We assess the potential of increased economic competition by examining whether Medicare beneficiaries are willing to switch to physicians who agree to accept all services on assignment. Data come from a survey of Medicare beneficiaries conducted in November 1988. Our principal finding is that beneficiaries are not sensitive to price when making decisions about whether or not to switch physicians. Less than one-half of 1 percent of the sample had switched physicians for economic reasons in the year prior to the survey. Furthermore, willingness to switch was not correlated with ability to pay. We conclude that policies aimed at altering consumer demand may not be the most effective way to control Medicare costs.