In a mixed duopoly environment, I study under which conditions the introduction of a voucher system for private schools can increase competition and as a result, social welfare. My model considers a market in which schools compete in qualities to attract students. Speci cally, I consider two settings: one with two private pro t-maximizing schools and one with a mixed duopoly, in which one of the schools maximizes social welfare. In the two situations, the quality level offered by the schools plays a crucial role in the students' enrollment decision. I nd that in both private and mixed duopoly, the voucher reduces the tuition fee and the quality of the high quality school. It also increases own pro ts and decreases the ones of its competitor. Thus, the voucher reduces the incentives of the high-quality school to invest on its quality, and this weakens the competition in the market. In the mixed duopoly scenario, particularly for having an increasing consumer surplus and social welfare, the social planner needs to implement a low voucher. The contrary needs to be implemented in the private duopoly. Finally, the low voucher policy can be successful as a high voucher is costly. Keywords: Mixed Duopoly, Voucher Programs, Educational System, Vertical and Horizontal Differentiation. JEL classi fications: D21, H52, I2, L13.