From the abstract:
The joint federal-state financing of the Medicaid program works through a matching mechanism known as the Federal Medicaid Assistance Percentage (FMAP). This mechanism determines the federal and state shares of Medicaid costs based on a state’s per capita personal income relative to the national average. While the FMAP formula has remained unchanged since the enactment of the Medicaid program in 1965, changes in per capita income have resulted in substantial changes in the federal and state shares of Medicaid costs in many states.
This issue brief describes the FMAP formula, analyzes how actual FMAPs have changed since the beginning of Medicaid and discusses the outlook for FMAPs in 2013 and beyond.