This paper offers an explanation for the counterintuitive relationship between physician competition and Medicaid participation found by many investigators. Contrary to standard predictions, a number of studies have found strong negative relationships between the supply of physicians and Medicaid participation and equally strong positive relationships between supply and the concentration of Medicaid patients in small numbers of large Medicaid practices. The model advanced here argues that the residential segregation of Medicaid patients and differences in the minimum-efficient scale of practice for treatment of Medicaid and private patients create strong incentives for physicians in competitive urban areas to: 1) take either few Medicaid patients or 2) many and 3) make it costly to maintain a Medicaid practice share between these two extremes. In less competitive areas, these incentives are weaker, if not altogether absent.