State and Local Welfare Reform and Fiscal Relief Act of 1979

State and Local Welfare Reform and Fiscal Relief Act of 1979 - Amends the program of Aid to Families with Dependent Children (AFDC) established by part A of title IV of the Social Security Act to establish a new formula for determining the amount of the Federal payment to each State for amounts expended by a State under such program. Provides for an annual cost-of-living increase in such amount. Requires that such increases be passed on to the recipients of aid under the program. Directs that each State plan for the operation of the State AFDC program provide for reimbursement of the political subdivisions of the State for the amount contributed to the program by the subdivisions.