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I'm confused as to how you see his earlier estimate as better at all, much less vastly better. Are you saying you'd be happy with a price tag which consists of the range $4000 to $1500000?
The chance of hitting the $1.5m upper end makes this price tag functionally identical to "idk, could be anything" for most people. Unless you have millions in assets then 1.5 million is already enough to ruin your life and put you in a place where you're probably staring down bankruptcy. Whether the cost caps out at 1.5 million or 1.5 billion is irrelevant to people who can pay neither of those numbers.
The important point is the conceptual realization that patients cannot consent without being informed. It's called informed consent. Part of being informed is being informed about the costs. Obviously, there is going to be a knowledge gap both in terms of the medical and financial costs/benefits. When it comes to medical cost/benefits, people mostly acknowledge the knowledge gap and say that it's important for doctors to find a way to explain the situation as they can to the patient. There is obviously a range of quality here, but the answer is that you have to try. When it comes to the financial side, they instead just say that it's impossible. They give up. They don't even try. (It's just a coincidence that doing this is in their interest.)
His prior answer gave a probability attached to a known unknown, conveying the information known by the doctor in a way that is very representative of the doctor's knowledge. First, it is obvious that they can do this sort of thing.
Second, as to the question of comparing the quality of the answers, suppose you were considering playing a lottery-style game. One just told you, "The range of payouts is between $5k and $1.5M." A second told you, "The payout is about $5k with about probability p, and the payout is about $1.5M with probability 1-p." Which of these answers do you think is better quality information? Which of these answers do you think is more helpful in analyzing whether you would like to play?
Third, the lingering question is whether/when it matters. It will obviously depend. It will depend on the dollar figures; it will depend on the probabilities; it can also obviously depend on how the individual's personal insurance is structured (common factors would be deductible, co-insurance, and out-of-pocket max). From there, we have a several-dimensional parameter sweep. We could sit down and generate plots. I'm sure we would see tons of regimes where having the information is basically useless. But I'm also confident that we would see tons of regimes where having the information is useful. I'm sure the good doctor we are talking to can come up with plenty of individual examples off the top of his head that are in the regime where it doesn't matter. Don't care. There are almost certainly also plenty of examples where it does matter; I would venture to guess that, actually, for the vast majority of regular, routine decisions, it can, in fact, matter. The standard party line is to just not even try, in any case, because there might be other cases where it doesn't matter. That's absurd. Moreover, it betrays a lack of understanding of economic thinking. There are always non-marginal cases. In no other area of economics do we say, "There are some extremely high/low value producers/consumers, and since their behavior won't be changed by [alteration to the price system], we should just completely blow up the price system and abandon it." Economists push back on this shoddy reasoning constantly. Sure, there might be someone who just loves eating exactly one apple every day so much that even if we blow up and get rid of the price system for apples, just don't tell anyone how much apples cost, and have them paid for via some complicated mechanism, they'll still buy exactly seven apples every week. Who cares? The price system is there for all of the other cases.
The challenge to someone saying that we should never talk about prices because they never matter is to actually show that they never matter, not that there are some cases in which they might not matter. I think they probably do matter to a hell of a lot more cases than they're willing to admit.
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