The price of admission: Who gets into private school, and how much do they pay?

I analyze how elementary and secondary private schools decide which students to admit from their applicant pool using mechanism design theory. The problem for an individual private school of who to admit and how much to charge in tuition, is complicated by the existence of peer-effects: the value students place on attending school is increasing with the average ability of the entire class at that school. This feature, coupled with the fact that students can always attend public school for free, places constraints on the types of classes the private school can admit. In my model, students have an ability type that is known to the school through testing, as well as a wealth type that is private information. Students report their wealth to the school and on the basis of the results from the ability test and wealth reports, the school institutes an allocation rule and a payment rule. Allocation rules which only admit all high ability students and no others, or all high wealth students and no others are not feasible. I utilize a simple example to show how in a revenue-maximizing allocation, the private school always under-admits the highest ability students relative to the allocation rule that maximizes social welfare.