We consider a  population of students with  heterogenous socioeconomic status, and study the dual design problem  of  allocating students to schools  and   choosing how to grade  students in school. We fully characterize  the welfare-maximizing school design, which exhibits: (a) stratification,  (b) a positive relationship between grade inflation and school rank, (c) coarse sorting, with students divided into just two  groups. We go on to show that the ability to strategically misreport socioeconomic status benefits students at the top of the ladder and reduces welfare of those at the bottom.