OPINION OF THE COURT
ALDISERT, Chief Judge.
Three principal issues are presented in this appeal from sentences imposed on a guilty verdict in a criminal antitrust prosecution: whether the proof at trial varied from the indictment charging a single, con[1188]*1188tinuing conspiracy; whether the government introduced sufficient evidence to prove the interstate commerce element of the Sherman Act violation; and whether this court should set aside or modify, on appeal, the one million dollar fine levied against defendant Fischbach & Moore. Appellants assert several less significant arguments, including the admission of an allegedly prejudicial government exhibit; prosecutorial misconduct during closing argument; errors in jury instructions; and the denial of a continuance to defendant Arbogast. Because we find no reversible error, we affirm the judgment of the district court.
I.
For approximately seven years, from 1974 to 1981, representatives of several electrical contracting companies met at the Duquesne Club in Pittsburgh. The purpose of these meetings was to allocate electrical construction projects, by bid rigging, at the Western Pennsylvania Works (Works) of United States Steel (USS). Whenever one of the companies desired to rig a bid, that company’s representative would telephone the other contractors and arrange a meeting. After deciding among themselves which firm would receive the contract, that firm’s representative would contact the other contractors and would tell them what bid to submit, ensuring that his firm’s bid would be the lowest. Some of the firms kept track of the allocations to ensure that each contracting company received its fair share of work.
As a result of investigating this bid rigging scheme, the government accused a number of the electrical contractors and their employees of antitrust violations. The indictment charged them with violating § 1 of the Sherman Act by conspiring to allocate electrical construction projects at the Western Pennsylvania Works, to fix the prices at which those projects were bid, and to submit noncompetitive, collusive, and rigged bids on those projects. Although some of the defendants plea bargained to the charges and avoided trial, three electrical contracting companies, Fischbach and Moore (F & M), Sargent Electric, and Lord Electric, and four individual employees, Paul Arbogast, Joseph Rodgers, Frederic Sargent, and Ralph Vryenhoek, stood trial on the charges. They are the appellants before us.
Prior to trial, one of the defendants, Paul Arbogast, was indicted and prosecuted in Montana for an unrelated Sherman Act violation. The district court postponed the Western Pennsylvania trial once because of the Montana action. In mid-January 1984, Arbogast again moved for a continuance, the Montana trial not having ended and the Western Pennsylvania trial scheduled to begin in early February. The court denied this motion. Arbogast was acquitted in Montana on January 21 and began trial in Pittsburgh on February 6.
To narrow the scope of the trial, the government issued a bill of particulars, which it later amended, identifying contracts within the scope of the conspiracy. The proof at trial related to some, but not all, of the contracts on this list. The government also introduced extensive evidence to prove the interstate commerce jurisdictional element. This evidence included Government Exhibit 32 (Govt. Ex. 32), a file of invoices and freight bills for electrical materials and equipment bought by USS from out of state vendors for use in electrical construction projects at the Works.
After a finding of guilty by the jury, the district court imposed both fines and prison sentences on the individual defendants. The three corporate defendants received fines of one million dollars each, the statutory maximum under § 1 of the Sherman Act. Defendants now appeal their convictions, and have asserted a long list of contentions, requiring this opinion to be more lengthy than what we believe to be appropriate in this court.
II.
Appellants raise three principal contentions. First, appellants F & M, Lord Electric, Sargent Electric, Paul Arbogast, and [1189]*1189Joseph Rodgers allege a variance between the proof and the indictment. In a related argument, F & M, Lord Electric, Ralph Vryenhoek, and Frederic Sargent allege that the government did not prove the interstate commerce element of the Sherman Act charge. In the third major contention, F & M alleges both that its sentence was illegal and that the trial court abused its discretion in imposing sentence.
The precepts guiding our review of the variance argument are familiar. Our polestar is to determine whether “there is substantial evidence, viewed in the light most favorable to the Government, to uphold the jury’s decision.” United States v. Palmeri, 630 F.2d 192, 203 (3d Cir.1980) (quoting Burks v. United States, 437 U.S. 1, 17, 98 S.Ct. 2141, 2150, 57 L.Ed.2d 1 (1978)), cert. denied, 450 U.S. 967, 101 S.Ct. 1484, 67 L.Ed.2d 616 (1981). Additionally, Kotteakos v. United States, 328 U.S. 750, 66 S.Ct. 1239, 90 L.Ed. 1557 (1946), sets forth the two-pronged test appellants must meet to succeed in this specific contention: (1) that there was a variance between the indictment and the proof and (2) that the variance prejudiced some substantial right of the defendants. Id. at 752, 756, 66 S.Ct. at 1241, 1243.
In the usual criminal case, our review of a sentence imposed by the district court is extremely circumscribed. United States v. Felder, 706 F.2d 135, 137 (3d Cir.1983).1 Generally, if the sentence falls within the statutory maximum, the matter is not reviewable on appeal. United States v. Dickens, 695 F.2d 765, 782 n. 26 (3d Cir.1982), cert. denied, 460 U.S. 1092, 103 S.Ct. 1792, 76 L.Ed.2d 359 (1983). We may review the sentence, however, if there is a showing of illegality or abuse of discretion. United States v. Fessler, 453 F.2d 953, 954 (3d Cir.1972). We now consider appellants’ variance argument.
III.
Appellants F & M, Sargent Electric, and Paul Arbogast argue that because the government’s evidence sought to establish multiple conspiracies and not the single, continuing conspiracy charged in the indictment, the convictions must fall as illegal. They allege variance in two respects: (1) that the government interpreted the indictment to charge that all electrical contracting bids were rigged during the time of the conspiracy, later reducing the number of bids in the bill of particulars and further reducing them at trial and (2) that the government proved not one continuing conspiracy, but a series of independent conspiracies, i.e., that each contract the government proved the defendants rigged constituted a separate conspiracy.
A.
The indictment charged that the defendants conspired to “allocate among themselves electrical construction projects” at the Works; to “fix the prices at which electrical construction projects” were bid; and to “submit noncompetitive, collusive, complementary and rigged bids.” App. at 21a-22a. But the indictment did not state that the conspiracy encompassed all bids or all contracts made during the seven-year period. Although the government so stated at a pre-trial conference, even if the appellants relied on these government representations or the bill of particulars as to the extent of proof, neither can modify the scope of the indictment. United States v. Critchley, 353 F.2d 358, 362 (3d Cir.1965) (bill of particulars).
Even had the indictment read in terms of “all construction projects” and “all bids,” the government still would have introduced sufficient evidence to prove the crimes charged. To prove a conspiracy to rig all bids, the government was not required to show that the defendants actually rigged all bids. United States v. Socony-Vacuum Oil Co., 310 U.S. 150, 224 n. 59, [1190]*119060 S.Ct. 811, 845 n. 59, 84 L.Ed. 1129 (1940). The defendants could have conspired to rig all bids, but failed to achieve that objective for one reason or another, e.g., because the bid lists included companies with which the defendants could not cooperate. Evidence of the fourteen rigged bids both proved that a conspiracy to rig bids existed and permitted the jury to conclude that the conspiracy encompassed all bids.
B.
We also conclude that the government introduced sufficient evidence to justify a jury finding of only a single conspiracy. The government proved that the defendants met, over a period of several years, at the Duquesne Club for the sole purpose of rigging bids and allocating contracts. The government introduced evidence to prove that all the participants knew the purpose of the club meetings and that they met as a group, thus negating the argument that separate groups of the defendants were conspiring together, with the same goal, but with their actions unconnected. More important, the government showed that some of the defendants kept records of which company received which job, ensuring that each firm would receive its fair allotment of the contracts. This recordkeeping indicated a single conspiracy that continued over time, and not separate conspiracies involving only certain contracts.
Because we hold that defendants did not prove a variance between the proof and the indictment, we need not consider the prejudice prong of Kotteakos.
C.
In a related argument, appellant Lord Electric maintains that the proof varied from the indictment in that the government proved one conspiracy, but that conspiracy had no effect on interstate commerce. As support for this contention, Lord Electric expressly declines to rely on Kotteakos, conceding that it suffered no prejudice from the variance alleged. Instead, appellant relies on the language of the Sherman Act requiring the conspiracy to restrain “trade or commerce among the several States.” 15 U.S.C. § 1.
As we understand this argument, Lord Electric contends that the government proved a single agreement to rig bids only at the time one of the defendants would telephone the others to arrange a meeting. This agreement, appellant states, was harmless and restrained no trade. Rather, the ensuing agreements reached at the meetings restrained trade, but those fourteen separate agreements were not charged in the indictment. We decline to adopt this convoluted construction of the offense charged in the indictment.
Lord Electric’s argument starts to collapse when it concedes, as it does, that it conspired to fix bids when one of the other conspirators made a telephone call. Because we cannot isolate the original telephone call from the subsequent action triggered by the call, the keystone of this argument falls out. These telephone calls and the meetings that followed were an integral part of the conspiracy to fix bids, to which appellant agreed. To view the conspiracy in terms of artificial separate and distinct phases would give no meaning to the agreement into which Lord Electric entered and for which it was indicted. Had the defendants not contemplated making the telephone calls, no reason existed for them to agree to rig bids if the calls were made. Rather, the calls and Duquesne Club meetings constituted concerted activity to further the conspiracy to rig bids. As such, anticompetitive effects of these actions cannot be separated from the initial agreement to rig bids.
IV.
In a more particularized argument, defendant Rodgers contends that the government did not introduce evidence sufficient for the jury to find that he knowingly joined the continuing conspiracy charged in the indictment. He argues that he began to attend the Duquesne Club meetings only as a casual observer to protect the [1191]*1191interest of his company, Foley Electric, and that his appearance was long after the other defendants entered into a conspiracy. To join a conspiracy, the government generally must prove two different types of intent: (1) the basic intent to agree, which is necessary to establish the existence of the conspiracy and (2) the more traditional intent to effectuate the object of the conspiracy. United States v. United States Gypsum Co., 438 U.S. 422, 443 n. 20, 98 S.Ct. 2864, 2877 n. 20, 57 L.Ed.2d 854 (1978).
In a situation very similar to that of Rodgers, in United States v. Continental Group, Inc., 603 F.2d 444 (3d Cir.1979), defendants were convicted of a 26-year continuing conspiracy to fix the price of consumer bags. One defendant, Chase Bag, maintained that the government had introduced insufficient evidence to support its conviction, arguing that its behavior was legitimate price followership. Id. at 448. We affirmed Chase Bag’s conviction, basing our decision on, among other things, Chase Bag’s adoption of an unpublished price list of a competitor, St. Regis. We stated:
Had the St. Regis incident been the only evidence against Chase Bag, we might agree that the government’s proof varied substantially from the indictment. We note, however, that Chase Bag’s participation in various meetings where prices were discussed, its exchange of price information with competitors, and its parallel pricing policies, although perhaps in-, nocent by themselves, are cast in a different light by [Chase Bag’s] apparent agreement with [St. Regis] to fix prices.
Id. at 455.
Although the issue is close, we are persuaded that the government introduced sufficient evidence to demonstrate that Rodgers knowingly entered the continuing conspiracy. Although he joined the Duquesne Club meetings at a point far into the conspiracy, his purpose in going there was to obtain contracts (specifically the contract designated as Govt. Ex. 23) for his company, Foley Electric. After it was agreed that Foley was to be the low bidder on this contract, Rodgers arranged the bid submissions on this contract by telephoning the other companies and telling them what prices to bid. The most damning evidence against Rodgers was his alleged reason for wanting this particular contract: “because he had cooperated with other people at the meeting and he felt that he should be given some consideration.” App. at 1826a-27a. Viewed in the light most favorable to the government, this remark evidences Rodgers’s knowledge both of the continuing nature and goals of the conspiracy and his intent to join the conspiracy and further its objectives. Rodgers’s actions only confirm his understanding of and familiarity with the conspiracy.
If the testimony pertaining to Govt. Ex. 23 was the only evidence on which the government relied, perhaps Rodgers would have had a stronger case. See, e.g., the one-time only exception we suggested in Continental Group, 603 F.2d at 455. But here the government introduced evidence of Rodgers’s involvement with another rigged contract, designated as Govt. Ex. 27. Although testimony was conflicting as to whether the contract was rigged over the phone or at a club meeting, viewed in the light most favorable to the government, the jury could have found that Rodgers also participated in rigging this contract. We therefore concluded that substantial evidence existed to tie Rodgers to the conspiracy.
We now turn to appellants’ interstate commerce argument.
V.
Appellants F & M, Lord Electric, Ralph Vryenhoek, and Frederic Sargent argue that the government did not prove the interstate commerce element of the Sherman Act charge.
Section 1 of the Sherman Act proscribes “every contract, combination ..., or conspiracy, in restraint of trade or commerce among the several States____” 15 U.S.C. § 1. The government may prove [1192]*1192the connection of the restraint to interstate commerce under either of two independent theories. McLain v. Real Estate Board of New Orleans, Inc., 444 U.S. 232, 242, 100 S.Ct. 502, 509, 62 L.Ed.2d 441 (1980). An “in commerce” theory requires that the government prove that (1) a substantial volume of interstate commerce is involved with the challenged activity and (2) the challenged activity is an essential, integral part of the transaction and is inseparable from its interstate aspects. Id. at 244, 100 S.Ct. at 510. An “effect on commerce” theory, applies to primarily intrastate activity. The government must show that (1) a substantial amount of interstate commerce was involved and (2) the challenged activity has a “not insubstantial effect” on interstate commerce. Id. at 245-46,100 S.Ct. at 510-11, see also Cardio-Medical Associates, Ltd. v. Crozer-Chester Medical Center, 721 F.2d 68 (3d Cir.1983).
The government may prove the nexus between interstate commerce and the challenged activity through either the activities of the target of the antitrust violation or defendant’s activities. Id. at 74. Because the activities involved in this case, price-fixing and bid rigging, are per se violations, Northern Pacific Railway Co. v. United States, 356 U.S. 1, 5, 78 S.Ct. 514, 518, 2 L.Ed.2d 545 (1958) (price fixing); United States v. Brighton Building & Maintenance Co., 598 F.2d 1101, 1106 (7th Cir.), cert. denied, 444 U.S. 840, 100 S.Ct. 79, 62 L.Ed.2d 52 (1979) (bid rigging); United States v. Flom, 558 F.2d 1179, 1183 (5th Cir.1977) (bid rigging), the government is not required to prove any adverse impact on interstate commerce. Northern Pacific, 356 U.S. at 5, 78 S.Ct. at 518.
Based on the trial testimony, we hold that the government introduced substantial evidence to support a jury finding that either the electrical contracting services were in commerce or that the defendants’ activities affected interstate commerce. As to the in commerce theory, the government introduced evidence to show that the contractors and USS ordered substantial amounts of materials from out of state for use on the USS jobs. Not only did the invoices show that pieces of equipment used in the Works jobs cost tens of thousands of dollars, but the evidence often showed that materials were shipped directly from out-of-state manufacturers to USS job sites. The electrical contracting services thus involved a substantial amount of interstate commerce. Because the materials were shipped into the state solely in connection with the contracting jobs, and were otherwise useless, the contracting services were an essential, integral part of interstate commerce.
Moreover, the evidence also serves to prove the interstate element of the Sherman Act by satisfying the affecting commerce theory. Clearly, a large amount of materials used in the contracting jobs traveled through interstate commerce. Per se violations in the electrical contracting field involving USS would have a marked effect on interstate commerce, especially by shifting purchases from one contractor to another.
We next consider F & M’s argument pertaining to its sentence.
VI.
F & M alleges both that its sentence was illegal and that the judge abused his discretion in imposing sentence. The illegality argument is based on the theory that the one million dollar fine is disproportionate, thus violating the eighth amendment. F & M contends that the judge abused his discretion by basing the fine on the one million dollar penalty accepted by another defendant, the Foley Company, as part of its plea bargain.
F & M relies on Solem v. Helm, 463 U.S. 277, 103 S.Ct. 3001, 77 L.Ed.2d 637 (1983), in arguing that its fine is disproportionate. The Supreme Court suggested three factors for a court to consider in reviewing a sentence for disproportionality: (1) the gravity of the offense and the harshness of the penalty; (2) the sentences imposed on other criminals in the same jurisdiction; and (3) the sentences imposed [1193]*1193for the commission of the same crime in other jurisdictions. Id. at-, 103 S.Ct. at 3011. Evaluating these factors, we hold that the district court’s sentence was not disproportionate and thus not illegal.
F & M brazenly committed a grave crime. The jury found the company guilty of conspiring to commit per se violations of the Sherman Act in a series of meetings that obviously were illegal. Moreover, F & M was one of the ringleaders of that conspiracy. As to the sentences imposed in the same jurisdiction, the penalties levied on the other defendants in this case provide a good example. Every individual defendant received a fine and a prison sentence; all the corporate defendants received one million dollar fines. Thus, in comparison, F & M’s fine does not appear severe. Moreover, in comparing the sentence with those received by defendants in other jurisdictions, F & M provided extensive statistics on the infrequency of the imposition of the maximum fine. These statistics, however, illustrate that defendants frequently are fined, and fined in large amounts. Although F & M’s one million dollar fine is substantial, its amount was the expression of the Congress, not the judiciary. Accordingly, we hold that the fine is not disproportionate to the gravity of the offense, the public policy considerations implicated, and the Congressional determinations.
F & M also contends that the district court abused its discretion by taking another defendant’s punishment into account when fining F & M. F & M argues that because the judge gave no reasons for the fine imposed, it is reasonable to believe that he relied on improper motives. This court does not require a judge to elucidate his sentencing rationale.2 United States v. Del Piano, 593 F.2d 539, 540 (3d Cir.) (per curiam), cert. denied, 442 U.S. 944, 99 S.Ct. 2889, 61 L.Ed.2d 315 (1979). Nor does F & M offer any evidence, other than the speculations of its excellent lawyers, of the judge’s reliance on improper factors in the sentencing process. In short, “aside from characterizing [the fine] as excessive, defendant ] [has] presented no reason which would justify a conclusion that the sentence[] [was] anything other than the result of a proper exercise of judicial judgment.” Government of the Virgin Islands v. Rodriguez, 423 F.2d 9, 11 (3d Cir.1970). For the above reasons, we decline to set aside F & M’s sentence.
VII.
We now consider defendants’ remaining arguments in turn.
Lord Electric contends that the district court should not have admitted Govt. Ex. 32, the file of purchase orders and invoices, because the exhibit was irrelevant. Additionally, it argues that even if Govt. Ex. 32 were relevant, the evidence was prejudicial and the trial judge should have excluded the exhibit pursuant to Rule 403, Federal Rules of Evidence. Because the initial relevancy decision implicates the interpretation and application of legal precepts, our review is plenary. In re Japanese Electronic Products Antitrust Litigation, 723 F.2d 238, 269 (3d Cir.1983); Universal Minerals, Inc. v. C.A. Hughes & Co., 669 F.2d 98, 101-02 (3d Cir.1981). The Rule 403 decision, however, is reviewed under an abuse of discretion standard. In re Japanese Electronic Products Antitrust Litigation, 723 F.2d at 269-70.
For evidence to be admissible under Rule 402, it must be relevant. “ ‘Relevant evidence’ means evidence having any tendency to make the existence of any fact that is of consequence to the determination of the action more probable or less probable than it would be without the evidence.” Rule 401, F.R.Evid. The Government sought to introduce exhibit 32 to prove the interstate [1194]*1194commerce element of Sherman Act jurisdiction.
As noted earlier, and contrary to what defendant Lord asserts, the interstate commerce activities of the target of the antitrust violation, as well as the defendant, are relevant to a finding on the interstate commerce element. Cardio-Medical Associates, 721 F.2d at 74. Because this evidence tended to make the existence of the consequential fact of involvement with interstate commerce more probable than if the evidence were not available, Govt. Ex. 32 was relevant.
Yet even if evidence is relevant, the court may exclude it “if its probative value is substantially outweighed by the danger of unfair prejudice, confusion of the issues, or misleading the jury, or by considerations of undue delay, waste of time, or needless presentation of cumulative evidence.” Rule 403, F.R.Evid. The defendant argues that Govt. Ex. 32 was more prejudicial than probative because the jury could not identify which invoices and freight bills related to the contracts at issue. The jury thus could have believed that evidence of every purchase of materials in interstate commerce contained in the file was relevant to proving the interstate commerce element of the crime.
Contrary to what Lord asserts, the jury could tie interstate purchases to particular contracts, by matching a project number to a job number. Although the process might be time consuming and the correlation not always perfect, this procedure removed the prejudice about which defendant was concerned, and tilted the balance in favor of admissibility.
Sargent Electric argues that it is entitled to a reversal because of allegedly improper remarks made by the prosecutor during his closing argument. In evaluating the prosecutor’s comments, our standard of review is “whether such remarks, in the context of the entire trial, were sufficiently prejudicial to violate defendant’s due process rights.” United States v. Scarfo, 685 F.2d 842, 849 (3d Cir.1982), cert. denied, 459 U.S. 1170, 103 S.Ct. 815, 74 L.Ed.2d 1014 (1983).
Sargent isolates three instances of misconduct to substantiate its contention. It states that the prosecutor expressed his subjective feelings as to its guilt, yet identifies no page in the transcript where this occurred. The government points to one remark of the prosecutor’s: “I submit to you that the defendants are guilty ... on the facts and the evidence____” App. at 3673a. By tying his remarks to evidence on the record, United States v. Schartner, 426 F.2d 470, 477 (3d Cir.1970), the prosecutor’s remarks were not prejudicial.
Likewise, defendant’s claims regarding other comments are baseless. The statement by the prosecutor that “[wjhat I would like to do is summarize what I think the issues in the case are ...,” app. at 3610a, was merely a figure of speech, and not an injection of his personal feelings into the trial. The reference to Sargent Electric’s financial reports, app. at 3651a, although the reports were not in evidence, was proper rebuttal to the defendant’s assertion that it had made a complete financial disclosure to USS. United States v. Somers, 496 F.2d 723, 740 (3d Cir.), cert. denied, 419 U.S. 832, 95 S.Ct. 56, 42 L.Ed.2d 58 (1974).
Sargent Electric makes one final related argument for reversal, arguing that the prosecutor’s rebuttal was so lengthy— one and a half hours — and non-responsive as to amount to a second closing argument, permitting surrebuttal on the part of the defense. The judge had the discretion to limit the prosecutor’s rebuttal and chose not to do so. In view of the complicated nature of the ease, the rebuttal was not overly long. Considering all the circumstances of the case, neither the rebuttal argument nor the prosecutor’s remarks in any way violated defendant’s due process rights.
[1195]*1195C.
Defendant Arbogast argues that the trial court should have granted his second request for a continuance because his Montana trial ended shortly before the Pittsburgh trial began. In reviewing the trial court’s decision, an appellate court will reverse the lower court only if the judge abused his discretion. Ungar v. Sarafite, 376 U.S. 575, 589, 84 S.Ct. 841, 849, 11 L.Ed.2d 921 (1964); Paullet v. Howard, 634 F.2d 117, 119 (3d Cir.1980) (per curiam). The factors a court should consider when presented with a motion for a continuance include: the efficient administration of criminal justice; the accused’s rights, including an adequate opportunity to prepare his defense; and the rights of other defendants whose trials are delayed because of the continuance. United States ex rel. Carey v. Rundle, 409 F.2d 1210, 1214-15 (3d Cir.1969), cert. denied, 397 U.S. 946, 90 S.Ct. 964, 25 L.Ed.2d 127 (1970).
In this instance, the trial court did not abuse its discretion. The judge’s denial of the second continuance neither abridged Arbogast’s right to due process nor was insupportable in light of the circumstances of the case.
Arbogast’s reasons for seeking the continuance included giving him more time to prepare his defense and permitting him to be defended by counsel of his choice. Although this case is a fairly complex antitrust suit, Arbogast was aware of the general perimeters of the ease against him when the district court first postponed the trial in October. Moreover, Arbogast discussed his defense for the Pittsburgh case with counsel during the Montana trial. Although Arbogast’s first choice as counsel did not represent him in Pittsburgh, another lawyer from the same firm took over the representation. Despite these circumstances, Arbogast had approximately two weeks to devote to his Pittsburgh defense. Courts have found no constitutional violation in appointment of counsel cases when the defendant and his attorney have had much less time to prepare. Ungar, 376 U.S. 575, 84 S.Ct. 841, 11 L.Ed.2d 921 (five days to answer show cause order); United States ex rel. Chambers v. Maroney, 408 F.2d 1186 (3d Cir.1969) (counsel appointed on day of trial).
Additionally, the judge already had continued the trial once, for a period of several months. To have postponed this complicated trial again would not only have contributed to calendar congestion, but, more important, would have made the other defendants involved continue to wait to have their day in court.
D.
Sargent Electric, Lord Electric, Frederic Sargent, and Ralph Vryenhoek argue that the judge erred in giving instructions: (1) by shifting the burden of proof to the defendants by an instruction that price-fixing is per se illegal; (2) by failing to charge the jury fully on sham bidding; (3) by his instruction removing the element of intent from the jury’s consideration; and (4) by his instruction on the “affecting commerce” theory pertaining to the interstate commerce element of the Sherman Act.
In evaluating the district court’s ruling on points for charge, the standard of review is abuse of discretion. United States v. American Radiator & Standard Sanitary Corp., 433 F.2d 174, 199 (3d Cir.1970). Once the court has given an instruction, we must “determine whether the charge, taken as a whole and viewed in the light of the evidence, fairly and adequately submits the issues in the case to the jury.” Ayoub v. Spencer, 550 F.2d 164, 167 (3d Cir.), cert. denied, 432 U.S. 907, 97 S.Ct. 2952, 53 L.Ed.2d 1079 (1977); see also United States v. Park, 421 U.S. 658, 675, 95 S.Ct. 1903, 1913, 44 L.Ed.2d 489 (1975). The trial court should be reversed only if the instruction was capable of confusing and thereby misleading the jury. Idzojtic v. Pennsylvania Railroad Co., 431 F.2d 1029, 1036 (3d Cir.1970) (Aldisert, J., dissenting). We now address defendants’ contentions seriatim.
The Supreme Court repeatedly has held that per se violations require no proof [1196]*1196of anticompetitive effect to constitute a violation of the Sherman Act. Northern Pacific Railway, 356 U.S. at 5, 78 S.Ct. at 518; United States v. Socony-Vacuum Oil Co., 310 U.S. 150, 220-22, 60 S.Ct. 811, 842-43, 84 L.Ed. 1129 (1940); United States v. Trenton Potteries Co., 273 U.S. 392, 396-97, 47 S.Ct. 377, 379, 71 L.Ed. 700 (1927). Consequently, an instruction to this effect would “fairly and adequately” submit the issue to the jury. Moreover, this argument that the instruction creates an irrebuttable presumption has been considered and rejected by several jurisdictions. See, e.g., United States v. Koppers Co., 652 F.2d 290, 293-96 (2d Cir.), cert. denied, 454 U.S. 1083, 102 S.Ct. 639, 70 L.Ed.2d 617 (1981); United States v. Manufacturers’ Association of the Relocatable Building Industry, 462 F.2d 49, 52 (9th Cir.1972).
Sargent Electric argues that the court should have given a more complete instruction on sham bidding. It maintains that the instruction should have identified several aspects of USS’s bidding procedures as potentially sham bidding and that the sham bidding instruction should have related to the rule of reason, rather than the per se, approach. The judge’s instructions, however, adequately presented the issue to the jury.
The court initially referred to sham bidding in general terms. The court then instructed the jury that if USS acquiesced in the allocation of contracts, they should find the defendants not guilty. The court thus presented the essence of the sham bidding defense to the jury, although not in terms of specific practices. Moreover, Sargent Electric never requested the court to give the instruction in any particular language. Thus, the court’s failure to adopt language other than that which it used is not reversible because the instruction did not represent “plain error resulting in a manifest denial of justice.” United States v. Palmeri, 630 F.2d 192, 201 (3d Cir.1980).
Additionally, no reason existed for the judge to couple the sham bidding instruction with a reasonableness instruction. Price-fixing and bid rigging are per se violations. Defendant’s conduct, even if USS were a monopsonist as defendant contends, did not fall in any “gray zone” requiring a reasonableness instruction. See United States v. Gillen, 599 F.2d 541 (3d Cir.), cert. denied, 444 U.S. 866, 100 S.Ct. 137, 62 L.Ed.2d 89 (1979). For the reasons stated above, the district court did not err in giving the challenged instruction.
Sargent Electric also alleges that the court’s instructions removed consideration of the element of intent from the jury. The court instructed that no showing of specific intent to disobey the law or restrain trade or knowledge of the illegality of the activities was necessary and defendants could be convicted if they knowingly formed the conspiracy or knowingly joined the conspiracy. App. at 3722a. Prior to this, the court also instructed that intent could be proved by showing that the acts of the defendants had the effect of bid rigging and the acts were undertaken with knowledge of the bid rigging; or defendants’ acts did not have any proscribed effects, but the defendants undertook those acts with a conscious purpose of bringing about the proscribed effects. Id. at 3721a-22a.
The trial court’s instructions avoided the problems of presuming intent simply from the commission of certain acts discussed in United States v. United States Gypsum Co., 438 U.S. 422, 98 S.Ct. 2864, 57 L.Ed.2d 854 (1978) and Sandstrom v. Montana, 442 U.S. 510, 99 S.Ct. 2450, 61 L.Ed.2d 39 (1979). Here, the jury was asked to find not only that the defendants knowingly joined or formed the conspiracy, but that they also meant to bring about or did bring about the effects proscribed by the Sherman Act. Moreover, not only did the instructions follow the language accepted by this court, especially as to specific intent, see United States v. Continental Group, Inc., 603 F.2d 444, 462-63 (3d Cir.1979), but part of the instructions followed the exact language of defendants’ proposed instruc[1197]*1197tion No. 14. App. at 3819a. Viewed as a whole, the instructions were a correct statement of the law and fairly and adequately presented this issue to the jury.
Appellants also object to the jury instructions pertaining to the “affecting commerce” theory. The judge stated that the jury need only find that the commerce involved was substantial and that they did not have to find a rise in prices or a shift in commerce and the judge instructed that the government could satisfy either the in commerce or affecting commerce theory to prove the interstate commerce element of the Sherman Act. The court’s instructions, however, correctly stated the law. Per se violations require no proof of an anti-competitive effect on commerce. Northern Pacific Railway, 356 U.S. at 5, 78 S.Ct. at 518. Also, evidence that supports either theory pertaining to the interstate commerce element is sufficient to establish a Sherman Act violation. McLain v. Real Estate Board of New Orleans, 444 U.S. at 242, 100 S.Ct. at 509.
E.
Relying on United States v. Kelly, 349 F.2d 720 (2d Cir.1965), defendant Rodgers alleges prejudice because the district court failed to marshal the evidence against him. A trial court, however, need not marshal the evidence, especially if the trial is complex. United States v. Gillilan, 288 F.2d 796, 798-99 (2d Cir.1961). Unlike Kelly, where the evidence did not connect the defendant to the single conspiracy charged, Rodgers suffered no prejudice by a failure to marshal the evidence because that evidence directly connected him to the conspiracy.
VIII.
We have carefully considered all contentions presented by the appellants. The judgment of the district court will be affirmed in all respects.