Can competition and the existence of profit-seeking actors in the school market improve educational quality? To see cost-efficient, long-term improvements, we identify the school system's capacity for knowledge-enhancing innovation as crucial and explore this question by examining Swedish tax-financed schooling. The Swedish school system was marketized in the early 1990s to an unparalleled degree but has only seen modest (if any) educational gains. This lack of progress is puzzling considering evidence from regular markets that competition and the presence of for-profit actors should spur innovation. Our analysis suggests that these factors are necessary but not sufficient conditions for innovation, tracing the obstacles to innovation in the Swedish school quasi-market to three sub-par institutional conditions. Together, they result in a significant epistemic problem, which impedes the beneficial effects of competition and the profit-motive. First, the view of knowledge (institutionalized in national curricula) does not entrust teachers with a real, knowledge-promoting mission. Second, the design of the grading system makes grades unreliable measures of knowledge, making it difficult for schools to compete and for users to choose along this dimension. Third, the information provided to users is insufficient and overly complicated, meaning user choice is less informed than it should be. Institutional reforms that improve actors' epistemic positions along these margins could improve the situation, paving the way for innovation and long-term improvements.