I say almost obvious, because it took a seminal paper by Kenneth Arrow in 1963 to spell out the argument; but when you "get" it, it seems obvious.
The conclusion:
All of this doesn’t necessarily mean that socialized medicine, or even single-payer, is the only way to go. There are a number of successful health-care systems, at least as measured by pretty good care much cheaper than here, and they are quite different from each other. There are, however, no examples of successful health care based on the principles of the free market, for one simple reason: in health care, the free market just doesn’t work. And people who say that the market is the answer are flying in the face of both theory and overwhelming evidence.
