what part of this scenario don't you understand

Resources are limited and medical demand is not. The medical response time if the President of the United States gets shot is less for than if anyone else gets shot. It's not possible to give everyone as much health protection as the president. So it's not a scenario. I can imagine each person as being the only person on earth with such care, and I can imagine imagining a single hypothetical world has each person with that level of care, but I can't actually imagine it.

there's a lot of intermediate points

That indicates that no argument about the type of thing to be done will be based on a difference in kind. It won't resemble saying that we should switch from what happens at present to "no-one being left to die just because they happen not to have a given amount of money". We currently allow some people to die based on rationing, and you are literally proposing the impossible to connote that you would prefer a different rationing system, but then you get tripped up when sometimes speaking as if the proposal is literally possible.

deciding how much we want to pay for

Declaring that someone has a right is declaring one's willingness to help that person get something from others over their protests. We currently allow multimillionaires, and we allow them to spend all their money trying to discover a cure for their child's rare or unique disease, and we allow people to drive in populated areas.

We allow people to spend money in sub-optimal ways. Resources being limited means that not every disease gets the same attention. Allowing people to drive in populated areas is implicitly valuing the fun and convenience of some people driving over the actuarially inevitable death and carnage to un-consenting pedestrians.

What this means specifically depends on the means available at any given time.

I don't understand how you want to ration or limit people, in an ideal world, because you have proposed the literally impossible as a way of gesturing towards a different rationing system (infinitely) short of that ideal and (as far as I can see) not different in kind than any other system.

By analogy, you don't describe what you mean when you declare "infinity" a number preferable to 1206. Do you mean that any number higher than 1206 is equally good? Do you mean that every number is better than its predecessor, no matter what? Since you probably don't, then...what number do you mean? Approximately?

I can perhaps get an idea of the function if you tell me some points of x (resources) and y (what you are proposing).