This paper studies a quality-then-prices game between public and private providers. There are two types of equilibria: one in which private providers are partially financed by vouchers, they offer higher quality than public providers, and everyone patronizes private providers, and one in which there is no voucher, public providers offer higher quality than private providers, and customers patronize both public and private providers. Under certain conditions, these two equilibria co-exist. Hence, an equilibrium with vouchers arises only when it induces private providers to provide higher quality than public providers would do if the whole budget were to be spent on publicly-provided quality. This result provides precise under which \citeaspos{Friedman1955} claim holds as an equilibrium outcome of our game.