Do price and value of degrees correlate much?
High cost and high quality are not related in the United States.

First, remember that there is a large fixed base cost of room and board, which amounts to around $10K-$15K, depending on location.  Just a quick glance at a few top schools will show that the cost of tuition beyond that is correlated primarily with state-run vs. private rather than quality:


Harvard: $43,938
MIT: $43,720
Berkeley: $12,972
University of Michigan: $13,977 (in-state)


Also, remember that many of the high-priced colleges do need-based rather than merit-based financial aid, so these numbers should be seen as a "ceiling" rather than an expected price: even a super-genius will pay based on what their parents make, rather than based on how smart they are.  That same Harvard article linked in the original post notes:


  During the 2012-2013 academic year, students from families with incomes below 
   $65,000, and with assets typical for that income level, will generally pay nothing toward the cost of attending Harvard College.  Families with incomes between $65,000 and $150,000 will contribute from 0 to 10 percent of income, depending on individual circumstances.  Significant financial aid also is available for families above those income ranges.


Thus, even at a super-expensive place like Harvard, the cost of education is completely uncorrelated with its quality.