The expected utility calculations now say choice 1 yields $14000 and choice 2 yields $17000.
The expected payoff calculations say that. Expected utility calculations say nothing since you haven’t specified a utility function. Neither can you say that choice 2 must be better because of the fact that for any reasonable utility function U($14k)<U($17k), because the utility of the expected payoff is not equal to the expected utility.
EDIT: pretty much every occurrence of “expected utility” in this post should be replaced with “expected payoff”.
The expected payoff calculations say that. Expected utility calculations say nothing since you haven’t specified a utility function. Neither can you say that choice 2 must be better because of the fact that for any reasonable utility function U($14k)<U($17k), because the utility of the expected payoff is not equal to the expected utility.
EDIT: pretty much every occurrence of “expected utility” in this post should be replaced with “expected payoff”.
You’re right, but I was looking at the question in terms of the (bad) assumption of linear utility for money.