Full opinion text
MEMORANDUM OPINION AND ORDER HAIGHT, District Judge: Plaintiffs Lucyle Kalish and Sol Joseph Kamen brought this derivative action on behalf of defendant Franklin Custodian Funds, Inc. (U.S. Government Securities Series) (the "Fund”) under the Investment Company Act of 1940, as amended, 15 U.S.C. § 80a-1 et seq. (the “Act”), to recoup allegedly excessive advisory fees paid by the Fund to its investment adviser. Franklin Custodian Funds, Inc. is a diversified open-end investment company registered with the Securities and Exchange Commission under the Act. The Fund is one of five series of Franklin Custodian Funds, Inc., and concentrates its investments in obligations of the Government National Mortgage Association (“GNMA”), with the objective of income through investment in securities of the U.S. Government or its instrumentalities. Plaintiffs Kalish and Kamen became shareholders of the Fund in 1986 and 1987 respectively and remained shareholders throughout the pertinent period. Defendant Franklin Distributors (“Franklin Distributors”) acted as the Fund’s investment adviser and manager until January 31, 1986, pursuant to contract. Defendant Franklin Advisers, Inc. (“Franklin Advisers”) has acted as the Fund’s investment adviser under a contract which became effective February 1, 1986 and has been subsequently renewed and modified. Franklin Distributors continues to act as principal underwriter of the Fund. Defendant Franklin Administrative Services, Inc. (“Franklin Services”) has acted as shareholder servicing agent, transfer agent and dividend paying agent for the Fund. Each of these companies is a wholly owned subsidiary of defendant Franklin Resources, Inc. (“Franklin Resources”). These entities are from time to time referred to collectively as “Franklin” or “defendants.” Plaintiffs filed their complaint on September 25, 1987, stating a cause of action under § 36(b) of the Act, 15 U.S.C. § 80a-35(b). Plaintiffs alleged that the fees paid by the Fund to Franklin Advisers were exorbitant, and that Franklin Advisers and the Fund’s directors had breached the fiduciary duty imposed upon them by the Act. The Court granted defendants’ motion to strike plaintiffs’ demand for a jury trial in a Memorandum Opinion and Order dated February 29, 1988. Following discovery, the case was tried to the Court. This Opinion constitutes the Court’s findings of fact and conclusions of law under Rule 52(a), Fed.R.Civ.P. BACKGROUND The Fund was formed in 1971. In 1983 its directors decided to emphasize investment in securities issued by GNMA, popularly known as “Ginnie Maes.” That has remained the focus of the Fund’s investment policy to this date. For purposes of limitations and streamlining of proof, this action has been deemed by stipulation to have been commenced on September 30, 1987. At issue are the fees paid by the Fund to Franklin Advisers during its fiscal years ending on September 30, 1987 and September 30, 1988. Those fees were paid pursuant to a series of one-year management agreements between the Fund and Franklin running from February to February, and approved by the Fund’s board of directors. The Fund has experienced dramatic growth since its inception, as revealed by the following table: Date # of Accounts Net Assets Outstanding Shares Dec. 31, 1984 178,428 $ 2,496,954,705 351,627,795 Dec. 31, 1985 450,980 $ 8,875,802,045 1,180,547,279 Sept. 30, 1986 679,542 $14,361,682,054 1,938,886,002 Dec. 31, 1986 694,579 $14,941,488,124 2,013,006,042 June 30, 1987 687,256 $14,267,717,200 1,994,862,976 Sept. 30, 1987 665,410 $13,024,436,878 1,895,183,448 Dec. 31, 1987 639,336 $12,650,664,753 1,805,885,572 June 30, 1988 621,240 $12,432,704,402 1,760,935,529 Sept. 30, 1988 609,925 $12,112,775,121 1,735,011,210 Dec. 31, 1988 599,227 $11,646,328,085 1,706,432,500 June 30, 1989 570,386 $11,454,854,549 1,639,288,165 During the relevant time period, virtually all the assets of the Fund have been invested in obligations of the GNMA. GNMA is an agency within the United States Department of Housing and Urban Development which acquires mortgages or mortgage purchase commitments, insured or guaranteed by other government agencies, and resells them to private mortgage lenders, such as mortgage bankers, commercial banks and saving and loan associations. These lenders assemble a pool of mortgages which, upon application, are guaranteed by GNMA. The private lenders, also known as “issuers,” create and sell to investors certificates representing fractional or total ownership of such. Securities dealers purchase the certificates created by the issuers and resell them to customers such as the Fund. The originator of a pool and issuer of its certificates receives a servicing fee of 44 basis points a year. GNMA receives 6 basis points a year as a guarantee fee. Ginnie Mae certificates are referred to as “pass-through” securities because the monthly payments of interest and principal on the mortgages in each pool are passed on by the pool originators to the certificate holders, after deduction of the foregoing fees. The nature of Ginnie Mae securities gives rise to certain complexities in respect of managing a fund consisting of them. Openend mutual funds such as the Fund are required to calculate their net asset values on a daily basis and to offer and redeem their shares on a daily basis. Because the individual mortgages making up the pool underlying the certificates might be prepaid as the result of changing interest rates, the calculation of net asset value on a daily basis poses some administrative problems. Uncertainty on prepayments also causes uncertainty in predicting yields, which impacts upon investment decisions. Throughout the relevant period the Fund has had five directors. Charles B. Johnson and Rupert H. Johnson, Jr. are affiliated with defendants. The three independent, non-affiliated directors are S. Joseph Fortu-nato, Harris J. Ashton, and Edmund H. Kerr. The fees paid by the Fund to its investment adviser-manager are approved by the board of directors and included in a contract between the Fund and the adviser. Franklin Distributors acted as the Fund’s investment adviser-manager until January 31, 1986. Franklin Advisers has acted as the Fund’s adviser-manager under a contract which became effective February 1, 1986, was renewed as of February 1, 1987, and amended in February 1988, effective April 30, 1988. The fees paid by the Fund to Franklin Advisers may be summarized as follows: Fee Schedule of the Fund February 1, 1986 through January 31, 1988: .625% on first $100 million of net assets .50% on next $150 million .45% on amounts over $250 million February 1, 1988 (effective April 30, 1988) to present: .44% on net assets in excess of $10 billion up to $12.5 billion .42% on net assets in excess of $12.5 billion up to $15 billion .40% on net assets in excess of $15 billion Considerable majorities of the Fund’s shareholders voted by proxy to approve each of the management agreements. Purchasers of shares of the Fund pay a sales charge in accordance with the terms of the prospectus. On a purchase of up to $100,000, the sales charge equals 4% of the gross amount invested. The scale then adjusts downwards by stages to a sales charge of .25% for purchases in excess of $2.5 million. The sales charge is paid with respect to both new purchases and rein-vestments of income dividends. One hundred percent of the initial sales charge is paid to securities dealers who sell the shares. The sales charge on reinvested income dividends is shared with the securities dealers. The sale charges received and retained in recent years may be summarized as follows: Year Amount Retained by Franklin Distributors Amount Paid to Securities Dealers Total 1985 $ 3,114,000 $169,066,000 $172,180,000 1986 $16,550,000 $315,271,000 $331,821,000 1987 $14,357,000 $ 99,672,000 $114,029,000 1988 $ 8,118,592 $ 38,224,436 $ 46,343,028 Pursuant to a separate contract, the Fund pays Franklin Services fees on a per-account basis of $6.00 annually. These fees are paid for Franklin Services’ work as transfer agent,, dividend disbursing agent and shareholder services agent. For fiscal years ending September 80, the fees have been: 1985 $1,508,043 1986 $3,350,669 1987 $4,473,316 1988 $4,239,240 The parties have stipulated to the Fund’s expense ratio, which is obtained by dividing expenses by Fund assets. The expense ratio for fiscal years ended September 30 has been as follows: Year g B Ui CD W P 1985 LO 1986 1C 1987 lO 1988 lO At the conclusion of the evidence, plaintiffs’ counsel argued in summation that there were three main branches to plaintiffs’ case. First, management failed to fully inform the directors, and in fact misled them concerning facts material to evaluation of the management fees. Second, the fees paid by the Fund were excessive by objective standards, whether or not the directors were misled. Third, contrary to the Act and the Fund’s agreements with the Franklin affiliates, the Fund improperly was made to shoulder distribution expenses which were properly the obligation of other Franklin entities. Tr. 533-34. As will be seen, these contentions overlap considerably. Defendants contend that plaintiffs have failed to prove that the fees paid by the Fund were excessive, or that Franklin and the Fund directors breached their fiduciary duty in that regard. DISCUSSION Section 36(b) of the Act provides: [T]he investment adviser of a registered investment company shall be deemed to have a fiduciary duty with respect to the receipt of compensation for services, or of payments of a material nature, paid by such registered investment company, or by the security holders thereof, to such investment adviser or any affiliated person of such investment adviser. The Act also provides that in actions such as that at bar, a plaintiff need not “allege or prove that any defendant engaged in personal misconduct,” but plaintiff does have “the burden of proving a breach of fiduciary duty.” § 36(b)(1). Approval of compensation by the board of directors of the investment company, and ratification by its shareholders, “shall be given such consideration by the court as is deemed appropriate under all the circumstances.” § 36(b)(2). The legislative history reveals that the statute does not forbid an adviser-manager from earning a profit on services provided by it to a fund; that a “cost-plus” type of contract is not required; and that the court is not authorized “to substitute its business judgment for that of a mutual fund’s board of directors in the area of management fees.” S.Rep. No. 91-184, 91st Cong., 1st Sess., reprinted, in [1970] U.S.Code Cong. & Ad.News 4897, 4902-03. A series of cases construing § 36(b) have been tried in this Court and appealed to the Second Circuit. See Gartenberg v. Merrill Lynch Asset Management, Inc,, 528 F.Supp. 1038 (S.D.N.Y.1981) (Pollack, J.), aff'd, 694 F.2d 923 (2d Cir.1982), cert. denied sub nom. Andre v. Merrill Lynch Ready Assets Trust, 461 U.S. 906, 103 S.Ct. 1877, 76 L.Ed.2d 808 (1983) (“Gartenberg T’); Gartenberg v. Merrill Lynch Asset Management, Inc., 573 F.Supp. 1293 (S.D.N.Y.1983) (Pollack, J.), aff'd, 740 F.2d 190 (2d Cir.1984) (“Gartenberg IF’); Schuyt v. Rowe Price Prime Reserve Fund, 663 F.Supp. 962 (S.D.N.Y.) (Ward, J.), aff'd, 835 F.2d 45 (2d Cir.1987), cert. denied, 485 U.S. 1034, 108 S.Ct. 1594, 99 L.Ed.2d 908 (1988); Krinsk v. Fund Asset Management, Inc., 715 F.Supp. 472 (S.D.N.Y.1988) (Walker, J.), aff'd, 875 F.2d 404 (2d Cir.), cert. denied, — U.S. -, 110 S.Ct. 281, 107 L.Ed.2d 261 (1989). See also Meyer v. Oppenheimer Management Corp., 609 F.Supp. 380 (S.D.N.Y.1984) (Sofaer, J.) reversed, 764 F.2d 76 (2d Cir.1985), on remand, 707 F.Supp. 1394 (S.D.N.Y.1988), 715 F.Supp. 574 (S.D.N.Y.1989) (Sweet, J.). From these cases a considerable body of instructive precedent has grown. In determining whether fund directors have breached their § 36(b) fiduciary duty, the test is essentially whether the fee schedule represents a charge within the range of what would have been negotiated at arm’s-length in the light of all the surrounding circumstances. It follows that: to be guilty of a violation of § 36(b), therefore, the adviser-manager must charge a fee that is so disproportionately large that it bears no reasonable relationship to the services rendered and could have not been the product of arm’s-length bargaining. Gartenberg I at 694 F.2d 928. The Second Circuit has identified a number of factors to be considered in evaluating the fairness of an adviser-manager’s fee. Gartenberg I holds that “the principal factor” in evaluating that fairness cannot be “the price charged by other similar advisers to funds managed by them,” since “the existence in most cases of an unseverable relationship between the adviser-manager and the fund it services tends to weaken the weight to be given to rates charged by advisers of similar funds.” Id. at 929. Given that circumstance, the court of appeals continued, “other factors may be more important in determining whether a fee is so excessive so as to constitute a ‘breach of fiduciary duty.’ ” Those other factors “include the adviser-manager’s cost in providing the service, the nature and quality of the service, the extent to which the adviser-manager realizes economies of scale as the fund grows larger, and the volume of orders which must be processed by the manager.” Id. at 930. In expanding the focus beyond fees charged by other advisers, the Second Circuit implemented the legislative history expressed in the Senate report, which made clear that Congress: intended that the court look at all the facts in connection with the determination and receipt of such compensation, including all services rendered to the fund or its shareholders and all compensation and payments received, in order to reach a decision as to whether the adviser has properly acted as a fiduciary in relation to such compensation. S.Rep. No. 91-184, supra [1970] U.S. Code Cong. & A.D. News at 4910, quoted at 694 F.2d 930. The Second Circuit in Gartenberg I did not eliminate the price charged by other similar advisers from all consideration; its analysis relates more to the weight to be accorded that factor, than its admissibility in the equation. Thus District Judge Walker (as he then was) felt at liberty in Krinsk to consider “the advisory fees charged” by other “central asset account funds,” although acknowledging that under Garten-berg I “such comparisons have limited value due to the lack of competition among advisers for fund business.” 715 F.Supp. at 497. The Second Circuit, affirming Judge Walker’s dismissal of the complaint in Krinsk, included “comparative fee structures” as a factor to be considered. After reiterating the Gartenberg I test of fairness, the court of appeals said in Krinsk: The following factors are to be considered in applying this standard: (a) the nature and quality of services provided to fund shareholders; (b) the profitability of the fund to the adviser-manager; (c) fall-out benefits; (d) economies of scale; (e) comparative fee structures; and (f) the independence and conscientiousness of the trustees. 875 F.2d at 409. As to comparative expense ratios and advisory fees, the Second Circuit noted the district court’s finding “that the Fund’s expense ratio and advisory fee are not only consistent with the industry norms, but have been among the lowest of any mutual fund in the industry,” although repeating the Gartenberg I caution “against providing much weight to this type of comparison.” Id. at 411-12. Accordingly, while I will give consideration to comparative fee structures in evaluating the fairness of defendants’ fees, I will place that factor last in the batting order, and first consider the evidence concerning (a) the nature and quality of Franklin Advisers’ services provided to Fund shareholders; (b) the profitability of the Fund to the adviser; (c) whether economies of scale were realized by the adviser-manager and shared with the shareholders; and (d) the role played by the Fund’s independent directors. That last factor breaks down into three questions: (1) the expertise of the independent directors; (2) whether they were fully informed about all facts bearing on the adviser-manager’s services and fee; and (3) the conscientiousness with which the independent directors performed their duties. Gartenberg I at 930. (a) The Nature and Quality of the Adviser-Manager’s Services Provided to the Shareholders. Individuals are drawn to open-end mutual funds by the opportunity to make investments perhaps not otherwise feasible for them; the certainty of professional management and the hope for profit; and liquidity of assets. To accomplish those purposes, funds make available a number of shareholder services. Advisers’ services consist in the main of devising an overall investment strategy, including analysis of current projected economic factors, the selection of securities, and the execution of trades. Shareholder services cover a wide range of functions centering around the opening of accounts, redeeming of shares, maintenance of records, and furnishing of information. Fund managers must also insure compliance with federal securities regulations and comparable regulations of the 50 states. Charles B. Johnson dep. 35-38. Franklin Advisers and Franklin Resources act as investment advisers and managers to a family of about 52 Franklin funds of which the Fund is one. At the times in question, five members of a research staff of about 35 spent more than half their time on the Fund, analyzing investment strategy, conducting portfolio research, executing transactions, and settling administrative problems. Rupert H. Johnson, Jr. dep. 8-9. As the Fund increased in size, Franklin Advisers hired additional people to handle the administrative side of managing trading in Ginnie Maes. Ashton Dep. 17-19. The Franklin group wrote some proprietary computer software to help process and control the administrative functions, but many entries must be made manually. Charles Johnson dep. at 26-27. Plaintiffs disparage these services. They argue in Proposed Finding of Fact 24 that Franklin Advisers relies upon securities dealers for investment expertise in selecting mortgage pools and does not perform the extensive in-depth research performed by the dealers. Counsel also argued in summation that according to defendants’ expert witness Kingman, “the principal function that Franklin performed was a back-office type of function,” adding that Kingman “conceded that back-office jobs typically on Wall Street garner less prestige and command lower salaries.” Tr. 576. I accept that the securities dealers who trade in Ginnie Mae certificates bring their own expertise to bear. However, as plaintiffs acknowledge, Franklin Advisers’ investment committee must make decisions as to the coupon rates at which the Fund will purchase securities; and that function is not performed in a vacuum. Consideration must be given to rate of interest projections. The fact that trading in Ginnie Mae certificates tends to be long term rather than the more hectic pattern of short term, in and out trading does not diminish the importance of sound investment analysis for long-term decisions. As for King-man, he did say in his deposition that back-office work “is not the glamor side of the business,” lacking “the prestige of the investment or marketing side”, dep. 33. However, he also said: “It is terribly important to have good managers in the back office or you are in deep trouble.” Ibid. More significant than these reflections on the social strata of the securities business is Kingman’s opinion, expressed in his position paper (DX AU), and unshaken on cross-examination at his deposition: Back office problems occur with trading and investing in all types of securities. However, mortgage-backed securities ... necessarily involve more operational problems because of the way the payments are received. Instead of semi-annual payments of interest with principal at maturity, the principal and interest are paid monthly along with any prepayments that have been made on the underlying mortgages. The accounting for these payments is therefore more expensive than for that on any other type of securities. In addition, the trading of mortgage backed securities has proved to be a time-consuming task for back office operations personnel. Problems experienced in trade settlement, payment tracking, and securities clearance are unlike that of any other security in the market. Kingman was qualified to express these opinions. There is no contrary expert opinion evidence in the record. On the issue of the nature of defendants’ services, I conclude that Franklin Advisers’ responsibilities to the Fund in respect of investment advice and management were relatively complex, certainly far more so than plaintiffs were prepared to concede at trial. As for the quality of these services, there is no evidence that Franklin performed its administrative and management duties in less than an efficient and satisfactory manner. Plaintiffs offered no specific complaints, on their part or in connection with any other investors. Plaintiffs did adduce evidence that in past years two of Franklin’s officers had been sanctioned by regulatory agencies for improper record keeping. That proof does not rise much above the level of establishing that defendants hired humans instead of recording angels. Plaintiffs’ evidence on the point is more than offset by a series of apparently unsolicited letters from investors praising the quality of Franklin employees’ services. See DX X. Furthermore, a 1988 independent industry survey of broker/dealers rated Franklin first in the quality of its services to those entities. DX BU. Given investors’ primary objective of making money, the most significant indication of the quality of an investment adviser’s services is the fund’s performance relative to other funds of the same kind. See Krinsk, 875 F.2d at 409. The traditional yardsticks measuring performance are yield and expense ratio. They determine what the investor gets and how much he pays for it. A leading source of statistics on mutual fund performances is Lipper Analytical Services, Inc. Lipper statistical tables in evidence (DX AD, BE), furnished to the Fund’s directors, show that for the fiscal years ending September 30, 1987 and 1988, in a universe of fixed income funds with assets in excess of $5 billion, the Fund had the highest total return of them all. All the funds in that universe were government securities funds. In a universe of fixed income funds with assets over $2 billion, most of which were government securities funds, the Fund ranked fourth out of 23 for the fiscal year ended September 30, 1987, and fourth out of 18 for the fiscal year ended September 30, 1988. Those impressive yields were coupled with an expense ratio comparing favorably with industry experience. Defendants offered two studies by Lipper comparing the fees and expense ratios of Franklin funds (including the Fund) with the fees and expense ratios of funds of similar objective and size managed by other firms. DX AA is a Lipper report dated July 30, 1987. The report analyzes the Fund’s expense ratio for the most recently reported fiscal year (September 30, 1986). Franklin placed second in a universe of 13, which means that only one of the funds in the 13-member peer group had lower expense ratios than the Fund. That study was updated in a report dated November 1989, DX BF, in which the Fund placed second in a peer group of 16. Plaintiffs called an expert to compare the Fund’s performance with another Ginnie Mae mutual fund, with results less favorable to Franklin. Plaintiffs’ expert witness, John Livingstone, holds a doctorate in business, teaches accounting and business strategy at the graduate level, and is a principal in a management consulting company advising corporations in accounting, finance and economics. Livingstone has never been a director of a Ginnie Mae fund, employed by an adviser of such a fund, or participated in the negotiation of a management fee for a Ginnie Mae fund. Livingstone focused upon the Vanguard GNMA Fund. He added Vanguard to the 13 funds the directors were given as part of management’s fee presentation. See DX 35 (pp. 1-3). The statistics show that Vanguard outperformed the Fund in respect of expense ratio and yield. As to expense ratio, Vanguard’s total expense ratio for the most recently reported fiscal year was 0.350%. The Franklin Fund ranked fifth lowest at 0.545%. The highest total expense ratio amassed in the universe of 14 was Colonial Government Securities Plus, at 1.102%. As to total yield, Livingstone compared Franklin and Vanguard. The comparison was complicated by the fact that the two funds have different fiscal years. Accordingly Livingstone compiled averages over the last five years, four years, three years, and two years. Taking “total return” as the addition of dividends and increases in net asset value, Livingstone computed a five-year average total return for Franklin of 10.03% as to Vanguard’s 11.32%; a four year average of Franklin 9.67%, Vanguard 11.35%; a 3-year average of Franklin 10.63%, Vanguard 10.99%; and a two-year average of Franklin 7.25%, Vanguard 8.13%. Defendants attack plaintiffs’ use of the Vanguard GNMA fund as a basis for comparison with the performance of the Franklin GNMA Fund. They contend that the structure of the Vanguard family of funds is unique. Specifically, Charles Johnson testified that characteristically the funds in the Vanguard family of funds own the management company, and that in consequence the management company renders services to the funds at cost, whereas in the Franklin family, Franklin Advisers seeks to make a profit. Tr. 401-404. Johnson also testified that the capital of “Vanguard Company is supplied by the various funds for which it is the manager,” making the operation comparable to “a mutual life insurance company as opposed to a stock life insurance company.” Tr. 402, 403. For those reasons, Johnson “totally reject[ed]” Livingstone’s comparison of the expense ratio of the Vanguard Ginnie Mae Fund with the Franklin Ginnie Mae Fund. Tr. 403. Defendants sought at trial to shore up that distinction by introducing a letter dated November 30, 1989 from a senior vice president of Lipper Analytical Services to Franklin Resources, commenting on the differences between the two funds. DX CA. The Court excluded the exhibit on defendants’ case under the rules of evidence, but admitted the document when plaintiffs offered it, thereby transforming the letter into PX CA. Lipper’s comments constitute something of a mixed bag. The letter concludes: The fundamental differences between the Vanguard Group and Franklin Resources makes a comparison between the Fund’s managed by the two companies a tenuous one. In the world of mutual funds, Vanguard funds are truly unique. However, the Lipper letter also indicates that Johnson was wrong in saying that the Vanguard GNMA fund received investment advice from a Vanguard manager at cost. The letter recites: The [Vanguard] GNMA Portfolio is managed by Wellington Management Company. In the fiscal year ended January 31, 1989 the GNMA portfolio paid 0.03% of its average net assets to Wellington. This extraordinarily low fee is possible because of the great buying power possessed by the Vanguard group. Acting on behalf of its shareholder constituency, The Vanguard Group has negotiated low advisory fees with Wellington, which manages the portfolios of fifteen Vanguard funds having assets of $16 billion at September 30, 1989, and twelve other money managers who oversee as many Vanguard fund portfolios. Note the advisors provide no other services beyond money management. As to “other services”, the Lipper letter states: The Vanguard Group reduces the costs of running mutual funds from the fund shareholders’ point of view by operating on an “at-cost” basis. All the Vanguard mutual funds receive corporate management, administrative, shareholder accounting, marketing and distribution services from the Vanguard Group. To that extent, Johnson’s distinction is valid. The conclusion to be drawn is that the Vanguard GNMA fund furnishes some basis for a comparison of performance with the Franklin Fund, but there are also significant differences in structure, peculiar to the Vanguard family of funds, which lessen the value of the comparison for purposes of this litigation. (b) The Profitability to Franklin of its Services to the Fund. In Gartenberg I the Second Circuit described the adviser-manager’s “cost in providing the service” as a factor pertinent to the fairness of its fee, but did not specifically refer to “profitability.” 694 F.2d at 930. In Krinsk the court listed “the profitability of the fund to the Adviser-Manager” as a significant factor, but did not specifically refer to costs. 875 F.2d at 409. In fact, profitability and costs are intertwined. In a presentation to the Fund’s directors, Charles Johnson described “profitability” in terms of “net income as a percentage of revenues.” DX X at p. 3. One arrives at net income by deducting appropriate costs from gross revenues. The parties dispute the propriety of certain cost deductions from Franklin Advisers’ fees paid by the Fund. I deal with that issue infra, when considering whether Franklin misled the Fund’s directors and whether the latter conscientiously performed their duties. But profitability may usefully be considered separately from those issues. As the Second Circuit observed in Gartenberg I, a fund’s directors may be fully informed and endeavor to act conscientiously; nevertheless, “an adviser-manager’s fee could be so disproportionately large as to amount to a breach of fiduciary duty in violation of § 36(b).” 694 F.2d at 930. Coopers & Lybrand, the certified public accountants retained by Franklin Resources, prepared a report dated January 4, 1988 to the boards of directors of the Franklin group of mutual funds. PX 7, DX AG. That report undertook to prepare statements of revenue and expenses by function, and statements of profitability by fund, for the fiscal years ended September 30, 1985 and 1986 and for the six months ended March 31, 1987. Coopers & Lybrand did not conduct an examination made in accordance with generally accepted auditing standards of the financial information furnished to it by Franklin, and accordingly did not express an opinion on that information. Letter of December 30, 1987 forwarding report at 2. The report sets forth two sets of statements of revenue and expenses by function for each of the three time periods, each using a different indirect costs allocation methodology. “One method uses function related revenue factors as the basis for allocating indirect expenses by function, and the other uses function related direct labor factors as the basis for allocating indirect expenses by function.” Id. at 1. Otherwise, the two sets of financial information used the same assumptions, definitions and methodologies for identifying or allocating revenue and expenses among the functional categories. Coopers and Lybrand stated in the letter accompanying its report: Based on the procedures included in our review, as indicated above, it appears that while other methods of allocation may be appropriate and could produce different results, the methods used by the Company [Franklin Resources] to identify or allocate revenue and expenses by function and fund in preparing the . statements referred to above appear to be methodologies that are reasonable under the circumstances. Using the method of indirect expenses allocated on the basis of revenue, the report shows profitability to Franklin Resources generated by the Fund for the fiscal years ending September 30, 1985 of 13.95%; for the fiscal year ending September 30, 1986 of 22.31%; and for the six months ending March 31, 1987, 30.44%. Using the method of function related direct labor factors as the basis for allocating indirect expenses by function, the report calculates profitability for the fiscal year ending September 30, 1985 of 14.27%; for the fiscal year ending September 30, 1986, 22.52%; and for the six months ending March 31, 1987, 30.65. Those profitability calculations depend upon a fully-distributed cost accounting set forth in the Coopers & Lybrand report. The accounting allocates indirect expenses incurred by Franklin Resources as among the following functions: “Underwriting,” “Transfer Agent,” “Management,” and “Other.” We now come to a hotly disputed area. Plaintiffs claim that Franklin Resources misled the Fund’s independent directors by misallocating expenses from its underwriting function to the management function, thereby artificially decreasing the legitimate profitability of the Fund to Franklin. Before considering the evidence on this issue, I must address defendants’ standing objection to plaintiffs’ “misalloeation” claim as falling outside the scope of the issues for trial identified by the complaint and the pre-trial order. As noted, the complaint alleged “in particular” a violation of § 36 of the Act. The pre-trial order provided in 111: The parties agree that the trial of this action shall be based upon this Final Pre-Trial Order and upon the pleadings. No claims or defenses are abandoned, and no claims or defenses other than those set forth in the pleadings and this Final Pre-Trial order may be asserted. The parties thereupon set forth, inter alia, their respective proposed findings of fact and conclusions of law. Previously defendants had taken the pretrial deposition of plaintiffs’ expert, Livingstone, and sought full disclosure of any opinions adverse to defendants that Livingstone might offer at trial. Defendants objected to plaintiffs' misal-location of expense theory at trial, and evidence in support thereof, because they regard the claim essentially as one falling under § 12(b) of the Act, which defendants say was not pleaded in the complaint or embraced by the pre-trial order. Section 12(b) provides that: It shall be unlawful for any registered openend company (other than a company complying with the provisions of section 80a-10(d) of this title) to act as a distributor of securities of which it is the issuer, except through an underwriter, in contravention of such rules and regulations as the [SEC] may proscribe as necessary or appropriate in the public interest or for the protection of investors. 15 U.S.C. § 80a-12(b). The SEC has promulgated Rule 12b-l, 17 C.F.R. § 270.12b-l, which provides in subsection (a)(2): For purposes of this section, such a company will be deemed to be acting as a distributor of securities of which it is the issuer, other than through an underwriter, if it engages directly or indirectly in financing any activity which is primarily intended to result in the sale of shares issued by such company, including, but not necessarily limited to, advertising, compensation of underwriters, dealers, and sales personnel, the printing and mailing of prospectuses to other than current shareholders, and the printing and mailing of sales literature. Rule 12b-l(b) further provides that a registered open-end management investment company may act as a distributor of securities of which it is the issuer if any payments made in connection with such distribution are made pursuant to a written plan conforming to the Rule. Franklin did not have a Rule 12b-l plan; but the more general concern raised by plaintiffs at bar is that articulated by Judge Ward in Schuyt at 663 F.Supp. 987: Under Rule 12b-l, the directors had an obligation to assure themselves that there was not an indirect use of Fund assets for distribution expenses. In Gartenberg I, Judge Pollack looked to § 12(b) of the Act and Rule 12b-l to determine whether certain processing costs “are of the character of forbidden ‘distribution’ expenses,” drawing the distinction in that regard between “managerial functions” and “promotional expenses.” 528 F.Supp. at 1052. I reject defendants’ contention that plaintiffs at bar cannot appeal to § 12(b) principles because that section of the Act is not specifically pleaded in the complaint or referred to in the pretrial order. The independent directors’ duty to prevent the indirect use of fund assets for distribution expenses, which may occur if “forbidden” distribution expenses are placed in the management column where they do not belong, forms an integral part of evaluating the fairness of the manager-adviser’s fee, as Schuyt and Gartenberg I indicate. Indeed, in Gartenberg I Judge Pollack considered § 12(b) and Rule 12b-l contentions within the context of plaintiffs’ § 36(b) claim, while refusing- plaintiffs’ “diversionary belated attempt” to expand the issues so as to assert claims under §§ 15(a) and 20(a) of the Act. Judge Pollack rejected those claims because “[t]he complaints in these suits allege but one cause of action — a claim for breach of fiduciary duty under Section 36(b),” 528 F.Supp. at 1065. See also 694 F.2d at 933-34. Claims under those other sections fell outside the scope of the § 36(b) pleading, but § 12(b) considerations did not. However, at the conclusion of Livingstone’s direct testimony I granted defendants’ motion to strike that testimony insofar as Livingstone undertook to describe specific instances of expense misallocation. I did so because Livingstone gave no such testimony at his deposition, although repeatedly pressed by defendants’ counsel to reveal all opinions he then held favorable to plaintiffs and adverse to defendants on any issue in the case. Furthermore, plaintiff’s proposed findings of fact do not deal with misallocations of expenses. Plaintiffs’ only specific reference to the cost study appears in Proposed Finding of Fact Í1 35: In 1987, Franklin undertook to make a cost study regarding the profitability of the Fund to Franklin. This was performed in consultation with Coopers & Lybrand, the regular auditors for Franklin as well as for the Fund. The cost study was finally completed and presented to the Board of directors of the Fund in early 1988. A discussion of the material contained in the report is set forth below. The only discussion “set forth below” uses figures and percentages derived from the Coopers & Lybrand report, but there are no specific references to misallocations of expenses. The purpose of a pre-trial deposition of the adverse party’s expert witness is to learn in advance of trial precisely what the expert will say, in order to prepare to meet it. Similarly, proposed findings of fact in a pre-trial order are intended to identify those factual assertions which the adverse party will make, equally necessary for trial preparation. It would not have been fair, in these circumstances, to permit Livingstone to give detailed opinion testimony with respect to misallocation of expenses. But the general principles involved are sufficiently familiar from case law, and subsumed by plaintiff’s § 36(b) claim, to permit me to consider the issue, to the extent that I comprehend it without the assistance of expert opinion testimony. Plaintiffs base their charge of improper allocation of distribution expenses to the investment management function primarily upon a comparison between Franklin Resources’ report to the Fund directors dated July 17, 1987 (PX 17), and the Coopers & Lybrand report dated January 4, 1988 (PX 7). The genesis of those reports and their consideration by the directors are considered infra. For present purposes it is sufficient to say that some rather startling differences between the two reports appear in the allocation of expenses among the several Franklin functions. The July 17, 1987 report was prepared by Franklin staff over a period of months. The report states that because the “cost and profit analysis is accounting oriented, the guidance and concurrence of Coopers & Lybrand was obtained on each significant step of development in the financial model.” The report deals first with Franklin Resources as a whole, and then performs a product-line study of each fund with respect to revenues and expenses. The report analyzes “direct cost — compensation,” and “indirect cost.” The report also contains a condensed income statement for Franklin Resources, broken down between “underwriting,” “transfer agent fee,” “management,” and “others.” Treating Franklin Resources as a whole, for fiscal year ended September 30, 1985 “management” produced investment management fees of $41,593,615 against total expenses allocated to management of $3,322,567. For the fiscal year ended September 30, 1986, those figures for “management” are $98,371,448 and $5,853,-453. For the first six months ended March 31, 1987, the figures are $75,463,061 and $4,261,835. PX 17 at p. 9. The total expenses allocated to the underwriting function for Franklin Resources as a whole were, for the fiscal year ended September 30, 1985, $18,524,853; for the fiscal year ended September 30, 1986, $39,-516,822; and for the six months ended March 30, 1987, $20,107,401. In succeeding pages, the report calculates “cost and profit results by function” with respect to each of the funds managed and advised by Franklin Resources. With respect to the Fund at issue, for fiscal year ending September 30, 1985 the report shows advisory fees of $17,670,249 against expenses allocated to the advisory function of $117,613; for the fiscal year ended September 30, 1986 the comparable figures are $50,999,954 and $336,054; and for the six months ending March 31, 1987 they are $33,942,407 and $579,724. Those same pages of the July 17, 1987 report allocated to the Fund expenses for the underwriting function in the fiscal year ended September 30, 1985 which totalled $10,066,356; for fiscal year ending September 30, 1986, $21,383,791; and for the first six months ending March 31, 1987, $8,477,-901. Turning now to Coopers & Lybrand’s January 4, 1988 report, PX 7, as noted the statements of revenue and expenses by function were computed by two methods in respect of the allocation of indirect expenses. The table below sets forth management revenues and expenses allocated to the management and underwriting functions of Franklin as a whole, first under that method using revenue factors to allocate indirect expenses, and then using direct labor factors to allocate indirect expenses: Using Revenue Factors to Allocate Indirect Expenses FYE 9/30/85 Management fees: $41,763,501 Management expenses: 37,177,657 Underwriting expenses: 2,704,873 FYE 9/30/86 Management fees: 98,535,011 Management expenses: 75,727,036 Underwriting expenses: 5,859,417 Six Months ended 3/31/87 Management fees: 75,504,188 Management expenses: 45,478,190 Underwriting expenses: 3,726,230 Using Direct Labor Factors To Allocate Indirect Expenses The total for management fees and management fees and management expenses do not change. The total expenses allocated to the underwriting functions are: FYE 9/30/85: $ 638,640 FYE 9/30/86: 1,382,661 Six months ended 3/31/87: 1,831,468 See PX 7 at pp. 3-8. When the Coopers & Lybrand report turns to an analysis of each fund, the following figures appear with respect to the Fund at issue. For the fiscal year ended September 30, 1985, the report shows management revenue of $17,670,249; expenses allocated to the management function of $13,281,076; and expenses allocated to the underwriting function of $1,584,494. For the fiscal year ended September 30, 1986, the comparable figures are $50,999,-954, $28,466,552, and $3,189,605. For the six months ending March 31,1987, the comparable figures are $33,942,407, $13,915,-550, and $1,478,972. Between these two reports, there are dramatic decreases in underwriting expense and equally dramatic increases in management expenses. Which allocation of expenses is correct? Did Franklin Resources attempt to mislead the independent directors of the Fund by misallocating expenses? If it did so, were those independent watchdogs deliberately inattentive or carelessly asleep in their kennels? I consider -these questions infra. For the present, I consider the effect of expense allocation upon profitability. It is necessary to quantify that effect, since the cases teach that an adviser’s fee may be fair or unfair, whether or not particular expenses are deducted from the adviser’s gross revenues. See Krinsk, 715 F.Supp. at 502 (“profitability to Merrill Lynch from fee based activity was well within the realm of reasonableness, even without downward adjustment for costs of financial consultants and sales assistance”); Gartenberg I at 528 F.Supp. 1052 (“The compensation accepted by the Adviser was not unfair whether viewed with or without consideration of the processing costs”). Defendants contend that, whatever the resolution of the other questions related to expense allocation, the whole issue makes no difference because its effect upon profitability is minimal. Defendants argue in substance that if Franklin Resources’ purpose in switching expenses from the shell of underwriter function to that of management was to take the independent directors’ eyes off the pea of profitability, the result was hardly worth the effort. Calculations of profitability derived from the July 17, 1987 report, pp. 10-12, give profitability figures of 17.65% for the fiscal year ended September 30, 1985, 25.72% for fiscal year ended September 30, 1986, and 32.53% for the six months ending March 31, 1987. The January 8, 1988 report gives profitability figures for those periods using method A for allocating indirect expenses of 13.95%, 22.31% and 30.43%; and, using method B 14.27%, 22.52%, and 30.64%. PX 7 at pp. 25, 27. These differences are not as dramatic. There is some force to this analysis, but it does not fully address the particular significance of proper allocation of distribution expenses in a section 36(b) claim, given the public policy concerns expressed in § 12(b) and Rule 12b-l. The Second Circuit in Krinsk approved Judge Walker’s recognition that “[c]osts within the CMA program must be properly allocated in any profitability study lest the Fund subsidize the costs of Merrill Lynch’s commission-generating activities.” 875 F.2d at 410. Judge Ward in Schuyt approved directors viewing data on distribution expenses to monitor the adviser’s performance, “just as long as they did not consider these expenses when they voted on the advisory agreement, lest they ignore the advice of counsel and improperly [give] the Adviser an excessive fee so that the Adviser could indirectly use Fund assets to promote the Fund.” 663 F.Supp. at 987-88. The issue is not so much whether shifting certain items of expense from one function to another dramatically reduces profitability calculations, but whether the independent directors, in assessing the profitability of the Fund to Franklin Advisers, should have disregarded certain distribution expenses altogether in voting upon the latter’s management fee. But defendants approach the matter in a second way. They grant plaintiffs’ point “and then some” (defendants’ post-trial brief at 13) by adding the full amount of expenses for “advertising” and “promotion” allocated by the Coopers & Lyb-rand report to the management function for Franklin Resources as a whole to the net income of the Fund at issue alone, and then recalculate profitability of the Fund to Franklin. Defendants net these expenses down by about 50% to reflect the after-tax effect. In fact, the figures appearing in the Coopers & Lybrand report imply a tax rate of 48.49%, as Livingstone recognized in his presentation, e.g., PX 32A, p. 6. In the calculations which follow, I will add to the Fund’s net revenues 51.51% of the expenses in question to show the post-tax effect of defendants’ approach: Fiscal year ended September 30, 1985: To net revenues of $3,505,511, add $2,756,-145 in after tax expenses (generated by pre-tax expenses of $4,990,340 for advertising and $373,948 for promotion), for a total of $6,268,656, or 25% of total revenues of $25,127,197. For fiscal year ended September 20, 1986: To net revenues of $15,965,195, add $6,214,255 in after tax expenses (generated by pre-tax expenses of $11,731,228 for advertising and $332,945 for promotion), for a total of $22,179,450, or 31% of total gross revenues of $71,550,595. For the six months ending March 31, 1987: To total net revenues of $13,973,434, add $3,384,324 in after tax expense (generated by pre-tax expenses of $6,367,601 for advertising and $202,627 for promotion), for a total of $17,357,758, or 37.8% of total gross revenues of $45,907,000. These calculations are based upon method A of allocating indirect costs. I do not think it necessary to repeat the exercise using Method B. As defendants point out in performing their own exercise, it is unreasonably favorable to plaintiffs to take the advertising and promotion expenses from Franklin Resources’ services to all the funds and add them to the net revenues of this Fund only. The actual profitability percentages are in all likelihood significantly less than those resulting from the Court’s calculations. The most that can be said is that, as in other cases involving multi-product services by an adviser-manager, the Court is left “with the problem of uncertain profitability.” Schuyt at 663 F.Supp. 978. See also Krinsk at 715 F.Supp. 489 (“At the outset, the Court recognizes the impossibility of arriving at an exact profitability figure.”) But it is most unlikely that the profitability of this Fund to Franklin at any time exceeded 35%. Dr. Livingstone regarded the profits the Fund generated for Franklin Advisers as excessive on two other bases, both of which I reject. Livingstone fashioned what he referred to as “yardsticks of profitability” based upon return on common equity, and net income as a percentage of revenues. He compared Franklin Resources’ return on common equity with a compilation with large broker firms, money center banks, insurance firms, mutual fund sponsors, public broker-dealers, personal loan companies, diversified financial groups, major regional banks, and a compendium of companies taken from Business Week’s “Top 1000.” As for net income as a percentage of revenues, Livingstone compared Franklin Resources with large broker firms, public broker-dealers, and New York Stock Exchange member firms. Livingstone’s approach in this regard, having the virtue of simplicity if nothing else, is that Franklin just plain made too much money. That is not an acceptable approach. Under the cases, to the extent that comparisons are probative at all, a mutual fund adviser-manager must be compared with members of an appropriate universe: adviser-managers of similar funds. Plaintiffs offer precisely the sort of profitability analysis which Judge Sweet rejected in Meyer v. Oppenheimer Management Corp., 715 F.Supp. at 576. Plaintiff in Meyer relied upon evidence that the profitability to the fund’s investment adviser was higher than that of broker-dealers and ten large banks. Judge Sweet found that evidence of no assistance to him: However, a return on assets or investment analysis adds little to the determination because a money market fund management company has no substantial net worth, is not capital intensive, and its activities differ from other types of financial services companies which provide services other than the management of money market funds from exclusive business funds. See also Gartenberg I at 694 F.2d 930 n. 3: Appellants’ argument that the lower fees charged by investment advisers to large pension funds should be used as a criterion for determining fair advisory fees for money market funds must also be rejected. The nature and extent of the services required by each type of fund differ sharply. As the district court recognized, the pension fund does not face the myriad of daily purchases and redemp-tions throughout the nation which must be handled by the Fund, in which a purchaser may invest for only a few days. In the case at bar, I give no weight to plaintiffs’ comparisons of the Fund’s profitability with a wide range of different sorts of companies, both within the broad boundaries of the “financial industry” and outside them. (c) Economies of Scale. The concept of “economies of scale” assumes that as a mutual fund increases in size, its operational costs decrease proportionally. If a fund realizes economies of scale, its willingness to let the shareholders participate in the resulting benefits becomes a factor in evaluating the reasonableness of the adviser-manager’s fees. Section 36(b) of the Act was specifically directed to economies of scale. In Fogel v. Chestnutt, 668 F.2d 100, 111 (2d Cir.1981), cert. denied, 459 U.S. 828, 103 S.Ct. 65, 74 L.Ed.2d 66 (1982), Judge Friendly wrote: The problem to which § 36(b) was addressed was that with which the SEC had dealt in pages 125-49, 154 of its Report on Public Policy Implications of Investment Company Growth (PPI), H.R.Rep. No. 2337, 89th Cong., 2d Sess. (1966). This was that advisers’ fees, generally stated as a percentage of the market value of the managed assets, which had been altogether reasonable when a fund was launched, may have become unreasonably high when the fund grew to enormous size. In Gartenberg I the Second Circuit looked again to legislative history: We do not suggest that rates charged by other adviser-managers to other similar funds are not a factor to be taken into account. Indeed, to the extent that other managers have tended “to reduce their effective charges as the fund grows in size,” the Senate Committee noted that such a reduction represents “the best industry practice [which] will provide a guide,” S.Rep. No. 91-184, supra, [1970] U.S.Code Cong. & Ad.News at 4902. 694 F.2d at 929. Thus the Second Circuit recognizes as a factor bearing upon the reasonableness of fees “the extent to which the adviser-manger realizes economies of scale as the fund grows larger,” Gartenberg I at 930. Krinsk lists “economies of scale” as one of the relevant factors. 875 F.2d at 409. The judges of this Court who have tried § 36(b) case have dealt with economies of scale: in Gartenberg I at 528 F.Supp. 1054-1055; in Schuyt at 663 F.Supp. 979-980 (and see 970 n. 25); and in Krinsk at 715 F.Supp. 496. Plaintiffs in prior cases have argued in substance that since a fund increased dramatically in size, economies in scale must have been realized. The courts reject that argument. In Krinsk, Judge Walker accepted the proposition that “economies of scale ‘relate to the costs incurred in doing a unit of something,’ ” and dismissed plaintiff’s exhibits as unpersuasive because they “fail[ed] to demonstrate that the per unit cost of Fund transactions ... decreases as the number of units increases.” 715 F.Supp. at 496. Judge Walker went on to find that merely because the ratio of fee based expenses to fee based revenues declined at a time when the Fund size grew, that fact does not establish that such a decline was necessarily due to economies of scale. Ibid. Affirming the dismissal of the complaint in Krinsk, the Second Circuit quoted that language with approval at 875 F.2d 411, and went on to say: Rather, to show economies of scale, plaintiff bore the burden of proving that the per unit cost of performing Fund transactions decreased as the number of transactions increased. Ibid. For that proposition the Court of Appeals cited the district court’s opinion in Gartenberg I, at 528 F.Supp. 1055, where Judge Pollack wrote: That processing costs do not significantly diminish as Fund assets increase accords with logic and common sense. While it may be almost as easy to invest a block of $100 million as a block of $10 million, it requires substantially more time, money and personnel to process 1 million shareholders than 100,000 orders. The ease and speed with which Fund shares can be bought or redeemed is crucial to the success of any money market fund, especially since the investor looses money for every minute his funds lie unemployed. Merrill Lynch added more than 3,000 non-sales personnel to handle the additional transaction volume caused by the Fund. I conclude from these cases that to demonstrate breach of fiduciary duty in respect of economies of scale, an investor must first prove that in fact the fund realized economies of scale. This requires proof of decreasing costs on a per-unit basis, as the fund increases in size. In Krinsk Judge Walker accepted the testimony of a defense witness that one must “try to create a detailed analysis of each element of a transaction ..., over an extended period of time, over different levels of activity, to determine whether or not there are economies of scale.” 715 F.Supp. at 496. While this was a defense witness, Judge Walker accepted his view, and the Second Circuit clearly bestowed its imprimatur of approval in the language I have quoted from its opinion affirming Krinsk. To place that burden of proof upon a plaintiff accords with logic and common sense, as Judge Pollack observed in Gartenberg I. Economies of scale do not exist in a vacuum. The concept is meaningful only if increased size of a fund (more shareholders, more assets under management) directly reduces the manager’s costs of processing each transaction and servicing each shareholder. A plaintiff must prove that the fund actually realized such economies of scale. If a plaintiff makes that showing, then the question becomes whether the fund has permitted shareholders to participate, at least in part, in the economies of scale it has realized. In Schuyt Judge Ward quoted with approval counsel’s advice to independent directors as to how a fund shares the benefits of economies of scale: The basic test is whether the directors can satisfy themselves that the information that is available provides a reasonable basis for judgment that the benefits of the economies of scale are in fact shared by the advisor with the Fund (e.g., by appropriately fixed “break-points” or alternatively, by means of a fee structure which, whether or not containing break-points, in effect incorporates economies of scale by virtue of a relatively low starting point which in effect subsumes economies of scale throughout). 663 F.Supp. 970 n. 25. See also Gartenberg I at 528 F.Supp. 1054 (“Clearly, the present schedule takes account of economies of scale; the rate of fees diminishes progressively.”) In the case at bar, as their expert Livingstone acknowledged, plaintiffs did not attempt a study to determine if the per-unit cost of each transaction for the Fund decreased as the number of transactions increased. Tr. 226. Rather, Livingstone offered two definitions of “economies of scale,” and contended that charts drawn from the Coopers & Lybrand report of January 4, 1988, PX 7, demonstrate that Franklin actually realized economies of scale. Livingstone began his definitions by testifying that “[ejconomies of scale are also sometimes referred to as ‘increasing returns to scale.’ ” He then said: As the volume or scale of operations increases, then economies of scale or increasing returns to scale may arise from either (a), decreasing average cost per unit produced; (b), increasing average revenue per unit produced. In either case, the result is increasing profit per unit produced. Thus, economies of scale are evidenced by, (a), decreasing percentage cost to revenue as the volume of operations increases; or (b), increasing percentage of profit to revenue as the volume of operations increases. Tr. 42. Fixed costs, which do not increase with volume, give rise to economies of scale of type (a). Livingstone then said: Case (b), that is, the case of increasing percentage of profit to revenue, can occur even if all costs are perfectly variable. All that would be required is f