded that defendants would most likely respond 'to attempted entries into the market by attempting to eliminate the new competition or co-opt the new competition into the cartel. From evidence that SFBT was already a part of the alleged cartel, and evidence that future entrants in the market would be co-opted into the cartel, Dr. Mak also concluded that Dolphin would be the “sole benefactor of the visitor traffic diversion” caused by Dolphin’s entry into the market at lower prices.

The defendants challenged Dolphin’s damage evidence by a motion for summary judgment. For purposes of the motion for summary judgment the district court assumed that the survey and the Report which Dolphin relied on were valid, and that Dolphin could establish the anticom-petitive activity which it alleged. The district court found that Dolphin’s survey evidence and the deposition testimony of Dolphin’s owner, J. Mark Lavelle, failed to account for the defendants’ potential competitive reaction to a loss in their volume of customers. Because of this failure the court concluded that Dolphin had not presented evidence from which the jury could arrive at a reasoned damage award. The district court also noted that Dolphin’s evidence failed to account for the potential entry of new competitors into the market.

JURISDICTION AND STANDARD OF REVIEW

The district court had jurisdiction over this matter pursuant to 28 U.S.C. § 1331 . We have jurisdiction over this appeal pursuant to 28 U.S.C. § 1291 . We review the grant of summary judgment de novo, viewing the evidence in the light most favorable to the non-moving party. Taylor v. Sentry Life Insurance Co., 729 F.2d 652, 654 (9th Cir.1984).

DISCUSSION

In order to recover under section 4 of the Clayton Act, Dolphin must establish that its injuries were caused “by reason of” the defendants’ anticompetitive activities. 15 U.S.C. § 15 . The “by reason of” language is the starting point for analyzing causation and damages, the two aspects of Dolphin’s prima facie case which are at issue here. Dolphins’ evidence linking the alleged violation of the antitrust laws to its injury must be more precise than the evidence establishing the amount of injury which it has suffered. Story Parchment Co. v. Paterson Parchment Paper Co., 282 U.S. 555, 562-63 , 51 S.Ct. 248, 250-51 , 75 L.Ed. 544 (1931); Van Dyk Research Corp. v. Zerox Corp., 631 F.2d 251, 255 (3d Cir.1980), ce rt. denied, 452 U.S. 905 , 101 S.Ct. 3029 , 69 L.Ed.2d 405 (1981); Flintkote Co. v. Lysfjord, 246 F.2d 368, 392 (9th Cir.), cert. denied, 355 U.S. 835 , 78 S.Ct. 54 , 2 L.Ed.2d 46 (1957). In order to establish causation under section 4, Dolphin must demonstrate that the anticompetitive activity was “a material cause of [its] injury.” Zenith Radio Corp. v. Hazeltine Research, Inc., 395 U.S. 100 , 114 & n. 9, 89 S.Ct. 1562 , 1571 & n. 9, 23 L.Ed.2d 129 (1969). Dolphin need not rule out “all possible alternative sources of injury.” Id; see also Mulvey v. Samuel Goldwyn Productions, 433 F.2d 1073 , 1075 n. 3 (9th Cir.1970), cert. denied, 402 U.S. 923 , 91 S.Ct. 1377 , 28 L.Ed.2d 662 (1971) (antitrust violation need not be the “sole” cause of the injury for causation to exist). To establish the amount of its injury Dolphin must provide evidence such that the jury is not left to “speculation or guesswork” in determining the amount of damages to award. Bigelow v. RKO Radio Pictures, Inc., 327 U.S. 251, 263-65 , 66 S.Ct. 574, 579-80 , 90 L.Ed. 652 (1946). See also Zenith Radio, 395 U.S. at 123-24 , 89 S.Ct. at 1576-77 .

Defendants argue that, given Dolphin’s failure to account for: (1) defendants’ potential legal competitive response to a loss in their market share; or (2) the entry of other competitors into the market, the district court correctly awarded summary judgment in their favor. Dolphin counters that Dr. Mak’s conclusions account for defendants’ potential competitive responses and the potential entry of third parties into the market. Under the facts of this case, we find that Dolphin has presented evidence from which a jury could determine that Dolphin had been injured by the defendants’ anticompetitive activity, and determine the amount of Dolphin’s injury without engaging in speculation.

I. CAUSATION.

Causation evidence under section 4 must establish that the injury which the plaintiff claims is attributable to the conspiracy, and not to other factors. See, e.g., Van Dyk Research Corp., 631 F.2d at 254-56 (plaintiff not entitled to recovery where injury was caused by cash flow problems, inability to raise money through new stock offerings, and failure of marketing arrangement); R.S.E., Inc. v. Pennsy Supply, Inc., 523 F.Supp. 954, 966 (M.D.Pa.1981) (plaintiff’s damage evidence was inadequate because of its failure to consider, among other things, twenty-five percent reduction in relevant market). Once the plaintiff has established that the anticompetitive activities were a material cause of some of its injury, the remainder of the damage inquiry is judged under the amount of damage standard. Zenith Radio, 395 U.S. at 114 n. 9, 89 S.Ct. at 1571 n. 9. For purposes of this appeal we assume, as did the district court, that Dolphin will be able to substantiate the alleged conspiracy among the defendants and that Dolphin’s survey evidence is valid and admissible. Operating under these assumptions we conclude that Dolphin has met its causation burden.

The Report is evidence from which the jury could conclude that Dolphin’s market share, and hence Dolphin’s profits, would have been larger but for the alleged conspiracy. The Report’s conclusion that, even if Dolphin and defendants offered tours at the same price, Dolphin could have attained a substantially larger market share than the two to five percent that it attained in spite of the alleged conspiracy is especially probative of causation. The Report’s conclusions are consistent with Dolphin’s claims that the defendants limited Dolphin’s access to the market by destroying promotional material for Dolphin’s tours displayed in hotels and stores, harassing Dolphin employees who tried to distribute promotional material, and taking kickbacks from gift shops which were made part of the defendants’ tours. Dolphin points to deposition and documentary evidence which arguably support these claims.

There is no evidence in the record attributing Dolphin’s injury to factors such as poor management or a general decrease in the market which would negate Dolphin’s evidence of causation. Defendants classify their arguments regarding Dolphin’s failure to account for defendants’ “competitive reaction” to Dolphin’s entry in the market or the potential entry of third parties into the market as causation arguments. On the facts of this case, however, we conclude that these arguments go only to the amount of Dolphin’s injury. Failure to estimate market share based on a competitive price differential between plaintiff and defendants may be a causation issue in some cases. See Murphy Tugboat Co. v. Crowley, 658 F.2d 1256, 1261-62 (9th Cir.1981), cert. denied, 455 U.S. 1018 , 102 S.Ct. 1713 , 72 L.Ed.2d 135 (1982) (where plaintiff had to make fourteen percent market share to make a profit, failure to account for defendant’s “competitive reaction” in estimating market share was a causation issue because plaintiff could not establish any injury without establishing that it would have achieved the fourteen percent market share). However, in this case the Report indicates that Dolphin would have attained a market share of roughly twenty percent even if Dolphin and defendants offered tours at the same prices. We conclude that Dolphin has presented evidence from which a jury could conclude that the conspiracy was a material cause of some portion of Dolphin’s losses.

II. AMOUNT OF DAMAGES.

The second question before us is whether Dolphin has presented sufficient evidence from which a jury could determine the amount of damages which Dolphin is entitled to without engaging in speculation. Defendants, whose illegal conduct operates to exclude others from the relevant market, should not benefit because their wrongdoing makes it more difficult for the plaintiff to establish the precise amount of its injury. See Story Parchment, 282 U.S. at 563 , 51 S.Ct. at 250 . The jury is allowed to act on probable and inferential proof in determining the amount of damages even though such an award may be an approximation. Id.

An antitrust plaintiff who is excluded from the relevant market by anticompetitive activity is entitled to recover his lost profits. See Moore v. Jas. H. Matthews & Co., 682 F.2d 830, 836 (9th Cir.1982); Murphy Tugboat, 658 F.2d at 1262-63 . See also Graphic Products Distributors, Inc. v. Itek Corp., 717 F.2d 1560, 1579-80 (11th Cir.1983); Grip-Pak, Inc. v. Illinois Tool Works, Inc., 694 F.2d 466, 474-75 (7th Cir.1982), ce rt. denied, 461 U.S. 958 , 103 S.Ct. 2430 , 77 L.Ed.2d 1317 (1983). In economic terms, the amount of damages is the difference between what the plaintiff could have made in a hypothetical free economic market and what the plaintiff actually made in spite of the anticompetitive activities. Bigelow, 327 U.S. at 264 , 66 S.Ct. at 579 (Antitrust damages measured by “comparison of profits, prices and values as affected by the conspiracy, with what they would have been in its absence under freely competitive conditions.”); Murphy Tugboat, 658 F.2d at 1262 . See generally, II Areeda & Turner, Antitrust Law 231-34 (1978); Antitrust Law Developments at 410-13.

Among the methods by which an antitrust plaintiff can establish lost profits are: (1) comparing the plaintiff’s profits before or after the alleged anticompetitive activity with the profits made while the plaintiff was subjected to the anticompetitive activity; (2) examining the profits of a business comparable to the plaintiff’s business which was not affected by the anticompetitive activity; or (3) projecting the market share which the plaintiff would have attained absent the anticompetitive activity, and then projecting plaintiff’s profits accordingly. See Antitrust Law Developments at 411-13. In this case Dolphin has attempted to establish its lost profits by projecting the market share that it would have attained absent the anticompetitive activity. In using this approach, Dolphin must presume the existence of rational economic behavior in the hypothetical free market. Murphy Tugboat, 658 F.2d at 1262 . This includes a rational price differential between Dolphin’s prices and defendants’ prices based on all competitors attempts to maximize their own profits, id.; R.S.E., 523 F.Supp. at 966 , and the potential entry of other competitors into the market. Coleman Motor Co. v. Chrysler Corp., 525 F.2d 1338, 1353 (3d Cir.1975); ILC Peripherals Leasing Corp. v. International Business Machines Corp., 458 F.Supp. 423, 435 (N.D.Cal.1978) aff'd mem. 636 F.2d 1180 (9th Cir.1980), cert. denied, 452 U.S. 972 , 101 S.Ct. 3126 , 69 L.Ed.2d 983 (1981).

There is some tension between the principle that difficulty in proving the amount of damage should not operate to benefit a defendant whose actions have made that proof difficult, and requiring an antitrust plaintiff to anticipate a hypothetical free market in establishing the amount of his injury. However, we conclude that the burden of anticipating this hypothetical market is appropriately placed on antitrust plaintiffs. In projecting free market profits, antitrust plaintiffs are not entitled to assume favorable aspects of an anticompetitive market such as an unnatural price differential between themselves and their competitors and limited competition from third parties because of the difficulty of entering the market. Such an approach would overestimate the profits an antitrust plaintiff would have made absent the anti-competitive activity and then under the antitrust laws treble this artificially high damage estimate.

In this case Dolphin has attempted to establish the profits it would have made in an economic free market through the Report. The Report estimates the market share which Dolphin would have attained at the existing price differential in Dolphin’s favor, and, more importantly, estimates the market share which Dolphin would have made had defendants and Dolphin offered tours at the same prices or at price differentials less favorable to Dolphin. Dr. Weiner, the accountant, then estimated the profits that Dolphin could have made at the various projected market shares. In this respect, Dolphin has provided the jury a reasonable basis for estimating Dolphin’s market sharé in a free market and ultimately determining its lost profits.

Dolphin’s damage evidence has some deficiencies however. Dr. Mak’s conclusion that Dolphin was not competing with any comparable American tour companies does not adequately address the possibility that Dolphin would have had competition in a free market where barriers to entry were not present. In order to evaluate this aspect of the hypothetical economic market the jury will need evidence regarding the likelihood of entry by comparable tour firms and the potential affect on Dolphin’s market share. Testimony by Dolphin’s owner and by Dr. Mak or other economic experts could provide the jury with this information at trial.

To this point Dolphin’s damage evidence also fails to address the possibility that Dolphin may not offer the lowest priced tours in the market. The Report indicates that those Japanese tourists who preferred the American firm’s tour over the Japanese firm’s tour at the same price were asked whether they would still choose the American tour if the Japanese firm’s tour was five, ten, or fifteen dollars cheaper. This portion of the survey response was not included in the Report’s estimates of Dolphin’s market share. Assuming that the survey and the Report will be found admissible, Dolphin could provide the jury with evidence of the market share it would have achieved if it were not the lowest priced tour operator in the market by tabulating this data in the same manner that it tabulated the survey responses for price differentials in Dolphin’s favor.

In spite of the current deficiencies in Dolphin’s' damage evidence, we conclude that the district court should have allowed the case to proceed to trial on the evidence before it. Dolphin has presented evidence from which a jury could reasonably estimate the amount of Dolphin’s injury without speculation if Dolphin’s damage evidence were filled in by testimony at trial and by tabulation of survey results which the record indicates are available to Dolphin. If Dolphin is unable to establish the validity of the Report or qualify Dr. Mak as an expert, then it may be unable to present sufficient evidence on the amount of its damages and a directed verdict or judgment notwithstanding the verdict may be appropriate. For purposes of avoiding summary judgment, however, Dolphin has provided sufficient evidence of the amount of its injury.

CONCLUSION

Operating on the same assumptions as the district court, we conclude that Dolphin has established a causal relationship between the assumed conspiracy and its injury. The Report, provides evidence that Dolphin would have achieved a larger market share in a free market than the market share it received as a result of defendants’ alleged anticompetitive activities.. We further conclude that Dolphin’s case should not have been dismissed for failure to provide sufficient proof of the amount of its injury. The Report provides the jury with a range of figures from which it can determine the market share Dolphin would have attained in a free market. Any deficiencies in Dolphin’s evidence of the amount of its injury can be filled in by testimony at trial and by supplementing the Report with data which is available to Dolphin.

REVERSED AND REMANDED.

. The defendant-appellees (defendants) are Paci-fico Creative Service, Inc.; Pacifico Creative Service (California), Inc.; Nippon Express U.S.A., Inc.; Kintetsu International Express (U.S.A.), Inc.; Pacific Leisure Management Corporation; Japanese Tour Operators Association; and, Franciscan Lines, Inc. . Dolphin estimated the characteristics of the total population of Japanese visitors to San Francisco by relying on the Hawaii Visitors Bureau's Annual Research Report, for 1981. . Our opinion is not intended as an indication of the validity of Dolphin’s evidence of conspiracy. This is an issue to be resolved in the course of the litigation. We review the evidence and accusations of conspiracy only as necessary to our assessment of causation. . We find the term competitive reaction misleading, see infra n. 6. . In some instances an antitrust plaintiff who is excluded from the relevant market may seek to recover the going concern value of his business as an alternative measure of damages. Graphic Products, 717 F.2d at 1579 ; ABA Antitrust Section, Antitrust Law Developments 410-11 (2d ed. 1984) (hereinafter “Antitrust Law Developments "). . The parties to this case, the district court, and some decisions, Murphy Tugboat, 658 F.2d at 1262 ; R.S.E., 523 F.Supp. at 966 , have referred to this component of the antitrust plaintiffs burden as a requirement that antitrust plaintiffs account for the "competitive reaction” of antitrust defendants. Although those courts which have used the term competitive reaction have essentially employed a lost profits analysis by stating that the antitrust plaintiff cannot estimate his market share and lost profits by assuming that defendants would not have reacted competitively by reducing their prices in response to plaintiffs entry in the market, we prefer not to use the term competitive reaction. Competitive reaction implies that we must determine whether the defendants would have continued cartel pricing or reacted competitively to Dolphin’s entry in the market by reducing their prices. But under Bigelow Dolphin’s measure of recovery is the difference between what it could have made in a free economic market and what it actually made in spite of the anti-competitive activity: A competitive price differential between Dolphin and defendants is presumed in order to measure what. Dolphin could have made in an economic free market, not because defendants would necessarily abandon their cartel in favor of competitive price reductions. Dolphin has lost only the difference between what it could have made in a hypothetical free market and what it actually made in spite of the anticompetitive activity. . For purposes of reviewing the grant of summary judgment it is reasonable for us to assume that the survey will not be given to the jury in isolation: It will likely be supported by testimony from Dr. Mak and Dolphin’s owner. During cross examination the defendants can bring out any problems with the survey or the Report and emphasize factors which they believe indicate that the Report overestimates the market share which Dolphin would have attained in a free market. . Defendants raise a number of other challenges to Dolphin’s evidence regarding the amount of injury. Some of these arguments may be considered in determining the admissibility of the survey and Report, and some may be introduced to rebut the Report if it is found admissible. For purposes of this appeal, however, none of defendants’ contentions indicates that the jury would have to engage in speculation in determining the amount of Dolphin's injury. . Dolphin also attempts to challenge the district court’s refusal to find the agreement between defendants Japan Travel Bureau International and Nippon Express U.S.A. a per se violation of the antitrust laws and grant summary judgment in its favor. Dolphin claims that the denial of summary judgment is appealable as inter alia a denial of preliminary injunctive relief. See Safe Flight Instrument Corp. v. McDonnell-Douglas Corp., 482 F.2d 1086, 1093 (9th Cir.), cert. denied, 414 U.S. 1113 , 94 S.Ct. 843 , 38 L.Ed.2d 740 (1973). However, the district court denied Dolphin’s motion for summary judgment and request for temporary injunctive relief on March 23, 1983. Dolphin's notice of appeal was not filed until July 7, 1984. Even were we to consider the denial of summary judgment on the per se violation issue appealable as a denial of temporary injunctive relief, the issue is not properly before us because Dolphin failed to file its notice within thirty days of the order denying injunctive relief as required under Fed.R. App.P. 4(a)(1).