Cambridge University Press v. J.L. Albert , 906 F.3d 1290 ( 2018 )


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  •              Case: 16-15726    Date Filed: 10/19/2018   Page: 1 of 25
    [PUBLISH]
    IN THE UNITED STATES COURT OF APPEALS
    FOR THE ELEVENTH CIRCUIT
    ________________________
    No. 16-15726
    ________________________
    D.C. Docket No. 1:08-cv-01425-ODE
    CAMBRIDGE UNIVERSITY PRESS,
    OXFORD UNIVERSITY PRESS, INC.,
    SAGE PUBLICATIONS, INC.,
    Plaintiffs-Appellants,
    versus
    J. L. ALBERT,
    in his official capacity as Georgia State University Associate Provost for
    Information Systems and Technology,
    KENNETH R. BERNARD, JR.,
    in his official capacity as member of the Board of Regents of the University
    System of Georgia, et al.,
    Defendants-Appellees.
    ________________________
    Appeal from the United States District Court
    for the Northern District of Georgia
    _______________________
    (October 19, 2018)
    Before WILLIAM PRYOR, MARTIN, and ROSENBAUM, Circuit Judges.
    Case: 16-15726     Date Filed: 10/19/2018    Page: 2 of 25
    WILLIAM PRYOR, Circuit Judge:
    This appeal requires us to decide whether the district court misinterpreted
    our mandate in an earlier appeal and misapplied the defense of fair use, 17 U.S.C.
    § 107, in a dispute between three academic publishers and Georgia State
    University about the University’s practice of distributing to students digital
    excerpts of copyrighted works without paying the publishers. After a bench trial,
    the district court ruled that the publishers established a prima facie case that 48
    digital excerpts infringed their copyrights but that the University prevailed on an
    affirmative defense of fair use for 43 of those excerpts. The publishers appealed.
    We upheld the district court’s analysis of the first and fourth fair-use factors,
    including its finding that widespread unlicensed use of 31 excerpts for which
    licenses existed could cause substantial harm to the potential markets. But we
    reversed and remanded for the district court to correct specific errors in its analysis
    of fair use. One such error was the use of a mathematical formula to balance the
    four statutory fair-use factors. Another was the insufficient weight the district court
    gave to the severe threat of market substitution. On remand, the district court ruled
    that the University prevailed on its fair-use defense for 44 of the 48 excerpts.
    Contrary to our instructions, the district court again applied a mathematical
    formula to balance the factors. It also revisited its market-harm analysis for the 31
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    licensed excerpts and found that the threat of market harm supported fair use in all
    but six of the 48 instances. Although the district court did not abuse its discretion
    when it declined to reopen the record to allow the publishers to present new
    evidence about the availability of digital licenses, the district court misinterpreted
    our earlier decision and misapplied the statutory test of fair use. We affirm in part,
    vacate in part, and remand with instructions.
    I. BACKGROUND
    We divide the background in three parts. First, we describe the facts and the
    original proceedings in the district court. Second, we describe our decision in the
    earlier appeal. Third, we describe the proceedings on remand.
    A. The Facts and the Original Proceedings in the District Court
    Cambridge University Press, Oxford University Press, Inc., and Sage
    Publications, Inc. publish academic works. Cambridge Univ. Press v. Patton
    (Cambridge II), 
    769 F.3d 1232
    , 1238 (11th Cir. 2014). The publishers “market
    their books to professors who teach at universities and colleges” so that the
    professors will “assign them as required reading” for their courses and “students
    will purchase them.” 
    Id. at 1238–39.
    The publishers also sell “licenses to use
    excerpts of [their copyrighted] works.” 
    Id. at 1276.
    In the past, professors
    commonly assigned—and students purchased—paper “coursepacks” of licensed
    excerpts. 
    Id. at 1239.
    But it has become more common for universities to distribute
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    digital excerpts electronically. 
    Id. The publishers
    license users “to photocopy [and
    to] digitally reproduce portions of their works.” 
    Id. at 1240.
    They offer such
    licenses, called “permissions,” both directly and through the Copyright Clearance
    Center. 
    Id. Georgia State
    University, a public university in Atlanta, Georgia, provides
    several ways to distribute excerpts of copyrighted works to students. The
    University pays to use licensed excerpts in paper coursepacks that the University
    bookstore assembles and sells to students. 
    Id. at 1241
    & n.4. The University also
    maintains two systems for electronic distribution of course materials, “ERes” and
    “uLearn.” 
    Id. at 1239.
    Both programs enable University personnel to upload digital
    copies of excerpts to University servers and allow students enrolled in a course to
    download the excerpts. 
    Id. Neither the
    University, see 
    id. at 1238,
    nor the students,
    see 
    id. at 1240,
    pay for the use of the digital excerpts. This approach is “popular.”
    
    Id. “For example,
    during the Spring 2009 term, paper coursepacks were offered for
    only about fifteen courses, while instructors in hundreds of courses made readings
    available on ERes.” 
    Id. In 2008,
    the publishers filed a complaint against officials of the University
    for direct, contributory, and vicarious copyright infringement, 17 U.S.C. §§ 106,
    501(a); see also Metro-Goldwyn-Mayer Studios Inc. v. Grokster, Ltd., 
    545 U.S. 4
                  Case: 16-15726     Date Filed: 10/19/2018    Page: 5 of 25
    913 (2005) (acknowledging limited third-party liability for copyright violations),
    and sought declaratory and injunctive relief. Cambridge 
    II, 769 F.3d at 1241
    –42 &
    n.6. The publishers alleged a pattern and practice of distributing substantial
    unlicensed excerpts of their copyrighted works, and they sought to prove their
    claims based on a representative sample of infringements. 
    Id. at 1241
    –42. The
    University asserted an affirmative defense of fair use, 17 U.S.C. § 107. Cambridge
    
    II, 769 F.3d at 1242
    .
    After a bench trial, the district court ruled that the University infringed the
    copyrights of the publishers in five instances. See Cambridge Univ. Press v. Becker
    (Cambridge I), 
    863 F. Supp. 2d 1190
    , 1363–64 (N.D. Ga. 2012). The district court
    found that the publishers established a prima facie case for 48 instances of
    infringement. See Cambridge 
    II, 769 F.3d at 1237
    . But it ruled that the University
    established its fair-use defense for 43 of the excerpts. 
    Id. We summarize
    its
    conclusions as relevant to this appeal.
    The Copyright Act enumerates four “factors to be considered” in finding that
    “the use made of a work in any particular case is a fair use” instead of an
    infringement. 17 U.S.C. § 107. The first factor is “the purpose and character of the
    use, including whether [it] is of a commercial nature or is for nonprofit educational
    purposes.” 
    Id. § 107(1).
    The second factor is “the nature of the copyrighted work.”
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    Id. § 107(2).
    The third factor is “the amount and substantiality of the portion used
    in relation to the copyrighted work as a whole.” 
    Id. § 107(3).
    And the fourth factor
    is “the effect of the use upon the potential market for or value of the copyrighted
    work.” 
    Id. § 107(4).
    The district court found that “factor one strongly favor[ed]” a finding of fair
    use for every excerpt because the University’s copying was for nonprofit
    educational uses. Cambridge 
    I, 863 F. Supp. 2d at 1225
    . It found that factor two
    “favor[ed]” fair use for every excerpt because the academic works were
    “informational in nature.” 
    Id. at 1226–27.
    It found that factor three favored fair use
    for 35 excerpts each of which was less than 10 percent or one chapter of the
    original work but favored infringement for 13 excerpts that exceeded those bounds.
    Cambridge 
    II, 769 F.3d at 1251
    . And it found that factor four “strongly favored” a
    finding of copyright infringement for 31 excerpts for which digital permissions
    were available and “favored” fair use for 17 excerpts for which the publishers
    failed to prove the availability of digital permissions. 
    Id. In its
    overall analysis of fair use for each excerpt, the district court “g[ave]
    each of the four factors equal weight” and “treat[ed] the four factors as a simple
    mathematical formula.” 
    Id. at 1260.
    That is, the district court simply “add[ed] up”
    its findings whether each factor favored fair use or infringement for each excerpt.
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    Id. It found
    that “fair use applied whenever at least three of the four factors favored
    [the University].” 
    Id. at 1251.
    But when it initially weighed the factors together in
    its overall analysis for some excerpts, the district court found a tie, with factor one
    strongly favoring fair use, factor two favoring fair use, factor three favoring
    infringement, and factor four strongly favoring infringement. See Cambridge 
    I, 863 F. Supp. 2d at 1260
    , 1263, 1268, 1274, 1278, 1358, 1362. For seven such excerpts,
    the district court broke the ties by reconsidering the weight of the third factor, the
    fourth factor, or both. See 
    id. at 1260,
    1263–64, 1268–69, 1274, 1278, 1358–59,
    1362–63. It found that evidence of the amount of past permissions revenues
    “strengthen[ed]” the showing in favor of infringement on the fourth factor in four
    instances, 
    id. at 1260,
    1268, 1278, 1363, but that it “undercut[]” the weight of the
    showing in two instances, 
    id. at 1264,
    1274. It did not change any of its findings
    that factor four favored infringement.
    The district court granted partial declaratory and injunctive relief to the
    publishers, but it awarded attorney’s fees and costs to the University, 17 U.S.C.
    § 505.
    B. The Earlier Appeal
    In the earlier appeal, we reversed, vacated, and remanded. Cambridge 
    II, 769 F.3d at 1284
    . As relevant here, we upheld the district court’s analysis of
    factors one and four. See 
    id. at 1267,
    1279, 1281, 1283. But we instructed the
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    district court to correct its “erroneous application of factors two and three” and its
    errors in “[weighing and] balancing the four fair use factors” in its overall analysis.
    
    Id. at 1283.
    We held that the district court got two things right in Cambridge I: its
    analysis of the first factor and its analysis of the fourth factor. On the first factor,
    we agreed that “the nonprofit educational nature” of the University’s use favored
    the fair-use defense. 
    Id. at 1267;
    see also 
    id. at 1283
    (“The District Court did not
    err in holding that the first factor . . . favors fair use.”). But we cautioned that the
    University’s “nontransformative” use, verbatim copying that served “the same
    intrinsic purpose” for which the works were originally published, 
    id. at 1263,
    made
    “the threat of market substitution . . . significant,” 
    id. at 1267.
    We also held “that the District Court’s analysis under the fourth factor was
    correct.” 
    Id. at 1279;
    see also 
    id. at 1281
    (“[T]he District Court did not err in its
    application of the fourth factor.”); 
    id. at 1283
    (“With regard to the fourth factor . . .
    the District Court did not err.”). But we held that “the District Court erred by not
    affording the fourth factor additional weight in its overall fair use calculus.” 
    Id. at 1281.
    Indeed, we found important errors in “the District Court’s overarching fair
    use methodology.” 
    Id. at 1259.
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    We held that the district court erred when it “g[ave] each of the four factors
    equal weight, essentially taking a mechanical ‘add up the factors’ approach,” and
    that it should not have “treat[ed] the four factors as a simple mathematical
    formula.” 
    Id. at 1260.
    We explained that “a given factor may be more or less
    important . . . under the specific circumstances of [a particular] case.” 
    Id. In this
    case, we emphasized that the district court “should have afforded [factor four]
    more significant weight in its overall fair use analysis” because “the threat of
    market substitution is severe.” 
    Id. at 1283;
    accord 
    id. at 1275,
    1276 n.31, 1281. We
    also reminded the district court that “the four statutory factors may not be treated
    in isolation, one from another. All are to be explored, and the results weighted
    together, in light of the purposes of copyright.” 
    Id. at 1260
    (alteration adopted)
    (quoting Campbell v. Acuff-Rose Music, Inc., 
    510 U.S. 569
    , 578 (1994)).
    We also held that the district court erred in its analyses of the second and
    third factors. Although the district court initially found that factor two favored fair
    use and weighed equally with the other three factors, we explained that “the
    District Court should have held that the second factor was neutral, or even
    weighted against fair use,” for excerpts in which “evaluative, analytical, or
    subjectively descriptive material” predominated, and that “the second fair use
    factor is of relatively little importance in this case.” 
    Id. at 1270.
    As for the third
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    factor, we held that the district court erred in creating “a 10 percent-or-one-chapter
    safe harbor” for fair use. 
    Id. at 1275.
    We explained that the district court was
    required to assess each excerpt “individually, considering the quantity and the
    quality of the material taken.” Id.. And we explained that it was required to
    determine “whether that taking was excessive in light of” not only “the educational
    purpose of the use” but also “the threat of market substitution.” 
    Id. at 1275.
    We
    also mentioned the “ample precedents that explain that excessive verbatim copying
    weighs against fair use under factor three.” 
    Id. at 1274
    n.30.
    We vacated the orders that granted partial declaratory and injunctive relief to
    the publishers and awarded attorney’s fees and costs to the University. 
    Id. at 1283–
    84. Because the relief that the district court ordered was based on its erroneous
    fair-use analysis, we remanded for the district court to correct its analysis to be
    “consistent with [our] opinion.” 
    Id. at 1284.
    C. The Proceedings on Remand
    On remand, the publishers moved to reopen the record to introduce new
    evidence that digital licenses had been available for the 17 excerpts for which the
    publishers did not establish license availability at trial. The district court dismissed
    the motion without prejudice. The publishers later filed the declaration of an
    officer of the Copyright Clearance Center, Debra J. Mariniello, stating that digital
    licenses were available in 2009 for the 17 excerpts. The district court refused to
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    admit the declaration and struck all references to it from the publishers’ brief.
    Cambridge Univ. Press v. Becker (Cambridge III), No. 1:08-cv-1425, slip op. at 18
    (N.D. Ga. Mar. 31, 2016).
    The district court changed its fair-use analysis in response to our decision in
    Cambridge II. In the new analysis, factor one “favor[ed] fair use in all cases,” but
    “not strongly.” 
    Id. at 11
    (internal quotation marks omitted); see also 
    id. at 18.
    The
    district court did not revisit its earlier first-factor analysis for any of the excerpts.
    Instead, in its new fair-use analysis for each excerpt, the district court simply
    repeated the finding that “[f]actor one favors fair use.” 
    Id. at 24,
    29, 34, 39, 43, 47,
    53, 56, 60, 64, 70, 73, 79, 83, 88, 91, 95, 98, 101, 103, 106, 110, 114, 120, 124,
    130, 133, 137, 140, 144, 146, 150, 155, 158, 161, 165, 170, 174, 179, 183, 187,
    191, 196, 201, 205; see also 
    id. at 20,
    52, 69.
    The district court changed its second-factor analysis for each excerpt. It
    found that factor two favored a finding of fair use in two instances, see 
    id. at 131,
    145, that it was neutral in 34 instances, see 
    id. at 22,
    26, 30, 44, 57, 61, 70, 74, 80,
    89, 93, 100, 102, 105, 108, 111, 115, 121, 135, 139, 142, 151, 156, 163, 166, 176,
    180, 184, 190, 193, 203, 206; see also 
    id. at 52,
    69, and that it favored
    infringement in 12 instances, see 
    id. at 37,
    40, 50, 54, 67, 85, 97, 125, 148, 159,
    172, 198.
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    The district court also changed its earlier third-factor analysis for each
    excerpt. It found that factor three favored fair use for 37 excerpts, 34 of which had
    benefited from its earlier 10-percent-or-one-chapter safe harbor. See 
    id. at 22,
    26,
    31, 44, 52, 54, 57, 61, 69, 71, 75, 80, 94, 100, 102, 105, 108, 111, 116, 121, 126,
    132, 135, 142, 145,148, 152, 156, 160, 164, 167, 172, 177, 180, 185, 193, 203. The
    district court also found that the third factor favored fair use for three excerpts that
    exceeded its earlier safe harbor. Compare 
    id. at 57,
    131–32, 176–77, with
    Cambridge 
    I, 863 F. Supp. 2d at 1273
    –74, 1310, 1346. For two excerpts, the
    district court found that the price of the unpaid permissions “would have been
    excessive” and that the high price “allow[ed]” the district court “to look more
    favorably” on the unpaid use of a greater “quantity” of material. Cambridge III,
    slip op. at 116, 176 (emphases omitted).
    The district court changed its fourth-factor analysis for the 31 excerpts for
    which it had originally found that “factor four strongly disfavored fair use.” 
    Id. at 11
    . Under its new analysis, the district court stated that factor four would only
    “initially favor [the publishers]” in those instances. 
    Id. at 12.
    Then, based on its
    reading of Cambridge II, the district court offered the University three ways to
    prove that the fourth factor actually favored fair use in a particular instance:
    [1] [T]he Court of Appeals held that Defendants may seek to prove
    that in fact, the demand for excerpts of a particular copyrighted work
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    was so limited that repetitive unpaid copying of excerpts from that
    work would have been unlikely even if unpaid copying of excerpts
    was a widespread practice in colleges and universities. In such a case
    the actions of Defendants in using unpaid excerpts would not have
    caused substantial damage to the potential market for the copyrighted
    work to such a degree that Plaintiffs would lose the incentive to
    publish the work. [2] Defendants may also seek to prove that their
    actions (even assuming widespread availability of unpaid excerpts)
    did not substantially affect the value of the copyrighted work in 2009.
    . . . [3] Defendants may also seek to prove that the portion of the
    market captured by unpaid use is so slight that it would have had no
    effect on the author’s or the Plaintiffs’ decision to propagate the work
    in the first place.
    
    Id. at 12–13.
    The district court suggested that the relevant evidence for these
    showings would generally come from “the records of permissions sales for
    excerpts from the book.” 
    Id. at 13.
    The district court also adjusted its method of balancing the four factors. It
    explained that the “initial, approximate respective weights of the four factors” were
    “25% for factor one, 5% for factor two, 30% for factor three, and 40% for factor
    four.” 
    Id. at 14.
    “If a particular factor ha[d] noteworthy strength or weakness, the
    weight of that factor w[ould] be adjusted” in the district court’s new analysis. 
    Id. at 13.
    Despite these changes to its analysis, the district court reached similar
    bottom-line results. It again found fair use for each of the 43 excerpts for which it
    had originally done so. And it found fair use in one instance where it had
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    previously found infringement. Compare Cambridge 
    I, 863 F. Supp. 2d at 1359
    (finding that the University’s use of two chapters from The Power Elite, by C.
    Wright Mills, was unfair), with Cambridge III, slip op. at 200–01 (finding that the
    use of The Power Elite was fair).
    The district court again found fair use for the vast majority of excerpts in
    large part because it reversed most of its original fourth-factor findings. On
    remand, the district court found that the fourth factor supported fair use in 42 of 48
    instances. See Cambridge III, slip op. at 24, 28–29, 34, 42, 46, 52, 55, 60, 63, 69,
    73, 83, 87, 91, 95, 98, 101, 103, 106, 109, 114, 119, 124, 129, 132, 136, 140, 143,
    146, 149, 154, 158, 160, 164, 169, 174, 177, 182, 186, 190, 195, 200. The district
    court left unchanged only six of its 31 original findings that the threat of market
    harm weighed against fair use for excerpts for which licenses were available. See
    
    id. at 38,
    52, 68, 78, 204, 210.
    The district court granted partial declaratory and injunctive relief against the
    University. But it ruled that the University was the “prevailing side and [was]
    entitled to an award of costs and attorneys’ fees.” 
    Id. at 212.
    After the Supreme
    Court decided Kirtsaeng v. John Wiley & Sons, Inc., 
    136 S. Ct. 1979
    (2016), the
    publishers moved for reconsideration of the fee award, but the district court denied
    the motion.
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    II. STANDARDS OF REVIEW
    “Fair use involves both questions of law and questions of fact.” Cambridge
    
    II, 769 F.3d at 1255
    . “After a bench trial, we review a district court’s conclusions
    of law de novo and a district court’s factual findings for clear error.” 
    Id. (alterations adopted)
    (quoting Proudfoot Consulting Co. v. Gordon, 
    576 F.3d 1223
    ,
    1230 (11th Cir. 2009)). “We review de novo the district court’s interpretation and
    application of this court’s mandate” in an earlier appeal. Cox Enters., Inc. v. News-
    Journal Corp., 
    794 F.3d 1259
    , 1272 (11th Cir. 2015) (emphasis added). And we
    review the denial of a motion to reopen the record for abuse of discretion. See
    Elston v. Talladega Cty. Bd. of Educ., 
    997 F.2d 1392
    , 1405 (11th Cir. 1993).
    III. DISCUSSION
    We divide our discussion in two parts. First, we explain that the district court
    misinterpreted our mandate and misapplied the test of fair use. Second, we explain
    that the district court did not abuse its discretion when it declined to reopen the
    record. Because we hold that the district court committed reversible errors, we
    reverse, vacate, and remand.
    A. The District Court Erred when It Made Its New Findings of Fair Use.
    The district court misinterpreted our mandate and misapplied the test of fair
    use on remand. In Cambridge II, we instructed the district court to correct its
    “erroneous application of factors two and three” and its errors in weighing the four
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    factors in its overall analysis of fair use for each excerpt. Cambridge 
    II, 769 F.3d at 1283
    . But the district court exceeded this limited mandate, revisiting its 31 earlier
    findings that factor four favored infringement and reversing all but six of them.
    The district court again applied a mathematical formula in its overall analysis of
    fair use. And it erroneously considered the high price of permissions when it found
    that factor three favored fair use for two excerpts.
    1. The District Court Erred when It Revisited Factor Four.
    The publishers argue that the district court “failed . . . to follow this Court’s
    remand instructions” when it revisited its earlier findings that factor four favored
    infringement. The University responds that the district court correctly changed its
    approach to reflect our decision in Cambridge II. We agree with the publishers.
    In deciding this appeal, we are bound by the decision in Cambridge II, just
    as the district court was bound to apply its mandate. The doctrine of the law of the
    case “preclude[s] courts from revisiting issues that were [already] decided.”
    Schiavo ex rel. Schindler v. Schiavo, 
    403 F.3d 1289
    , 1291 (11th Cir. 2005). In
    particular, “findings of fact and conclusions of law by an appellate court are
    generally binding in all subsequent proceedings in the same case in the trial court
    or on a later appeal.” Transamerica Leasing, Inc. v. Inst. of London Underwriters,
    
    430 F.3d 1326
    , 1331 (11th Cir. 2005) (quoting Heathcoat v. Potts, 
    905 F.2d 367
    ,
    370 (11th Cir. 1990)). And under the mandate rule, which “is nothing more than a
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    specific application of the ‘law of the case’ doctrine,” 
    id. (quoting Piambino
    v.
    Bailey, 
    757 F.2d 1112
    , 1120 (11th Cir. 1985)), “[a] district court[,] when acting
    under an appellate court’s mandate, ‘cannot vary it, or examine it for any other
    purpose than execution; or give any other or further relief; . . . or intermeddle with
    it, further than to settle so much as has been remanded,’” Litman v. Mass. Mut. Life
    Ins. Co., 
    825 F.2d 1506
    , 1510–11 (11th Cir. 1987) (quoting In re Sanford Fork &
    Tool Co., 
    160 U.S. 247
    , 255 (1895)). “The trial court must implement both the
    letter and the spirit of the mandate, taking into account the appellate court’s
    opinion and the circumstances it embraces.” 
    Piambino, 757 F.2d at 1119
    (citations
    omitted).
    The district court interpreted our earlier decision to instruct it to change its
    fourth-factor analysis for the 31 excerpts for which digital permissions were
    available, Cambridge III, slip op. at 11–13, but the district court misinterpreted our
    mandate. In its original decision, the district court found that the fourth factor
    “weigh[ed] heavily” against fair use in all 31 instances where the publishers made
    digital licenses available. See Cambridge 
    I, 863 F. Supp. 2d at 1239
    . Our decision
    in Cambridge II upheld those 31 findings. We held that “the District Court did not
    err in its application of the fourth factor.” Cambridge 
    II, 769 F.3d at 1281
    ; see also
    
    id. at 1279
    (“[T]he District Court’s analysis under the fourth factor was correct
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    . . . .”); 
    id. at 1283
    (“With regard to the fourth factor . . . the District Court did not
    err.”). The only error we identified in the district court’s treatment of the fourth
    factor was that, in weighing and balancing the relative importance of the factors, it
    undervalued the “severe” threat of market harm posed by the University’s
    “nontransformative” copying. 
    Id. at 1283;
    see also 
    id. at 1267,
    1275, 1281.
    We did not instruct the district court to revisit its earlier findings that factor
    four favored infringement when we instructed it to reweigh the factors on remand.
    Indeed, we explained that, “[a]lthough . . . the District Court’s method for
    weighing the four factors against one another was erroneous, this does not mean
    that the District Court’s reasoning under each of the four factors [was] also
    necessarily flawed.” 
    Id. at 1260.
    And we repeatedly held that, although it should
    have weighed both factor one and factor four differently, the district court “did not
    err” in its application of those two factors. See 
    id. at 1283
    . On remand, the district
    court correctly declined to revisit its first-factor analysis for any of the excerpts. It
    followed our instruction to change only how “strongly” factor one weighed in
    favor of fair use in its overall analysis for each excerpt. See Cambridge III, slip op.
    at 11, 18. In contrast, the district court changed all but six of its original findings
    that factor four favored infringement instead of giving those findings “more
    significant weight in its overall fair use analysis,” Cambridge 
    II, 769 F.3d at 1283
    .
    18
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    The University contends that the district court correctly revisited its earlier
    findings that factor four favored infringement because Cambridge II announced a
    new standard of market harm, but the University misreads our earlier decision. It
    stresses that we described the “central question under the fourth factor” as whether
    a use “would cause substantial economic harm such that allowing it would frustrate
    the purposes of copyright by materially impairing [the publishers’] incentive to
    publish the work.” 
    Id. at 1276
    (emphasis omitted). But we used this description of
    market harm—which merely echoed longstanding precedent, see 
    Campbell, 510 U.S. at 590
    ; Peter Letterese & Assoc., Inc. v. World Inst. of Scientology Enter.,
    Int’l, 
    533 F.3d 1287
    , 1315 (11th Cir. 2008)—to explain that the earlier “analysis
    under the fourth factor was correct.” Cambridge 
    II, 769 F.3d at 1279
    .
    In short, we held in Cambridge II that the district court’s original fourth-
    factor analysis was correct. That holding precluded the district court from
    revisiting the fourth factor in Cambridge III. On remand, the district court must
    reinstate its original findings that the fourth factor strongly disfavors fair use for
    the 31 excerpts for which the publishers proved the availability of digital licenses.
    2. The District Court Erred when It Weighed and Balanced the Factors in Its
    Overall Calculus of Fair Use for Each Excerpt.
    The publishers argue that the district court erred by again “appl[ying] a
    mathematical formula” in its overall analysis of fair use for each excerpt. The
    19
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    University contends that, “[a]lthough the district court provided approximate initial
    weights of the four factors at the outset of its remand decision,” it adjusted that
    formula in its overall analysis for each excerpt. We again agree with the publishers.
    In Cambridge II, we identified two distinct ways in which, in its original
    analysis, the district court failed to recognize that “a given factor may be more or
    less important . . . under the specific circumstances of [a particular] case.”
    Cambridge 
    II, 769 F.3d at 1260
    . First, we explained that “the District Court erred
    in giving each of the four factors equal weight.” 
    Id. Second, we
    explained that the
    district court erred “in treating the four factors as a simple mathematical formula,”
    which we also described as an “arithmetic approach.” 
    Id. On remand,
    the district court corrected the first of these errors but again
    committed the second. The district court assigned “initial, approximate respective
    weights of the four factors as follows: 25% for factor one, 5% for factor two, 30%
    for factor three, and 40% for factor four.” Cambridge III, slip op. at 14. Although
    the district court heeded our instructions in Cambridge II when it recognized that
    some factors are more important than others, it failed to break free of its erroneous
    “arithmetic approach” and to give each excerpt the holistic review the Act
    demands.
    20
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    As the Supreme Court has explained and as we reiterated in Cambridge II,
    “the four statutory factors may not be treated in isolation, one from another. All are
    to be explored, and the results weighed together, in light of the purposes of
    copyright.” Cambridge 
    II, 769 F.3d at 1260
    (alteration adopted) (quoting
    
    Campbell, 510 U.S. at 578
    ). We emphasized that “fair use is not a mechanical
    determination,” 
    id. (alteration adopted)
    (quoting Wright v. Warner Books, Inc., 
    953 F.2d 731
    , 740 (2d Cir. 1991)), and that a court must “weigh[] . . . the four factors in
    light of the facts of a given case,” 
    id. at 1259.
    To be sure, the district court described its arithmetic weights as “initial” and
    “approximate,” and it stated that it would “adjust[]” them when it found
    a “noteworthy strength or weakness” among the factors. 
    Id. at 13.
    But the district
    court made such adjustments only four times, each time to bolster the importance
    of the third factor’s weighing against fair use. See 
    id. at 38,
    68, 140, & 201. And,
    on those four occasions, the district court did nothing to adjust the other factors in
    the overall fair-use calculus. We conclude that the district court’s quantitative
    rubric was an improper substitute for a qualitative consideration of each instance of
    copying in the light of its particular facts.
    The district court failed to give each excerpt the holistic review that the Act
    demands. On this remand, the district court must not apply a mathematical formula
    21
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    at any step of its analysis. We reiterate our holding in Cambridge II that “the fourth
    factor looms large in the overall fair use analysis” for each excerpt in this 
    appeal, 769 F.3d at 1275
    , but we instruct the district court to evaluate the four factors
    qualitatively, not quantitatively, and to take care to consider them holistically “in
    light of the purposes of copyright.” 
    Campbell, 510 U.S. at 578
    .
    3. The District Court Erred when It Considered the Cost of Purchasing
    Licenses in Finding that the Third Factor Favored Fair Use.
    The district court twice erred in applying the third factor of the statutory test
    of fair use when it considered whether the cost of licensing was “excessive” in the
    light of the publishers’ “marginal cost for authorizing digital copies . . . , [which]
    would not vary no matter how many digital copies were authorized.” Cambridge
    III, slip op. at 116, 176. The district court reasoned that high prices “allow[ed] [it]
    to look more favorably on the quantity of [the University’s] use than it otherwise
    would.” 
    Id. at 11
    6, 176 (emphases omitted). In these two instances, the district
    court deviated from the language of the Act.
    The third factor of the statutory fair-use test is “the amount and
    substantiality of the portion used in relation to the copyrighted work as a whole.”
    17 U.S.C. § 107(3). This provision of the Act does not direct courts to consider the
    price of the unpaid use. If it did, then the district court’s reasoning could tilt the
    third factor in favor of fair use even in cases of extensive verbatim copying. After
    22
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    all, it is always the case that a publisher’s “marginal cost for authorizing digital
    copies would be virtually nil, and would not vary no matter how many digital
    copies were authorized.” Cambridge III, slip op. at 116, 176. When we instructed
    the district court to correct its analysis under the third factor on remand, we did not
    include this consideration. See Cambridge 
    II, 769 F.3d at 1275
    . The district court
    erred when it twice considered the price of the unpaid use as relevant to the third
    factor.
    B. The District Court Did Not Abuse Its Discretion when It Declined To
    Reopen the Record.
    The publishers argue that they should have been permitted to supplement the
    record on remand with evidence that digital permissions were available for the 17
    works for which it did not previously provide this evidence. They argue that this
    evidence “was offered to fill a purported evidentiary gap that existed through no
    fault of [the publishers]” because “[t]he district court failed to put [them] on
    notice” of the need to prove license availability at trial. They stress that the
    availability of digital licenses took on greater importance after our decision in
    Cambridge II clarified the importance of factor four.
    These arguments are unpersuasive. The question whether to reopen the
    record on remand is “left to the sound discretion of the trial court.” Jones &
    Laughlin Steel Corp. v. Pfeifer, 
    462 U.S. 523
    , 551 (1983). And the district court
    23
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    was entitled to conclude that it would be inappropriate to admit new evidence of
    license availability that was “offered years after the close of the trial and entry of
    the judgment and after review by the Court of Appeals.” Cambridge III, slip op. at
    18. Nor can the publishers excuse their delay by asserting that they were ignorant
    of the importance of this evidence. Indeed, they similarly “complain[ed]” in the
    earlier appeal “that they were not notified at trial that they were required to show
    license availability for 2009 in particular.” Cambridge 
    II, 769 F.3d at 1278
    n.33.
    And we responded that the publishers “were—or should have been—aware that the
    relevant evidentiary question was whether a market existed at the time of the
    purported infringements.” 
    Id. The district
    court was not required to reopen the
    record to allow the publishers to introduce new evidence on this topic.
    IV. CONCLUSION
    We AFFIRM in part, VACATE in part, and REMAND for proceedings
    consistent with this opinion. We affirm the order denying the publishers’ request to
    reopen the record, but we vacate the judgment entered on remand. The district
    court must reinstate its earlier findings that factor four strongly disfavors fair use
    for 31 of the 48 excerpts. The district court must eschew a quantitative approach to
    the weighing and balancing of the fair-use factors and give each excerpt the
    holistic, qualitative, and individual analysis that the Act demands. And the district
    court must omit any consideration of price from its analysis of the third factor.
    24
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    Because the district court’s award of attorney’s fees and costs was based on its
    erroneous fair-use analysis, we also VACATE that award and the underlying
    determination that the University is the prevailing party.
    25