I think this gives an answer reasonably close to what you're looking for (from the NYTimes article, "In climbing the income ladder, location matters," featuring research by Raj Chetty, Emmanuel Saez, and others).
The team of researchers initially analyzed an enormous database of earnings records to study tax policy, hypothesizing that different local and state tax breaks might affect intergenerational mobility.
What they found surprised them, said Raj Chetty, one of the authors and the most recent winner of the John Bates Clark Medal, which the American Economic Association awards to the country’s best academic economist under the age of 40. The researchers concluded that larger tax credits for the poor and higher taxes on the affluent seemed to improve income mobility only slightly. The economists also found only modest or no correlation between mobility and the number of local colleges and their tuition rates or between mobility and the amount of extreme wealth in a region.
Note that the study is primarily about income and social mobility, but they also mention that tey find modest or no correlation between tuition rates and amounts of extreme wealth in a region.