Prompted by widespread concerns about public school quality, a growing empirical literature has measured the effects of greater choice on school performance. This paper contributes to that literature in three ways. First, it makes the observation that the overall effect of greater choice, which has been the focus of prior research, can be decomposed into demand and supply components: knowing the relative sizes of the two is very relevant for policy. Second, using rich data from a large metropolitan area, it provides a direct and intuitive measure of the competition each school faces. This takes the form of a school-specific elasticity that measures the extent to which reductions in school quality would lead to reductions in demand. Third, the paper provides evidence that these elasticity measures are strongly related to school performance: a one-standard deviation increase in the competitiveness of a school's local environment within the Bay Area leads to a 0.15 standard deviation increase in average test scores. This positive correlation is robust and is consistent with strong supply responsiveness on the part of public schools, of relevance to the broader school choice debate.