Even in Sweden adults have something they pay, but it is capped on a yearly basis.
Medicare also has a copay and deductible.
http://www.house-call-physicians.com/medicare_info.htmLike any other insurance, Medicare has deductibles and copays. If a system has a cost, it will lower demand because of the economic formula you showed. But in a pure private system, the cost is so high, only the well off can afford good care, and the poor get no care, and the middle gets somewhere in between.
In a system with no government intervention then it is all based on market forces where having money means getting care.
In a regulated system a progressive element is added. If you are poor health care is cheap, but even that cheap price is alot for the poor person, so it does not spike demand.
A middle class person can also have lower price care because of a progressive tax on the rich.
The system that includes deductibles and copays makes it not free, and more importantly what cost 20$ as a deductable, to a poor person is even more of a reduction of demand then what cost 1000$ for a millionaire.
There is another factor, currently in the world production capability is far more then demand. This creates a mandatory unemployment, many people still think of economics in the way of 200 years ago, when production was lower then demand.
Because of demand falling below production, sectors of employment have to be created. Not just for their need, but also to give people some work to do, since work is a vital part of both individual and social well being.
One of the ways to do this is increase demand for different sectors, war and consumerism does this. But instead of creating demand just for throw away things. Why not create some demand for health care, then returning soldiers can get education in nursing field, or even doctors, and expanse to education facilities can create even more demand in education sectors.
And as you state, we do not have a free market health system, in Sweden Insurance companies are not allowed to also own health centers. In part that stops just elevating prices(when gov. paid for) for self profit, it also hinders lack of care as a motivator for profit reasons.
And if we had a non monopoly system, laws of supply and demand could be argued, but since both vertical and horizontal price fixing and monopolies exist, the effect is not supply and demand on care, this can be shown to be true because of increases in profits of companies in health industries while care has become more expensive and available for fewer people.
But many make the argument you speak of but actually have some similar thoughts as listed below. The thoughts listed are ones that are so unpalatable many things like bad arguments are given when actually the items here are the real thoughts on the issue.
A few arguments more centered around extreme think tanks that do not share their goals in public conversation.
(It should be noted that 5 years ago, in part because of Canada medical care, and fearing US medical care changes, schools that teach doctors lowered the amount of new people they allowed in, to add another argument to private health care. Or at least it was in the news.
Also those that want control over the work force want people to be in fear, if people fear going broke from an illness then they will not be able to leave job. That means they can not strike, they can not quit because of unreasonable demands or poor pay, and they can not start small businesses, that can challenge big corporate control. So for some it has nothing to do with making people healthier, it is about keeping people scared so they can be controlled.
There is also a fringe, but influential group that have many people, some in think groups. They fear good health care will help people live, and helping poor or middle class people live is against lower population goals of some groups. Also some think on lower classes as waste, and do not want them to replicate. Some of the anti health care, and even cost increase is a form of social warfare. There are many examples of some groups saying 'good' people as they define it should be promoted to have more and healthier kids, while lower people should be hindered from having healthy kids.
There are also some that really think driving people into poverty is a good thing, they believe it will make people more susceptible to control by a few masters. They consider loss of houses for medical care and things like that a good thing. Those people mostly think of things in zero sum gains, as people lose money they get it, so driving people into poverty is good for them. If they are forced to rent, then they can collect that rent, if they lose their house, then a well off person can buy it cheaper.)