That can't be true of either health care or college.
Why? Virtualization. Colleges now offer online courses, which do away with a lot of the labor-intensive work (grading papers, giving the same lecture/course over and over again). Additionally, with health care, you have robotics and telemedicine which can decrease the amount of labor.
Even if the cost disease is correct, the problem is that it doesn't apply to those fields. Yes, they can be labor intensive, but technology can make them more productive - that is if they bother with it. In some cases, thanks to market distortion, that doesn't always happen, as the government doesn't care about efficiency or productivity increases.
For example, in Ohio, we have multiple K-12 virtual academies - all of them are cheaper than brick & mortar schools. Why? Costs are lower, as one teacher can handle more kids thanks to automation. Of course, the typical public schools hate this, because it takes away funding, regardless if there is a qualitative advantage via virtual education.
Back from the dead, I'm afraid.







