Just to add some fact. According to Yale's financial statement [1], their operating expenses in 2015 was around $3.2 billion. So tuition doesn't come close to covering their operating costs. And it looks like they typically spend around 5% of their endowment (the spending level most foundations target because that is the minimum a foundation must spend to maintain their status).

[1] http://finance.yale.edu/sites/default/files/2014-2015%20Annu...