For libertarians, the question is quite unworthy for discussion. So far as the patient is willing to pay and there is no coercion or deceit, charging dearly is not wrong. For instance, you would not object to Lionel Messi’s salary however high it may be. Libertarians favor free market. People should be free to decide what to do with their money. Taxation is unjust because it jeopardizes the ownership. To go one step further, libertarians also believe that people own their bodies and their lives, and therefore do not support moral laws such as those against prostitution.
In contrast, the utilitarian philosophy considers how we may maximize happiness and minimize pain. For example, Jeremy Bentham proposed building beggar workhouses in the 18th century. According to the scheme, beggars in the streets were to be locked up. They would then have to work to pay for the expenses of the workhouses. Bentham reasoned that other citizens would be happier with no beggars in the streets, at a small cost of a few beggars who might be forced to live in places they did not like. The overall happiness, or utility, of the society would nevertheless increase.
At first glance, we may think that utilitarians must support low doctor fees. Patients would be happier, or at least feel less pain, if they can pay less for the same service. However, utilitarians would point out that it depends on whether lowering doctor fees would result in fewer competent doctors joining the profession and deteriorating health care. In the latter case, the utility of the society would actually decrease.
Utilitarian principles are difficult to apply. Above all, happiness cannot be quantified but utilitarians try to measure everything in the same scale. Even if measurement is possible, a popular policy among the majority does not mean it is right. In the era of the Roman Empire, prisoners were forced to fight with tigers and die a brutal death for the entertainment of Roman citizens. Tens of thousands of people were enchanted at the expense of a few prisoners who would die from other punishments anyway, but yet we find the practice hard to accept. Surely overall or average happiness cannot be the sole yardstick we go after.