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Re: Profile Evaluation for fall 2020 - thanks in advance!!
Just a couple things to note. This is a Fall '21 profile, since you'll be entering in the Fall of 2021, to avoid any confusion. The Fall 20 cohort has already begun their classes.
Anyway, given the university that you're from, your best bet would be to see where past students have gotten into. I presume that there shouldn't be any asymmetry of information if you're from somewhere like Oxbridge or UCL/LSE, since you won't be the first from there to arrive in the school's applicant pool, and they'll most likely know how to assess you.
Is there any particular reason why you're getting a letter from a maths professor?
As it stands, if you are from the abovementioned schools, Top 30 is definitely possible (as a very conservative estimate), but you should see where students in the past have gone on to.
Do note that this coming cycle will be arguably more competitive since a number of schools would have students (from the Fall 20 cohort) who deferred entry due to the virus situation. Therefore, they might take in fewer students.
Lastly, I don't know if this needs mentioning, but given what you state as interests, you might want to look into Public Policy PhD programmes in the top schools too. They are quite econ-centric, in terms of the coursework preparation so you should consider applying to a couple of those too.