This paper investigates the impact of public provision on competition within the Brazilian higher education sector. We develop and estimate an empirical model of demand for higher education that incorporates tuition-free institutions and consumer choice constraints. Our model produces more realistic substitution patterns than a logit model without constraints, indicating that selectivity is an essential dimension of product differentiation. We find that the most selective public programs exert comparable competitive pressure to the most selective private programs, but the least selective public programs exert more competitive pressure than the least selective private programs. Our estimates of the supply response of private institutions suggest that, in the absence of public programs, tuitions would be about 7 percent higher. These findings provide important insights into the competitive dynamics of Brazilian higher education and highlight the role of public provision in promoting competition in this sector.