Not so sure you are right. Last figure I heard close to one medical dollar in three goes to administration in the U.S. This is not just insurance company admin costs and profits (which are actually a minority of such costs) but administrative costs having to do with meeting insurance company requirements. Comparable costs for Canada are around 15%. (Again not just the cost of health authority itself which is very small, but internal hospital, clinic and private practice admin costs.) So a 15% savings off the total medical dollars is pretty substantial. Then if single buyer leverage reduced drug costs to Canadian levels, that could get you another 4% or so. More preventative care, and poorest of the poor not being treated in emergency rooms gets you another percent or so - so you could save at least 20% of the medical dollar with a single payer system. That gives you an improvement in overall medical quality for everyone even with including the uninsured.
Beyond that , it makes solving the other problems possible. Single buyer leverage can do a great deal about inflated drug costs. and can help negotiate a better deal with doctors as well. And you don't have to do it exactly like Canada either. I've often thought that combining global budgeting with pay per service could avoid perverse incentives that come with either method alone. Agree on a price per treatment as U.S. insurance does now. But also have a global budget.
Don't micromanage the followup. A Dr. can prescribe treatments at the listed price as she pleases up to the limits of her global budget.
Exceed the global management, or want to prescribe something not on the list? then you have to deal with some micromanagement. But the latter should not happen much. The list should be negotiated between the single payer authority and professional associations. So every type of non-quack treatment should be on there. No it does not work for everything. You have to have special global budgets for emergency situations (earthquakes, explosions in chemical factories and such).
But I think that basic principle could go along way towards allowing cost control without the inefficiencies of micromanagement.
There are some other things that should happen at the same time. As you say a ban on drug company advertisements. Also some serious actions to reduce medical errors - a major killer in the U.S. medical system, and a major contributor to health care costs as well.
BTW I sometimes hear U.S. costs blamed on "overuse" of hight tech medicine. Well, could be , but Japan makes much more extensive use of high tech than we do - and get good results at a reasonable cost. (They have a higher MRI to population ratio than the U.S., for example)
I am completely with Jenny Brown that primary emphasis on the crappy health care most insured people get rather than the uninsured would be more of a winning strategy - without of course ignoring the uninsured. In the Oregon single payer initiative campaign a lot of uninsured people were unaware they would be covered under the initiative - they are so used to these things applying only to other people.
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