In two separate actions filed in the Superior Court, seven Massachusetts hospitals (see note 4, infra, and accompany*449ing text) and one managed health care organization that disproportionately provide medical care to the poor allege that the Secretary of the Executive Office of Health and Human Services (Secretary) has violated her obligation to reimburse them for the reasonable costs incurred in providing medical services to enrollees in MassHealth, the Massachusetts Medicaid program that is jointly funded by Federal and State legislative appropriations and serves the needs of those persons “whose income and resources are insufficient to meet the costs of necessary medical services.” Title XIX of the Social Security Act, codified at 42 U.S.C. § 1396-1 (Supp. IV 2010).3 A judge in the Superior Court granted the Secretary’s motion for judgment on the pleadings in one case and the Secretary’s motion to dismiss in the other, concluding as a matter of law that the plaintiffs could not prevail even if their allegations were true. The plaintiffs filed timely notices of appeal, and on the parties’ joint motion the appeals were consolidated in the Appeals Court. We transferred the cases to this court on our own motion, and now affirm the decisions denying the plaintiffs’ claims.
General background. The plaintiffs in the first action are the Boston Medical Center Corporation (BMC) and the Boston Medical Center Health Plan, Inc. (Health Plan). According to the amended complaint, BMC is the largest provider of medical care to “underserved, low-income, and vulnerable populations in Massachusetts”; only nineteen per cent of its patients are covered by private insurers. The Health Plan is a managed care organization that provides health care services to approximately 240,700 members, of whom approximately 170,000 are enrolled in MassHealth. The plaintiffs in the second action are Holyoke Medical Center, Inc., and two other hospitals (collectively, the Holyoke plaintiffs).4 The defendant in both actions is the Secretary, who administers MassHealth.
*450The judge allowed the Secretary’s motion for judgment on the pleadings as to the complaint brought by BMC and the Health Plan in a carefully reasoned memorandum of decision and order. She allowed the Secretary’s motion to dismiss as to the complaint brought by the Holyoke plaintiffs, stating that her legal analysis in the first case “applies here in nearly all respects” and addressing in her memorandum and order only the differences between the two cases.
In reviewing the judge’s two orders, “we examine the same pleadings as the motion judge and therefore proceed de novo.” Dartmouth v. Greater New Bedford Regional Vocational Tech. High Sch. Dist., 461 Mass. 366, 373 (2012) (Dartmouth) (motion to dismiss). See Wheatley v. Massachusetts Insurers Insolvency Fund, 456 Mass. 594, 600-601 (2010) (judgment on pleadings). Those pleadings include contracts and public documents that are referenced in the complaints and that were provided to the motion judge. See Marram v. Kobrick Offshore Fund, Ltd., 442 Mass. 43, 45 n.4 (2004), citing Mass. R. Civ. P. 10 (c), 365 Mass. 752 (1974). We accept as true the allegations in the complaints and draw every reasonable inference in favor of the plaintiffs. Curtis v. Herb Chambers I-95, Inc., 458 Mass. 674, 676 (2011), citing Warner Lambert Co. v. Execuquest Corp., 427 Mass. 46, 47 (1998). “We consider whether the factual allegations in the complaint are sufficient, as a matter of law, to state a recognized cause of action or claim, and whether such allegations plausibly suggest an entitlement to relief.” Dartmouth, supra at 374, citing Iannacchino v. Ford Motor Co., 451 Mass. 623, 636 (2008). Because issues relevant to the plaintiff hospitals are distinct from issues raised by the Health Plan, we consider first the claims relevant only to the hospitals and then consider the additional claims raised by the Health Plan. We conclude by examining the remaining claims that are asserted by all plaintiffs.
The hospitals’ claims. 1. Background. The rates paid by Mass-Health for medical services provided by hospitals generally are *451established by contract between the hospital and the Secretary. G. L. c. 118G, § 11. Since 1991, the Secretary has established payment rates for hospitals through an annual rate setting process. The Secretary publishes a Request for Applications (RFA) that informs each hospital of the payment rates for each MassHealth-eligible patient that the hospital may treat, as well as the methodology used to calculate each hospital’s payment rates. The RFA, at least for rate year 2009,5 is an approximately one hundred page document that primarily focuses on describing the types of hospital services that will be “reimbursed” by MassHealth, and the methodology used by the Secretary to calculate various reimbursement rates to be paid for different types of care. Under G. L. c. 118E, § 36, and the terms of the REA, a hospital that enters into a contract to accept MassHealth patients must agree to accept, “as payment in full,” the amounts paid under these rates.
One rate at issue in this lawsuit and defined in the RFA is the “Standard Payment Amount Per Discharge” (SPAD). A SPAD payment is a flat-fee paid by the Secretary for the first twenty days of inpatient care, regardless of the reason for the hospitalization or the actual cost incurred by the hospital to care for the admitted patient, and regardless whether the patient actually remains in the hospital for twenty days. A second rate at issue is the “Payment Amount Per Episode” (PAPE), which similarly is a flat-fee paid by the Secretary for outpatient care. The rate of the SPAD or PAPE payment determines whether a hospital makes a profit or takes a loss on the care of MassHealth patients.
The SPAD and the PAPE rates differ for each hospital, because the rates adjust the Statewide average costs of providing service with a complicated algorithm based in part on a hospital’s particular “casemix.”6 A hospital’s “casemix index” is defined in the RFA as a “categorization of a hospital’s patient population according to criteria approved by [the Secretary] including, *452but not limited to, primary and secondary diagnoses, primary and secondary procedures, illness severity, patient age and source of payment.” The index is intended to take into account the differences among hospitals in the types of medical problems they treat and the patient populations they serve that will affect their average costs, so that a hospital that treats more serious or complex medical problems requiring expensive procedures or longer hospitalizations or that treats patient populations in poorer health or with special needs will have SPAD and PAPE rates above the Statewide average.7
An appendix to the REA is a document titled “MassHealth Hospital Contract” (contract), which is a ten-page form contract. If a particular hospital accepts the REA, including the detailed description of payment rates, the hospital executes and returns the REA and contract indicating its acceptance. Either party is allowed to terminate the contract with at least thirty days’ prior written notice for any reason.
According to the terms of the contract, the Secretary “may revise payment rates, methodology [and] may amend any term of this [c]ontract, as it determines necessary” and with few exceptions not relevant to this appeal, “shall provide the [hospital] with [thirty] days’ written notice prior to implementing any amendment to the terms of the contract.” If the hospital does not respond to a proposed amendment, the Secretary “may exercise [her] discretion either to terminate for cause ... or continue the [hospital’s] participation,” in which case the Secretary “shall notify the [hospital] whether pre- or post-amendment methodology, rates, and [c]ontract provisions shall apply.”
BMC and the Holyoke plaintiffs are disproportionate share hospitals, which means that at least sixty-three per cent of their “gross patient service revenue” comes from Medicare, Medicaid, free care, or other government payors.8 G. L. c. 118G, § 1. *453Under G. L. c. 118G, § 11 (a), “[f]or disproportionate share hospitals, the [Secretary] shall establish rates that equal the financial requirements of providing care to recipients of medical assistance.” “Financial requirements” is defined as “a hospital’s requirement for revenue which shall include, but not be limited to, reasonable operating, capital and working capital costs, the reasonable costs of depreciation of plant and equipment and the reasonable costs associated with changes in medical practice and technology.” G. L. c. 118G, § 1.
As alleged by the plaintiffs, the Secretary issued the rate year 2009 RFA in August, 2008, but amended the RFA on September 19, raising payment rates. On October 1, the Secretary issued a “Notice of Final Agency Action,” lowering payment rates and stating that the calculation of payment rates would be “derived from the statewide average hospital cost per admission in rate year 2006, standardized for casemix differences and wage area variation” and that the Secretary would adopt a minimum efficiency standard to cap reasonable hospital costs used in calculating MassHealth payments. In an amendment on December 7, the Secretary again lowered payment rates. All of the Holyoke plaintiffs signed the amended RFA contracts, but the BMC did not. The BMC, however, along with the other plaintiff hospitals, continued to participate in MassHealth, treated MassHealth enrollees, and accepted payments from the Secretary.
The plaintiff hospitals have brought four claims challenging this reduction in rate payments, which we address in turn.
2. Violation ofG. L. c. 118G, § 11. The four plaintiff hospitals assert that the Secretary’s methodology and rate payments for rate year 2009 violated G. L. c. 118G, § 11, because the MassHealth rate payments yielded by that methodology did not “equal the financial requirements of providing care to recipients of medical assistance.”9 Section 11 (a) imposes a statutory duty *454on the Secretary to set MassHealth payment rates for disproportionate share hospitals that equal the financial requirements of providing care to those patients. The statute does not, however, expressly waive sovereign immunity and create a private right of action for a hospital to claim that the Secretary committed a breach of this duty by imposing unreasonably low payment rates in the RFA. The plaintiff hospitals ask us to imply such a waiver and a private right of action, arguing such implication is necessary because otherwise the statute would be ineffective.
In general, we have “been reluctant to infer a private cause of action from a statute in the absence of some indication from the Legislature supporting such an inference.” Loffredo v. Center for Addictive Behaviors, 426 Mass. 541, 544 (1998) (Loffredo). Where a private right of action inferred from a statute would permit a claim against the Commonwealth, the Legislature must also waive sovereign immunity. See Lopes v. Commonwealth, 442 Mass. 170, 175 (2004) (Lopes) (“Sovereign immunity bars a private action against a State in its own courts absent consent by the Legislature or abrogation of sovereignty by Congress acting under its Fourteenth Amendment powers”). See also Alden v. Maine, 527 U.S. 706, 745, 754-756 (1999). “The rules of construction governing statutory waivers of sovereign immunity are stringent.” Ware v. Commonwealth, 409 Mass. 89, 91 (1991), quoting Woodbridge v. Worcester State Hosp., 384 Mass. 38, 42 (1981) (Woodbridge). We have found a waiver of sovereign immunity only where consent to suit is “expressed by the terms of a statute, or appear[s] by necessary implication from them.” Lopes, supra at 175-176, quoting Woodbridge, supra.
Here, the statutory scheme strongly suggests that the Legislature did not intend to waive sovereign immunity and provide hospitals with a private right of action to challenge the reasonableness of MassHealth payment rates. In G. L. c. 118G, § 9, *455the Legislature allowed medical providers administratively to challenge before an impartial hearing officer MassHealth payment rates set by the Secretary that the provider contends were unreasonable, with judicial review available under G. L. c. 30A. However, the Legislature explicitly excluded hospital rates established under § 11 from this appeal process. See G. L. c. 118G, § 9 (appeal of rate setting to hearings officer “[ejxcept for rates established pursuant to [§ ll]”).10 It “weighs heavily against recognizing a private right of action,” Salvas v. Wal-Mart Stores, Inc., 452 Mass. 337, 373 (2008) (Salvas), that the Legislature has expressly provided medical providers aggrieved by unreasonable MassHealth payment rates with an avenue of administrative appeal, along with judicial review, but has expressly excluded from this remedy the MassHealth rates set for hospitals pursuant to § 11.
Nor are we persuaded that a private right of action and waiver of sovereign immunity is a “necessary implication” of a statutory duty under § 11 (a) to establish rates for disproportionate care hospitals that equal the “financial requirements” of providing care to MassHealth patients. A statutory duty by itself does not necessarily imply a judicial remedy to challenge the executive branch’s compliance with that duty. See, e.g., Massachusetts Redemption Coalition, Inc. v. Secretary of the Executive Office of Envtl. Affairs, 68 Mass. App. Ct. 67, 68-70 (2007) (Mass. Redemption) (statute mandating that “secretary [of environmental affairs] shall promulgate . . . regulations” creates “purely political question . . . best left to the executive branch” and does not create private right to challenge compliance in court). The Legislature often imposes obligations on officials in the *456executive branch to act in accordance with specified standards, but it does not always create a private right of action and waive sovereign immunity to allow private parties to enforce compliance with those standards in a judicial or administrative adjudication against the Commonwealth. See, e.g., Salvas, supra at 372-373 (Attorney General has duty to enforce statute; no private right of action); Sullivan v. Chief Justice for Admin. & Mgt. of the Trial Court, 448 Mass. 15, 38 (2006) (“we discern no legislative intent to create a private cause of action to enforce environmental laws that the plaintiffs seek to have recognized”); Woodbridge, supra (“tenor of G. L. c. 123 [which declares the rights of patients receiving treatment through Department of Mental Health] is one of aspiration and encouragement, rather than of the creation of a formal system of actionable guaranties”).
Finally, in determining whether a private right of action and waiver of sovereign immunity are a “necessary implication” of a statutory duty, we consider whether it would be reasonable as a matter of public policy for the Legislature to have intended a statutory duty without a judicial remedy. See Bates v. Director of Office of Campaign & Political Fin., 436 Mass. 144, 174 (2002) (considering whether “reasons of ‘justice and public policy’ argue for the application of sovereign immunity”); Morash & Sons v. Commonwealth, 363 Mass. 612, 623 (1973) (same). Judicial review of a hospital’s payment rates set by the Secretary would be complex and difficult. The Legislature imposed on the Secretary a duty to establish rates “that equal the financial requirements of providing care to recipients of medical assistance,” G. L. c. 118G, § 11 (a). General Laws c. 118G defines “[financial requirements” as “a hospital’s requirement for revenue” to reimburse its “reasonable” costs, which include not only “reasonable” operating costs, but also “reasonable” capital costs, depreciation, and “reasonable costs associated with changes in medical practice and technology.” G. L. c. 118G, § 1. That same statute also defines a hospital’s “[a]ctual costs” as “all direct and indirect costs incurred by a hospital ... in providing medically necessary care and treatment to its patients, determined in accordance with generally accepted accounting principles.” Id. Where a hospital’s “actual costs” are not reasonable, “financial requirements” need not *457equal “actual costs.” See Cliff House Nursing Home, Inc. v. Rate Setting Comm’n, 16 Mass. App. Ct. 300, 304 (1983) (“reasonable costs are distinguishable from and may be less than actual costs”). Therefore, any review of a hospital’s payment rates must consider not only the hospital’s actual costs, but also whether its actual costs are reasonable.11
*458Judges have decided issues of comparable difficulty and complexity, but not without substantial time, effort, and expense. As the motion judge found, the “Secretary’s performance of the task assigned to her necessarily calls for the application of technical expertise that the [cjourt lacks, and the exercise of judgment and discretion that the [Ljegislature has not entrusted to the [c]ourt.” It would be reasonable for the Legislature to conclude that the fair and cost-effective provision of hospital services to MassHealth patients would not be furthered by judicial review. See Cummings v. Secretary of Envtl. Affairs, 402 Mass. 611, 617 (1988) (“A policy that places final determination as to the necessity of an [environment impact report] in the hands of a disinterested public official with expertise in environmental matters, shared by his or her staff but not ordinarily shared by judges, cannot be characterized as unsound”).12
*459For these reasons, the judge did not err in concluding that the plaintiff hospitals’ claims that the Secretary violated her statutory duty under § 11 must be denied because the Legislature neither created a private right of action to enforce this statutory duty nor waived sovereign immunity.
3. Breach of contract. The plaintiff hospitals do not allege that the Secretary failed to make payments as required by the hospital provider RFA and contract. What they do allege is that the Secretary is contractually required to comply with applicable statutes in determining reimbursement rates, including the statutory obligation in § 11 (a) to “establish rates that equal the financial requirements of providing care to recipients of medical assistance,” and that the Secretary committed a breach of this contractual obligation. “[A] contractual claim does not arise under a statute unless the Legislature has explicitly expressed the intent to waive sovereign immunity and create a contractual remedy.” Lopes, supra at 178, quoting Hollstein v. Contributory Retirement Appeal Bd., 47 Mass. App. Ct. 109, 114 (1999). Our conclusion that the Legislature did not intend to waive sovereign immunity therefore defeats the plaintiffs’ contractual claim.
The Holyoke plaintiffs additionally allege that the Secretary violated the “implied covenant of good faith and fair dealing” in her actions. But the basis for this claim is the alleged statutory violation that the Secretary did not “set reimbursement rates . . . based on the actual financial requirements” of the plaintiff hospitals (emphasis added). To the extent that this claim rests on an alleged statutory violation, we have already concluded that it must fail on grounds of sovereign immunity. To the extent that it rests on the claim that the hospitals were entitled under § 11 (a) to reimbursement of their actual costs, we have already noted that the statutory scheme distinguishes between actual and reasonable costs, and only requires the Secretary to reimburse reasonable costs. To the extent that it rests on more traditional grounds of bad faith or unfair dealing, it also must fail because, where the Holyoke plaintiffs agreed in *460the contract to accept the rates of payment in their RFA, the Secretary cannot be found to have acted in bad faith or to have dealt unfairly by failing to provide reimbursement at higher rates. “[T]he implied covenant [of good faith and fair dealing] does not create rights or duties beyond those the parties agreed to when they entered into the contract.” Curtis v. Herb Chambers I-95, Inc., 458 Mass. 674, 680 (2011), and cases cited. The judge did not err in denying the claims of breach of contract and breach of the implied covenant of good faith and fair dealing.
4. Preemption under the supremacy clause. Under 42 U.S.C. § 1396a(a)(30)(A) (Supp. IV 2010) of the Federal Medicaid Act (§ 1396a[a][30][a]), a State Medicaid plan, such as MassHealth, must “provide such methods and procedures relating to . . . the payment[] for care and services available under the plan ... as may be necessary ... to assure that payments are consistent with efficiency, economy, and quality of care and are sufficient to enlist enough providers so that care and services are available under the plan at least to the extent that such care and services are available to the general population in the geographic area.” The hospital plaintiffs allege that the Secretary’s “improper rate-setting process” and her reduction in payments “based solely on the Commonwealth’s budgetary concerns” were contrary to the requirements of § 1396a(a)(30)(A) because the Secretary did not consider whether the payments were “consistent with efficiency, economy, quality of care, and access to care.”
The hospital plaintiffs concede that, under Federal law, providers do not have a private right of action under § 1396a(a)(30)(A). See Long Term Care Pharmacy Alliance v. Ferguson, 362 F.3d 50, 56-57, 59 (1st Cir. 2004) (“nothing in [§ 1396a(a)(30)(A)] expressly provides that those who furnish Medicaid services have any enforcement rights or, indeed, have any specific rights to procedural (e.g., notice and comment) or substantive (e.g., just and reasonable rates) protections”; “if [providers] think that state reimbursement is inadequate — and cannot persuade the Secretary [of the United States Department of Health and Human Services] to act — they must vote with their feet”).13 The hospital plaintiffs attempt to sidestep this obstacle by claim*461ing that the Secretary’s rate setting process and rate payments “are preempted under the Supremacy Clause of the United States Constitution.” We conclude that, where the plaintiffs have no private right of action directly to claim a violation of § 1396a(a)(30)(A), they cannot accomplish the same result by claiming a violation of the supremacy clause.
“The purpose of the Supremacy Clause is . . .to ensure that, in a conflict with state law, whatever Congress says goes.” Douglas v. Independent Living Ctr. of S. Cal., Inc., 132 S. Ct. 1204, 1212 (2012) (Roberts, C.J., dissenting) (Douglas). The supremacy clause is “ ‘not a source of any federal rights;’ rather, it ‘ “secure[s]” federal rights by according them priority whenever they come in conflict with state law.’ ” Dennis v. Higgins, 498 U.S. 439, 450 (1991), quoting Chapman v. Houston Welfare Rights Org., 441 U.S. 600, 613 (1979). The plaintiffs, however, essentially attempt to make the supremacy clause a source of Federal rights by claiming that it provides a private right of action that is not available under § 1396a(a)(30)(A). We agree with Chief Justice Roberts’s view on the matter, as expressed in Douglas:
“[I]f Congress does not intend for a statute to supply a cause of action for its enforcement, it makes no sense to claim that the Supremacy Clause itself must provide one. *462Saying that there is a private right of action under the Supremacy Clause would substantively change the federal rule established by Congress in the Medicaid Act. That is not a proper role for the Supremacy Clause, which simply ensures that the rule established by Congress controls.”
Douglas, supra at 1212-1213 (Roberts, C.J., dissenting).14
Even if the plaintiffs could bring their cause of action under the supremacy clause, the claim would still be barred by the Commonwealth’s sovereign immunity. “The Constitution, by delegating to Congress the power to establish the supreme law of the land when acting within its enumerated powers, does not foreclose a State from asserting immunity to claims arising under federal law merely because that law derives not from the State itself but from the national power.” Alden v. Maine, 527 U.S. 706, 732 (1999). Except where Congress exercises its enforcement power under § 5 of the Fourteenth Amendment to the United States Constitution, a State retains sovereign im*463munity from private suit in its own courts unless it consents to suit. Id. at 754-756. See Lopes, supra at 175; Morris v. Massachusetts Maritime Academy, 409 Mass. 179, 184-185 (1991) (States retain sovereign immunity unless Congress explicitly abrogates State sovereign immunity). The judge correctly denied the plaintiffs’ claims under the supremacy clause.15
5. Taking without lawful compensation. The hospital plaintiffs allege that the low payment rates established by the Secretary constitute a taking without lawful compensation, in violation of art. 10 of the Massachusetts Declaration of Rights and the Fifth and Fourteenth Amendments to the United States Constitution. We recognize that, where a property owner is legally compelled to engage in a price-regulated activity, the inadequacy of the regulated price may give rise to a constitutional claim of a regulatory taking. See Bluefield Water Works & Improvement Co. v. Public Serv. Comm’n of W. Va., 262 U.S. 679, 690 (1923) (public utility entitled under Fourteenth Amendment to rates sufficient to yield reasonable rate of return on value of its property); Boston Gas Co. v. Department of Pub. Utils., 368 Mass. 780, 789 (1975) (“Under the Federal and State Constitutions, the company is entitled to earn a fair and reasonable return on its investment”). But “where a service provider voluntarily participates in a price-regulated program or activity, there is no legal compulsion to provide service and thus there can be no taking.” Garelick v. Sullivan, 987 F.2d 913, 916 (2d Cir.), cert. denied, 510 U.S. 821 (1993) (Garelick), and cases cited. See Franklin Memorial Hosp. v. Harvey, 575 F.3d 121, 129 (1st Cir. 2009). A hospital’s participation in the MassHealth program is voluntary in that no hospital is required to execute the contract set forth in the RFA and participate in MassHealth. See G. L. c. 118E, § 36 (“Participation in the medical assistance programs established under this chapter shall be limited to providers of services who . . . indicate their intention to the division to so *464participate”); Hennessey v. Berger, 403 Mass. 648, 650 (1988) (“participation by health care providers in Medicaid is voluntary” under Federal and State law).
The hospital plaintiffs argue that their participation in MassHealth was voluntary in theory but not in reality. BMC claims that it is compelled by a “statutory mandate” to participate in MassHealth, because the enabling statute that authorized its creation from the merger of Boston City Hospital and Boston University Medical Center Hospital declared that “the mission of the new medical center . . . shall be to consistently provide excellent and accessible health care services to all in need of care, regardless of status or ability to pay.” St. 1995, c. 147, § 1 (b). The Holyoke plaintiffs similarly claim that, as nonprofit, tax-exempt public charities, they are “legally required to provide health care services to all in need of care, regardless of status or ability to pay.” All the hospital plaintiffs argue that they would be unable to provide medical care to those in need without participating in MassHealth.
We acknowledge that it would be difficult, perhaps impossible, for these disproportionate share hospitals to survive financially if they were to refuse to participate in MassHealth, and that such a refusal would burden their MassHealth patients who would have to go elsewhere to seek nonemergency care.16 A painful choice, however, is nonetheless a choice; a disproportionate share hospital retains the option, difficult as it may be, to refuse to participate in MassHealth, even if doing so may put its continued existence as a financially viable hospital at risk and endanger the quality of health care available to its MassHealth patients. As a matter of law, despite the “business realities” and “the strong financial inducement to participate” in MassHealth, a hospital’s decision to participate is voluntary and its voluntariness deprives the hospital of any claim of a regulatory taking. Minnesota Ass’n of Health Care Facilities, Inc. v. Minnesota Dep’t of Pub. Welfare, 742 F.2d 442, 446 (8th Cir. 1984), cert. denied, 469 U.S. 1215 (1985). See id., quoting Minnesota Ass’n *465of Health Care Facilities, Inc. v. Minnesota Dep’t of Pub. Welfare, 602 F.2d 150, 154 (8th Cir. 1979) (“It is, of course, only through voluntary participation in the state’s Medicaid program that a nursing home falls within the purview of [the statute]. ‘If appellants find that the reimbursement rates are insufficient, then they may either make their homes more efficient and economical or terminate their relationship with Medicaid and no longer accept Medicaid recipients as residents’ ”). See Painter v. Shalala, 97 F.3d 1351, 1357 1358 (10th Cir. 1996) (physician voluntarily provided services knowing amount reimbursed under Medicare); Garelick, supra at 917 (“All court decisions of which we are aware that have considered takings challenges by physicians to Medicare price regulations have rejected them in the recognition that participation in Medicare is voluntary”).
Many businesses financially may have little choice but to do business with the government at rates below what they would like to receive, but that does not mean that they may bring a regulatory taking claim. See, e.g., German v. Commonwealth, 410 Mass. 445, 451 (1991) (statute establishing “new [lower] rate of compensation for State employees” not taking). See also Hughes Communications Galaxy, Inc. v. United States, 271 F.3d 1060, 1070 (Fed. Cir. 2001), quoting Sun Oil Co. v. United States, 572 F.2d 786, 818 (Ct. Cl. 1978) (“ ‘the concept of a taking as a compensable claim theory has limited application to the relative rights of party litigants when those rights have been voluntarily created by contract.’ . . . Taking claims rarely arise under government contracts because the Government acts in its commercial or proprietary capacity in entering contracts, rather than in its sovereign capacity”); Detroit Edison Co. v. United States, 56 Fed. Cl. 299, 303 (2003) (noting it is inappropriate to permit plaintiff “to pursue a takings remedy in order to circumvent the limitations inherent in its contractual relationship with the Government”).
The Health Plan’s claims. 1. Background. In 2006, the Legislature passed comprehensive health care legislation that had as one of its goals to change the way that medical providers would be compensated for serving patients with no health coverage who could not pay for their care. See St. 2006, c. 58 (“An Act providing access to affordable, quality, accountable Health Care” *466[Act]). Under § 122 of the Act, the Secretary was required in fiscal years 2007, 2008, and 2009 to reimburse BMC and hospitals operated by the Cambridge public health commission “at levels consistent with their net supplemental payments of $287,000,000 in fiscal year 2006.” In addition, § 122 provided, “For fiscal year 2009, subject to appropriation, the [Secretary] shall hold harmless said amount of $287,000,000 in funding by allocating $160,000,000 in net supplemental payments from the Commonwealth Care Trust Fund and by increasing actuarially sound rates to the maximum extent allowable and eligible for financial participation, including the balance from other financing mechanisms . . . .” BMC and the Health Plan were entitled to two-thirds of the $287 million, or approximately $191.3 million.
The Legislature authorized a lump-sum payment of $106.7 million to BMC, and there is no dispute that the Secretary made this payment in fiscal year 2009. The health Plan alleges that, under § 122, the Secretary was required to pay the remaining $84.6 million by increasing “to the maximum extent allowable” the monthly amount that the Secretary paid for each MassHealth member who was enrolled in its managed care health organization, known as the monthly “capitation rate.” Instead, the Secretary reduced the capitation rates she had initially set, which were already allegedly inadequate because those rates were based on data from calendar years 2005 and 2006, and held the capitation rates at the levels established for fiscal year 2008. On November 10, 2008, the Health Plan executed the Secretary’s amendment to its managed care organization contract with the reduced capitation rates, albeit under a reservation of rights, “because failure to do so would have resulted in the [Secretary’s] immediate transfer of enrollees out of [the Health Plan].”
2. Violation of St. 2006, c. 58, § 122. The Health Plan alleges that the Secretary disregarded the requirement in § 122 to increase the capitation rate in fiscal year 2009 “to the maximum extent allowable” in order to generate the $84.6 million balance that it was due. The Secretary argues that, under § 122, she need not have increased the capitation rate “to the maximum extent allowable” so long as the total funding level, consisting *467of the total capitation payment, the fixed supplemental payment of $106.7 million to the BMC, and any additional payments from “other financing mechanisms,” was at least equal to what was paid to the BMC in 2006, which she contends it was.
We conclude, as did the judge below, that the Health Plan’s claims under § 122 of the Act cannot prevail for the same reasons that the plaintiff hospitals cannot prevail on their claims under G. L. c. 118G, § 11: the Legislature did not provide a private right of action to enforce the “hold harmless” provisions of § 122, or waive sovereign immunity, and waiver is not a “necessary implication” of this statutory duty.
Claims applicable to all plaintiffs. We now turn to claims asserted by all the plaintiffs.
1. Quantum meruit. The plaintiffs allege that they may recover for services provided to MassHealth patients on a theory of quantum meruit. The plaintiffs, however, provided these services pursuant to contracts entered into with the Secretary, at rates set under those contracts. A plaintiff is not entitled to recovery on a theory of quantum meruit where there is a valid contract that defines the obligations of the parties. See York v. Zurich Scudder Invs., Inc., 66 Mass. App. Ct. 610, 620 (2006); Restatement (Third) of Restitution and Unjust Enrichment § 2 (2011) (“A valid contract defines the obligations of the parties as to matters within its scope, displacing to that extent any inquiry into unjust enrichment”).
The BMC claims that it never entered into a contract for 2009 because it refused to sign the December amendment to the rate year 2009 REA that established the new payment rates. This contention is incorrect as a matter of law. The BMC had in 1998 executed a “provider agreement” with the Department of Public Welfare (department) that “continue[d] in effect until terminated by either party” where the department would “reimburse the Provider at rates . . . contained in the applicable [department fee schedules.” The BMC does not allege that it terminated that provider agreement. After being given full notice of the terms of the proposed contract in the rate year 2009 REA, including notice of the rates it would receive under the amended contract, BMC did not terminate the agreement but instead continued to provide services with knowledge of the *468payment rates. There is no dispute that the Secretary exercised her discretion under the contract to “continue [BMC]’s participation,” at the rates set forth in the RFA.
The Holyoke plaintiffs argue that they had no legally valid rate year 2009 contract with the Secretary because the payment rates provided in the contract did not equal the financial requirements of providing care to recipients of medical assistance and therefore the contract was illegal and in violation of public policy. Where providers have no private right of action to claim a violation of G. L. c. 118G, § 11 (a), or 42 U.S.C. § 1396a(a)(30), we will not provide them with this “back door” means of accomplishing the equivalent through a quantum meruit claim that would provide judicial review of the reasonableness of the Secretary’s rates for disproportionate share hospitals.
The Health Plan claims that its contract is void because it was entered into and performed under duress. We note at the outset that this argument is incorrect in that economic duress renders a contract voidable, not void. See Cabot Corp. v. AVX Corp., 448 Mass. 629, 637 (2007) (Cabot), and cases cited. We treat the Health Plan’s claim as seeking to void retroactively its allegedly voidable contract with the Secretary.
When the Health Plan executed the agreement on November 10, 2008, with the Secretary that lowered its capitation rate, it attached a document that it called a “reservation of rights” that declared that the Health Plan “signs the Amendment under duress” (emphasis in original).17 “The assertion of duress must be proved by evidence that the duress resulted from defendant’s wrongful and oppressive conduct and not by plaintiff’s necessities.” Cabot, supra at 638, quoting International Underwater Contrs., Inc. v. New England Tel. & Tel. Co., 8 Mass. App. Ct. 340, 342 (1979). All that the Secretary is alleged to have done here was to set unreasonably low capitation rates, and inform the Health Plan that it was free to reject these rates and not renew its managed care operator contract. This conduct falls *469well short of the requisite “wrongful and oppressive conduct” intended to coerce the Health Plan to accept the contract. See Cabot, supra at 639 (“Absent any legally cognizable restraint, [a party is] free to drive whatever bargain the market would bear”). The judge did not err in denying the quantum meruit claims.
2. Certiorari, mandamus, and declaratory judgment. The plaintiffs sought certiorari review of the Secretary’s actions under G. L. c. 249, § 4.18 “Certiorari is a limited procedure which may be used to correct substantial errors of law committed by a judicial or quasi-judicial tribunal (but not administrative, political, or legislative decisions).” St. Botolph Citizens Comm., Inc. v. Boston Redev. Auth., 429 Mass. 1, 7 (1999). “If the proceeding or hearing involves ‘unsworn statements by interested persons advocating or disapproving the proposed new policy’ rather than ‘sworn testimony by witnesses subject to cross-examination in a hearing preceded by specific charges,’ the hearing is more likely to be legislative or regulatory, rather than quasi-judicial, in nature.” School Comm. of Hudson v. Board of Educ., 448 Mass. 565, 576 (2007). The judge was correct to deny this review where the Secretary was exercising her regulatory power granted by the statute, and the rate setting process bore none of the indicia of judicial or quasi judicial decision-making.
The plaintiffs similarly also sought relief in the nature of mandamus, pursuant to G. L. c. 249, § 5.19 “A complaint in the *470nature of mandamus is ‘a call to a government official to perform a clear cut duty,’ and the remedy is limited to requiring action on the part of the government official.” Simmons v. Clerk-Magistrate of the Boston Div. of the Hous. Court Dep’t, 448 Mass. 57, 59-60 (2006), quoting Doe v. District Attorney for the Plymouth Dist., 29 Mass. App. Ct. 671, 675 (1991). Here, as the motion judge found in denying the mandamus claim, the Secretary’s statutory duty is to set rates of reimbursement for services provided under MassHealth and to enter into contracts with providers who agree to accept the rates set. The Secretary did exactly that. “Mandamus is not an appropriate remedy to obtain a review of the decision of public officers who have acted and to command them to act in a new and different manner.” Harding v. Commissioner of Ins., 352 Mass. 478, 480 (1967). See Doherty v. Retirement Bd. of Medford, 425 Mass. 130, 134 (1997), quoting Reading v. Attorney Gen., 362 Mass. 266, 269 (1972) (“mandamus is a remedy for [administrative] inaction and [is] not available where action has already been taken”).
The plaintiffs also sought, under G. L. c. 231 A, § 1, a judgment declaring that the Secretary’s reimbursement rates and capitation rates, and her methodology for determining these rates, are unreasonable, and in violation of G. L. c. 118G, § 11 (a); 42 U.S.C. § 1396a(a)(30); and St. 2006, c. 58, § 122.20 Where a provider has a private right of action to challenge the Secretary’s rate determination, a claim for declaratory judgment would be appropriate if the Secretary had promulgated regulations and the plaintiffs were challenging the validity of those regulations, claiming them to be illegal, arbitrary, or capricious. See Salisbury Nursing & Rehabilitation Ctr., Inc. v. Division of Admin. Law Appeals, 448 Mass. 365, 371 (2007), and cases cited. But here the Legislature has declined to give the plaintiff providers any private right of action and what is at issue is the reasonableness *471of the payment rates established by the Secretary and the methodology used to calculate those rates, not the validity of any regulation. If the plaintiffs could seek declaratory judgment here, they would for all practical purposes have a private right of action to challenge the reasonableness of payment rates. A declaratory judgment cannot be used to circumvent a legislative judgment denying a provider the opportunity to seek administrative or judicial review of the reasonableness of payment rates. See Green v. Mansour, 474 U.S. 64, 73 (1985) (declaratory judgment not available where result “would be a partial ‘end run’ ” around prohibition in Eleventh Amendment to United States Constitution).
*470“[T]he superior court . . . may on appropriate proceedings make binding declarations of right, duty, status and other legal relations sought thereby, either before or after a breach or violation thereof has occurred in any case in which an actual controversy has arisen and is specifically set forth in the pleadings and whether any consequential judgment or relief is or could be claimed at law or in equity or not. . . .”
*471Conclusion. We affirm the motion judge’s allowance of the Secretary’s motion for judgment on the pleadings as to the claims brought by BMC and the Health Plan, and of the motion to dismiss as to the claims brought by the Holyoke plaintiffs. We honor the legislative judgment that the plaintiffs’ redress for claims that the Secretary committed a breach of her statutory duties in calculating the reimbursement and capitation rates paid for the provision of medical care to MassHealth patients rests in the political arena, not in the courts. See Franklin Memorial Hosp. v. Harvey, 575 F.3d 121, 130 (1st Cir. 2009) (provider’s “better course of action is to seek redress through the state’s political process”).
So ordered.
A second major program, Medicare, is a Federal medical insurance program available to the disabled or elderly. See Title XVm of the Social Security Act, codified at 42 U.S.C. §§ 1395c, 1395j (Supp. IV 2010). In addition to Medicare and Medicaid, there are other private and government programs available in Massachusetts, including the Health Safety Net Trust Fund (Health Safety Net), see G. L. c. 118G, §§ 34-39, which reimburses hospitals that provide care to those who are without private or government insurance and “are determined to be financially unable to pay for their care, in whole or in part.” Id. at § 34.
The other hospital plaintiffs are Quincy Medical Center, Inc., and Brockton *450Hospital, Inc., doing business as Signature Healthcare Brockton Hospital. Three other hospitals (Berkshire Medical Center, Inc.; Essent Healthcare of Massachusetts, Inc., doing business as Merrimack Valley Hospital; and Cape Cod Hospital) were plaintiffs in the lawsuit but do not join in the appeal.
The record appendix includes a copy of the Request for Applications (RFA) hospital provider contract for rate year 2009.
For rate year 2009, the methodology used to calculate each hospital’s “Standard Payment Amount per Discharge” (SPAD) rate was defined over two pages of the RFA. The methodology used to calculate the “Payment Amount Per Episode” (PAPE) rate is approximately one page long.
In rate year 2009, the final SPAD rates varied from $3,424.85 (Nantucket Hospital) to $15,089.45 (Dana-Farber Cancer Institute). The SPAD rates for the plaintiff hospitals were $9,232.43 (Boston Medical Center), $6,516.24 (Holyoke Medical Center), $7,626.07 (Quincy Hospital) and $5,227.26 (Brock-ton Hospital). The PAPE rates varied from $138.53 (Wing Memorial Hospital) to $1,433.97 (Dana-Farber Cancer Institute) and show similar individual hospital variation.
The “[g]ross patient service revenue” is defined as “the total dollar *453amount of a hospital’s charges for inpatient services rendered in a fiscal year.” G. L. c. 118G, § 1. “Free care” is also defined by that statute as care “provided to individuals determined to be financially unable to pay for their care, in whole or in part.” Id. Hospitals can seek reimbursement for this care from the Health Safety Net trust fund. See G. L. c. 118G, §§ 34, 36, 39.
The relevant text of G. L. c. 118G, § 11, provides:
“All rates of payment to acute hospitals and non-acute hospitals under Title XIX shall be established by contract between the provider *454of such hospital services and the division of medical assistance, except as provided in subsections (a) and (£>), or otherwise permitted by law. All rates shall be subject to all applicable Title XIX statutory and regulatory requirements and shall include reimbursement for the reasonable cost of providing competent interpreter services ....
“(a) For disproportionate share hospitals, the executive office shall establish rates that equal the financial requirements of providing care to recipients of medical assistance.”
The relevant text of G. L. c. 118G, § 9, provides:
“Except for rates established pursuant to [§ 11], any person, corporation or other party aggrieved by an interim rate or a final rate established by the division [of health care finance and policy], or by failure of the executive office to set a rate or to take other action required by law and desiring a review thereof shall, within thirty days after said rate is filed with the state secretary [of health and human services] or may, at any time, if there is a failure to determine a rate or take any action required by law, file an appeal with the division of hearings officers established by [G. L. c. 7, § 4H], . . . Judicial review shall be governed by [G. L. c. 30A, § 14,] to the extent not inconsistent with the provisions of this section.”
Determining a hospital’s “reasonable” costs, or even its actual costs, would likely prove to be a difficult and subjective evaluation:
“Unfortunately, ‘reasonable’ remains murky and ill-defined. . . . [F]or hospitals and physicians, a strong case can be made that ‘prevailing’ or ‘usual’ or ‘customary’ charges are not necessarily ‘reasonable’
“For hospitals, current pricing structures are mysterious at best. As noted in Doe [v. HCA Health Servs. of Term., Inc., 46 S.W.3d 191, 194 (Tenn. 2001)], hospitals commonly use an internal document called a ‘charge master.’ It lists the hospital’s official billing charges for thousands of goods and services. Charge masters are usually kept confidential, even from most of the hospital’s employees, and typically are adjusted from week to week. . . .
“[A] charge master [is] not necessarily based on any analysis of the costs of providing various goods and services. In Doe, the hospital employee who set the charge master acknowledged in testimony that ‘he has never conducted studies to determine the actual costs of delivering goods and services in setting the Charge Master rates. Instead he just “estimates it”.’
“In fairness to hospitals, basing charges on the actual costs of providing services can be very difficult. For instance, internal cost-shifting is widespread, in which prices for some common items are set high, to generate extra revenue to cover some of the costliest goods and services. For this and other reasons, determining the actual cost of providing a given service will ordinarily require considerable resources to track down its myriad sub-costs. There is little incentive to undertake such an effort, given that payors reimburse care according to actual or negotiated charges, not hospitals’ actual costs. The net result is little, if any, correlation between a charge master price and the price that the same service or product might have if purchased in a direct, supply- and-demand economy.”
Morreim, High-Deductible Heath Plans: New Twists on Old Challenges from Tort and Contract, 59 Vand. L. Rev. 1207, 1251-1254 (2006).
Here, the Legislature has provided little guidance for a court to use in determining what is a “reasonable” cost. See, e.g., G. L. c. 118G, § 7 (setting out ways to review provider costs, including “peer group costs analyses; ceilings on capital and operating costs; [and] productivity standards” but then *458stating “this section shall not apply to . . . hospitals [except] for services under the workers’ compensation act”). This lack of guidance further reinforces our view that the Legislature did not intend for the judiciary to review hospital payment rates.
The plaintiff hospitals cite Todino v. Wellfleet, 448 Mass. 234 (2007) (Todino), and Bates v. Director of the Office of Campaign & Political Fin., 436 Mass. 144 (2002) (Bates), in support of their contention that a private right of action and waiver of sovereign immunity are a “necessary implication” of the Secretary’s statutory duty under G. L. c. 118G, § 11. Both cases are distinguishable.
In Todino, the Legislature had waived sovereign immunity and provided police officers and fire fighters with a private right of action under G. L. c. 41, § 111F, to enforce their right to be protected from any “loss of pay” arising from an incapacitating injury sustained without fault in the performance of their duties. Id. at 236-238. We concluded that, where the statute “clearly expresses an intent to protect injured officers fully from all reductions in the worth of their compensation, including by temporary loss of use of funds,” id. at 237, “[t]he recovery of interest is necessarily implied by the potent language of § 11 IF that requires timely payments and prohibits any reduction of pay.” Id. at 239.
In Bates, the Massachusetts Clean Election Law (since repealed) was approved by popular initiative. Id. at 146. We concluded that the “power to bind the Commonwealth to payments of public funds by the process of certification is required ‘by necessary implication’ from the clean elections law.” Id. at 173, quoting Woodbridge v. Worcester State Hosp., 384 Mass. 38, 42 (1981). We imputed to the voters who enacted the law an intent to waive sovereign immunity to enforce the Commonwealth’s obligation to pay qualifying candidates public funds for their political campaigns, and saw “no reasons of ‘justice and public policy’ [that would] argue for the application of sovereign *459immunity.” Bates, supra at 173-174. In the circumstances here, we do not impute an intent to waive sovereign immunity to the Legislature, and understand why the Legislature would conclude that public policy does not require a waiver of sovereign immunity.
Nor does 42 U.S.C. § 1396a(a)(30)(A) (Supp. IV 2010) (§ 1396a[a][30][A]) *461grant the hospitals a right that would be separately enforceable under 42 U.S.C. § 1983 (2006). See Long Term Care Pharmacy Alliance v. Ferguson, 362 F.3d 50, 57 (1st Cir. 2004) (“[The plaintiff’s] best argument [to enforce § 1396a(a)(30)(A)] would have been to rely upon section 1983 as providing an explicit automatic private right of action .... However, the Supreme Court recently closed that door as well in Gonzaga University v. Doe, [536 U.S. 273, 283 (2002)]”). See also Equal Access for El Paso, Inc. v. Hawkins, 509 F.3d 697, 702-704 (5th Cir. 2007), cert. denied, 555 U.S. 811 (2008); Mandy R. v. Owens, 464 F.3d 1139, 1147-1148 (10th Cir. 2006), cert. denied, 549 U.S. 1305 (2007); Westside Mothers v. Olszewski, 454 F.3d 532, 542-543 (6th Cir. 2006); Sanchez v. Johnson, 416 F.3d 1051, 1058-1062 (9th Cir. 2005); Pennsylvania Pharmacists Ass’n v. Houstoun, 283 F.3d 531, 541-542 (3d Cir.), cert. denied, 537 U.S. 821 (2002); In re NYAHSA Litig., 318 F. Supp. 2d 30, 39 (N.D.N.Y. 2004), aff’d sub nom. New York Ass’n of Homes & Servs. for the Aging, Inc. v. Debuono, 444 F.3d 147, 148 (2d Cir. 2006). Contrast Pediatric Specialty Care, Inc. v. Arkansas Dep’t of Human Servs., 443 F.3d 1005, 1015-1016 (8th Cir. 2006), partially vacated on other grounds sub nom. Selig v. Pediatric Specialty Care, Inc., 551 U.S. 1142 (2007) (providers can enforce § 1396a[a][30][A] through 42 U.S.C. § 1983).
In Douglas v. Independent Living Ctr. of S. Cal, Inc., 132 S. Ct. 1204 (2012) (Douglas), the United States Supreme Court granted certiorari to decide “[w]hether Medicaid recipients and providers may maintain a cause of action under the Supremacy Clause to enforce [§ 1396a(a)(30)(A)] by asserting that the provision preempts a state law reducing reimbursement rates.” Id. at 1212 (Roberts, C.J., dissenting). After oral argument, the Federal agency in charge of administering Medicaid, the Centers for Medicare & Medicaid Services (CMS), approved several of the State’s amendments to its Medicaid plan and the State withdrew its request for approval of the remaining amendments. Id. at 1209. A five-member majority of the Court vacated the judgments of the United States Court of Appeals for the Ninth Circuit, which held that Medicaid providers and beneficiaries could bring a private action based on the supremacy clause, id., and remanded it for further argument on the ground that CMS approval of the rate reductions placed the cases “in a different posture.” Id. at 1210. The majority did “not address whether the Ninth Circuit properly recognized a Supremacy Clause action to enforce this federal statute before the agency took final action.” Id. at 1211.
In his dissent, joined by the other three Justices, Chief Justice Roberts concluded that the Court should have decided the question presented on certiorari and that no remand was necessary because, “[t]o decide this case, it is enough to conclude that the Supremacy Clause does not provide a cause of action to enforce the requirements of [§ 1396a(a)(30)(A)] when Congress, in establishing those requirements, elected not to provide such a cause of action in the statute itself.” Id. at 1212 (Roberts, C.J., dissenting). Therefore, four of the Justices have concluded that the supremacy clause does not provide a cause of action to enforce the requirements of § 1396a(a)(30)(A), while five Justices have yet to reach the issue.
The Supreme Court in Douglas noted that, where the CMS has approved a State’s payment rate plan, an aggrieved medical provider could likely seek review of the agency determination under the Administrative Procedure Act, 5 U.S.C. §§ 701 et seq. (2006 & Supp. IV 2010) “to obtain an authoritative judicial determination of the merits of their legal claim.” Id. at 1210. The defendant in such a case would be the United States Secretary of Health and Human Services, not the Massachusetts Secretary. See 5 U.S.C. §§ 701, 702.
Even if a hospital did not participate in MassHealth, it would be paid at MassHealth rates for any emergency care it provided to MassHealth patients. See G.L. c. 118G, § 11 (b), G.L. c. 118E, § 17A; G.L. c. 111, § 70E, fifth par., (k) & (n). See also 42 U.S.C. § 1395dd (Supp. IV 2010).
The Secretary’s Medicaid director immediately replied in writing that, if the Health Plan “did not intend to accept the Amendment unconditionally, including all payment terms as payment in full, and would prefer instead not to renew [its] [c]ontract,” then it was free to do so and should notify the Secretary of its decision. The Health Plan did not respond to this letter, and continued to provide services to its MassHealth members.
The relevant text of G. L. c. 249, § 4, provides:
“A civil action in the nature of certiorari to correct errors in proceedings which are not according to the course of the common law, which proceedings are not otherwise reviewable by motion or by appeal, may be brought in the supreme judicial or superior court.... Where such an action is brought against a body or officer exercising judicial or quasi-judicial functions to prevent the body or officer from proceeding in favor of another party, or is brought with relation to proceedings already taken, such other party may be joined as a party defendant by the plaintiff or on motion of the defendant body or officer or by application to intervene. ...”
The relevant text of G. L. c. 249, § 5, provides: “A civil action to obtain relief formerly available by writ of mandamus may be brought in the supreme judicial or superior court. . . .”
The relevant text of G. L. c. 231 A, § 1, provides: