You have no comparison here, or maybe you do how as the cost of private universities going in the US?
The way I see it is there are some places that capitalism works very well, to me these seem to be places where the power between consumers and producers is relatively equal. Capitalism needs competition to function properly, health care (especially with monopolies offered by patents) you get the choice of dying or paying exorbitant amounts. The moment you introduce monopolies/oligopolies companies become just as inefficient as government because the have no incentive to be more efficient. In fact its the opposite high cost just become a justification for charging people more. Health insurance just makes the situation worse because you now separate the actual payment with the premiums so people don't care how much it costs when paying and won't shop around. You have 2 groups that prefer higher costs, the medical industry because they make more money and insurance because without high costs why would you need health insurance in the first place.
Of course governments organizations are like monopolies from the start, they don't have any incentive to be more efficient either, since they can just say we need more money from the tax payer. But at least they don't have the underlying goal of making as much money as possible.