Could you please cite somewhere in the world where the free market is working for health care? Every other first world country either has socialized medicine or a tightly regulated health industry.
Basically everyone has to maintain a fund (the government pay into it for the poorest) for healthcare. This is what they spend when they have healthcare needs.
Because the people are making the purchasing decisions themselves (as opposed to the insurance company doing it) they have a far stronger incentive to demand value and to be informed, and you get genuine competition between providers (as if you don't like them this time you'll go elsewhere next time with no insurance company mandating who you can see).
The government then picks up the few areas that aren't well catered for by this system.
I think it costs about 40% of what the US system costs (possibly even less) and Singapore has a typical life expectancy of 80.
And with that, you're no longer in a free market.
... has a price- and service-controlled market, set not by the healthcare industry but by the Singaporean government (you know, the guys that cane graffiti artists and banned gum-chewing?) They also provide government subsidies to citizens as well as permanent residents (though not as much) for their compulsory Medisave program. So, their invisible hand is very visible and it's called "their government regulates or pays for alot of their care".