EASTERBROOK, Circuit Judge.
Does the Individuals with Disabilities Education Act, 20 U.S.C. §§ 1400-87, entitle a local school district to reimbursement from the state for some or all of the expense when the district must reimburse parents for a child’s private education? A court may direct a school district to pay for private education “if the court ultimately determines that such placement, rather than a proposed iep [individualized education program], is proper under the Act.” Burlington School Committee v. Massachusetts Department of Education, 471 U.S. 359, 369, 105 S.Ct. 1996, 85 L.Ed.2d 385 (1985). Such an order was entered in both of the cases now on appeal. Magistrate Judge Denlow, presiding by consent under 28 U.S.C. § 636(c), concluded that Oak Park’s school district had made so many procedural and substantive errors in preparing an iep for Kelly E. that her parents are entitled to reimbursement for private education. 21 F.Supp.2d 862 (N.D.I11.1998). District Judge Moran enforced an administrative decision that T.H.’s parents are entitled to reimbursement for an intensive home-based educational program. 55 F.Supp.2d 830 (N.D.I11.1999). Both school districts have accepted these decisions; the only remaining dispute is whether the state must chip in. Our cases appear to be the first to present that question to a court of appeals.
The magistrate judge directed the state to pay for Kelly E.’s private education and half of her parents’ legal expenses. He gave two principal reasons. 21 F.Supp.2d at 883, reconsideration denied, 1999 WL 91899, 1999 U.S. Dist. Lexis 1612. First, he viewed the state as a guarantor of every local school district’s compliance with the Act, and therefore responsible for part of the cost. Second, he concluded that state statutes and regulations offering to pay for private placements at approved schools are not generous enough to comply with Florence County School District v. Carter, 510 U.S. 7, 114 S.Ct. 361, 126 L.Ed.2d 284 (1993), which the magistrate judge understood as calling for state reimbursement of local districts’ expenses for private education. Illinois law provides (105 ILCS 5/14-7.02):
A school district making tuition payments pursuant to this Section is eligible for reimbursement from the State for the amount of such payments actually made in excess of the district per capita tuition charge for students not receiving special education services....
If a child has been placed in an approved individual program and the tuition costs including room and board costs have been approved by the Review [934]*934Board, then such room and board costs shall be paid by the appropriate State agency subject to the provisions of Section 14-8.01 of this Act.
An implementing regulation adds: “A program not approved in accordance with the requirements of this Part shall not be used by school districts to serve students with disabilities under Section 14-7.02 of the School Code.” 23 Ill. Adm. Code § 401.10. This means that a non-approved program is ineligible for reimbursement under § 14-7.02, not that such a program “shall not be used” at all.' Still, the magistrate judge thought that the statute and regulation steered school districts away from placements that might be educationally best for students, and toward either continued education in the public schools or approved private placements that were educationally less desirable (but cheaper for the local school districts). To counteract this incentive, the magistrate judge directed the state to pay for half of Kelly’s education even though state law does not authorize the outlay. By contrast, the district judge in T.H. declined to order the state to contribute toward the cost of the home education. The judge explained: “If the [Palatine school] district was concerned about its ability to recoup expenses in excess of the district per capita tuition charge for students not receiving special education services, see 105 ILCS § 5/14-7.02, it could have worked harder to develop an appropriate placement that was approved by the state.” 55 F.Supp.2d at 847. Judge Moran disagreed with the magistrate judge’s conclusion that the state must either ensure local districts’ compliance or insure their compliance costs.
Illinois, as appellant in the Oak Park case and appellee in the Palatine case, leads off with a flurry of objections to the very possibility of litigation. Local school districts lack standing, the state insists; if they suffer injury in fact, they do not meet prudential standards for adjudication; and if the local districts may sue, still the state is not a proper defendant given the eleventh amendment. None of these arguments was presented in the district court — though if they establish an absence of subject-matter jurisdiction we must consider them anyway. But they are feeble, individually and collectively.
Although, as Illinois stresses, the school districts are not the persons for whose benefit the Act is designed, they have been injured in fact by the need to pay for Kelly E.’s and T.H.’s private education. Although the injury may not be traceable to acts of Illinois, in seeking to recover part of their outlay the school districts are asserting a claim for contribution. Federal courts regularly resolve disputes about contribution. E.g., McDermott, Inc. v. AmClyde, 511 U.S. 202, 114 S.Ct. 1461, 128 L.Ed.2d 148 (1994); Akzo Nobel Coatings, Inc. v. Aigner Corp., 197 F.3d 302 (7th Cir.1999). Until now, no one has expressed doubt that cross-claims among joint wrongdoers present cases within the scope of Article III. Perhaps the Act does not authorize awards of contribution, but a party’s failure to establish a claim for re lief differs from a deficiency in subject-matter jurisdiction. Steel Co. v. Citizens for a Better Environment, 523 U.S. 83, 89-90, 118 S.Ct. 1003, 140 L.Ed.2d 210 (1998); Bell v. Hood, 327 U.S. 678, 682, 66 S.Ct. 773, 90 L.Ed. 939 (1946). Recast as a claim that local districts do not fall within the zone of interests protected by the Act and thus lack “prudential” standing, the state’s position fares no better, if only because we have held, see United Transportation Union v. Surface Transportation Board, 183 F.3d 606, 611 (7th Cir. 1999) (citing cases), that prudential considerations in general, and the zone-of-interests test in particular, are forfeited if not presented in a timely fashion. Illinois asks us to overrule this line of cases, but we decline; requiring litigants to raise zone-of-interests arguments at an early opportunity is compatible with, if not compelled by, decisions of the Supreme Court. See, e.g., Air Courier Conference v.
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EASTERBROOK, Circuit Judge.
Does the Individuals with Disabilities Education Act, 20 U.S.C. §§ 1400-87, entitle a local school district to reimbursement from the state for some or all of the expense when the district must reimburse parents for a child’s private education? A court may direct a school district to pay for private education “if the court ultimately determines that such placement, rather than a proposed iep [individualized education program], is proper under the Act.” Burlington School Committee v. Massachusetts Department of Education, 471 U.S. 359, 369, 105 S.Ct. 1996, 85 L.Ed.2d 385 (1985). Such an order was entered in both of the cases now on appeal. Magistrate Judge Denlow, presiding by consent under 28 U.S.C. § 636(c), concluded that Oak Park’s school district had made so many procedural and substantive errors in preparing an iep for Kelly E. that her parents are entitled to reimbursement for private education. 21 F.Supp.2d 862 (N.D.I11.1998). District Judge Moran enforced an administrative decision that T.H.’s parents are entitled to reimbursement for an intensive home-based educational program. 55 F.Supp.2d 830 (N.D.I11.1999). Both school districts have accepted these decisions; the only remaining dispute is whether the state must chip in. Our cases appear to be the first to present that question to a court of appeals.
The magistrate judge directed the state to pay for Kelly E.’s private education and half of her parents’ legal expenses. He gave two principal reasons. 21 F.Supp.2d at 883, reconsideration denied, 1999 WL 91899, 1999 U.S. Dist. Lexis 1612. First, he viewed the state as a guarantor of every local school district’s compliance with the Act, and therefore responsible for part of the cost. Second, he concluded that state statutes and regulations offering to pay for private placements at approved schools are not generous enough to comply with Florence County School District v. Carter, 510 U.S. 7, 114 S.Ct. 361, 126 L.Ed.2d 284 (1993), which the magistrate judge understood as calling for state reimbursement of local districts’ expenses for private education. Illinois law provides (105 ILCS 5/14-7.02):
A school district making tuition payments pursuant to this Section is eligible for reimbursement from the State for the amount of such payments actually made in excess of the district per capita tuition charge for students not receiving special education services....
If a child has been placed in an approved individual program and the tuition costs including room and board costs have been approved by the Review [934]*934Board, then such room and board costs shall be paid by the appropriate State agency subject to the provisions of Section 14-8.01 of this Act.
An implementing regulation adds: “A program not approved in accordance with the requirements of this Part shall not be used by school districts to serve students with disabilities under Section 14-7.02 of the School Code.” 23 Ill. Adm. Code § 401.10. This means that a non-approved program is ineligible for reimbursement under § 14-7.02, not that such a program “shall not be used” at all.' Still, the magistrate judge thought that the statute and regulation steered school districts away from placements that might be educationally best for students, and toward either continued education in the public schools or approved private placements that were educationally less desirable (but cheaper for the local school districts). To counteract this incentive, the magistrate judge directed the state to pay for half of Kelly’s education even though state law does not authorize the outlay. By contrast, the district judge in T.H. declined to order the state to contribute toward the cost of the home education. The judge explained: “If the [Palatine school] district was concerned about its ability to recoup expenses in excess of the district per capita tuition charge for students not receiving special education services, see 105 ILCS § 5/14-7.02, it could have worked harder to develop an appropriate placement that was approved by the state.” 55 F.Supp.2d at 847. Judge Moran disagreed with the magistrate judge’s conclusion that the state must either ensure local districts’ compliance or insure their compliance costs.
Illinois, as appellant in the Oak Park case and appellee in the Palatine case, leads off with a flurry of objections to the very possibility of litigation. Local school districts lack standing, the state insists; if they suffer injury in fact, they do not meet prudential standards for adjudication; and if the local districts may sue, still the state is not a proper defendant given the eleventh amendment. None of these arguments was presented in the district court — though if they establish an absence of subject-matter jurisdiction we must consider them anyway. But they are feeble, individually and collectively.
Although, as Illinois stresses, the school districts are not the persons for whose benefit the Act is designed, they have been injured in fact by the need to pay for Kelly E.’s and T.H.’s private education. Although the injury may not be traceable to acts of Illinois, in seeking to recover part of their outlay the school districts are asserting a claim for contribution. Federal courts regularly resolve disputes about contribution. E.g., McDermott, Inc. v. AmClyde, 511 U.S. 202, 114 S.Ct. 1461, 128 L.Ed.2d 148 (1994); Akzo Nobel Coatings, Inc. v. Aigner Corp., 197 F.3d 302 (7th Cir.1999). Until now, no one has expressed doubt that cross-claims among joint wrongdoers present cases within the scope of Article III. Perhaps the Act does not authorize awards of contribution, but a party’s failure to establish a claim for re lief differs from a deficiency in subject-matter jurisdiction. Steel Co. v. Citizens for a Better Environment, 523 U.S. 83, 89-90, 118 S.Ct. 1003, 140 L.Ed.2d 210 (1998); Bell v. Hood, 327 U.S. 678, 682, 66 S.Ct. 773, 90 L.Ed. 939 (1946). Recast as a claim that local districts do not fall within the zone of interests protected by the Act and thus lack “prudential” standing, the state’s position fares no better, if only because we have held, see United Transportation Union v. Surface Transportation Board, 183 F.3d 606, 611 (7th Cir. 1999) (citing cases), that prudential considerations in general, and the zone-of-interests test in particular, are forfeited if not presented in a timely fashion. Illinois asks us to overrule this line of cases, but we decline; requiring litigants to raise zone-of-interests arguments at an early opportunity is compatible with, if not compelled by, decisions of the Supreme Court. See, e.g., Air Courier Conference v. Postal Workers Union, 498 U.S. 517, 522-23 & n. 3, 111 S.Ct. 913, 112 L.Ed.2d 1125 (1991).
[935]*935Section 604(a) of the idea, 20 U.S.C. § 1403(a), provides that “[a] State shall not be immune under the eleventh amendment to the Constitution of the United States from suit in Federal court for a violation of this chapter.” Language this direct satisfies the clear-statement requirement. Illinois contends that abrogation exceeds Congress’s powers under § 5 of the fourteenth amendment, see Kimel v. Florida Board of Regents, — U.S.-, 120 S.Ct. 631, 145 L.Ed.2d 522 (2000); Florida Prepaid Postsecondary Education Expense Board v. College Savings Bank, 527 U.S. 627, 119 S.Ct. 2199, 144 L.Ed.2d 575 (1999); Boerne v. Flores, 521 U.S. 507, 117 S.Ct. 2157, 138 L.Ed.2d 624 (1997), but this is beside the point. Having enacted legislation under its spending power, Congress did not need to rely on § 5. States that accept federal money, as Illinois has done, must respect the terms and conditions of the grant. South Dakota v. Dole, 483 U.S. 203, 107 S.Ct. 2793, 97 L.Ed.2d 171 (1987). One string attached to money under the idea is submitting to suit in federal court. Bradley v. Arkansas Department of Education, 189 F.3d 745, 752-53 (8th Cir.1999), rehearing en banc granted on a different issue, 197 F.3d 958 (1999) (argued January 14, 2000). Although § 604(a) does not use words such as “consent” or “waiver,” it is hard to see why that should matter. Congress did what it could to ensure that states participating in the idea are amenable to suit in federal court. That the power comes from the spending clause rather than (as Congress may have supposed) the commerce clause or the fourteenth amendment is not relevant to the issue whether the national government possesses the asserted authority. Otherwise we require the legislature to play games (“guess which clause the judiciary will think most appropriate”). What matters, or at least should matter, is the extent of national power, rather than the extent of legislative prevision. Thus we hold that states must take the bitter with the sweet; having accepted the money, they must litigate in federal court. See also 20 U.S.C. § 1415(f)(2). Suit is of course limited to enforcing the federal terms and conditions; local school districts can’t piggyback claims based on state law. We must assume that Illinois has complied with all of its own statutes and regulations; school districts that want a more generous reimbursement policy under 105 ILCS 5/14-7.02 and 23 Ill. Adm. Code § 401.10 must resort to a state forum. See Pennhurst State School and Hospital v. Halderman, 465 U.S. 89, 104 S.Ct. 900, 79 L.Ed.2d 67 (1984). But if the idea itself entitles a local school district to reimbursement from a state, then the eleventh amendment does not stand in the way.
Thus we arrive at the principal question: does the Act prescribe a particular allocation of expenses between local and state bodies? Magistrate Judge Den-low did not identify a statutory source of authority for his award against the state, and 20 U.S.C. § 1415(f)(3)(A) does not by itself supply what is needed. (In 1997 Congress extensively amended the Act. All of our citations are to the current version.) Uncommon as it is for a municipality to sue a state (or the reverse) under federal law, compare Illinois v. Chicago, 137 F.3d 474 (7th Cir.1998), with Chicago v. Lindley, 66 F.3d 819, 823 n.6 (7th Cir.1995), § 1415(i) may allow this under some circumstances. When a parent disagrees with a local decision about a pupil’s iep, an administrative appeal lies to a state agency, see § 1415(g), and § 1415(f)(2) allows “[a]ny party aggrieved by the [state agency’s] findings and decision” to contest the outcome by suit under § 1415(f)(3). A local board of education therefore may sue the parent asking the court to upset the state’s decision and to restore the local board’s preferred educational plan. Perhaps, by analogy to federal administrative law, it may sue the state as the decision-maker (just as employers and unions sue the NLRB). But nothing in this subsection authorizes awards of financial relief in favor of local educational officials. Cases such as Texas Industries, Inc. v. Radcliff Materials, Inc., 451 U.S. 630, 101 S.Ct. [936]*9362061, 68 L.Ed.2d 500 (1981), and Northwest Airlines, Inc. v. Transport Workers, 451 U.S. 77, 101 S.Ct. 1571, 67 L.Ed.2d 750 (1981), show that simple grants of jurisdiction along the lines of § 1415(i)(3)(A) do not permit courts to reallocate loss among joint wrongdoers.
Title VII of the Civil Rights Act of 1964 authorizes suit in language similar to the idea. See 42 U.S.C. § 2000e-5(f)(3). A collective bargaining agreement between Northwest Airlines and a union representing some of its employees contained provisions that were held to violate Title VII, leading to an award of damages exceeding $20 million. Blaming the union for this loss, the employer sought an award of contribution — and lost. The Supreme Court assumed that an employer may be a person aggrieved for the purpose of filing a charge under § 2000e-5(b) and later filing suit. Northwest Airlines, 451 U.S. at 90, 101 S.Ct. 1571. But it held that the grant of federal jurisdiction, understood in light of the norm that federal courts do not adjust accounts among wrongdoers without statutory authorization, is not enough to authorize contribution. Only if something else in Title VII authorized contribution would such an award be proper. Texas Industries reached the same conclusion for antitrust litigation. Because § 1415(f)(3) is no more explicit about contribution than is § 2000e-5(f)(3), the state is entitled to prevail unless something else in the idea requires it to reimburse local school districts.
One possibility is § 1403(b): “In a suit against a State for a violation of this chapter, remedies (including remedies both at law and in equity) are available for such a violation to the same extent as those remedies are available for such a violation in the suit against any public entity other than a State.” This is the language on which Oak Park and Palatine principally rely. But it says only that a state is liable to the same extent as any other public entity. It does not say what that extent may be. If a state may not recover contribution from a local board of education, then under § 1403(b) a local board can’t recover contribution from a state. Whether a state may recover from a board, or a board from a state, can’t be answered from the language of § 1403(b).
But it can be answered, with some confidence, by parsing § 611 of the Act, 20 U.S.C. § 1411, which specifies the allocation of funds between state and local educational entities. Each state that receives money under the Act may keep as much as 25% to pay for direct educational services (a state may run schools of its own), administration, technical assistance, training, hearings, and subgrants for “capacity-building and improvement”. 20 U.S.C. § 1411(f)(4)(A). Each state must distribute to local educational agencies at least 75% of the federal grant, see § 1411(g), under a formula that takes as its annual base the amount each local agency received before the 1997 amendments. That amount depended on the number of pupils with disabilities enrolled in each school system; a state was required to apportion the 75% among local districts so that each received approximately the same amount per pupil with a special educational program. See § 611(d) of the former statute, 108 Stat. 3931. This system tells us two things: first, any school district that receives less than the allocation prescribed by § 1411(g) is entitled to a remedy under § 1403(b); second, if the local district has received its full allocation for a given year, it is not entitled to more.
The statutory allocation formula gives local districts a stipend per disabled pupil. This supplement per pupil is supposed to be 30% of the average cost of primary education in the United States. 20 U.S.C. § 1411(a)(2). (The statute specifies 40%, but the state is entitled to keep a quarter of this for itself.) Many pupils with disabilities can be educated for less than 130% of the national average, but others cost substantially more. Over time, things should average out so that the grant covers aggregate costs. Instead of directing the states to calculate expenses for each pupil and distribute funds among local dis[937]*937tricts accordingly, Congress directed states to apply a formula to the total number of pupils with disabilities. That system would collapse if local districts could in essence make a profit from some pupils with disabilities (those for which the 30% supplement exceeds the costs of special services) while suing the states for more whenever the costs exceeded the average per-pupil grant, as it did for T.H. and Kelly. Then the states, having distributed 75% off the top (as the statute requires), would be required to dip into (maybe exceed) the 25% retainage to cover the additional expenses of the most costly pupils.
Neither Oak Park nor Palatine contends that Illinois has distributed less than the 75% to which the local educational agencies are entitled. Their claims for contribution in this case therefore boil down to arguments that each local educational agency is entitled to an annual base derived from 75% of the state’s grant, plus per-pupil supplements whenever the Act requires (or permits a parent to choose) private education. Nothing we can find in 20 U.S.C. § 1411 or any other section of the idea supports such double dipping. A local educational agency that has received its share of the federal appropriation must provide for services out of that share; it cannot collect more from the state by way of contribution. States may of course agree to pay more out of their own budgets; 105 ILCS 5/14-7.02 appears to represent such a promise. But states may set their own conditions for this largess and, as we have observed already, federal courts are not entitled to enforce state laws against the states themselves.
A few words about Garter bring this opinion to a close. Both school districts rely heavily on this opinion, but it has nothing to do with relative shares of state and local districts. Carter holds that parents may be entitled to reimbursement for private education even though the school they select does not meet all requirements of 20 U.S.C. § 1401(a)(8) — and, in particular, does not meet all standards set by the state’s educational bureaucracy. The court observed that officials who disagreed with the need for private education were unlikely to give their approval, but that they could not so easily block parents’ entitlement to obtain a good education for their child. According to Oak Park and Palatine, the combination of Carter with 105 ILCS 5/14-7.02 leaves them in a bind: they can’t get state reimbursement unless the private school has been approved, but they also can’t use the lack of approval to avoid reimbursing parents for what may be a costly private placement. That may well be so, but it does not follow that the idea requires the state to contribute more than the amount allocated under § 1411(g). In Carter itself the Justices had this to say about the school district’s contention that the Court’s holding would break the bank:
[P]ublie educational authorities who want to avoid reimbursing parents for the private education of a disabled child can do one of two things: give the child a free appropriate public education in a public setting, or place the child in an appropriate private setting of the State’s choice. This is idea’s mandate, and school officials who conform to it need not worry about reimbursement claims.
Moreover, parents who, like Shannon’s, “unilaterally change their child’s placement during the pendency of review proceedings, without the consent of state or local school officials, do so at their own financial risk.” Burlington, supra, at 373-374, 105 S.Ct. 1996. They are entitled to reimbursement only if a federal court concludes both that the public placement violated idea and that the private school placement was proper under the Act.
Finally, we note that once a court holds that the public placement violated idea, it is authorized to “grant such relief as the court determines is appropriate.” 20 U.S.C. § 1415(e)(2). Under this provision, “equitable considerations are relevant in fashioning relief,” Burlington, 471 U.S. at 374, 105 S.Ct. 1996, and the court enjoys “broad discretion” in so doing, id., at 369, 101 S.Ct. 1571. Courts fashioning discretionary equitable relief [938]*938under idea must consider all relevant factors, including the appropriate and reasonable level of reimbursement that should be required. Total reimbursement will not be appropriate if the court determines that the cost of the private education was unreasonable.
510 U.S. at 15-16, 114 S.Ct. 361 (emphasis in original). Neither Oak Park nor Palatine took advantage of the options mentioned in the first paragraph of this passage, and neither district contends that the cost of private education was unreasonable and therefore should not be fully reimbursed under the third paragraph.
Whatever assistance a state may provide, beyond the block grant that the idea requires, must be worked out through the state’s political and judicial processes. The judgment in the Palatine case is affirmed. The judgment in the Oak Park case is vacated to the extent it requires the state to pay for any of Kelly E.’s private education, and the case is remanded for entry of a new judgment in conformity with this opinion. Illinois already has paid its assigned share of Kelly E.’s private education in years past, but it need not continue to do so and need not reimburse Oak Park for any portion of the attorneys’ fees awarded to Kelly’s parents.