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Non-technical summary• A simple model is presented where states decide on, and finance, universities which are attended by local but also by non-resident, mobile students.• The efficient allocation is characterised. By means of an example, it is shown that efficiency may require to concentrate mobile students in a small number of "elite" universities.• Un-coordinated decisions by the states are shown to satisfy the same first order conditions as the efficient allocation provided that the universities have the right to charge a tuition fee reflecting the costs induced by an additional student.• If tuition is banned or capped by the federal government, inefficient quality choices and insufficient admission numbers are likely to emerge.• The analysis supports the assignment of responsibility for higher education