The fact that it's so much cheaper to teach the liberal arts, yet the same tuition is charged, means that they are already much less subsidized. If you work out tuition paid by students and compare it to department salaries/expenses, humanities departments often turn a net profit for their universities (http://campuscomments.wordpress.com/2010/03/25/ah-bartleby-a...). If you charged students proportionally to the amount it cost to educate them for every credit-hour (i.e. equal subsidies across fields), STEM tuitions would be 20% to 50% higher.
On the other hand, I don't see much reason to subsidize medical education or research across the board, given the huge profits in it; income from patent royalties ought to be sufficient to pay for most of the needed research and education. An exception is harder-to-monetize research, like running clinical trials for old generic medications where it's not profitable for the private sector to do so (since they wouldn't be able to patent the result), or studying diseases that primarily affect poor countries.
On the other hand, I don't see much reason to subsidize medical education or research across the board, given the huge profits in it; income from patent royalties ought to be sufficient to pay for most of the needed research and education. An exception is harder-to-monetize research, like running clinical trials for old generic medications where it's not profitable for the private sector to do so (since they wouldn't be able to patent the result), or studying diseases that primarily affect poor countries.