I'm wondering to what extent money is a factor in phd admissions? For example, does an admissions committee limit the number of students admitted in a year depending on how much the department can afford that year? and approximately what percentage of the departments funds go to graduate funding(I am asking mostly in regards to US universities that rank in the top 20 for math.)?
And also, are qualified students who are less expensive more likely to get admitted because it wont cost the department much, if anything at all, since at many institutions certain groups receive their funding from the central administration rather than the department(such as women and minorities)?
Below is a source where the writer says
Even as faculty members on committees expressed philosophical commitment to diversity, Posselt observed financial motivations at play. Some universities offer extra funds for minority graduate students, so that a fellowship might be paid for from general university funds and not departmental funds. Where such incentives exist, they appear to have a strong impact, Posselt writes.
and in What do admission committees look for in a diversity essay?, Paul Garrett says:
being a woman in a STEM field (Science, Tech, Engineering, Math), or of ethnic origin other than northwestern European . . . opens certain money-pots to both the department and to the individual.