my comment doesn't assume too much about the shape of your utility curve except that it is continuous and monotonic. multiplying everything by a billion does c

my comment doesn't assume too much about the shape of your utility curve except that it is continuous and monotonic. multiplying everything by a billion does change things, but it doesn't say anything about the rationality of the people who choose 1 dollar now over 10 in the future. we're also not comparing 100 billion dollars to the love a woman. we're comparing 1 dollar now to 10 dollars in a year. my argument is that if you have any kind of sane (rational) discounting system, comparing 1 dollar now to 10 in the future is at worst like comparing 1 dollar now to 7.6 dollars now, with the only uncertainty being your changing utility preferences for dollars. if you honestly believe that the probability that your utility preference for marginal dollars will change by more 7.6 times in one year is greater than 0.5, then choosing 1 dollar may not be irrational. but for most people, that is highly unlikely. thus, your discounting system and thus preferences may be irrational.