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Some reasons American medicine is very expensive:
1. Health insurance, but not treatment, is fully tax deductible. So if you buy your own penicillin, it's with after tax money, but if your insurance company buys it, it's pre-tax money. That's one of the reasons that health insurance is so widespred in America even for routine medicine like antibiotics and checkups. That's a major contributing factor in why the administrative costs are so high.
2. There's a shortage of doctors in America, and qualified doctors from other countries are not allowed to practice medicine in the United States. So there's good doctors from Canada, England, Japan, wherever that'd love to practice in the USA, but can't. This artificially inflates doctor's wages by restricting supply.
3. American doctors are typically required to get an undergraduate degree, medical degree, and do a below market, crazy hours residency in order to be able to practice medicine. That's 8-10 years of study and below market working to practice medicine. Now, medicine is very important and needs to be done right, but I don't believe for a second that a focused apprenceship couldn't teach a very specific kind of medicine - say arithscopic surgery - in just 2-4 years under a highly trained doctor, but this isn't an option.
4. The Food and Drug Administration requires new drugs to be proven not only for safety, but also efficacy. That's an incredibly high and expensive burden to meet - that means that drugs need to be proven to work to a certain standard, instead of just not harm. This adds years of development time and millions of dollars in cost to the new drug development cycle.
Those are all legislated reasons that increase the cost of medical insurance, doctors, and drugs. They'd be fairly easy to remove -
1. All medical and health expenses can be written off taxes regardless of insurance. Employees can choose to convert som of their wages to a medical or health plan tax free to both the employer and employee. (Currently, under most circumstances, only employer-provided health insurance can is tax free)
2. Allow any doctor in a country with reasonably competent medical standards to practice in the United States.
3. Require that doctors be able to demonstrate that they can practice their area of medicine capably. Be flexible in how they demonstrate that. Note: This will incur high opposition from medical schools and current doctors who are currently enjoying the wage premium and had to go through the very long, difficult, and expensive system.
4. Change the drug standard from "safety and efficacy" to only safety. Drugs will come to market much faster and cheaper. There's plenty of people and organizations that will test proven safe drugs for efficacy for free or nominal cost once drugs hit market, and efficacy will get understood with time. Put this way - a proven safe but questionably effective treatment against heart disease being held off the market for five years and costing much more to get to market is not a good thing. If it's certainly safe, then let people make the decisions with their physicians, instead of having the FDA take such a strong gatekeeping stance.
Technology has progressed such that we don't need government protection from ourselves as much any more. The current set of legislation has greatly increased the costs of doctors and medicine. Regardless of political position, and regardless of stance on other health issues, addressing these four points will make the medical system fairer, more effective, and and less expensive with relative ease.
Admittedly, there's some powerful entrenched interests that are winning in the current arrangement, and will oppose these simple improvements.