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On this end of the scale, it grows (I'm not sure if it's exponential), but it doesn't grow indefinitely; eventually it starts falling.
What function is that? I thought human utility over money was roughly logarithmic, in which case loss of utility per cent lost would grow until (theoretically) hitting an asymptote. (Also, why would it make sense for it to eventually start falling?)
I have no idea what function it is. I also don't really have a working understanding of what "logarithmic" is. It starts falling because when you're dealing in the thousands of dollars, the next dollar matters less than it did when you were dealing in the tens of dollars.
Oh, okay, I think we're talking about the same function in different terms. You're talking in terms of the utility function itself, and I was talking about how much the growth rate falls as the amount of money decreases from some positive starting point, since that's what Hul-Gil seemed to be talking about. (I think that would be hyperbolic rather than exponential, though.)
The utility function itself does grow indefinitely; just really slowly at some point. And at no point is its own growth speeding up rather than slowing down.
So you're saying that being broke is infinite disutility. How seriously have you thought about the realism of this model?
Obviously I didn't mean that being broke (or anything) is infinite disutility. Am I mistaken that the utility of money is otherwise modeled as logarithmic generally?
Then what asymptote were you referring to?
It was in response to the "indefinitely" in the parent comment, but I think I was just thinking of the function and not about how to apply it to humans. So actually your original response was pretty much exactly correct.
It was a silly thing to say.
I wonder if it's correct, then, that the marginal disutility (according to whatever preferences are revealed by how people actually act) of the loss of another dollar actually does eventually start decreasing when a person is in enough debt. That seems humanly plausible.