
524 F.3d 726 (2008)
MICHIGAN DIVISION-MONUMENT BUILDERS OF NORTH AMERICA et al., Plaintiffs-Appellants,
v.
MICHIGAN CEMETERY ASSOCIATION et al., Defendants-Appellees.
Michigan Division-Monument Builders of North America et al., Plaintiffs-Appellees,
v.
Michigan Cemetery Association, Arborcrest Memorial Park (07-1168); Michigan Memorial Park, Inc. (07-1169); White Chapel Memorial Association (07-1171), Defendants-Appellants.
Nos. 06-2524, 07-1168, 07-1169, 07-1171.
United States Court of Appeals, Sixth Circuit.
Argued: March 13, 2008.
Decided and Filed: May 1, 2008.
*728 ARGUED: Barbara H. Kramer, Kramer & Kramer, Rydal, Pennsylvania, for Plaintiffs. Frederick R. Juckniess, Miller, Canfield, Paddock & Stone, Ann Arbor, Michigan, Jay W. Tower, Bingham Farms, Michigan, Jeffrey C. Gerish, Plunkett & Cooney, Bloomfield Hills, Michigan, Anthony F. Caffrey III, Cardelli, Lanfear & *729 Buikema, Grand Rapids, Michigan, for Defendants. ON BRIEF: Barbara H. Kramer, Mitchell A. Kramer, Kramer & kramer, Rydal, Pennsylvania, David A. Nacht, David Blanchard, Nacht & Associates, Ann Arbor, Michigan, for Plaintiffs. Frederick R. Juckniess, Miller, Canfield, Paddock & Stone, Ann Arbor, Michigan, Jay W. Tower, Bingham Farms, Michigan, Jeffrey C. Gerish, Plunkett & Cooney, Bloomfield Hills, Michigan, L. David Lawson, Winegarden, Haley, Lindholm & Robertson, Grand Blanc, Michigan, Robert D. Goldstein, Garan Lucow Miller, Grand Blanc, Michigan, Timothy J. Jordan, Garan Lucow Miller, Detroit, Michigan, for Defendants.
Before: MOORE, GILMAN, and SUTTON, Circuit Judges.

OPINION
RONALD LEE GILMAN, Circuit Judge.
This case involves allegations of anticompetitive behavior in the market for burial monuments in the state of Michigan. Three independent monument builders and a nonprofit trade association of monument buildersthe Michigan Division of the Monument Builders of North America  (collectively, the Builders) filed the present lawsuit against 20 cemetery operators and the Michigan Cemetery Association (collectively, the Cemeteries). The lawsuit alleges that the Cemeteries are engaged in (1) an illegal tying arrangement, in violation of § 1 of the Sherman Act, (2) an illegal conspiracy to restrain competition and monopolize trade, also in violation of § 1 of the Sherman Act, (3) an illegal conspiracy to restrain trade, in violation of § 2 of the Sherman Act, and (4) violations of the Michigan Prepaid Funeral and Cemetery Sales Act, M.C.L. § 328.225.
The district court dismissed the Builders' claims after concluding that the proposed geographic market as set forth in the complaint was too narrow as a matter of law. Subsequently, the district court denied motions for sanctions against the Builders that were filed by several of the cemetery operators. For the reasons set forth below, we AFFIRM the judgment of the district court on the merits of the antitrust claims, but VACATE its denial of sanctions and REMAND the case for further proceedings on that issue.

I. BACKGROUND

A. Factual background
The Builders allege that the Cemeteries "have been engaging in a continuing unlawful combination and conspiracy to unreasonably restrain trade and engage in unlawful tying arrangements in cemeteries in the sale and installation of memorials and monuments and related items." According to the Builders' second amended complaint (the Complaint), the Cemeteries employ various tactics to prevent the independent monument builders from competing in the market. These tactics form the basis of the alleged Sherman Act violations. Three independent monument builders have brought claims on their own behalf against the named defendants only, while the Monument Builders trade association seeks relief on behalf of a class of all monument builders in Michigan against a defendant class comprised of all cemeteries in the state that engage in one or more practices that restrict free trade for monuments. Monetary damages are sought by the independent builders and injunctive relief is sought by the trade association. The Builders' collective claims are identical, however, with respect to all of the legal and factual issues.
The Cemeteries are individually identified in paragraph 9 of the Complaint, but *730 the Complaint contains no specific allegations of wrongdoing by the individual cemeteries. Instead, the Complaint alleges generally that "each of the defendants, and each member of the defendant class, has engaged in all or certain of the following anticompetitive actions and activities." The Builders then assert four claims against the Cemeteries, although each claim is presented twice, once as a claim by the three independent builders (Counts I through IV) and once as a claim by the trade association (Counts V through VIII). The relevant geographic market for all four claims is defined in the Complaint as "each individual cemetery in the State of Michigan." Each cemetery is its own market, according to the Builders, "[b]ecause of the uniqueness of land and the fact that once a grave is purchased[,] the owner or his or her family who wish to memorialize the deceased must install the memorial or monument in that cemetery."
Count I (and Count V) allege an illegal tying arrangement in violation of Section 1 of the Sherman Act, 15 U.S.C. § 1. Specifically, the Builders allege that the Cemeteries "have sufficient economic power in the tying productthe cemetery burial lotsto impose restrictions in the tied product or service, monuments and memorials and related products and installation of monuments and memorials and related products and servicesand a substantial volume of commerce in said market was in fact restrained."
In Count II (and Count VI), the Builders allege that the Cemeteries are engaged in an illegal conspiracy to restrain competition and monopolize trade, also in violation of Section 1 of the Sherman Act. The alleged conspiracy is designed to "drive plaintiffs out of business by engaging in the predatory practices set forth in paragraph 32, in particular, by exclusion of plaintiffs from defendant cemeteries and by price fixing, thereby impeding plaintiffs' ability to sell or install monuments, memorials, foundations, benches, mausoleums, and other related items for the memorialization of the dead." According to the Builders, this conspiracy is part of a historical practice by cemeteries to "eliminate competition by adopting practices that violate the antitrust laws." The Builders explain that "[t]his avowed position to pursue illegal practices in violation of antitrust laws was articulated by Mr. C.H. Shackelfold, past president of the American Cemetery Association, in his speech in February 1982, in San Antonio, Texas." In that speech, Shackelfold said:
The cemeterian is not going to give up the installation rule until he is told to do so by the Supreme Court that he has to. If it reaches that point, you and I are going to have a lot more problems than we have now. Cemeteries will figure out other ways to collect these charges through maintenance, supervision and bookkeeping charges.
The Complaint makes no allegation, however, that Shackelfold is involved in the present litigation.
According to the Builders, "[h]aving secured the agreement from major private cemeteries that sell monuments and memorials, defendants, individually and through the aegis of the Michigan Cemetery Association, have attempted to bring smaller cemeteries into the conspiracy." The attempts to bring in smaller cemeteries are allegedly demonstrated by a letter from Leonard Krawczyk, President of Hillcrest Memorial Gardens and a Director of the Michigan Cemetery Association, that was sent to Jeff Davis of Great Lakes Monument Co. in December of 2004. A copy of the letter is attached to the Complaint as Exhibit 1. The letter discusses a dispute between Hillcrest and Great Lakes regarding the costs associated with placing *731 two monuments in Hillcrest's cemetery. In addition to being sent to Mr. Davis at Great Lakes, the letter was sent to the Shiawassee County Prosecutor, Suzanne Jolicour of the State Cemetery Commission, and a number of other cemeteries and monument builders.
Count III (and Count VII) alleges a "conspiracy to restrain trade and/or attempt to monopolize" in violation of Section 2 of the Sherman Act, 15 U.S.C. § 2. The Builders allege that because of their proposed geographic marketwith each individual cemetery being a market unto itselfthe Cemeteries "have sufficient market power to come dangerously close to monopolizing the defined market" in burial memorials and monuments.
Finally, in Count IV (and Count VIII), the Builders allege a number of violations of the Michigan Prepaid Funeral and Cemetery Sales Act. Among the alleged state-law violations is a failure to comply with price disclosure rules.

B. Procedural background
The Builders filed their initial complaint in December of 2005. In January of 2006, and again in August of 2006, the Builders were allowed to amend their complaint. Most of the Cemeteries then filed a joint motion to dismiss pursuant to Rule 12(b)(6) of the Federal Rules of Civil Procedure. The others filed their own separate motions to dismiss.
Finding that the Builders' proposed geographic market was inadequate as a matter of law, the district court granted the Cemeteries' motions to dismiss the federal antitrust claims in October of 2006. The court also declined to exercise supplemental jurisdiction over the Builders' state-law claims, thereby dismissing them without prejudice. A timely appeal was filed by the Builders, with the issues limited to the federal antitrust claims.
Meanwhile, four of the individual cemeteries filed motions for sanctions against the Builders pursuant to Rule 11 of the Federal Rules of Civil Procedure, 28 U.S.C. § 1927, and the court's inherent authority. The district court denied the motions without explanation. That decision has been cross-appealed by the individual cemeteries seeking the sanctions.

II. ANALYSIS

A. Standard of review
We review de novo a district court's dismissal of a complaint pursuant to Rule 12(b)(6) of the Federal Rules of Civil Procedure. Marks v. Newcourt Credit Group, Inc., 342 F.3d 444, 451 (6th Cir.2003). In reviewing a Rule 12(b)(6) motion to dismiss, which is based on the failure to state a claim upon which relief can be granted, "[f]actual allegations must be enough to raise a right of relief above the speculative level, . . . on the assumption that all the allegations in the complaint are true (even if doubtful in fact)." NicSand, Inc. v. 3M Co., 507 F.3d 442, 461 (6th Cir.2007) (quoting Bell Atl. Corp. v. Twombly, ___ U.S. ___, 127 S.Ct. 1955, 1965, 167 L.Ed.2d 929 (2007)). The court need not, however, accept as true legal conclusions or unwarranted factual inferences. Gregory v. Shelby County, 220 F.3d 433, 446 (6th Cir.2000).
In the antitrust context, the Supreme Court has noted that although district courts must "be cautious before dismissing an antitrust complaint in advance of discovery," they must not forget that "proceeding to antitrust discovery can be expensive." Bell Atl., 127 S.Ct. at 1966-67. It specifically commented that "a district court must retain the power to insist on some specificity in pleading before allowing a potentially massive factual controversy to proceed." Id. at 1967 (quoting Associated *732 Gen. Contractors of Cal., Inc. v. Carpenters, 459 U.S. 519, 528 n. 17, 103 S.Ct. 897, 74 L.Ed.2d 723 (1983)).

B. The tying claim and the relevant market
The Builders allege that the Cemeteries are using improper tying arrangements to require consumers to purchase a burial memorial from the Cemeteries once they have purchased a burial plot. These allegedly improper sales practices form the basis for all three of the Builders' claims arising under the Sherman Act. In granting the Cemeteries' motions to dismiss, the district court concluded that the Builders' antitrust claims fail because the geographic market, as proposed by the Builders, was too narrow as a matter of law. On appeal, the Builders argue that the district court erred in granting the motions to dismiss on the basis of alleged infirmities in the proposed geographic market. The Builders claim that they have satisfied the pleading requirements of the Federal Rules of Civil Procedure and are entitled to proceed to discovery in an attempt to prove that the geographic market they have proposed is sufficient to sustain an antitrust action.
A tying arrangement is defined "as an agreement by a party to sell one product . . . only on the condition that the buyer also purchases a different (or tied) product, or at least agrees that he will not purchase that product from any other supplier." N. Pac. Ry. Co. v. United States, 356 U.S. 1, 5-6, 78 S.Ct. 514, 2 L.Ed.2d 545 (1958). In other words, "[a] supermarket that will sell flour to consumers only if they will also buy sugar is engaged in tying. Flour is referred to as the tying product, sugar as the tied product." Jefferson Parish Hosp. Dist. No. 2 v. Hyde, 466 U.S. 2, 33, 104 S.Ct. 1551, 80 L.Ed.2d 2 (1984) (O'Connor, J., concurring) (emphasis in original). The typical tying case "involve[s] a seller's attempt to exploit its economic power over one product or in one market to force a less desirable, tied product on a buyer." Highland Capital, Inc. v. Franklin Nat. Bank, 350 F.3d 558, 565 (6th Cir.2003). Illegal tying therefore occurs only "if the seller has `appreciable economic power' in the tying product market and if the arrangement affects a substantial volume of commerce in the tied market." PSI Repair Servs., Inc. v. Honeywell, Inc., 104 F.3d 811, 815 (6th Cir.1997) (quoting Eastman Kodak Co. v. Image Technical Servs., Inc., 504 U.S. 451, 462, 112 S.Ct. 2072, 119 L.Ed.2d 265 (1992)).
"[A]ny inquiry into the validity of a tying arrangement must focus on the market or markets in which the two products are sold, for that is where the anticompetitive forcing has its impact." Jefferson Parish, 466 U.S. at 18, 104 S.Ct. 1551. Requiring proof of market power regarding the tying product "is important because, without market power, a seller cannot engage in the forcing necessary to establish a § 1 violation." PSI, 104 F.3d at 818. "Even though market power is normally established by controlling a substantial share of the market, market power also exists `when the seller offers a unique product that competitors are not able to offer.'" Id. at n. 3 (quoting Jefferson Parish, 466 U.S. at 17, 104 S.Ct. 1551).
The idea that all land is unique, however, is insufficient to support a finding of market power. In Northern Pacific, the Supreme Court concluded that specific real estate holdings were sufficient to give the defendant market power because the land was "strategically located in checkerboard fashion amid private holdings and within economic distance of transportation facilities.. . . [T]his particular land was often prized by those who purchased or leased it *733 and was frequently essential to their business activities." 356 U.S. at 7, 78 S.Ct. 514.
The holding of Northern Pacific has been interpreted to mean that "uniqueness of location is not in itself adequate to establish market power[;] . . . there must be other evidence showing that the location lends the defendant a competitive advantage others cannot meet." Baxley-DeLamar Monuments, Inc. v. Am. Cemetery Ass'n, 938 F.2d 846, 852 (8th Cir.1991). In a more recent case relevant to whether uniqueness alone is sufficient to presume market power, the Supreme Court reiterated that "in all cases involving a tying arrangement, the plaintiff must prove that the defendant has market power in the tying product." Ill. Tool Works Inc. v. Indep. Ink, Inc., 547 U.S. 28, 46, 126 S.Ct. 1281, 164 L.Ed.2d 26 (2006) (abrogating the long-standing presumption that the simple possession of a patent automatically conferred market power upon the patentee).
In addition to defining the relevant product market and demonstrating the defendant's power in that market, the plaintiff in an antitrust case must also define the relevant geographic market and demonstrate that the defendant's actions produced anticompetitive effects in that defined area. Found. for Interior Design Educ. Research v. Savannah Coll. of Art & Design, 244 F.3d 521, 531 (6th Cir.2001). The selected geographic market must "both correspond to the commercial realities of the industry and be economically significant." Brown Shoe Co. v. United States, 370 U.S. 294, 336-37, 82 S.Ct. 1502, 8 L.Ed.2d 510 (1962) (citations and internal quotation marks omitted). "What this usually boils down to in practice is the area of actual or potential competition between the parties involved in the case." City of Cleveland v. Cleveland Elec. Illuminating Co., 734 F.2d 1157, 1167 (6th Cir.1984).
The geographic market "includes the geographic area in which consumers can practically seek alternative sources of the product, and it can be defined as `the market area in which the seller operates.'" Double D Spotting Serv., Inc. v. Supervalu, Inc., 136 F.3d 554, 560 (8th Cir.1998) (quoting Tampa Elec. Co. v. Nashville Coal Co., 365 U.S. 320, 327, 81 S.Ct. 623, 5 L.Ed.2d 580 (1961)). As we have previously noted, "[m]arket definition is a highly fact-based analysis that generally requires discovery." Found. for Interior Design, 244 F.3d at 531. But the fact that market definition generally requires discovery has not prevented this court, and others, from affirming grants of motions to dismiss on the basis of an insufficiently pled or totally unsupportable proposed market.
In Double D, for example, the plaintiff alleged that the defendants engaged in anticompetitive behavior by requiring truck drivers to use a certain unloading service at a specified storage facility. Based on the plaintiff's complaint, "the product market is defined as unloading services and the geographic market is alleged to be the Supervalu warehouse in Urbandale, Iowa, which is a suburb of Des Moines." 136 F.3d at 560. The district court, in dismissing the plaintiff's complaint, concluded that the proposed geographic market was too narrow as a matter of law. In affirming the dismissal of the plaintiff's claim, the Eighth Circuit explained its rationale as follows:
At issue is one contract between the owner of one particular warehouse within the Des Moines metropolitan area and one unloading service provider. The contract provides that this one unloading service provider has the right, subject to an agreed upon price schedule, to provide all of the unloading services at this *734 particular warehouse. Supervalu's one warehouse in Urbandale does not amount to a relevant market for unloading services of this type. Rather, the market for unloading services would seem to be more properly defined as including all warehouses within, at least, the entire Des Moines, Iowa, metropolitan area, if not an even larger area.
Id. at 560-61.
The Fifth Circuit similarly affirmed a Rule 12(b)(6) dismissal on the basis of an inadequate geographic market in Apani S.W., Inc. v. Coca-Cola Enterprises, Inc., 300 F.3d 620 (5th Cir.2002). In Apani, the plaintiff alleged that Coca-Cola had illegally conspired with the City of Lubbock, Texas to obtain an exclusive contract to supply all nonalcoholic beverages to facilities owned by the city. Apani contended that the relevant geographic market consisted of "only the twenty-seven facilities owned by the City." Id. at 628. In affirming the dismissal of Apani's claims, the Fifth Circuit concluded that the "alleged geographic market did not correspond to the commercial realities of the industry and was not economically significant." Id. at 633. The court explained that "Apani has simply attempted to artificially narrow a broader economic market, the City of Lubbock, to specific venues. Such pleading maneuvers may not be used for the purpose of creating a fictitious market." Id.
The district court below relied heavily on Foundation for Interior Design, 244 F.3d 521, a case from this circuit. Although that case did not involve an insufficient geographic market per se, we affirmed a Rule 12(b)(6) dismissal because of an inadequate product-market definition. The defendant's antitrust counterclaims in Foundation for Interior Design were premised on the allegation that the plaintiff "abused its market power in the `market for accredited interior design programs' by restricting output and suppressing competition." Id. at 531. We affirmed the dismissal of the counterclaims because "the [defendant] competes with schools that have non-accredited interior design programs and with schools that have accredited programs. Thus, the relevant market in this case includes all interior design programs." Id.
The Builders define the tied product market as "granite and bronze grave monuments, memorials, foundations, benches, mausoleums, and related items for memorialization of the dead, and the installation of the same." With respect to the tying product, the burial lots, and the geographic market, the Builders' position is as follows:
Because of the uniqueness of land and the fact that once a grave is purchased the owner or his or her family who wish to memorialize the deceased must install the memorial or monument in that cemetery, each cemetery constitutes a unique and separate market. Therefore, the relevant geographic market is each individual cemetery in the State of Michigan.
The Builders further contend that "[a] cemetery lot, being real estate, is unique, and cemeteries are distinct enterprises and have a unique public function."
But the Builders'argument ignores the fact that each individual cemetery has nothing close to exclusive control over burial lots outside of the four corners of its own land. Moreover, the uniqueness of land is insufficient to serve as support for defining a geographic market absent a showing of competitive advantage on the basis of the land's particular characteristics. Baxley-DeLamar Monuments, Inc. v. Am. Cemetery Ass'n, 938 F.2d 846, 852 (8th Cir.1991) (concluding that although cemetery lots are unique, "as all land is *735 unique," the plaintiffs had failed to show that the uniqueness provided them with a competitive advantage). Counsel for the Builders in fact acknowledged during the district court's hearing on the Cemeteries' motion to dismiss that "of itself, the uniqueness of land[] does not make for a tying case. It did at one time. It does not anymore."
Furthermore, the acceptance of the Builders' proposed geographic market would make any proof of market power unnecessary. There can be no competition for the sale of burial lots within a market that contains only one provider of burial lots. Market power under these circumstances would be unavoidable. The Builders appear to acknowledge this aspect of their argument when they state that "there are no real substitutes for the tying product, interment rights within a particular cemetery." They in essence are urging us to merge the geographic-market analysis and the tying-product-market analysis into one determination, rendering one or the other unnecessary.
In a final attempt to explain their geographic-market argument, the Builders state in their Reply Brief that "competition between cemeteries for the sale of interment rights is not relevant to the market issues in this case. With respect to the tying market, Plaintiffs rely upon the uniqueness of the tying product, not market share, to establish the requisite power." But this argument seems to contradict their previously cited arguments, based on each cemetery's "exclusive control" over its own interment rights. Moreover, the only allegations of uniqueness in the Complaint are (1) the uniqueness of land, (2) the fact that after a grave is purchased, the purchaser must place the memorial in that cemetery, and (3) that cemeteries are "distinct enterprises and have a unique public function."
The Builders have acknowledged, however, that the uniqueness of land is insufficient by itself to support the Builders' proposed market. Focusing on what happens only after a grave site is purchased also ignores the competitive market for the initial sale of burial lots. And finally, the fact that cemeteries "have a unique public function" is a comment on the general role of cemeteries in society, but does not support the conclusion that each individual cemetery in Michigan is in some way unique from every other cemetery in a way that can be recognized by the antitrust laws.
Moreover, even if we were to accept the truth of all of the Builders' claims, we would still find that their prosed geographic market is too narrow as a matter of law. We have no doubt that the market for burial plots is heavily influenced by personal preferences (religious, geographic, and familial), but to conclude as a result of such personal preferences that each individual cemetery is its own geographic market removes any chance of defining a geographic market that "correspond[s] to the commercial realities of the industry." See Brown Shoe Co. v. United States, 370 U.S. 294, 336, 82 S.Ct. 1502, 8 L.Ed.2d 510 (1962) (citations and internal quotation marks omitted).
The Builders also assert that the district court incorrectly limited the market-power analysis to a question of market share, thereby avoiding the Supreme Court's recognition that market power may exist "when the seller offers a unique product that competitors are not able to offer." Jefferson Parish Hosp. Dist. No. 2 v. Hyde, 466 U.S. 2, 17, 104 S.Ct. 1551, 80 L.Ed.2d 2 (1984). But the Complaint, even when its factual allegations are taken as true, does not support a conclusion that each of the 3,800 individual cemeteries in the state of Michigan truly offers a unique *736 product that cannot be realistically offered by one or more of the other cemeteries. Moreover, the cases cited by the Builders in support of their argument that the uniqueness factor requires a market defined as each individual cemetery make clear that uniqueness, in the antitrust context, serves as an alternative method for proving product market share, not as a method of defining a geographic market. See id.; see also N. Pac. Ry. Co. v. United States, 356 U.S. 1, 7, 78 S.Ct. 514, 2 L.Ed.2d 545 (1958) (concluding that specific real estate holdings were sufficient to give the defendant market power because the land was "strategically located in checkerboard fashion amid private holdings and within economic distance of transportation facilities. . . . [T]his particular land was often prized by those who purchased or leased it and was frequently essential to their business activities").
The cases that both parties cite regarding antitrust claims against cemeteries support the conclusion that the Builders' proposed geographic market is deficient as a matter of law. In each case, the plaintiffs identified an economically realistic geographic market, and any discussion of uniqueness was in the context of determining product market share, not the relevant geographic market. For example, in Monument Builders of Greater Kansas City, Inc. v. American Cemetery Association of Kansas, 891 F.2d 1473, 1476 (10th Cir. 1989), the plaintiffs alleged that "approximately 70-75% of interments each year in the Kansas City area take place in [the defendants'] cemeteries." The geographic market was the "Kansas City area" rather than each individual cemetery. If the Builders' proposed geographic market here had been applied in Monument Builders of Greater Kansas City, there would have been no need to allege the market share, because each cemetery fully controls the interments within its own boundaries.
The Builders borrowed the line in their Complaint that "cemeteries are distinct enterprises and have a unique public function" from Rosebrough Monument Co. v. Memorial Park Cemetery Association, 666 F.2d 1130, 1143 (8th Cir.1981). In Rosebrough, the Eighth Circuit explained that "[a] cemetery lot, like any piece of real estate, is unique." Id. Yet that court also focused on a defined geographic areaSt. Louisand noted that the defendants "accounted for 22 percent of the burials performed in the market area in 1978." Id. Likewise, in Moore v. Jas. H. Matthews & Co., 550 F.2d 1207, 1211 (9th Cir.1977), the plaintiffs focused on Lane County in Oregon, where the defendant cemeteries "accounted for 78% of all interments."
One district court has commented that in both Rosebrough and Moore, "the Courts of Appeal referred to the uniqueness of individual cemetery plots as providing the Defendants with the necessary market power in that market. . . . However, the opinions also note that in both cases, the defendants controlled a substantial share of the cemetery market within a limited geographic area." Fla. Monument Builders v. All Faiths Mem'l Gardens, 605 F.Supp. 1320, 1322 (S.D.Fla. 1984) (emphasis in original). No similar geographic area has been proposed by the Builders here. Despite numerous cases alleging antitrust violations by cemeteries, the Builders have not offered a single case that supports their argument that the relevant geographic market for their tying claim is each individual cemetery in Michigan.
As the district court below noted, the Builders' geographic-market argument, with its focus on what occurs after a burial lot has been purchased, is very similar to the "lock-in" theory of antitrust. *737 Market power may exist in a lock-in case where once a customer buys one product, he or she is locked in to buying another product because of the seller's rules. See PSI Repair Servs., Inc. v. Honeywell, Inc., 104 F.3d 811, 817-18 (6th Cir.1997) (alleging that there was an illegal tie between the defendant's equipment and the defendant's replacement parts). Under the lock-in theory of antitrust, proof of market power in the tying market is not necessary if the defendant has monopoly power in an aftermarket product, such as replacement parts or repair services. Eastman Kodak Co. v. Image Tech. Servs., Inc., 504 U.S. 451, 477, 112 S.Ct. 2072, 119 L.Ed.2d 265 (1992) (holding that "it is clearly reasonable to infer that [the defendant] has market power to raise prices and drive out competition in the aftermarkets" for service and parts despite an undisputed lack of market power in the initial product).
But a lock-in claim requires specific factual allegations in the complaint that the defendant either changed its rules after the initial sale was made or concealed its rules from its customers. PSI, 104 F.3d at 820 (rejecting the plaintiff's lock-in claim because "there are no allegations that [the defendant] changed its parts-restrictive policy in order to lock-in customers, nor has [the plaintiff] alleged that [the defendant]'s policy was not generally known"). No such allegations are made in the Builders' Complaint, and they have expressly stated in their briefs that they are not pursuing a lock-in theory.
We therefore conclude that the district court did not err in determining that the Builders' proposed geographic market is too narrow as a matter of law. Because the flaw in the proposed market is fatal to all of the Builders' antitrust claims, the Cemeteries' motion to dismiss was properly granted.

C. Cross-appeals for sanctions
Following the dismissal of the Builders' Complaint, four of the individual cemeteries filed motions for sanctions against the Builders. The district court, after establishing the relevant legal framework, denied the motions without analysis, simply stating that "[w]hile this Court ultimately concluded that Defendants' motions to dismiss should be granted, the Court does not believe the sanctions under 28 U.S.C. § 1927, Rule 11, or the Court's inherent authority, are warranted in this action." On appeal, the cemeteries argue that the district court abused its discretion in failing to sanction the Builders despite what the cemeteries claim was an inadequate basis in law and fact for the Builders' antitrust claims. The cemeteries seek an award of their fees and costs or, in the alternative, a remand to the district court for further explanation of that court's decision to deny their requests for sanctions.
At the outset, the Builders argue that one of the cemeteries, White Chapel Memorial Association, did not timely appeal the denial of its motion for sanctions. White Chapel's motion for sanctions was denied by an order dated November 22, 2006. In its notice of appeal, filed January 3, 2007, White Chapel mistakenly stated that the order it was appealing was entered on December 1, 2006 rather than November 22, 2006. The Builders argue that White Chapel appealed the wrong order. Moreover, according to the Builders, White Chapel's appeal was filed "33 days after the last order in the case and 42 days after the first notice of appeal was filed," and was thus untimely. The first notice of appeal referred to by the Builders was their own notice of appeal of the district court's order granting the Cemeteries' motions to dismiss, which they filed on the same date (November 22, 2006) that the *738 court denied White Chapel's motion for sanctions.
We find no merit in the Builders' argument. Pursuant to Rule 4(a) of the Federal Rules of Appellate Procedure, a notice of appeal is generally required to be filed "within 30 days after the judgment or order appealed from is entered." But "[i]f one party timely files a notice of appeal, any other party may file a notice of appeal within 14 days after the date when the first notice was filed, or within the time otherwise prescribed by this Rule 4(a), whichever period ends later." Fed. R.App. P. 4(a)(3). The Builders correctly point out that the last order in the case was entered on December 1, 2006, 33 days before White Chapel's notice of appeal was filed. But they are incorrect in stating that White Chapel's notice was filed 42 days after the relevant first notice of appeal. The relevant notice of appeal, as far as White Chapel is concerned, was that filed by the Michigan Cemetery Association and Arborcrest Memorial Park on December 20, 2006, 14 days before White Chapel's notice of appeal. Therefore, despite being outside of the 30-day window for directly appealing the denial of its motion for sanctions, White Chapel's notice of appeal was within the 14-day window expressly provided by Rule 4(a)(3).
White Chapel mistakenly thought, however, that the December 1, 2006 order, rather than the November 22, 2006 order, was the one that denied its motion for sanctions. But such a technical error in a notice of appeal should be treated as harmless in the absence of a showing of prejudice. See Higginson v. United States, 384 F.2d 504, 508 (6th Cir.1967) (rejecting the appellee's argument that a notice of appeal was defective because "[t]he mistake was such as could have been made by a clerk or stenographer" and "affected no substantial rights"); see also McLaurin v. Fischer, 768 F.2d 98, 102 (6th Cir.1985) (holding that the error was harmless where a party appealed only the final order of the district court and did not explicitly appeal certain earlier rulings). Moreover, White Chapel's appeal on its motion for sanctions is identical to the other appeals regarding sanctions. The notice of appeal: (1) includes the correct case number from the district court, (2) identifies White Chapel's counsel and specifically notes that it is being filed by the "Attorneys for Defendant, White Chapel Memorial Association," and (3) refers to a sanctions order in the body of the notice. These factors, together with the filing of the appeal, would assuredly alert the Builders that the appeal concerns the November 22, 2006 order. The Builders have not offered any argument regarding prejudice and we find none. White Chapel's appeal should therefore be allowed to proceed despite its misidentification of the appealed-from order.
We now turn to the merits of the motions for sanctions. Reasonable costs and attorney fees are available under 28 U.S.C. § 1927 where an attorney "so multiplies the proceedings in any case unreasonably and vexatiously." Sanctions may be warranted "when an attorney knows or reasonably should know that a claim pursued is frivolous, or that his or her litigation tactics will needlessly obstruct the litigation of nonfrivolous claims." Jones v. Cont'l Corp., 789 F.2d 1225, 1230 (6th Cir. 1986).
Rule 11(b) of the Federal Rules of Civil Procedure, on the other hand, states that by filing a "pleading, written motion, or other paper" with the court, an attorney is certifying that "to the best of the person's knowledge, information, and belief, formed after an inquiry reasonable under the circumstances. . . [,] the claims, defenses, and other legal contentions are warranted *739 by existing law or by a nonfrivolous argument for extending, modifying, or reversing existing law or for establishing new law." "[I]n this circuit, the test for the imposition of Rule 11 sanctions is whether the individual attorney's conduct was reasonable under the circumstances." Mann v. G & G Mfg., Inc., 900 F.2d 953, 958 (6th Cir.1990).
We review a district court's decision to grant or deny sanctions, whether arising from § 1927 or Rule 11, under the abuse-of-discretion standard. Ridder v. City of Springfield, 109 F.3d 288, 298 (6th Cir.1997) ("As with Rule 11 sanctions, we review an order awarding attorney fees under § 1927 for an abuse of discretion."). "This court has defined an abuse of discretion as a definite and firm conviction that the trial court committed a clear error of judgment." Arban v. W. Publ'g Corp., 345 F.3d 390, 404 (6th Cir.2003) (citation and internal quotation marks omitted). Such an error occurs "when the district court applies the wrong legal standard, misapplies the correct legal standard, or relies on clearly erroneous findings of fact." Geier v. Sundquist, 372 F.3d 784, 789-90 (6th Cir.2004).
Both parties devote the bulk of their briefs to rearguing the underlying merits of the Builders' antitrust claims. In addition to arguing the merits, however, the cemeteries cite a number of cases that "have held that Rule 11 sanctions are appropriate where frivolous or unsupported antitrust claims are made." The Eastern District of Michigan, for example, awarded sanctions where the antitrust plaintiff and its counsel failed to recognize the lack of factual support for its claim after lengthy discovery and instead "hurled groundless accusations, advanced unsupported conspiracy theories, and proposed untenable market definitions that were `reverse engineered' to link the facts to some superficially appealing theory." B & H Medical, LLC. v. ABP Admin., Inc., 354 F.Supp.2d 746, 750 (E.D.Mich.2005); see also Fla. Monument Builders v. All Faiths Mem'l Gardens, 605 F.Supp. 1324, 1326 (S.D.Fla. 1984) (sanctioning an antitrust plaintiff's attorney for failing to "examine the rules and regulations of the Defendant cemeteries on file in the state capital to determine if any `parallel conduct' existed before filing a pleading alleging a conspiracy"); Danik, Inc. v. Hartmarx Corp., 875 F.2d 890, 895-96 (D.C.Cir.1989) (affirming sanctions under Rule 11 on the basis of "obvious deficiencies" in the prefiling investigation of the facts underlying the plaintiffs' antitrust claims), aff'd in part, rev'd in part on other grounds, 496 U.S. 384, 110 S.Ct. 2447, 110 L.Ed.2d 359 (1990).
No case has been cited, however, that grants the primary relief that the cemeteries seekthe imposition of sanctions by an appellate court in the first instance despite the district court's denial of the request on the same record. Under the highly deferential abuse-of-discretion standard, we are not surprised that the cemeteries have been unable to locate such a precedent.
The cemeteries base their claim of frivolousness on the district court's conclusions that the geographic market proposed by the Builders "blatantly ignore[d] economic and commercial reality and the facts in the record," and that the conspiracy claims were "practically and economically implausible." Furthermore, the cemeteries claim that the Builders were inconsistent in advancing their arguments, such as appearing to assert a "lock-in" antitrust claim in their written filings followed by express disavowals of such a theory during oral argument before the district court. According to the cemeteries, the district court's conclusions regarding the weakness of the Builders' claims, coupled with the *740 Builders' litigation behavior, demonstrate that sanctions are warranted in this case.
The district court obviously came to a contrary conclusion, but unfortunately provided no analysis that would allow us to review the soundness of its decision. This court dealt with a similar situation in Palmer v. Nationwide Mutual Insurance, Co., 945 F.2d 1371 (6th Cir.1991), where we vacated a district court's denial of a motion for sanctions because no explanation was given for the denial. Id. at 1377-78. The district court in Palmer had stated that the issue of sanctions was "a close question, because I almost find this an abuse of process." Id. at 1377. In vacating the district court's decision, we stated that "particularly in the close or serious sanction cases, . . . the district court should set out its analysis and discrete findings with respect to its decision on the allowance or rejection of sanctions." Id. (internal quotation marks omitted).
This court's decision in Eagles, Ltd. v. American Eagle Foundation, 356 F.3d 724 (6th Cir.2004), does not require a contrary result. Eagles involved the voluntary dismissal of the plaintiff's claim and subsequent motions for attorney fees and costs under both 15 U.S.C. § 1117(a) (which governs attorney fees in trademark cases) and 28 U.S.C. § 1927. This court affirmed the district court's denial of sanctions because "[t]he district court addressed the parties' arguments and applied the correct legal standard," and adequately "[gave] the reasons for the denial." Id. at 727.
As we explained in Eagles, "[t]he adequacy of a district court's statement is determined by this Court's ability to understand its reasoning, not by the number of sentences it uses." Id. at 727-28. Unlike in Eagles, the district court in the present case did not adequately give the reasons for the denial. Nor did the district court address the parties' arguments. This lack of explanation by the district court greatly hinders our ability to understand its reasoning.
In response to the cemeteries' request for a remand, the Builders assert that "this Court has never announced a blanket rule requiring a lengthy opinion each time a motion for sanctions is denied." No such blanket rule need be announced in the present case either, but this court has required an "analysis and discrete findings" in "`close' or serious sanction cases," Palmer, 945 F.2d at 1377, an approach that makes particular sense when the explanation for the ruling is not otherwise apparent from the record. This is such a case.

III. CONCLUSION
For all of the reasons stated above, we AFFIRM the judgment of the district court on the merits of the antitrust claims, but VACATE its denial of sanctions and REMAND the case for further proceedings on that issue.
