Here’s a chart showing some of the cost-increasing effects of privatizing payment for healthcare.
Under the Ryan proposal, Medicare beneficiaries would be given a voucher to purchase private health insurance or services rather than having access to Medicare’s single-payer plan. As a result, government spending goes down but total healthcare spending goes up because the private insurance companies lack Medicare’s purchasing power and cost controls.
(via Yglesias » Medicare Privatization Will Increase Health Care Spending)