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It probably a selection bias thing. More people who want to pursue medicine go to U of M and end up applying to medical school. Lets be honest U of M is the highest ranked school for undergrad in MI.That, plus it's crazy and annoying how there's just too many pre-meds at UM. Every medical school in Michigan has its greatest number of matriculants from UM, mostly because of the sheer number of applicants.
Good research! Seems that general funding is a good catch-all category. I did some light digging and found the state of Michigan's FY 16 budget for the purpose of this exercise.
http://www.michigan.gov/documents/budget/Budget_all_together_2016_final_481096_7.pdf?20160914164311
UofM - Ann Arbor received slightly over $300 mil in state funding. If all this was diverted to the med school (not logical) - it would account for 4% of the total budget.
EDIT: We would also have to consider the portions of health care funding now directly tied to the university that would go to the school. It would be a crapshoot guessing here and probably makes up a good portion of state funds.
Of interesting note, IS/OOS tuition accounts for $7mil of the budget or a staggering 0.10% - and some think med school is TOO expensive.
Yeah difficult to assess that piece of it, the state only foots the bill for medicaid, but its state employee insurance probably contracts with them, It is a large web of dollars.