
327 F.Supp. 844 (1971)
Julius W. HOBSON, individually and on behalf of Jean Marie Hobson and Julius W. Hobson, Jr., et al., Plaintiffs,
v.
Carl F. HANSEN, Superintendent of Schools of the District of Columbia, the Board of Education of the District of Columbia, et al., Defendants.
Civ. A. No. 82-66.
United States District Court, District of Columbia.
May 25, 1971.
*845 Peter F. Rousselot, Washington, D. C., for plaintiffs.
C. Francis Murphy, Acting Corp. Counsel for District of Columbia, and John A. Earnest, Matthew J. Mullaney, Jr. and Thomas R. Nedrich, Asst. Corp. Counsel for District of Columbia, for defendants.
J. SKELLY WRIGHT, Circuit Judge[*]:
On May 19, 1970, Julius W. Hobson, an original plaintiff in the class action which led to this court's prior judgment and decree of June 19, 1967, 269 F.Supp. 401, affirmed, sub nom. Smuck v. Hobson, 132 U.S.App.D.C. 372, 408 F.2d 175 (1969) (en banc), filed an amended motion for both further relief and enforcement of the decree. Under the relief requested the per-pupil expenditures from the regular District of Columbia budget at each elementary school would not be allowed to deviate by more than five per cent from the average per-pupil expenditure for all elementary schools in the system; the five per cent variation might be exceeded only for adequate justification, which would be defined to include provision of compensatory education for educationally deprived pupils in accordance with the 1967 decision, or provision for special educational services for the mentally retarded or physically handicapped. To understand the meaning of plaintiffs' motion for further relief and enforcement, it is necessary briefly to review the beginnings of this long litigation.

I
In 1967 the basic question presented to the court was whether the defendants, the Superintendent of Schools and the members of the Board of Education, in the operation of the public school system here, were unconstitutionally depriving the District's Negro and poor public school children of their right to equal educational opportunity with the District's white and more affluent public school children. 269 F.Supp. at 406. The court concluded that they were, and its decree permanently enjoined the District of Columbia school board from discriminating on the basis of racial or economic status in the operation of the public school system. 269 F.Supp. at 517.
This decree was based in part upon the court's finding of a systematic discrimination favoring the west of Rock Creek Park schools in the distribution of District educational resourcesin the age and condition of school buildings, in school congestion, in quality of faculty and of textbooks, in curricula and special programs such as kindergarten, and lastly in per-pupil expenditures. With reference to these documented inequalities, the court held:
"* * * However the Supreme Court ultimately decides the question of a school board's duty to avoid pupil-assignment policies which lead to de facto segregation by race and class, it should be clear that if whites and Negroes, or rich and poor, are to be consigned to separate schools, pursuant to whatever policy, the minimum the Constitution will require and guarantee is that for their objectively measurable aspects these schools be run on the basis of real equality, at least unless any inequalities are adequately justified." *846 269 F.Supp. at 496. The court went on to comment:
"The constitutional principle from which this modern separate-but-equal rule draws its sustenance is, of course, equal protection. Orthodox equal protection doctrine can be encapsulated in a single rule: government action which without justification imposes unequal burdens or awards unequal benefits is unconstitutional. The complaint that analytically no violation of equal protection vests unless the inequalities stem from a deliberately discriminatory plan is simply false. Whatever the law was once, it is a testament to our maturing concept of equality that, with the help of Supreme Court decisions in the last decade, we now firmly recognize that the arbitrary quality of thoughtlessness can be as disastrous and unfair to private rights and the public interest as the perversity of a willful scheme.
"Theoretically, therefore, purely irrational inequalities even between two schools in a culturally homogeneous, uniformly white suburb, would raise a real constitutional question. But in cases not involving Negroes or the poor, courts will hesitate to enforce the separate-but-equal rule rigorously. Through use of a generous de minimis rule or of a relaxed justification doctrine, or simply in the name of institutional comity, courts will tolerate a high degree of inequality-producing play, and delay, in the joints of the educational system. But the law is too deeply committed to the real, not merely theoretical (and present, not deferred) equality of the Negro's educational experience to compromise its diligence for any of these reasons when cases raise the rights of the Negro poor. * * *"
Id. at 497.[1] (Footnotes omitted.)
In its 1967 decree, the court attacked de jure segregation in the District directly, ordering the track system and optional attendance zones abolished and calling for integration of school faculties. The court held further that per-pupil expenditure is a measure which summarizes most other relevant distributions of educational resources. But on the assumption that compliance with other items of the 1967 decree would have the secondary effect of equalizing overall resource distribution, the court deferred any more specific remedy for the inequality in per-pupil expenditures. The thrust of plaintiffs' 1970 amended motion for further relief and enforcement was that this hoped for secondary effect of the original decree has not occurred. Plaintiffs returned to the court asking for further relief in view of the fact that the spread in total expenditures per pupil at various District elementary schools had increased by over 100 per cent since 1964, the last year for which complete figures were available at the time of the original litigation.[2] Plaintiffs requested a more specific remedy to alleviate these inequalities.

II
After a year of discovery and argument by memoranda,[3] the record now before the court indicates that a striking *847 *848 differential in per-pupil expenditures for teachers' salaries and benefits[4] exists between schools east and west of the Park and that the differential is greater in fiscal 1971 than it was in fiscal 1970. The area west of the Park,[5] where despite voluntary busing the public school population is today 74 per cent white, is decidedly favored over the rest of the city where the school population is 98 per cent black, and is especially favored over Anacostia, one of the most poor and black sections of the city.[6] The following tables show the extent of existing inequities by comparison of pupil-teacher ratios, average cost per teacher, and average teacher cost per child for both fiscal 1970 and fiscal 1971.[7]


*849
            DIFFERENCES BETWEEN WEST OF THE PARK ELEMENTARY
            SCHOOLS AND SCHOOLS IN THE REMAINDER OF THE CITY
                      (excluding special schools)           
                              Fiscal 1970
                         |--------------|--------------|----------------|
                         |              |  Remainder   | West of Park   |
                         | West of Park |  of City     | Advantage      |
                         |--------------|--------------|----------------|
Pupil-teacher ratio      |       21.4/1 |     22.9/1   |   7.0% smaller |
                         |--------------|--------------|----------------|
Average teacher cost     |      $11,734 |    $10,167   |  15.4% greater |
                         |--------------|--------------|----------------|
Teacher expenditures     |              |              |                |
  per pupil              |         $552 |       $444   |  24.3% greater |
                         |--------------|--------------|----------------|
                              Fiscal 1971
                         |--------------|--------------|----------------|
Pupil-teacher ratio      |       18.1/1 |     20.9/1   |  15.5% smaller |
                         |--------------|--------------|----------------|
Average teacher cost     |      $12,118 |    $11,048   |   9.7% greater |
                         |--------------|--------------|----------------|
Teacher expenditures     |              |              |                |
  per pupil              |         $669 |       $528   |  26.7% greater |
                         |--------------|--------------|----------------|
            DIFFERENCES BETWEEN WEST OF THE PARK ELEMENTARY
                SCHOOLS AND ANACOSTIA ELEMENTARY SCHOOLS   
                              Fiscal 1970
                         |--------------|--------------|----------------|
                         |              |              | West of Park   |
                         | West of Park |  Anacostia   | Advantage      |
                         |--------------|--------------|----------------|
Pupil-teacher ratio      |       21.4/1 |     24.6/1   |  14.9% smaller |
                         |--------------|--------------|----------------|
Average teacher cost     |      $11,734 |    $10,046   |  16.8% greater |
                         |--------------|--------------|----------------|
Teacher expenditures     |              |              |                |
  per pupil              |         $552 |       $413   |  33.7% greater |
                         |--------------|--------------|----------------|
                              Fiscal 1971
                         |--------------|--------------|----------------|
Pupil-teacher ratio      |       18.1/1 |     22.6/1   |  24.9% smaller |
                         |--------------|--------------|----------------|
Average teacher cost     |      $12,118 |    $10,775   |  12.5% greater |
                         |--------------|--------------|----------------|
Teacher expenditures     |              |              |                |
  per pupil              |         $669 |       $478   |  40.0% greater |
                         |--------------|--------------|----------------|

*850 Particularly in view of the 1967 opinion and decree in this case, these figures make out a compelling prima facie case that the District of Columbia school system operates discriminatorily along racial and socio-economic lines. As the Fifth Circuit taught us in Brooks v. Beto, 366 F.2d 1, 9 (1966), "figures speak and when they do, Courts listen." If plaintiffs' strong prima facie case of racial discrimination in the administration of the District school system is not rebutted, then these results can only be justified by a "compelling state interest."[8] The thrust of the defense in this case has not, however, been with the demonstration of such compelling interests, but rather with various attempts to undermine the preliminary finding of discrimination in the dispensation of educational opportunity.

III
A. The first of the defenses to plaintiffs' prima facie case is the argument that, conceding expenditures for teachers' salaries per pupil to be higher west of the Park than in the rest of the city and recognizing that the west of the Park area has traditionally been a bastion of the white and wealthy, more is required for a finding of discrimination in 1971. Specifically, defendants have asked the court to notice that busing undertaken to relieve overcrowding has diluted the concentration of white students and has raised the percentage of black students at many of the west of the Park schools. But the fact remains that, when all 13 schools west of the Park are considered together in 1971, they are still 74 per cent white as compared with all the rest of the schools in the system, which average 98 per cent black.[9] The west of the Park area continues to have schools which are identifiably more white and wealthy. Although they have received some bused students, the west of the Park schools remain 10 per cent less crowded than schools in the remainder of the city.[10] That the west of the Park schools have 27 per cent higher expenditures per pupil for teachers' salaries and benefits in 1971 is prima facie evidence of discrimination.
Nor do defendants succeed in undercutting this prima facie case by pointing out that there are substantial differences in per-pupil expenditure existing in the approximately 130 elementary schools in the system and by suggesting that consequently "it is possible for anyone to cull a small atypical grouping of elementary schools which yields an average per pupil expenditure substantially different from the city-wide average."[11] What defendants fail to recognize is that the schools west of the Park constitute both a geographic and an historical entity.[12] If defendants were correct that the observed teacher expenditures per pupil west of the Park were a random or freak phenomenon, then defendants should be able to find other such "atypical" clusters of schools and to demonstrate that the unusually high expenditures at such clusters were unrelated to impermissible racial or socio-economic discrimination. But the only other high expenditure "atypical" group of elementary schools mentioned by defendants is that comprising the Model Schools Division, in which the pupils are predominantly black and from the lowest income level families. In 1971 the schools in this model project had teacher expenditures per pupil of $548, or $15 above the citywide average.[13] This de minimis advantage hardly compares, however, with that of the west of the Park schools which were $136 above the citywide average. Moreover, there is a lawful reason *851 for the favorable treatment of the Model Schools Division program; it serves as a model of compensatory education and is justified by the court's 1967 holding that
"[w]here because of the density of residential segregation or for other reasons children in certain areas, particularly the slums, are denied the benefits of an integrated education, the court will require that the plan include compensatory education sufficient at least to overcome the detriment of segregation * * *."
269 F.Supp. at 515. Because the Model Schools Division program is designedly compensatory, it would not be bound by plaintiffs' proposed five per cent equalization order.
The higher than average teacher expenditures per pupil out of regular funds at the Model Schools Division schools are further accounted for by the fact that the administration has designated these schools to receive all Title I money extended to the District of Columbia under the Elementary and Secondary Education Act. Federal law requires that Title I funds be spent only to meet the special educational needs of disadvantaged children. To obtain Title I funds from the federal government, local school administrators must first demonstrate that the designated receiving schools are already given at least equal treatment with other schools in the system as measured by objective inputs out of regular budgetary funds.[14] Thus both because they are part of the city's own compensatory program and because it is a prerequisite to their receiving Title I funds, Model Schools Division schools lawfully receive slightly higher than average teacher expenditures per pupil. But by what lawful justification do the elementary schools in the white and wealthy west of the Park area receive strikingly higher teacher expenditures per pupil, out of regular appropriations uniquely within defendants' control, as compared with all of the city's black and generally poorer schools, including those of the Model Schools Division? As will be seen below, this is a question for which defendants have no satisfactory answer.
B. As an adjunct to their claim that the schools west of the Park constitute an unfair or "atypical" sample, defendants have offered evidence purporting to show that, when looked at overall, children from poor homes fare as well or better than their wealthier counterparts in the allotment of expenditures. By defendants' calculations, the statistical correlation between the fiscal 1970 per-pupil expenditure and the 1959 median family income is -0.08. "No statistical relationship at all exists; the rank distribution is completely random." According to plaintiffs, however, defendants have not computed this correlation correctly. The correct correlation is +.053small, but positive. Plaintiffs state that when one looks at the correlation between income and expenditures per pupil for teachers' salaries in fiscal 1970the focus which the court has most recently requestedthe correlation is a significant +.100; and that it rises to +.172 when special schools for the mentally retarded and physically handicapped are excluded (as they would be under plaintiffs' proposed equalization order).
Fortunately, the court does not find it necessary to arbitrate this abstruse statistical dispute between the parties. Even if defendants have computed the correlation correctly, all they have demonstrated is that random high per-pupil expenditures in favor of some children from poor, black neighborhoods east of Rock Creek Park at the expense of other children from poor, black neighborhoods east of Rock Creek Park are so great that they obscure the systematic discrimination in favor of white children from wealthy neighborhoods west of *852 Rock Creek Park. Put another way, if there is a "crazy quilt" or random nature to the spending pattern, it is concentrated among some low income area schools where there appears to be no significant correlation among race, neighborhood income, and per-pupil expenditures. Whereas white children in wealthy neighborhoods have only a slight chance of being assigned to elementary schools where the expenditure per pupil is less than the citywide average, children in poorer black neighborhoods face a substantial probability of such assignment. Defendants' own scatter diagrams serve only to reinforce plaintiffs' argument that per-pupil expenditures for teachers' salaries in District public schools are "random," if at all, only for the black and the poor. The wealthy and the white are virtually guaranteed more moneyin almost every instance substantially more than five per cent above the citywide average.
C. Defendants have also attempted to account for the observed discrepancies in expenditures solely on the basis of true economies of scale. A brief review of the contentions of opposing parties in the economies of scale debate will serve to indicate the added difficulties which beset the truth finding process when it is necessary to rely upon easily manipulated statistical analyses. When the evidence first presented indicated wide discrepancies in overall expenditures per pupil favoring the west of the Park schools, defendants took the position that economies of scale were the real reason for what plaintiffs attributed to discrimination. In this respect, defendants directed the court's attention to an article by June O'Neill and Arlene Holen published in the Washington Post on October 15, 1970.[15] Adopting the June O'NeillArlene Holen article's reasoning, defendants stated in their November 17 memorandum to the court that they "must here again emphasize that it is not the blackness or whiteness of the school, nor the poorness or richness of the school that causes a high or low per pupil expenditure figure. It is the size of the school."[16]
Plaintiffs have demonstrated to this court's satisfaction, however, that defendants' initial explanation of the observed discrepancies in per-pupil expenditures *853 solely on the basis of economies of scale is scientifically invalid. Plaintiffs' Michelson analysis aptly noted first that the conclusions reached in the June O'NeillArlene Holen article were based upon the unstated premise that the quality of education given at schools throughout the city was constant. This approach begs precisely the ultimate factual question posed by this litigation whether all children in the District school system are being given equal educational opportunity or whether some children are favored over others. If the larger schools east of the Park show substantially lower expenditures per pupil, it is of course possible that these lower expenditures may be explained by true economies of scale; but it is equally possible that they also reflect lower inputs of resources and generally inferior, thus less expensive, education. Dave O'Neill's analysis,[17] offered by defendants in response to Michelson's analysis, though it differs from Michelson's in other respects, is in agreement with Michelson that the June O'NeillArlene Holen newspaper article is facile and unreliable. The Michelson analysis, in addition to showing that the O'Neill Holen article begs the ultimate question posed by this litigation, also demonstrates that, when variables other than sizesuch as average teachers' salaries, teacher-pupil ratio, or capacity utilization are also considered, then size alone can be said to explain only somewhere between 7.5 per cent and 15 per cent of the observed differences in per-pupil expenditures for teachers' salaries. Thus defendants' initial claim that the differential is legitimate because it arises solely, or even substantially, from their alleged ability to run comparable quality schools more cheaply if they are larger has been convincingly refuted, not only by Michelson, but by their own expert as well.[18]


*854 IV
In the preceding portion of this opinion, the court has considered and rejected defendants' argument that the observed wide discrepancies in teacher expenditures per pupil favoring schools west of the Park are random and do not favor any particular racial group or economic class of children. The court has also rejected defendants' position that, even if an objective pattern of discrimination exists, it does so solely or primarily for technological reasons (i. e. economies of scale) which are beyond defendants' control and which cannot be remedied by a court order. Now the court comes to defendants' ultimate defense: that even if a pattern of unequal expenditures does exist, and even if the differential expenditures per pupil are within defendants' control, the resulting real resource differentials are nonetheless inconsequential as they relate to equal educational opportunity.
Teacher expenditure per pupil is a sum, of course, which reflects both the size of the class in which a given student finds himself and the salary paid his teacher. With regard to the average teacher salary component of teacher expenditures per pupil, defendants take the position that the different salaries paid teachers are primarily rewards for experience, and that experience has not been shown to have a significant correlation with a teacher's productivity measured by student achievement tests. The short response to this position is that defendants are seeking to reopen and relitigate an issue which has already been decided in the 1967 Hobson opinion.[19]
It is almost an affront to common sense to say, as do defendants, that a pattern of spending so discriminatory on its face as the one which exists in the District reflects no discrimination in "educational opportunity." To overcome the heavy burden against them, defendants lean in part on an argument by their expert, Dave O'Neill, that only teacher experience of six years and less has educational consequence. But even *855 if this assumption, which O'Neill admits is really an "intuitive hunch," were true, the west of the Park school is still favored in that it has a higher percentage of teachers with six years or more experience than schools in the rest of the city.[20] Moreover, as the court reads them the rather inconclusive educational studies tell us only that teachers seem to be overcompensated for experience relative to their productivity. That is, researchers consistently find some relationship between experience and achievement, though not so great as is traditionally paid for. In the absence of more conclusive studies, large differentials such as exist in the District of Columbia cannot be condoned.
Moreover, the Board cannot be allowed in one breath to justify budget requests to the Congress and to the District of Columbia City Council by stressing the connection between longevity and quality teaching, and then in the next breath to disavow any such connection before the court. Speaking before the City Council on the subject of teacher salary legislation, the chairman of the school board said:
"The Board recognizes that to achieve quality education in the District of Columbia public schools it is imperative that students must be housed in educational facilities conducive to learning and be taught by a highly motivated and well-trained teaching staff. It believes that in order to accomplish this objective, it must begin to offer a salary schedule attractive enough to retain its experienced master teachers. * * *"[21]
Under these circumstances, where teacher experience has not been proved to be unrelated to educational opportunity, where the administration itself has chosen to reward experience, and where a pattern of racial and socio-economic discrimination in expenditures continues in the District, the law requires either that experienced teachers be distributed uniformly among the schools in the system or that some offsetting benefit be given to those schools which are denied their fair complement of experienced teachers.[22]*856
*857 Defendants have also alleged that the observed variations in pupil-teacher ratios the second and larger component of the widely disparate teacher expenditures per pupilare of no consequence in terms of educational performance or opportunity. Without here going into this contention exhaustively, the court rejects it for much the same reasons as those given in the discussion of the value of teacher experience. The outside studies referred to in the Michelson and O'Neill reports are themselves inconclusive. There are so many other variables to be controlled in a study of the relationship between teacher-pupil ratio and educational product that the indefiniteness of the studies made to date is not the least bit surprising. To give only one example, the studies upon which O'Neill relies all concern achievement test results, and we do not know what the consequences of smaller class sizes might be on other measures of school outcomes. O'Neill himself has computed that "about 2/3 of the children in the D. C. system are in classes with pupil classroom teacher ratios of between 24.4 and 28.4. No empirical studies of school inputs could isolate any effect within this range of class size on educational quality."[23] But even accepting his findings arguendo, the negative implication would seem to be that a third of the children in the system, or approximately 30,000 children, are in schools outside this pupil-teacher range, and that at least some empirical studies have found a discriminatory effect outside this range. In the absence of more knowledge about the effect of class size on productivity, the large variation which still exists in the sizes of classes in the District of Columbia cannot be condoned.
In the end the court finds itself most persuaded, once again, by defendants' own words, uttered before the lawyerly rationalization process began in earnest. In his supplemental affidavit of August 12, 1970, at 5, Acting Superintendent Henley stated that the "reduction of overcrowding has produced rich benefits; the primary one is the reduction in teacher-pupil ratios [sic], which maximizes opportunities for optimum teaching and learning." And again, in the program justification for the 1972 fiscal budget we read that "class size is one of the most important factors in maximizing education achievement. As discussed above, the teacher works with individual children, and the larger the span of control, or span of instruction, within the classroom, the more difficult it is to provide optimal instruction to each child."[24] Thus do defendants put *858 themselves in the awkward position of asking to be applauded for their expensive efforts to reduce class sizes generally and of requesting funds for further reduction of class sizes under the rationale of productivity, while inconsistently maintaining for purposes of this litigation that no discrimination results when class sizes remain significantly smaller in west of the Park schools as compared with those in the rest of the city.
Plaintiffs' prima facie case of discrimination in the provision of educational opportunity, based upon the pattern of unequal expenditures which favors the schools west of the Park, is strongly buttressed by further evidence in the record concerning the results of citywide sixth grade reading achievement tests. The record shows that the west of the Park elementary schools produced an average reading achievement test score that was significantly higherindeed 2.4 grades higherthan the average for the rest of the city.[25] Obviously, these results tend to corroborate the presumption created by the pattern of expenditures that the city provides a better educational opportunity to its richer, white students. Defendants' dubious argument that the smaller classes and higher proportion of experienced teachers in the schools west of the Park do not give students there a better chance for a good education than can be had elsewhere in the city is still less convincing in the light of this testing evidence.
These achievement test results suggest that not only are the children in schools east of the Park being denied an educational opportunity equal to those west of the Park, but also they in fact are not being as well educated. Thus these test scores reflect the result of the discrimination against the east of the Park children in per-pupil expenditure. The burden of establishing that these test results reflect something other than the proven discriminatory distribution of educational opportunity falls upon defendants. And once again defendants have failed to meet their burden.
In an effort to suggest to defendants the kind of evidence they should be presenting if they were to prevail, the court ordered sua sponte on January 28, 1971 that
"defendants file in the record not later than February 15, 1971 such statistics and studies as will show the effect of the voluntary busing program on the achievement test scores of the children participating. These statistics should be on a school-by-school basis so that the improvement, if any, of the children in each receiving school may be discerned."
The court's idea in issuing this order was that a study of the improvement or lack of improvement in achievement test performance by students in the voluntary busing program, by providing a control for the factor of socio-economic background,[26] would be probative of whether west of the Park schools provide *859 a better education than schools in the rest of the city.
On February 16, 1971, however, defendants moved the court to rescind this order on grounds that it "imposes an unduly burdensome task upon the defendants and that the order will not lead to probative evidence." The gist of the memorandum in support of defendants' motion was that no systematic records of test results had been kept, and that those bused children who had been tested had been given different brands of tests for which conversion scales are unavailable thus rendering meaningful comparisons impossible. While the court does not charge defendants with a lack of candor, it does seem incredible that a school system under injunction to provide equal educational opportunity to all its students would not have shown more interest in studying the effect upon individual student achievement of a voluntary busing program which permits students to transfer from allegedly inferior to allegedly superior schools. That defendants have failed to keep any systematic records of the achievement test results of these bused students raises questions about their effectiveness as administrators, if not about their good faith as parties to this case.

V. Conclusions
Plaintiffs' motion for an amended decree and for further enforcement has now been argued and reargued via a series of motions and written memoranda for one full year. During this time the unfortunate if inevitable tendency has been to lose sight of the disadvantaged young students on whose behalf this suit was first brought in an overgrown garden of numbers and charts and jargon like "standard deviation of the variable," statistical "significance," and "Pearson product moment correlations." The reports by the experts one noted economist plus assistants for each sideare less helpful than they might have been for the simple reason that they do not begin from a common data base, disagree over crucial statistical assumptions, and reach different conclusions. Having hired their respective experts, the lawyers in this case had a basic responsibility, which they have not completely met, to put the hard core statistical demonstrations into language which serious and concerned laymen could, with effort, understand. Moreover, the studies by both experts are tainted by a vice well known in the statistical tradedata shopping and scanning to reach a preconceived result; and the court has had to reject parts of both reports as unreliable because biased. Lest like a latter day version of Jarndyce v. Jarndyce this litigation itself should consume the capital of the children in whose behalf it was brought, the court has been forced back to its own common sense approach to a problem which, though admittedly complex, has certainly been made more obscure than was necessary. The conclusion I reach is based upon burden of proof, and upon straightforward moral and constitutional arithmetic.
As has already been documented, the record now before the court shows a current differential in teacher expenditures per pupil every bit as striking as the differential in total expenditures per pupil noted in the 1967 opinion. The record also shows that this differential, which favors the schools west of the Park, has increased in percentage terms from fiscal 1970 to fiscal 1971. Today in Washington the 74 per cent white schools west of the Park enjoy a 27 per cent advantage in teacher expenditures per pupil over the 98 per cent black elementary schools in the rest of the city.
Four years after this court's first Hobson opinion, defendants have by their own admission failed to equalize the access of all students to dollar resources for teachers' salaries and benefits. Although defendants have argued strenuously that there is no proven connection between the showing that black students have unequal access to dollars and the crucial constitutional showing *860 that black students are denied equal educational opportunity, the court has found otherwise. For reasons discussed more fully above, the court has concluded that both lower class size and greater teacher experience (at least in certain ranges present in this case) contribute to the quality of a child's education. The court holds that defendants have failed to rebut plaintiffs' strong prima facie case that, despite an injunction against further racial and economic discrimination in the operation of the school system, defendants have continued to offer an education of higher quality to the white and wealthier students west of the Park as compared with the black and poorer students elsewhere in the city.
The court finds further that defendants have failed to offer the legal justification or compelling state interest necessary to overcome the presumptive invalidity of awarding benefits which affect the fundamental interests of and results in discrimination against a racial minority. Defendants argue, citing Dandridge v. Williams, 397 U.S. 471, 90 S.Ct. 1153, 25 L.Ed.2d 491 (1970), and McInnis v. Shapiro, N.D.Ill., 293 F.Supp. 327 (1968), affirmed, sub nom. McInnis v. Ogilvie, 394 U.S. 322, 89 S.Ct. 1197, 22 L.Ed.2d 308 (1969), that the rational relationship test should be applied to this case. But whatever the restrictive impact of Dandridge and McInnis on the reach of the equal protection clause with regard to the poor, the law is clear beyond doubt that, where a racial minority is treated in a discriminatory fashion, there is a presumptive constitutional violation demanding exacting scrutiny by the court and imposing a heavy burden of justification on defendants.[27]Compare James v. Valtierra, 402 U.S. 137, 91 S.Ct. 1331, 28 L.Ed.2d 678 (April 26, 1971), with Hunter v. Erickson, 393 U.S. 385, 89 S.Ct. 557, 21 L.Ed.2d 616 (1969), in which the Court specifically stated:
"Because the core of the Fourteenth Amendment is the prevention of meaningful and unjustified official distinctions based on race, * * * racial classifications are `constitutionally suspect' * * * and subject to the `most rigid scrutiny' * * *. They `bear a far heavier burden of justification' than other classifications * * *."
Id. at 391-392, 89 S.Ct. at 561. Moreover, as the cases establish, the court's duty to scrutinize alleged discrimination against a racial minority is especially high when the right of the minority affected is the right to equal educational opportunity. Brown v. Board of Education of Topeka, 347 U.S. 483, 74 S.Ct. 686, 98 L.Ed. 873 (1954); Swann v. Charlotte-Mecklenburg Board of Education, 402 U.S. 1, 91 S.Ct. 1267, 28 L.Ed.2d 554 (April 20, 1971). It is precisely the Brown requirement that public education be made available to racial *861 minorities on equal terms which plaintiffs seek to effect in Hobson. 347 U.S. at 493, 74 S.Ct. 686.
Whatever may be the differences in constitutional concern between purely de facto and purely de jure segregation, it is too late for defendants to suggest that discrimination of constitutional dimension does not arise where a school board has knowingly favored in an unjustified and substantial way predominantly white schools over predominantly black schools. Since 1967, following the rationale of Hobson, several of the circuits have rejected the rational relationship test in finding a violation of the equal protection clause where the state has acted affirmatively and where the direct effect of the challenged state action was inescapably discriminatory to the enjoyment of an important right by a racial minority. See, e. g., Hawkins v. Town of Shaw, 5 Cir., 437 F.2d 1286, 1291-1292 (1971); Kennedy Park Homes Association v. Lackawanna, 2 Cir., 436 F.2d 108, 114-115 (1970); Southern Alameda Spanish Speaking Organization v. City of Union City, California, 9 Cir., 424 F.2d 291, 295-296 & n. 9 (1970); Norwalk CORE v. Norwalk Redevelopment Agency, 2 Cir., 395 F.2d 920, 931-932 (1968); Keyes v. School District No. 1, D.Colo., 313 F.Supp. 61, 82-83 (1970). Unlike these cases, defendants here are already under an injunction to refrain from discrimination. Thus defendants' burden of justification here is greater, and the court's duty to scrutinize defendants' actions is even more exacting.

VI. The Remedy
To end this lingering invidious discrimination, it is time to find a remedy which, in the words of Green v. County School Board of New Kent County, 391 U.S. 430, 439, 88 S.Ct. 1689, 1694, 20 L.Ed.2d 716 (1968), "promises realistically to work, and promises realistically to work now." (Emphasis in original.) The remedy must be one which can be easily understood and effectuated by the school administration and which will once and for all relieve plaintiffs of the burden of coming forth to demonstrate that discrimination continues. In framing relief, the court has kept these goals in mind and has relied upon the teaching of Swann v. Charlotte-Mecklenburg Board of Education, supra, that once a right and a violation have been shown, United States District Courts have exceptionally broad equity powers to shape decrees to meet the complex problems of protecting the constitutional right of school children to equality of educational opportunity. 402 U.S. at 16, 91 S.Ct. at 1276; and see Johnson v. San Francisco, N.D.Cal., No. C-70 1131 SAW (Memorandum and Order Requiring the Parties to File Plans for School Desegregation, April 28, 1971). While accepting the Board's decision to maintain a neighborhood school system, and without requiring further mandatory busing, the court has sought to make a reality of its 1967 holding that
"if whites and Negroes, or rich and poor, are to be consigned to separate schools, pursuant to whatever policy, the minimum the Constitution will require and guarantee is that for their objectively measurable aspects these schools be run on the basis of real equality."
269 F.Supp. at 496.
Though defendants have objected strenuously to plaintiffs' suggested remedy,[28] it is significant that they have *862 proposed no remedies themselves. The recent Swann case also teaches that, in default by the school authorities of their obligation to proffer acceptable remedies for constitutional violations, a District Court has the duty and the power to frame a remedy itself. 402 U.S. at 15, 91 S.Ct. at 1276. For reasons already discussed, the court finds that plaintiffs' initially requested relief requiring equalization of total expenditures per pupil across the system would sweep too broadly and would require the school administration to equalize some inputs which have little or nothing to do with educational opportunity. But upon careful consideration, the court does find that the equalization order approach is a good *863 one, provided it is focused upon expenditures per pupil for teachers' salaries and benefits, so as to cover only inputs which do have a direct bearing on the quality of a child's education.
Having found continuing substantial discrimination, the court cannot agree with defendants' expert that an equalization order would amount to "much ado about nothing."[29] Defendants stress that implemenation of the proposed order would result merely in an increase of $3.39 per black child across the city.[30] But looked at from the perspective of individual disadvantaged schools and children, the impact of the observed unequal spending is seen to be very serious indeed. Defendants' figure of $3.39 per child masks the fact that some individual black schools are shockingly far below the citywide average expenditure per pupil level. Thus, to take one of many possible examples, if teacher expenditures per pupil in fiscal 1971 at the Draper School (actually $362) had been at the citywide average ($497), they would have increased by $135 per pupil. The increase in total teacher expenditures would then have been approximately $147,000. Under salary scales currently in effect, this would have permitted the addition of perhaps 15 new teachers at Draper. This addition would have reduced the pupil-teacher ratio from the present 25/1 to 18/1.[31] Even defendants' expert seems to concede that such a reduction has a beneficial effect on school outcomes when measured by achievement test scores.
A review of relevant cases reveals that many courts have ordered equalization of per-pupil expenditures in all schools within a single school district, and that such an order provides a judicially manageable standard. See, e. g., Kelley v. Altheimer, 8 Cir., 378 F.2d 483, 499 (1967); United States v. Jefferson County Board of Education, 5 Cir., 372 F.2d 836, 899-900 (1966), affirmed per curiam on rehearing en banc, 380 F.2d 385, cert. denied, 389 U.S. 840, 88 S.Ct. 67, 19 L.Ed.2d 103 (1967); United States v. Plaquemines Parish School Board, E.D.La., 291 F.Supp. 841, 846 (1967), affirmed as modified, 5 Cir., 415 F.2d 817 (1969); Hill v. LaFourche Parish School Board, E.D.La., 291 F. Supp. 819, 822-823 (1967); Lee v. Macon County Board of Education, M.D. Ala., 267 F.Supp. 458, 488-489, affirmed, sub nom. Wallace v. United States, 389 U.S. 215, 88 S.Ct. 415, 19 L.Ed.2d 422 (1967). And see also the Department of Health, Education and Welfare Memorandum to Chief State School Officers: "Subject: Advisory Statement on the Development of Policy on Comparability," regarding implementation of the 1970 amendments to the Elementary and Secondary Education Act, September 18, 1970, page 7 et seq.
Under all these circumstances, the court believes it should now use its broad equitable powers to set a standard for expenditures which will not interfere with the successful operation of the school system but which will ensure that it operates in a substantially nondiscriminatory fashion.
Wherefore it is ORDERED, ADJUDGED and DECREED that
1. On and after October 1, 1971, per-pupil expenditures for all teachers' salaries and benefits from the regular District of Columbia budget (excluding Title I ESEA funds, UPO funds, and, in general, all funds not from the regular congressional appropriation) in any single elementary school (not "administrative unit") shall not deviate by more than five per cent from the mean perpupil *864 expenditure for all teachers' salaries and benefits at all elementary schools in the District of Columbia school system as that mean is defined in this paragraph. The five per cent limit may be exceeded only for adequate justification on an individual school basis shown to this court in advance. "Adequate justification" shall include provision of compensatory education for educationally deprived pupils at certain schools or provision of special educational services for the mentally retarded or physically handicapped at certain schools or for other "exceptional" students. It shall also include a showing that variance above or below the five per cent limit is accounted for solely on the basis of economies or diseconomies of scale. For purposes of this order, the "mean" shall be computed after excluding from the computation total expenditures for all teachers' salaries and benefits and total average daily membership at all schools for which permission to exceed the five per cent limitation because of compensatory education or education of "exceptional" students is sought and granted.
2. By October 1, 1971, by June 1, 1972, and by October 1 of each succeeding year thereafter, defendants shall serve on plaintiffs and file with the clerk of this court information sufficient to establish compliance with this order for equalization of per-pupil expenditures for all teachers' salaries and benefits. At a minimum, such information shall include, in tabular form for every elementary school (not administrative unit), data in the following categories: (a) Name of school; (b) income level of the neighborhood from latest available United States census data; (c) average daily membership; (d) total number and percentage of students of each race as of a date not more than 30 days preceding the filing deadline; (e) building percentage over- and undercapacity and surplus or deficit of seats based on data filed in answer to category (c) above; (f) total number of teachers (for purposes of this calculation the only teachers to be included shall be those whose salaries and benefits are included in items (j) and (k) below); (g) pupil-teacher ratio (item (c) divided by item (f)); (h) total operating expenditures from the regular District of Columbia congressional appropriation only; (i) per-pupil operating expenditures from the regular District of Columbia congressional appropriation only; (j) total expenditures for all teachers' salaries and benefits from the regular District of Columbia congressional appropriation only; (k) per-pupil expenditures for all teachers' salaries and benefits from the regular District of Columbia congressional appropriation only; (l) total expenditures from impact aid funds; (m) per-pupil expenditures from impact aid funds; (n) total expenditures under Title I of the Elementary and Secondary Education Act of 1965; (o) per-pupil expenditures under Title I of ESEA; (p) total expenditures from UPO funds; (q) per-pupil expenditures from UPO funds; (r) total expenditures from all sources; (s) per-pupil expenditures from all sources.
The tabular form shall also include the mean as defined in paragraph 1 above, together with the upper and lower dollar bounds from that mean computed by adding to and subtracting from that mean five per cent of that mean.
3. In each report filed and disseminated pursuant to the requirements of paragraph 2 above, there shall be prominent and specific identification of the respects, if any, that the methods of computing the data in that report differ from the methods used in computing the comparable data for the preceding year.
4. At some future time, the Board and the school administration may adopt specific, measurable and educationally justifiable plans which are not consistent with the present order. At such time, upon a prima facie showing that the plans are reasonably designed in substantial part to overcome the effects of past discrimination on the basis of socio-economic and racial status, the court may modify the present order.
NOTES
[*]   Sitting by designation pursuant to 28 U.S.C. § 291(c).
[1]  See the discussion of law in text at pages 859-861 and Note 22 infra.
[2]  Affidavit of Julius W. Hobson, December 2, 1970, at 4.
[3]  On July 6, 1970, defendants opposed plaintiffs' amended motion. Defendants filed a motion of their own to vacate the decree of June 19, 1967 and to dismiss the original complaint, which plaintiffs in turn opposed on July 14, 1970, asking for judgment on the pleadings. In the memorandum of points and authorities filed in support of their opposition and motion of July 6, defendants contended that "the extent of integration of faculties and demountables to relieve overcrowding is not believed to have had a substantial impact on the 1967-68 per pupil expenditure figures as it would have on later years." To check this contention, the court, by order filed July 16, 1970, required defendants to file by August 10, 1970 certain categories of expenditure data for the 1970 fiscal year and to detail their compliance with that part of the court's 1967 opinion calling for compensatory education to de facto segregated schools. Matter responsive to this order was filed by defendants on August 10 and 12, 1970, in the form of an affidavit and a supplemental affidavit of Benjamin J. Henley, Acting Superintendent of Schools, and three volumes of exhibits. On August 12, 1970, the court sua sponte required defendants to develop and to file with the court certain tables displaying family income and per-pupil expenditures for fiscal 1970, as well as a calculation of the statistical correlation between deviations from mean per-pupil expenditure out of regular funds and deviations from mean 1959 median family income.

On August 17, 1970, plaintiff moved for production of additional information, which motion defendants opposed. By order filed August 31, 1970, the court granted plaintiffs' motion in part, denied it in part, and established a schedule for memoranda responding to exhibits previously filed and under order soon to be filed. The court's order of August 31 directed defendants to file in the record, inter alia, "projected per-pupil expenditure out of regular funds for teacher services rendered at each public elementary school in the District of Columbia for the school year 1970-71, as well as the per-pupil expenditure out of regular funds for teacher services rendered at each public elementary school in the District of Columbia during the school year 1969-70."
On the following day, September 1, 1970, in a memorandum opinion and order, this court stated:
"The best data now available to this court indicates that there still is a substantial differential in per-pupil expenditure which favors the elementary schools west of the Park. The area west of the Park is the richest in the District. The elementary school population of that area is also the whitest in the city. * * * A prima facie case of violation of the 1967 decree seems to have been made out. * * *"
(Footnotes omitted.)
In response to plaintiffs' May 19 proposal for further relief, defendants had urged that there were fundamental reasons, for the most part beyond the school system's control, which contributed to the alleged expenditure disparities and would make adherence to a 5% range of variation a devastating and unjustified burden on their management of the school system. Of the reasons given by the school board for variations in expenditures, some seemed truly to be beyond their control. Examples are differences in the amount and cost of vandalism occurring at different schools, in the age of different school buildings and the consequent cost of upkeep, and in the size of school plants and consequent variations in cost of opperations attributable to economies of scale. Without precluding defendants from introducing more precise and updated figures about expenditures or from rebutting the prima facie case of violation of the 1967 decree based on the figures then in the record, the court therefore sought to focus the attention of the parties on those aspects of school management which appeared to contribute substantially to the apparent disparities in per-pupil expenditure and which also appeared to be within defendants' control. In its September 1 memorandum opinion, the court ordered that defendants
(1) "indicate, by memorandum filed in the record in this case, why the school board should not devise a plan to equalize within a five per cent variation expenditures for teaching costs out of regular funds among all District of Columbia elementary schools for the 1971 fiscal year." and
(2) "indicate, by memorandum filed in the record in this case, why busing of pupils from low-income area, overwhelmingly black, overcrowded schools in the District to high-income area, whiter and underpopulated schools would not eliminate unnecessary differences in per-pupil expenditures relating to over- and undercrowding, which defendants concede to be one of the causes of the lingering and spectacular inequality in overall per-pupil expenditures."
Pursuant to the order of August 31, 1970, defendants filed enrollment-capacity data and racial data for each elementary school as of September 21, 1970. In accord with defendants' motion, the court amended its orders of August 31 and September 1, 1970 to require further exhibits on November 2, 1970 and the show cause memorandum by defendants relating to overcrowding and teaching costs on November 16, 1970. Defendants subsequently filed on November 2, 1970 exhibits dealing with teaching status, race, experience, actual per-pupil costs for teacher expenditures for fiscal 1970, and projected per-pupil costs for teacher expenditures for fiscal 1971. Defendants filed further data in the record on November 6, 17 and 27, 1970. On November 17, 1970, defendants also filed their show cause memorandum relating to overcrowding and teaching costs. Plaintiffs filed a memorandum responding to defendants' exhibits and show cause memorandum on December 8, 1970, along with affidavits by Julius Hobson and Stephan Michelson, Research Associate at the Center for Educational Policy Research, Harvard University. Defendants have filed a reply memorandum to the court, along with a separate analysis of variation in teacher expenditures per pupil among District elementary schools by Dave M. O'Neill, Burton Gray and Stanley A. Horowitz, on January 18, 1971. At the court's request, plaintiffs filed a rebuttal memorandum to the O'Neill report on February 11, 1971. Defendants filed a rejoinder memorandum on March 9, 1971.
Finally, and in response to a March 15, 1971 order of the court, counsel for the parties conferred; in lieu of proposed findings of fact, they subsequently submitted seven joint memoranda, supplemented by other separate memoranda where agreement was not possible, stipulating to the basic facts upon which this opinion is grounded.
[4]  In the course of this litigation, the court has shifted the focus of attention of the parties from total expenditures per pupil to expenditures per pupil for teachers' salaries and benefits, or "teacher expenditures per pupil." For the reasons, see the 4th paragraph of Note 3, supra.
[5]  Rock Creek Park itself runs the length of the city from north to south, and sets off the area to its west, roughly a fourth of the city, as a discrete geographic entity. The Park serves as a natural boundary for school attendance zones and makes cross-park districting, at least without mandatory busing, impractical. The area west of Rock Creek Park has been and continues to be by general agreement not only the most wealthy but also the only predominantly white section of Washington.
[6]  The percentage racial breakdown for 1971 comes from Joint Stipulation S-14. Joint Stipulation S-5 shows that in 1970 west of the Park schools were 77% white, while schools in the rest of the city were 98% black. The record before the court contains various indices of the economic status of different regions of the District of Columbia measured in several different years. All indices in all years show that the region west of the Park is by far the wealthiest in the city. With regard to the relative economic status of the Anacostia area vis-à-vis the area west of the Park, see the affidavit of Edward M. Brooks, former director of the Research Division of the United Planning Organization, in "Defendants' Further Separate Memorandum on the Relevance and Materiality of the Various Indicia of Wealth by Regions of the City," May 3, 1971. During 1968 and 1969 Mr. Brooks helped develop for UPO a poverty index for the District of Columbia which has the advantage that it can be updated annually on the basis of locally generated data. The latest available data using the UPO index is for 1968. In his affidavit Mr. Brooks states that "the six most affluent tracts in the city were West of Rock Creek Park, and, further, all of the tracts West of the Park were more affluent tha[n] any tract East of the Anacostia River." Like the west of the Park area, Anacostia is physically separated from the rest of the city by a geographical boundarythe Anacostia River. Anacostia has 37 elementary schools and a population of approximately 35,000 students. Defendants' Separate Memorandum re Tables S-17, 18, 19, and 20, April 27, 1971, at 2.
[7]  These data are taken from Joint Stiputions Nos. S-1, S-2, S-6 and S-7. The data base used includes kindergarten and prekindergarten students, special teachers, and counselors and librarians. Ideally, the court would have preferred to separate out counselors and librarians from teachers, but separate data for teachers only was unavailable in fiscal 1970, and the court wished above all to use the same data base in comparing pupil-teacher ratios, average teacher costs, and expenditures per pupil for teacher costs in fiscal 1970 and fiscal 1971.
[8]  See the discussion of law in text at pages 859-861 and Note 22 infra.
[9]  Joint Stipulation S-14.
[10]  Joint Stipulation S-16.
[11]  Defendants' Memorandum to the Court, November 17, 1970, at 20.
[12]  See Note 5 supra and Hobson v. Hansen, 269 F.Supp. 401, 410 (1967).
[13]  Defendants' Revised Submission to the Court, November 6, 1970, and Joint Stipulation S-6.
[14]  20 U.S.C. §§ 241a and 241e (1964), as amended by Public Law 91-230, § 109 (a), 91st Cong., 2d Sess., April 13, 1970. And see Memorandum to Chief State School Officers: "Subject: Advisory Statement on the Development of Policy on Comparability," September 18, 1970.
[15]  The article reads in part as follows:

"Large schools have relatively low expenditures per pupil and small schools have higher expenditures. This is just what would be predicted by the time-honored principle of economies of scale, which describes the general tendency of costs per unit of outputin this case, one child's educationto fall as the scale of operationin this case, the size of schoolincreases.
"Schools west of the park are smaller, 305 pupils per school on the average. Schools east of the park are newer and larger, 744 pupils per school on the average. The principle of economies of scale then, would lead one to expect higher expenditures west of the park where the schools are so much smaller. Such a differential need not reflect discriminatory practices.
"An appropriate comparison is made in the accompanying chart. When schools of equal size are compared, it is clear there are no significant east-west differences. If anything, schools of the same size east of Rock Creek have somewhat higher per-pupil expenditures than their western counterparts. The figures used here are D. C. expenditures only, and do not include federal Title I or impacted area funds.
"It is also striking that expenditures per pupil consistently decrease as the size of school increases. And this happens on both sides of the park.
"The reason for this phenomenon of declining costs, which is widely recognized in industry, is the greater spreading out of high fixed costs over more pupils in the larger schools. For example, school principals get similar salaries, but in larger schools the principal's salary cost per pupil will be much lower. This greater spreading out of costs applies to all those items in the school budget which cannot be provided in direct proportion to the number of pupilsadministrative costs, building and maintenance costs, library, special teacher and guidance services, etc."
[16]  Defendants' Memorandum to the Court, November 17, 1970, at 23. "Size" is defined as the number of pupils in attendance, not in terms of the physical dimensions of the building.
[17]  The two O'Neills should not be confused. June, the wife, wrote her Washington Post article on economies of scale first. Dave, the husband, appeared later, as defendants' expert.
[18]  June O'Neill, of course, had written in October about economies of scale in total expenditures per pupil. Dave O'Neill focuses, as the court had suggested in September, on teaching costs alone. As to the first component of teaching costaverage teacher salaryDave O'Neill finds there can be economies of scale. According to Dave O'Neill, variation in average teacher salary with size reflects "only the fact that old teachers tend to be in old (and therefore small) buildings." He criticizes the Michelson technique quite convincingly when he writes that "the fact that there is a built-in negative correlation between average teacher salary and school size has introduced much confusion into * * * previous discussions." Dave O'Neill does find, however, that the second component of teaching costsclass sizemay be subject to economies of scale, although "there will always be the problem that larger classes in the larger schools could result in both lower costs and lower quality." It is thus only for special teachers that absolutely untainted economies of scale may be possible. Small schools everywhere in town tend to have more special teachers than large ones; and because special teachers in small schools tend to be itinerant, the time they spend traveling may mean that students in large schools receive just as much classroom time per special teacher as students in small schools do. If this is true, Dave O'Neill concludes, "then it would appear that, as between sides of the park, significant differentials in the quality of schooling do not emanate from the [special teacher] differential." Although interesting, Dave O'Neill's economies of scale argument is speculative and unproved. At the moment, we cannot know how much of the existing variation in expenditures for special teachers is absolutely necessary because of economies of scale and how much could have been eliminated by more economical scheduling of special teachers. And even if Dave O'Neill's theory is correct, it would only explain away that part of the differential in teacher expenditures per pupil which relates to special teachers. Without prejudging this issue, the court will note at this point that an equalization order could be framed in such a way as to leave open exceptions to the permissible range of variation where defendants can prove that these were due purely to economies of scale. With respect to reporting special teacher expenditures per pupil, this court in any future studies will require that the salaries of special teachers who teach at more than one school be prorated among the schools according to the time spent at each school.

Although plaintiffs and defendants now seem to be in agreement that economies of scale are quite small, the question still arises whether they might be sufficiently large to account for teacher expenditures per pupil outside the requested 5% equalization range in a small number of exceptionally large or small schools. The question, of course, is not how much variation in teacher expenditure per pupil is explained by size, but rather what might be the magnitude in dollars and cents of the economies of scale factor. The Michelson analysis concluded that a 5¢ per child scale economy was possible, and this led to the realization that schools more than 1,000 pupils different in size might have scale economies accounting for teacher expenditure per pupil differentials outside the 5% range. But this finding, of course, goes to the viability of the proposed remedy, and not to the early and clearly unfounded claim of defendants that the observed discrepancies were legitimately accounted for on the basis of economies of scale. I shall come back to the secondary question in the remedy section.
[19]  volunteered the information, confirmed by the Task Force report, that teachers in the `older schools with stable or declining enrollments,' namely, the white elementary schools west of the Park, have had significantly greater teaching experience than the faculties at the Negro elementary schools. * * * Defendants, however, denigrate the significance of this attribute, picturing the young teacher fresh from the university who may predictably turn in the superior teaching performance. All this may be true, but it remains beyond denial that, other factors equal, experience is a real asset for a teacher, as it is for any professional. The Washington school system's pay scale, in proportioning salary to the number of years of teaching experience, is a testimonial to this fact. Moreover, it cannot be questioned that the initial few years of teaching make an enormous contribution to a teacher's competence. A superior percentage of teachers at the predominantly (85-100%) white schools, the Task Force report shows, have these vital first years of experience to fall back on. * * *"
269 F.Supp. at 434-435.
[20]  O'Neill Analysis at 9. Moreover, even accepting O'Neill's "intuitive hunch" arguendo, his own analysis, Table 3 at 16, shows that 68.3% of the teachers west of the Park, but only 60.4% of the teachers east of the Park, are "highest quality" as judged by the standard of six years or more of experience.
[21]  Statement of Mrs. Anita F. Allen, Chairman, Committee on Teachers' Salary Legislation, District of Columbia Board of Education, Before the City Council Regarding Teacher Salary Legislation, October 31, 1969, at 5. "First, the massive turnover rate of teachers must be stopped. And the District of Columbia schools can no longer afford to be a training ground for neighboring suburban school districts." D. C. Police, Firemen and Teachers' Pay Legislation Hearings before the Subcommittee on Fiscal Affairs of the Committee on the District of Columbia, United States Senate, on S. 1511, S. 2102, S. 2623, S. 2659 and S. 2679, November 15, 1967 and February 14, 1968, Statement of Dr. William R. Manning, Superintendent of Schools, District of Columbia Board of Education, at 119.

The other major component of teachers' salaries is graduate degrees obtained, and it is interesting to note that defendants do not allege inapplicability of this criterion, although it has fared less well than teacher experience in the studies which have been run to determine what makes a difference for pupil achievement. From defendants' submission "Degrees Held by TeachersOctober 20, 1966," revised in pencil to October 16, 1969, plaintiffs have calculated that 21.6% of the teachers west of the Park have master's degrees or higher, while only 11.8% of teachers in Anacostia are similarly qualified. The court also notes that under the administration's salary scale, expenditures attributable to experience alone are not completely separable from those attributable to degree status. For these reasons, it would be impossible to frame an equalization order which excludes solely longevity pay.
[22]  At the same time they argue that the longevity component of teachers' salaries is unrelated to the effectiveness of their performancean argument which I reject for the reasons outlined abovedefendants seek to justify the current spending pattern and to prove themselves innocent of discriminatory intent by giving several alternative reasons why a policy which rewards longevity might be employed. In this regard, defendants seek first to "explain" the presence of the most experienced and most educated teachers in the schools west of the Park as being merely "historical." As the O'Neill analysis puts it, "old teachers tend to be in old (and therefore small) buildings," and it happens that the oldest buildings are west of the Park. The very fact that defendants would make this argument at this stage of the Hobson litigation indicates a misunderstanding of the 1967 opinion and the nature of plaintiffs' complaint. In 1967 this court found that defendants in their operation of the school system were in at least some important respects intentionally discriminating against poor and black children. Active discrimination was found in the use of optional zones and in the assignment of teachers to schools on the basis of race. The ensuing injunction against further discrimination necessarily required defendants to take an active role in undoing whatever discrimination then existed in the system as well as in refraining from further discrimination in the future. If the inequalities in access to important educational resources, demonstrated by plaintiffs in this second phase of the litigation, are not the product of a continuing disciminatory intent by defendants, then they are at the very least the product of a "freezing in" of earlier discrimination. As the Fifth Circuit has stated in Henry v. Clarksdale School District, 409 F.2d 682, 688 (1969), "a relationship otherwise rational may be insufficient in itself to meet constitutional standardsif its effect is to freeze-in past discrimination." The present unequal distribution of experienced teachers in the District of Columbia school system, clearly favoring the white and wealthier children west of the Park, can by no means, therefore, be justified at this time on the ground that the causes of this distribution pattern are "historical."

In addition to their attempted historical justification, defendants maintain that there are at least three sound theoretical economic reasons why length of service might be compensated in excess of its associated productivity increases. According to defendants:
"(1) Turnover costs supply a rationale for an age-earnings profile that starts with earnings below productivity and, as experience accumulates, begins to pay wages in excess of productivity. * * *
"(2) The market for teachers' services has a supply side as well as a demand side. Union pressures are another possible explanation for salary patterns. If more experienced teachers control the union, they will use negotiations to get high salaries for themselves relative to new teachers. * * *
"(3) A third reason why the relative pay of experienced teachers may be higher than their relative productivity has to do with costs which are the same for all teachers, regardless of experience. Examples of such costs are hiring costs and the cost of providing a classroom for the teacher. * * *"
Any worry that shifts in teaching personnel necessitated by an equalization order "would breach the contract which has been effected with the Washington Teachers Union" (Benjamin Henley, Acting Superintendent of Schools, Supplemental Affidavit of August 12, 1970) is quickly allayed by reference to the contract itself which provides that "the fundamental transfer policy shall take into consideration the following factors: * * * legal requirements as ordered by the courts or Congress" and that "if any provision of this Agreement is or shall at any time be contrary to law, then such provision shall not be applicable or performed or enforced, and substitute action, if any, shall be subject to appropriate consultation and negotiation between the parties." Article IV B and Article XXII A respectively. The other alternative reasons offered by defendants for rewarding experience without regard to productivity smack of post hoc rationalization, are extremely speculative, and are essentially makeweights. Without pursuing them in detail in this opinion, the court rejects them.
When this court held in 1967 that "if whites and Negroes, or rich and poor, are to be consigned to separate schools, pursuant to whatever policy, the minimum the Constitution will require and guarantee is that for their objectively measurable aspects these schools be run on the basis of real equality, at least unless any inequalities are adequately justified," the phrase "adequately justified" was included primarily so as not to preclude unequally large inputs for systematically deprived children denied the benefit of an integrated education lauded so highly in Brown v. Board of Education of Topeka, 347 U.S. 483, 74 S.Ct. 686, 98 L.Ed. 873 (1954); that is, while setting a minimum standard, the court did not wish to preclude the school administration from focusing, if it saw fit, on equality of output, in terms of giving each student an equal opportunity to attain his own unique potential, rather than on equality of inputs. But the minimum required was that there be an equality of imputs in terms of objective resources. Under injunction to refrain from further discrimination, defendants have failed to comply with this "minimum." The court having found that an unequal distribution of the most experienced and highly paid teachers in favor of the predominantly white west of the Park area does favor this area as well in educational opportunity, no excuse for this continuing racial discrimination short of a "compelling state interest" is worthy of this court's attention at this late date in the history of the case.
[23]  O'Neill Analysis at 37.
[24]  "* * * Furthermore, as the overall pupil-teacher ratio increases, it becomes increasingly difficult to provide classes at all grade levels in small schools, and to balance out variations in student population in all schools, without resorting to some oversized classes. Under the current pupil-teacher level of 25:1, there are variations in class size of from ten to forty-five students, with over five hundred classes between thirty and forty-five students. A second teacher is assigned to some of the classes with over forty students." Fiscal Year 1972 Operating Budget Approved by the District of Columbia Board of Education, at 01-12a. In the same document, under the heading of "Alternative II, `Minimal Needs Budget,'" we read: "Under this level of funding the present pupil-teacher ratio of 25:1 would be maintained. In addition, a pupil-teacher ratio of 20:1 would be established in thirty Target Schools, where the pattern of academic achievement is most deficient." Ibid.
[25]  The court has made this calculation from 6th grade reading scores which were part of the output of tests given in grades 3 through 9 during September 1970. The results of these tests were provided by Mr. Robert B. Farr, Director of the Pupil Appraisal Division, and are listed in the O'Neill Analysis at 52.
[26]  In an effort to diminish the discrimination against children in overcrowded schools east of the Park, this court in its 1967 decision ordered the Board to bus, on a voluntary basis, the primarily black and poor children from the overcrowded schools to the underpopulated, predominantly white and nonpoor schools west of the Park. Several thousand children have been participating in the program during the past three years. Achievement test results from these children taken before they left the sending school compared with their annual test results at the receiving schools would have provided an indication, at least, of any discrepancy in the quality of education available at the schools on one side of the Park vis-à-vis the other side.
[27]  Both Dandridge and McInnis involved challenges to programs of statewide application. In McInnis a three-judge court upheld a statewide educational resource allocation formula which permitted school districts with a higher dollar value of taxable property per pupil to raise more money to support education than poor school districts. In addition to the crucial distinction that neither Dandridge nor McInnis involved allegations of racial discrimination, the court also notes that McInnis did involve the difficult problem of balancing a request for inter-district equality against a rational justification of inequality based upon the existence of local, inter-district diversity and the need for autonomy as among local political subdivisions. The Hobson case is easier because it involves a single district and a request for intra-district equality only. In granting plaintiffs' request for relief, the court follows what has been the law of the land at least since Plessy v. Ferguson, 163 U.S. 537, 16 S.Ct. 1138, 41 L.Ed. 256 (1896). See Wertz, Equal Opportunity in the Allocation of Public School Faculties, 39 Geo.Wash.L.Rev. 341, 365-366 (1971). For a list of decisions by other courts requiring intra-district equalization see text at page 863 infra. See generally J. Coons, W. Clune & S. Sugarman, Private Wealth and Public Education (1970).
[28]  Defendants oppose an equalization order on several grounds: (1) Defendants argue first that imposition of an equalization plan would conflict with the Academic Achievement Project, commonly known as the "Clark Plan" after its originator, Dr. Kenneth Clark. But the Clark Plan, it must be remembered, would reward teachers, not schools. If in one year a certain school has more than its share of superior teachers, the most obvious way to compensate poorly performing schools, without destroying incentives to teachers, would be to distribute the superior teachers equally throughout the system. This is the basis of school equalization, and it is manifestly compatible with redefining the criterion of teacher "quality" which, as this court understands it, is essentially all that the Clark Plan is designed to do.

(2) A related objection by defendants is that the proposed order would require mass teacher transfers and force upon black school children teachers who, despite long experience in white schools west of the Park, are either unsuited or disinclined to teach in a "ghetto school." Whether the school administration chooses to redefine the criterion of teacher "quality" or to stick by its current system of rewarding more experienced teachers on the assumption that they are better, quality teachershowever identifiedshould be distributed equally across the system. If, however, such distribution proves impractical, the proposed order is sufficiently flexible to permit alternative approaches to the problem of providing equal opportunity measured by objective inputs. If spreading the most highly paid teachers equally around the school system were in fact to prove the "devastating requirement in terms of personnel transfers and assignments" that defendants now fear, then, as has already been suggested in this court's show cause order of September 1, 1970, the "schools which do not have their share of such teachers [could instead] be compensated with a corresponding benefit." Both lower class size and higher teacher experience (at least in certain ranges) have a positive effect upon educational productivity. At the moment, the only way known to measure how much of one compensates for a loss in another is by their price. There is no doubt about the school department's right to assign a teacher to a school. However, if in practice teachers do not react well to this kind of policy, the compensatory policy is still viable. Children in poor schools can be compensated for not having equivalent quality teachers by having more teachers and thus smaller classes.
(3) Defendants have also attempted to demonstrate that the proposed equalization order would amount to "much ado about nothing." Even if blacks would gain from the Hobson proposal, defendants argue, the overall gain would be small. "The expenditure differential between all Negro and all non-Negro pupils comes to $67.54." But "since Negroes comprise 95% of all students * * * an equalization order would have the effect of raising expenditures of the average Negro student by only $3.39." The flaw in this reasoning is discussed in text at page 863 infra. Defendants also state that an equalization order would mean deprivation of current resources for some poor students. According to defendants, approximately 40% of the free lunch students, or over 13,000 students, would suffer a withdrawal of educational resources since they are in schools which would fall above the 5% equalization mark. From the court's perspective this particular argument is a red herring, whether or not defendants' figures, which plaintiffs challenge, are correct. Once a finding of significant variations in expenditures is made, and once a finding is also made that these variations adversely affect the poor and black children in attaining their right to equal educational opportunity, it is wrong to dwell on citywide gains and losses or upon correlations or averages. The existing discrepancies in teacher expenditures per pupil at particular schools have very severe consequences for the students attending these schools, as has been demonstrated in text at page 863 infra. All considered, the court cannot agree with defendants that plaintiffs are seeking an "artificial, meaningless symmetry of expenditure figures." What plaintiffs have been denied and are now seekingequal access to objectively measurable educational inputs is simply the very minimum they are entitled to under the Constitution.
Having considered defendants' objections to equalization carefully, the court rejects them as being without merit.
[29]  O'Neill Analysis at 38.
[30]  Ibid.
[31]  These calculations are based upon the most recent data at the court's disposal. The calculations include kindergarten and prekindergarten students and regular and itinerant teachers, but exclude counsellors and librarians.
