I think so because I doubt that most people (regardless of how good they are at math) can trust their current selves to compare utility from consumption to disutility from having to pay back (meaning that their future self will often disagree strongly with their current self.) This is not to say that someone else should be trusted with decisions about savings and loans other than the saver/borrower (forcing someone to put money into a pension fund on the grounds that they're irrational and then not really paying the pension back is a bit too common for my taste), just that "by default, don't get into debt" is good advice.
More generally, IMO quite often clever utilitarian maximization works worse than simple rules designed to keep you out of trouble first, and seek "utility" later. (I guess I don't quite believe in people being utility-seeking machines, not to mention ones having stable preferences, nor do I believe that a person is truly better off having achieved more utility per unit of time.)
I realize it's not a satisfactory argument, of course, if one does believe in utility maximization as a good way to think about these things, and I really wish I could back this up so it's more than a hunch...
Correct idea, incorrect math. The optimum is found with (11+r)/(2 + 2r) consumption in year 1 and (11+r)/2 consumption in year 2, for a total utility of 2 log(11+r) - 2 log(2) - log(1+r); at (10%, 20%, 50%) interest rates this yields (3.33, 3.26, 3.09) total utility.
Key idea is that since utility is concave, smoothing it out is a win. Now just trade off the gains from smoothing against the losses from financing, and you are golden.
Concavity is a way of formalizing this intuition; it means, roughly speaking, that f(2x) <= 2f(x).
Econ uses log(x) as a simple model, but the same idea would apply to any convex function albeit with different arithmetic.
This is however an argument for poll taxes (e.g., "every adult must pay $1000") being unfair, as well as sales taxes on inferior goods (warning: technical term) if the regressive effects aren't compensated by a quasi-fixed-dollar tax rebate.
And you are saying that the last 5% of a millionaire's income has the same utility as the last 5% of a different person's income that makes 25k/year?
Note that this assumes that you are already able to spend an optimal amount on food.
If I gave you the choice of only eating $1 of Cup-Noodles every day for 30 days ($30 total), or one single $300 meal at a high class restaurant, and nothing for 29 days, which is the smarter choice?
Shortening the time period just lowers the financing costs.
Suppose I have utility = log(consumption), but my income is volatile. If I have 1 income in year 1 but 10 income in year 2, and use no credit, my utility is log(1)+log(10) = 2.3.
If I use credit, I can have utility log(5.5 / (1+r)), with r the interest rate. At 10% interest, that's 3.2. At 20% interest that's 3.0. At 50% interest that's 2.6.
So even at 50% interest I'm increasing my utility by 10% due to the use of credit.