DAVID A. NELSON, Circuit Judge.

This is an appeal by the Secretary of Agriculture from a district court decision holding that the Secretary acted improperly when he amended his regulations in 1986 to categorize "workfare" benefits as unearned income for purposes of determining eligibility for food stamps under 7 U.S.C. § 2014(e). A cross-appeal raises the question whether the Secretary must continue federal financial assistance to the State of Ohio for the period of the state's compliance with the district court's order. The Secretary challenges this court's jurisdiction over the cross-appeal.

We conclude that the 1986 change in the regulations was not arbitrary or capricious; the judgment of the district court will therefore be reversed. The cross-appeal presents no justiciable case or controversy, in our view, and the cross-appeal will be dismissed.

I

The plaintiffs are individuals who, at the onset of this litigation, worked at public service jobs as a condition to receiving benefits under Ohio's "general relief" program, as it was then called. Plaintiff were eligible to receive food stamps under the Food Stamp Act of 1964, 7 U.S.C. § 2011 et seq.

Eligibility to receive food stamps, and the size of food stamp allotments, depend on household income. In calculating allotments, recipients who work are permitted a deduction — currently 20 percent of earned income — "to compensate for taxes, other mandatory deductions from salary, and work expenses. . . ." 7 U.S.C. § 2014(e). The deduction tends to make allotments larger than they would be without it.

As amended in 1978, the regulations of the Department of Agriculture, the federal agency that oversees the food stamp program, provided that "[a]ssistance payments from programs which require, as a condition of eligibility, the actual performance of work without compensation other than the assistance payments themselves, shall be considered earned income to the extent that the payments actually substitute for wages or salaries." 43 Fed.Reg. 47903 (Oct. 17, 1978). Prior to 1978, however, Ohio refused to allow plaintiffs to take the earned income deduction for payments they received under the general relief program. That policy led plaintiffs to file suit against the state. Although the then-Secretary of Agriculture was named as a defendant, he agreed with the plaintiffs on the merits of their claim.

On December 6, 1978, the district court entered a summary judgment granting plaintiffs the declaratory and injunctive relief they had requested. The court ordered that money received by the plaintiffs under the general relief program should be deemed to constitute income from employment, which income would be subject to the earned income deduction. The court denied the plaintiffs' claim for money damages, finding that claim barred by the Eleventh Amendment.

In 1982 the Secretary of Agriculture proposed to amend his regulations by removing "workfare" from the definition of earned income and amending the definition of "unearned income" to provide that assistance payments from programs which require, as a condition of eligibility, the actual performance of work without compensation other than the assistance payments themselves, shall be considered unearned income." 47 Fed.Reg. 52185, 52189 (Nov. 19, 1982). The Secretary's notice of proposed rulemaking offered three reasons for the change: Congressional intent, consistency with the Community Work Experience Program (a "workfare type program which State agencies may establish for recipients of Aid to Families with Dependent Children"), and encouragement of gainful employment over workfare. Id. at 52187-88.

The proposed change in the regulations was adopted in 1986. 51 Fed.Reg. 10764, 10786 (March 28, 1986) (codified at 7 C.F.R. § 273.9(b)(2)(i)). The preamble to the final rule said, among other things, that the new regulations (which incorporated a number of other changes as well) would "reduce Program costs and simplify administration." Id. at 10764.

The state defendant then moved the district court for relief from the 1978 order. The plaintiffs, for their part, moved to enforce the judgment. The district court granted the plaintiffs' motion, after certain proceedings not pertinent here, and the appeal and cross-appeal followed.

II

Under the Administrative Procedure Act, regulations adopted by the Secretary pursuant to the broad authority conferred on him by the Food Stamp Act must be sustained if they are not arbitrary or capricious or contrary to law. 5 U.S.C. § 706. The standard is the same whether or not the position reflected in the regulations represents a change on the Secretary's part. See Motor Vehicle Mrs. Ass'n v. State Farm Mut. Auto. Ins. Co., 463 U.S. 29, 40-44, 103 S.Ct. 2856, 2865-67, 77 L.Ed.2d 443 (1983); see also Chevron, U.S.A., Inc. v. Natural Resources Defense Council, Inc., 467 U.S. 837, 863-64, 104 S.Ct. 2778, 2791-92, 81 L.Ed.2d 694 (1984) ("An initial agency interpretation is not instantly carved in stone. On the contrary, the agency, to engage in informed rulemaking, must consider varying interpretations and the wisdom of its policy on a continuing basis.").

In Chevron, the Supreme Court set forth the following approach to review of a challenged regulation:

"First, always, is the question whether Congress has directly spoken to the precise question at issue. If the intent of Congress is clear, that is the end of the matter; for the Court, as well as the agency, must give effect to the unambiguously expressed intent of Congress. If, however, the Court determines Congress has not directly addressed the precise question at issue, the Court does not simply impose its own construction on the statute, as would be necessary in the absence of an administrative interpretation. Rather, if the statute is silent or ambiguous with respect to the specific issue, the question for the Court is whether the agency's answer is based on a permissible construction of the statute."

467 U.S. at 842-43, 104 S.Ct. at 2781-82.

Applying the Chevron analysis to the case at bar, we find that Congress has not spoken directly to the precise question of whether workfare income ought to be considered earned income. It may be true that Congress contemplated the inclusion in "earned income" of allowances received in government training programs. See H.R. Rep. No. 464, 95th Cong., 1st Sess., 61-62, reprinted in 1977 U.S. Code Cong. Admin. News 1704, 2039-40. The Secretary contends, however, that "[t]raining allowances are actual compensation given in exchange for the work received," while the recipient of workfare is not being compensated for work as such; the work is simply a condition of eligibility for benefits. The fact that such benefits are not subject to the taxes and "other mandatory deductions from salary" of which Congress spoke in 7 U.S.C. § 2014(e) lends support to the Secretary's contention.

The Secretary offers the following rationale for his conclusion that workfare should not be treated as earned income. First, he says, the purpose behind the earned income deduction was "to compensate" for the taxes, other mandatory deductions from salary, and work expenses alluded to in 7 U.S.C. § 2014(e). Individuals on workfare do not need to have their taxes and so forth compensated for, the Secretary says, because they do not pay income or social security taxes and they are often reimbursed for other expenses. (He concedes that reimbursement may not fully cover such expenses.)

Second, the Secretary argues, there is a close relationship between the Food Stamp Program and the Community Work Experience Program of the AFDC program, 42 U.S.C. § 609 et seq. Workfare benefits received under the latter program are not considered earned income, and in the interest of consistency and administrative convenience, the Secretary says, workfare benefits from any source ought to be considered unearned income.

Third, the Secretary argues that the narrower definition of earned income provides an incentive for individuals to leave workfare for more productive employment — and the goal of the earned income deduction "is to encourage household members to work." H.R. Rep. 95-464, at 61, reprinted in 1977 U.S. Code Cong. Admin. News 2039.

Plaintiffs respond that the Secretary's interpretation is unreasonable because the factual situation today is exactly the same as it was in 1978, when the Secretary agreed with their position. The Secretary, they say, is relying on the same legislative history that would have been considered in 1978. The preamble to the 1978 rule implementing the deduction said that payments which "contemplate" the performance of work are "more properly considered as earned income." 43 Fed.Reg. 47864 (Oct. 17, 1978) (referring to Conservation Service payments). There has been no relevant change in the statutory framework on which the 1978 regulation was predicated.

The plaintiffs argue further that the second element in the Secretary's rationale, a need to harmonize the Food Stamp Act and the AFDC statute, must fail because it is inconsistent with recent Supreme Court caselaw. See Lukhard v. Reed, 481 U.S. 368, 107 S.Ct. 1807, 95 L.Ed.2d 328 (1987), rejecting the assertion that AFDC and the Food Stamp Act should be presumed to have a common definition of income. In Reed the Court noted that "[t]he explicit differences between the definition of `income' in the Food Stamp program . . . on the one hand and the AFDC statute on the other are simply too great to permit any such presumption." Id. at 377, 107 S.Ct. at 1813.

Finally, plaintiffs contend that the Secretary's policy argument is not well grounded in fact and is not supported by legislative history. They argue that Congress intended to distinguish not between types of employment, as the Secretary contends, but between working and not working. Plaintiffs point to a House report stating that "the term `earned income' [should] be construed to apply to any household member who is involved in any training program recognized by any federal, state, or local government agency." H.R. Rep. No. 464, 95th Cong., 1st Sess., 61-62, reprinted in 1977 U.S. Code Cong. Admin. News 2039-40. They contend that a workfare program is comparable to a training program and is not intended to be a "makework" system.

The Secretary remains unmoved, and we cannot say that the Secretary acted arbitrarily and capriciously in electing to treat workfare benefits as unearned income. The Secretary has provided a reasoned analysis in support of his position, even though some parts of the analysis are certainly debatable, and we do not find that the regulations are in conflict with the statute.

"A reviewing court may not set aside an agency rule that is rational, based on consideration of the relevant factors, and within the scope of the authority delegated to the agency by the statute. . . . The scope of review is narrow and a court is not to substitute its judgment for that of the agency." State Farm Mutual, 463 U.S. at 42-43, 103 S.Ct. at 2866.

That the change in the Secretary's judgment may have been "related to the election of a new President of a different political party" is immaterial:

"A change in administration brought about by the people casting their votes is a perfectly reasonable basis for an executive agency's reappraisal of the costs and benefits of its programs and regulations. As long as the agency remains within the bounds established by Congress, it is entitled to assess administration records and evaluate priorities in light of the philosophy of the administration." Id. at 59, 103 S.Ct. at 2875 (Rehnquist, J., concurring in part and dissenting in part) (footnote omitted).

Although the district court did not find it necessary to reach the plaintiffs' claim that the challenged regulation violates the Equal Protection Clause of the Fourteenth Amendment, the court nonetheless expressed a belief that the distinction between food stamp recipients who are workfare participants and those who are regular employees bore no rationale relationship to a legitimate government interest and thus was unconstitutional. Plaintiffs attempt to press this argument on appeal, but the attempt is unavailing.

The constitutional safeguard of equal protection is violated "only if the classification rests on grounds wholly irrelevant" to the achievement of a proper government interest. See McGowan v. Maryland, 366 U.S. 420, 425, 81 S.Ct. 1101, 1104, 6 L.Ed.2d 393 (1961). The classification will not be set aside "if any state of facts reasonably may be conceived to justify it." Id. A desire "to reduce Program costs" is a legitimate government interest, and the regulatory change can be justified as a cost-reduction measure, among other things. The burden of the cost saving is borne by people who are not paying income taxes or social security taxes, and whose work assignments, under the pertinent Ohio statute, may not "result in the displacement of persons who are already employed as regular full-time or part-time employees. . . ." Ohio Rev. Code § 5101.83(B). The desire to give food stamp recipients an incentive to become "regular full-time or part-time employees" is a legitimate governmental purpose, and plaintiffs' equal protection claim has no merit. If the policy adopted by the Secretary in 1986 be thought undesirable, the remedy lies in the same political processes that led to the earlier policy being changed in the first place.

III

The cross-appeal brought by the state will be dismissed for want of a case or controversy within the meaning of those terms as used in Article III, Section 2 of the Constitution. The Secretary has made no claim for recoupment, and this court has no way of knowing whether he ever will.

The judgment of the district court is REVERSED, and the cross-appeal is DISMISSED.