In the United States, the federal government grants colleges access to a student's Free Application for Federal Student Aid (FAFSA) which facilitates substantial price discrimination. This paper is the first to estimate the consequences of allowing colleges to use the FAFSA in their pricing decisions. I build and estimate a structural model of college pricing and simulate counterfactuals wherein some or all of the FAFSA information is restricted. I find that if FAFSA information were restricted, 13 percent of students attending elite colleges would be inefficiently priced out of the elite market. Nevertheless, student welfare would rise as colleges charged the majority of students lower prices. Colleges do use the FAFSA to transfer resources from high- to low-income students on average, but this redistribution is highly imprecise: allowing colleges to use the FAFSA harms one-third of low-income students while one in seven high-income students actually benefit.