Correction: I originally wrote that, under the permanent benefits model, it is optimal to spend our whole budget at once. This is not true. I arrived at this result by making incorrect assumptions in my proof. Rather than proving that utility of spending is non-concave, I should have determined the concavity of the utility of spending at time t_0 minus the utility of spending at time t_1. This function is concave. I don’t yet have a full picture of how this affects optimal behavior under this model (I will update the post once I do), but I wanted to point out the error as soon as possible.
Correction: I originally wrote that, under the permanent benefits model, it is optimal to spend our whole budget at once. This is not true. I arrived at this result by making incorrect assumptions in my proof. Rather than proving that utility of spending is non-concave, I should have determined the concavity of the utility of spending at time
t_0minus the utility of spending at timet_1. This function is concave. I don’t yet have a full picture of how this affects optimal behavior under this model (I will update the post once I do), but I wanted to point out the error as soon as possible.I have now updated the post.