then under the constraint of x+y=const the optimal solution is going to be an even split.
Yeah, but unless you actually end up at that point, that's hardly relevant. If people donated rationally, we would always be at that point, but people don't, and we aren't.
and our normal utility functions definitely don't have that behavior.
We're normally only dealing with one person. If you play videogames, you quickly get to the point where you don't want to play anymore nearly as much, so you do something else. If you save someone's life, there's still another guy that needs saving, and another guy after that, etc. You can donate enough that the charity becomes less efficient, but you have to be rich and the charity has to be small.
Also, consider: If you wanted a shirt, and I bought you one, you'd stop wanting a shirt and spend your money on something else, just like if you bought the shirt. If you wanted to donate $100 to X charity, and I told you that I already did, would you respond the same?
Yeah, but unless you actually end up at that point, that's hardly relevant. If people donated rationally, we would always be at that point, but people don't, and we aren't.
I don't understand how what you just said relates to my example. To recap, I meant my example, where the maximum is at the even split, to refute the claim that any smooth utility function will obtain its maximum along one "most efficient" axis. The whole argument is only about the rational behavior.
...We're normally only dealing with one person. If you play videogames, you qu
If it's worth saying, but not worth its own post, even in Discussion, it goes here.