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byrnema comments on On dollars, utility, and crack cocaine - Less Wrong
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"For someone with $ << 0, the marginal utility of $5 to them is minimal. "
I'm a newbie, which will soon be obvious, but I don't think the utility function is being applied correctly. At each value of U (the worth that a person has at his disposal in goods), we have the utility that can be purchased with U. (So u is negative for U<0 because you get negative things for owing money.)
I understand that if someone is greatly in debt, their utility may not change much if you increase or decrease their debt by some amount. This is why the utility function would be shallow for $ << 0. Thus, I agree that someone with $ << 0 who happens to find $5 on the ground would have little incentive to use $5 to pay off their debt.
However, let's use the function to see what utility they can purchase with their $5...
The fact that they are spending it on gambling or drugs means they are NOT moving from U=(-X) to U=(-X+5) (they're not using the $5 to pay off their debt). They are staying at U=(-X) and spending their $5 as true disposable income -- in other words, exactly as though U=0.
A person with U=0 gets a steep benefit from the spending of $5.
I think there's some confusion here as to what the utility function is defined over. And to be fair, the post itself is somewhat confused in this respect.
The argument that it might be more or less rational to gamble is an entirely different matter to whether it is more or less rational to smoke crack.
The shape of the utility function over money can make it more or less rational to accept particular money gambles: risk aversion is after all a property of the shape of the utility function.
The shape of the utility function over money cannot affect whether specific, non-risky choices about how to spend that money (e.g. whether to smoke crack) are more or less rational. If crack is you best option, that's already reflected in your utility function for money; if it's not, then that too, is already built in.
NB: This comment is not as precise as it should be in distinguishing decision-utility, experienced-utility etc. I think the fundamental point is right though.