Medicare faces significant financial challenges because of rising health care costs. In response, Medicare reform efforts have been testing various payment and service delivery models, including accountable care organizations (ACOs), aiming to reduce expenditures while preserving or enhancing the coordination of quality care. The idea behind ACOs is to form an organizational network to coordinate all care for Medicare beneficiaries and in so doing, at least theoretically, improve quality of care and hopefully reduce medical costs. The purpose of this research is to apply Data Envelopment Analysis (DEA) to assess the potential savings of Medicare obtainable through optimally efficient implementation of ACOs and Medicare Advantage plans. DEA comparisons across plans achieve this purpose by identifying which Medicare plans operate relatively more efficiently and which are inefficient, and additionally, for inefficient plans, the DEA analysis generates target levels of "inputs" and "outputs" required to bring the plan into efficient operation. Knowing sources of inefficiency can also provide insights into Medicare reform, such as Medicare privatization and innovation models. Our results show that Medicare Advantage plans are more efficient in reducing health expenditures but incur higher administrative costs. Health expenditure savings can also be achievable by promoting government-sponsored managed Medicare such as ACOs. Finally, compared to the profit efficiency of Medicaid managed care plans, Medicare Advantage should have the potential for more Medicare market penetration from the supply (insurer) side.