It seems that the mistake that people commit is imagining the the second scenario is a choice between 0.34*24000 = 8160 and 0.33*27000 = 8910. Yes, if that was the case, then you could imagine a utility function that is approximately linear in the region 8160 to 8910, but sufficiently concave in the region 24000 to 27000 s.t. the difference between 8160 and 8910 feels greater than between 24000 and 27000… But that’s not the actual scenario with which we are presented. We don’t actually get to see 8160 or 8910. The slopes of the utility function in the first and second scenarios are identical.
“Oh, these silly economists are back at it again, asserting that my utility function ought to be linear, lest I’m irrational. Ugh, how annoying! I have to explain again, for the n-th time, that my function actually changes the slope in such a way that my intuitions make sense. So there!” ← No, that’s not what they’re saying! If you actually think this through carefully enough, you’ll realize that there is no monotonically increasing utility function, no matter the shape, that justifies 1A > 1B and 2A < 2B simultaneously.
It seems that the mistake that people commit is imagining the the second scenario is a choice between 0.34*24000 = 8160 and 0.33*27000 = 8910. Yes, if that was the case, then you could imagine a utility function that is approximately linear in the region 8160 to 8910, but sufficiently concave in the region 24000 to 27000 s.t. the difference between 8160 and 8910 feels greater than between 24000 and 27000… But that’s not the actual scenario with which we are presented. We don’t actually get to see 8160 or 8910. The slopes of the utility function in the first and second scenarios are identical.
“Oh, these silly economists are back at it again, asserting that my utility function ought to be linear, lest I’m irrational. Ugh, how annoying! I have to explain again, for the n-th time, that my function actually changes the slope in such a way that my intuitions make sense. So there!” ← No, that’s not what they’re saying! If you actually think this through carefully enough, you’ll realize that there is no monotonically increasing utility function, no matter the shape, that justifies 1A > 1B and 2A < 2B simultaneously.