POSNER, Chief Judge.

This is a suit under 42 U.S.C. § 1983 by a nonprofit corporation that operates a residential facility for the mentally retarded in Wisconsin, by three current residents of the facility, and by four prospective residents from out of state. The defendants, state and local Wisconsin officials and a local government, are charged with violating these retarded persons’ federal constitutional right to travel, and some of their federal statutory rights as well, by enforcing certain state laws and federal Medicaid regulations. In a series of judgments, one rendered after a trial on one of the plaintiffs’ right to travel claims, the district court upheld the constitutionality of the state laws and federal regulations. Insofar as the suit seeks damages from a state official in his official capacity, it is clearly barred by the Eleventh Amendment. E.g., Edelman v. Jordan, 415 U.S. 651, 663, 94 S.Ct. 1347, 1355, 39 L.Ed.2d 662 (1974). But the injunctive claim against him can proceed, Ex parte Young, 209 U.S. 123, 28 S.Ct. 441, 52 L.Ed. 714 (1908), as there is no suggestion that the relief sought would invade the sovereign rights of Wisconsin, Idaho v. Coeur D’Alene Tribe of Idaho ,—U.S.-,-, 117 S.Ct. 2028, 2043, 138 L.Ed.2d 438 (1997), and so can the claims, both legal and equitable, against the other defendants.

Bethesda Lutheran’s facility is located in Watertown, Wisconsin, in Jefferson County. It offers long-term care to the severely retarded. Its residents come from all over the United States. The three current residents on whose behalf the suit was filed range in age from 35 to 40 and have lived in the facility for between 14 and 29 years. All are classified under the federal Medicaid regulations, however, as residents of Illinois because that is where their parents lived when these plaintiffs were admitted to the facility. We shall see that, as Illinois residents, they are entitled to Medicaid benefits from neither Wisconsin nor Illinois, if the regulations are valid; and without those benefits they cannot afford to remain in the Watertown facility. The four prospective residents on whose behalf the suit was also filed range in age from 22 to 42, and they live either with their parents or, in one case, in a group home, all outside Wisconsin. The Wisconsin laws that they challenge prevent them from relocating to the Watertown facility, as they (or more likely their guardians) would like to do. All seven plaintiffs are gravely retarded — their IQs range from 10 to 34 — and none is competent to manage his or her own affairs. They are, however, private, paying (with or without the help of Medicaid) patients; and Bethesda Lutheran, the owner of the Wisconsin facility, has standing, along with the patients themselves, to challenge in federal court laws that forbid it to sell its services to potential customers or limit the prices it can charge. Craig v. Boren, 429 U.S. 190, 194-97, 97 S.Ct. 451, 455-56, 50 L.Ed.2d 397 (1976); Rothner v. City of Chicago, 929 F.2d 297, 301 (7th Cir.1991); Wedg *445 es/Ledges of California, Inc. v. City of Phoenix, 24 F.3d 56, 61 (9th Cir.1994).

We begin with the claim involving the four nonresidents. The Watertown facility is classified under Wisconsin law as a “facility for the developmental^ disabled,” more commonly referred to as an “intermediate care facility for the mentally retarded.” Wisconsin law permits the admission of a person to such a facility only (unless there’s an emergency) upon the recommendation of the social services agency of the “individual’s county of residence,” Wis. Stat. § 50.04(2r); Wis. Admin. Code § HFS 134.52(2)(b), plus — if the person is found to be mentally incompetent — upon a court order of “protective placement” in response to a petition “filed in the county of residence of the person to be protected.” Wis. Stat. § 55.06(3)(e). See also Wis. Stat. § 55.06; Wis. Admin. Code § HFS 134.52(2)(e). In context, it is apparent, as both sides agree, that by “residence” the statutes mean domicile, rather than where the person happens to be (on the distinction, see, e.g., In re Estate of Daniels, 53 Wis.2d 611, 193 N.W.2d 847, 849 (1972)), and that the references to a “county” are to a Wisconsin county. The upshot is that to be admitted to the Watertown facility the prospective resident must first establish his residence in a Wisconsin county. So nonresidents of Wisconsin are ineligible.

States do not violate the Constitution by giving preference to residents seeking admission to state universities and other facilities owned by the state or its subdivisions. Camps Newfound/Owatonna, Inc. v. Town of Harrison, — U.S.-,-, 117 S.Ct. 1590, 1606, 137 L.Ed.2d 852 (1997); W.C.M. Window Co. v. Bemardi, 730 F.2d 486, 494-96 (7th Cir.1984); SSC Corp. v. Town of Smithtown, 66 F.3d 502, 510-13 (2d Cir.1995); Swin Resource Systems, Inc. v. Lycoming County, 883 F.2d 245, 248-51 and n. 2 (3d Cir.1989). But Bethesda Lutheran is a private facility. For Wisconsin to prohibit its admitting nonresidents is like Illinois’ forbidding nonresidents to stay at the Chicago Hilton or attend Northwestern University. Such a law would prima facie violate the right to travel or relocate from one state to another, a right that the Supreme Court has held to be protected by the privileges and immunities clauses in Article IV and the Fourteenth Amendment, the equal protection clause of the Fourteenth Amendment, and the commerce clause of Article I. See Attorney General of New York v. Soto-Lopez, 476 U.S. 898, 901-05, 106 S.Ct. 2317, 2319-22, 90 L.Ed.2d 899 (1986); Shapiro v. Thompson, 394 U.S. 618, 627-38, 89 S.Ct. 1322, 1327-33, 22 L.Ed.2d 600 (1969); Edwards v. California, 314 U.S. 160, 173-74, 62 S.Ct. 164, 166-67, 86 L.Ed. 119 (1941); id. at 181-86, 62 S.Ct. at 171-72 (concurring opinion); Zobel v. Williams, 457 U.S. 55, 73-81, 102 S.Ct. 2309, 2319-23, 72 L.Ed.2d 672 (1982) (concurring opinion). It would be. more extreme than the law that the Court invalidated in Camps Newfound/Owatonna, which merely gave a special tax break to charities operated primarily for the benefit of the state’s residents.

Yet there is no doubt that Wisconsin can, without violating the Constitution, establish procedures, such as the protective-placement procedure in section 55.06, for making sure that people are not confined to institutions for the mentally incompetent unless they actually are incompetent. It makes no difference whether the institution is public or private, except that if it is public the state would be required by the federal Constitution to adopt such a procedure, Secretary of Public Welfare v. Institutionalized Juveniles, 442 U.S. 640, 649-50, 99 S.Ct. 2523, 2527-28, 61 L.Ed.2d 142 (1979); Heller v. Doe, 509 U.S. 312, 113 S.Ct. 2637, 125 L.Ed.2d 257 (1993); see also Kansas v. Hendricks, —U.S.-,---, 117 S.Ct. 2072, 2079-80, 138 L.Ed.2d 501 (1997); Parham v. J.R., 442 U.S. 584, 606-07, 99 S.Ct. 2493, 2505-06, 61 L.Ed.2d 101 (1979); Addington v. Texas, 441 U.S.-418, 425-27, 99 S.Ct. 1804, 1808-09, 60 L.Ed.2d 323 (1979), while, if it is private, presumably all the state must do to comply with its constitutional duties is not to place its coercive powers behind private commitments to the institution. Spencer v. Lee, 864 F.2d 1376, 1378-82 (7th Cir.1989) (en banc). The state is not required, even if not constitutionally forbidden, to sit by while greedy or selfish relatives herd the elderly or impaired into private facilities that are more restrictive than the *446 committed individual actually needs. The plaintiffs’ challenge, however, is not to their being required to undergo the protective-placement procedure; it is to their being required to become residents (in the sense of domiciliaries) of the state before doing so, which is to say, required to move into the state at the beginning of the process without intending to leave it. Since anyone who is approved for protective placement is by definition incapable of living outside the Water-town facility or its equivalent in restrictiveness, it is unclear where in Wisconsin the applicant for admission to the facility is supposed to live while the placement petition is being processed.

The Attorney General of Wisconsin assures us that the applicant doesn’t have to show up in the state until the very day of the hearing' on his petition, and if the petition is granted on the spot he can go directly to the Watertown facility. But what if it isn’t granted on the spot? And more important, how can someone establish residence whose intent (or, more to the point in these cases, his guardian’s intent) is that he shall remain in Wisconsin only if his petition is granted? The legal principles governing the acquisition of a new domicile would not make a person who came to Wisconsin to play the Wisconsin lottery, and announced that if he won he would in gratitude stay in Wisconsin permanently, a Wisconsin resident on the day he arrived, before even playing, let alone winning, the lottery. See Baker v. Wisconsin Dep’t of Taxation, 246 Wis. 611, 18 N.W.2d 331, 333 (1945); Julson v. Julson, 255 Iowa 301, 122 N.W.2d 329 (1963); Vickerstaff v. Vickerstaff, 392 S.W.2d 559, 561-62 (Tex.Civ. App.1965); Gates v. Commissioner, 199 F.2d 291, 294 (10th Cir.1952). It is the same here — and were it not, the state would have no ground for opposing the applications of these plaintiffs for admission to the Water-town facility. They would have only to set foot in Jefferson County, intending to remain if their applications were granted, and, presto, they would be residents of Jefferson County.

That is wrong, of course; yet if the Attorney General is correct that the Wisconsin authorities wink at violations of the residency requirement for placement in a restrictive facility, the requirement is not much of an obstacle to the facility’s attracting nonresidents. But it is some obstacle; not everyone is comfortable flouting the law even when invited to do so in a brief signed by the state’s highest legal officer. And since it is an obstacle, it has to be justified, if it is to pass constitutional muster, by reference to some legitimate interest of the state. Attorney General of New York v. Soto-Lopez, supra, 476 U.S. at 904, 906 and n. 6, 106 S.Ct. at 2321, 2322 and n. 6; Hooper v. Bernalillo County Assessor, 472 U.S. 612, 618, 105 S.Ct. 2862, 2866, 86 L.Ed.2d 487 (1985). Several makeweight justifications are advanced in the state’s brief — for example, that the requirement of residence in the state is necessary in order to empower the courts of the state to exercise personal jurisdiction over institutionalized persons. The state does not mean “personal jurisdiction” in the sense of wanting to make these people amenable to service of process (not that that would be a problem); it just wants to make sure that it can protect them — that is, that they are within the protective jurisdiction of the state. Obviously they are.

When asked about justifications at oral argument for the residency requirement, the assistant attorney general who argued the case for the defendants made no reference to the arguments in the brief, but instead shrugged and acknowledged that he couldn’t think of any justifications. In a supplemental filing addressed to this question, however, he told us without elaboration that the requirement is “necessary to establish which Wisconsin county is the financially and pro-grammatically responsible public entity.” This seems pretty odd; why isn’t the responsible county the one in which the person is living? But we glean hints from the record that in some previous era, before the county of original residence was made the responsible county, the counties in which institutions housing mentally infirm people were concentrated bore a heavy financial burden because they had to provide social services to people who had moved into their institutions from other counties. For example, a patient who was originally from Milwaukee and underwent the protective-placement procedure *447 there, but was institutionalized in a Jefferson County facility, became the responsibility of the Jefferson County social services agency. The current method of allocation assigns this patient to Milwaukee County as the county of the patient’s residence and thus spares Jefferson County any financial responsibility for him. The state argues that if the patient comes from outside the state, there is no originating Wisconsin county, so the burden falls on Jefferson County. This is no argument at all for the state to be making, for how can it matter to the state which county pays? It is a petty argument, at best, when made by Jefferson County. The state could easily assign the out-of-staters for fiscal purposes to counties randomly, equalizing the burden; its failure to do this is not a good reason for impairing a constitutional interest.

The argument that we expected to be made for the residency requirement is that the state (or a county — but it doesn’t matter which county) may eventually have to pick up part of the tab for the people now living as private patients in the Watertown facility and that this gives the state an interest in confining eligibility for the facility to “real” Wisconsinites. But this argument, as distinct from the petty intercounty-equity argument reconstructed above (though not actually made, at least in a readily comprehensible form), is not made, and might, as we shall see, run afoul of decisions by the Supreme Court. In any event there is nothing to support the argument, making our hotel analogy apropos. Although the Watertown facility receives Medicaid payments on account of some of its patients, payments that come in part out of the state’s pocket (Medicaid is jointly financed by the states and the federal government), a state, as we are about to see, is not required to provide Medicaid assistance for nonresidents. The requirement, though challenged by the individual plaintiffs who are already patients in the Watertown facility, is assumed to be valid by the state. This makes Wisconsin’s insistence on confining eligibility for the Watertown facility to state residents perverse from even the state’s standpoint.

Some of these nonresidents, it is true, may become Wisconsin residents at some future time. Under the Medicaid regulations, an institutionalized incompetent becomes a resident of the state in which he is living if his parents abandon him, 42 C.F.R. § 435.403(i)(2)(iv), and perhaps “abandonment” includes death. We needn’t decide; the expected fiscal burden on the state has not been quantified, or even crudely estimated — and in fact the state does not advance this potential fiscal burden as a justification for its residency requirement, although it hints around it. We conclude that the residency requirement is an unjustifiable interference with interstate mobility, because it is an interference and because no plausible justification for it has been suggested. The plausible justifications were not argued at all, and the implausible ones were abandoned at the oral argument.

We turn to the claim of the plaintiffs who are currently living at the Watertown facility. They are Medicaid recipients, and as just mentioned the Medicaid program does not require a state that participates in it to provide assistance under it to nonresidents, 42 U.S.C. § 1396a(b)(2); 42 C.F.R. § 435.403(a), or even to its residents who have gone out of state for care, unless the state of residency lacks facilities for providing the services that these residents need or there are other special circumstances, such as a medical emergency. 42 C.F.R. §§ 431.52(b)(l)-(4), 435.403(a). The regulations define the state of residence of an institutionalized incompetent who became incompetent before the age of 21 as the state of his parents’ residence when he entered the institution. 42 C.F.R. § 435.403(i)(2)(ii); see also Wis. Admin. Code § HFS 103.03(e)la. The current-resident plaintiffs came to the Watertown facility from Illinois, where their parents did and do live, and so for Medicaid purposes these residents of the Watertown facility are residents of another state. So neither Wisconsin nor Illinois (because of the regulation limiting the duty of a state to pay Medicaid benefits for services rendered to its residents outside of the state) is required by the Medicaid regulations to pick up the tab for services rendered to these plaintiffs. If it were merely a question of which state must pay, it would be as trivial as the question which county is responsible for providing social services to *448 these patients. The problem is that neither state will pay. The Medicaid regulations make it difficult for indigent incompetent nonresidents to obtain institutional care in Wisconsin, by disentitling them to Medicaid benefits, and makes it impossible for Bethesda Lutheran, the owner of the Watertown facility, to obtain Medicaid reimbursement for any of the expenses of treating these plaintiffs. The appellants argue that the regulations are unconstitutional and therefore that the defendants may not use them to deny Medicaid assistance. We asked the Department of Health and Human Services to submit a brief addressed to this question and it has done so.

The constitutional right to travel' or to relocate from state to state is usually thought of as a right against the states rather than a right against the federal government. The leading modern ease, Shapiro v. Thompson, supra, struck down state laws conditioning eligibility for welfare benefits on residence within the state for a period of time. It seems odd as an original matter to suppose the federal government constitutionally obligated to provide financial assistance to indigents in a form that will encourage them to seek medical treatment in distant states, especially since, if adequate treatment is unavailable in their home state, the Medicaid regulations obligate that state to support the provision of treatment in another state. 42 C.F.R. § 431.52(b)(3). If accepted, the plaintiffs’ argument, when it is combined with the argument that we have already accepted against the state’s residency requirement, might make Wisconsin a magnet for the parents and guardians of indigent incompetents throughout the United States merely because it has superior facilities — for which the federal government would be picking up a major part of the tab.

But we are not writing on a clean slate. The Supreme Court has made clear that the right to travel or relocate is a right against the federal government as well as against the states. Kent v. Dulles, 357 U.S. 116, 125-27, 78 S.Ct. 1113, 1117-18, 2 L.Ed.2d 1204 (1958); Aptheker v. Secretary of State, 378 U.S. 500, 505-06, 84 S.Ct. 1659, 1663-64, 12 L.Ed.2d 992 (1964); Haig v. Agee, 453 U.S. 280, 306-07, 101 S.Ct. 2766, 2781-82, 69 L.Ed.2d 640 (1981). Shapiro v. Thompson itself invalidated along with state duration-ofresidenee requirements a similar requirement that Congress had imposed on the District of Columbia. 394 U.S. at 641-42, 89 S.Ct. at 1334. So the right to travel does bind the federal government. The Department of Health and Human Services does not argue otherwise.

The Medicaid regulations do not forbid anyone to change his state of residence. But neither did the welfare provisions struck down in Shapiro v. Thompson. All that either set of provisions does or did is impose a severe monetary penalty on indigents who move from one state to another. Shapiro teaches that this is an infringement of the “right to travel” and must therefore be justified. The Court did not, it is true, require states to provide welfare benefits to nonresidents; it is plain that they have no such obligation. See Martinez v. Bynum, 461 U.S. 321, 328-29, 103 S.Ct. 1838, 1841-42, 75 L.Ed.2d 879 (1983). But the plaintiffs in ornease are not arguing that Wisconsin must provide benefits to nonresidents who are receiving treatment in the state. The plaintiffs in Shapiro were residents; they just hadn’t been residents for long. The plaintiffs in ornease concede that they have to be residents of Wisconsin in order to be entitled to the Medicaid benefits that they are seeking, but they argue that the Medicaid regulations prevent them from establishing that (once the unconstitutional provisions of state law are swept to one side) they are indeed residents of Wisconsin. Vlandis v. Kline, 412 U.S. 441, 453, 93 S.Ct. 2230, 2236, 37 L.Ed.2d 63 (1973), holds that the power of a state to confine its public services to residents does not entitle the state to establish arbitrary barriers to a nonresident’s becoming a resident.

To change one’s domicile from State A to State B requires an intent to go to B and remain there. So one must have sufficient mental capacity to form such intentions, and we may assume (without having to decide— not an entirely easy question under the cases, which generally do not consider a determination of incapacity to manage one’s *449 own affairs determinative on the question, see, e.g., Coppedge v. Clinton, 72 F.2d 531, 533 (10th Cir.1934); Long v. Sasser, 91 F.3d 645, 647 (4th Cir.1996); Rishell v. Jane Phillips Episcopal Memorial Medical Center, 12 F.3d 171 (10th Cir.1993); Restatement (Second) of Conflicts of Law § 23 comment a (1971)) that a person with an IQ of 34 or less does not have this capacity. In many jurisdictions the power to choose the person’s domicile passes in such cases to his guardian (otherwise the domicile of infants could not be changed), constrained only by the duty to act exclusively for the best interest of his ward. E.g., Grier v. Estate of Grier, 252 Minn. 143, 89 N.W.2d 398, 403 (1958); Rishell v. Jane Phillips Episcopal Memorial Medical Center, supra, 12 F.3d at 174; Restatement, supra, § 23 comment f. Some eases, however, deny the guardian’s power to change the ward’s state of domicile; a brief dictum, not mentioned by any of the parties, aligns Wisconsin with this position. Town of Carlton v. State Dep’t of Public Welfare, 271 Wis. 465, 74 N.W.2d 340, 343 (1956). The significance of Wisconsin’s position on the question is unclear, as we are not told what state’s law controls in a change of domicile case. Most of the cases that deny the guardian’s power to change the ward’s domiciliary state are, moreover, like Town of Carlton, pretty old, as well as inconsistent with the treatment of infants; and the most recent case, Long v. Sasser, supra, 91 F.3d at 647-48, arose in a rather special setting. The guardian was seeking to change his ward’s domicile in order to create diversity of citizenship. The idea of trundling an incompetent from state to state in search of procedural advantages is distasteful. To deny the guardian all power to change the ward’s residence to the state in which the best treatment for his ward is available might seem equally distasteful. In any event, none of the parties denies that the guardians of the current-resident plaintiffs can change the state of domicile of their wards, that they want to change it to Wisconsin, or that this change, to permit their wards to reside in the Water-town facility, would indeed be in the wards’ best interests. Any argument, therefore, that these plaintiffs’ challenge to the Medicaid regulations is moot because they couldn’t become Wisconsin residents even if the regulations were invalidated has been waived.

We must decide whether this curtailment of them right to travel can be justified. The federal government, like the state government, advances a number of makeweight arguments, such as that it is important to have a clear rule for determining the state of residency of a Medicaid recipient. No doubt it is important. But if as we doubt there is substantial uncertainty in determining the recipient’s common law state of domicile (and that could only be in a case in which the incompetent lacked a guardian and his mental incapacity to form an intent to remain in a state was in question), the regulations could make the state in which the recipient was living his state of residence for Medicaid purposes, and there would then be no lack of clarity.

The government’s only substantial argument is that its rule is necessary to prevent Medicaid recipients from flocking to the states that provide the best care, which, because there is no uniform nationwide payment schedule for Medicaid services, would be costly for the federal government and for those states and which could lead to a competition among the states to provide as little care as they could get away with. This strikes us as an excellent argument, but it is the exact argument-the need to prevent migration for better benefits-that the Supreme Court rejected in Shapiro v. Thompson, deeming the argument not merely outweighed by competing considerations, but inadmissible. 394 U.S. at 629-33, 89 S.Ct. at 1328-30. We are given no reason to suppose that the argument is any more plausible in the present setting. We need not decide whether the Constitution would be satisfied by Wisconsin’s paying no higher Medicaid benefits to persons who come from out of state than such persons would be entitled to in the states of their origin. The constitutional violation is patent where, as in this case (like Shapiro), the destination state refuses to pay any benefits at all.

The plaintiffs’ other arguments are either waived (as in the case of their appeal to the Religious Freedom Restoration Act, which has anyway been since declared unconstitu *450 tional) or too insubstantial to warrant discussion (as in the case of their claim that the Medicaid regulations violate the Americans with Disabilities Act). Nevertheless the judgment of the district court must be reversed and the case remanded for the entry of appropriate relief. Both sets of challenged provisions, the state and the federal, violate the right to travel that has been held to be conferred against both state and federal action by the Constitution.

Reversed and Remanded.