Here’s an attempt to formalize the “is partying hard worth so much” aspect of your example:
It’s common (with some empirical support) to approximate utility as proportional to log(consumption). Suppose Alice has $5M of savings and expected-future-income that she intends to consume at a rate of $100k/year over the next 50 years, and that her zero utility point is at $100/year of consumption (since it’s hard to survive at all on less than that). Then she’s getting log(100000/100) = 3 units of utility per year, or 150 over the 50 years.
Now she finds out that there’s a 50% chance that the world will be destroyed in 5 years. If she maintains her old spending patterns her expected utility is .5*log(1000)*50 + .5*log(1000)*5 = 82.5. Alternately, if interest rates were 0%, she might instead change her plan to spend $550k/year over the next 5 years and then $50k/year subsequently (if she survives). Then her expected utility is log(5500)*5+.5*log(500)*45 = 79.4, which is worse. In fact her expected utility is maximized by spending $182k over the next five years and $91k after that, yielding an expected utility of about 82.9, only a tiny increase in EV. If she has to pay extra interest to time-shift consumption (either via borrowing or forgoing investment returns) she probably just won’t bother. So it seems like you need very high confidence of very short timelines before it’s worth giving up the benefits of consumption-smoothing.
Here’s an attempt to formalize the “is partying hard worth so much” aspect of your example:
It’s common (with some empirical support) to approximate utility as proportional to log(consumption). Suppose Alice has $5M of savings and expected-future-income that she intends to consume at a rate of $100k/year over the next 50 years, and that her zero utility point is at $100/year of consumption (since it’s hard to survive at all on less than that). Then she’s getting log(100000/100) = 3 units of utility per year, or 150 over the 50 years.
Now she finds out that there’s a 50% chance that the world will be destroyed in 5 years. If she maintains her old spending patterns her expected utility is .5*log(1000)*50 + .5*log(1000)*5 = 82.5. Alternately, if interest rates were 0%, she might instead change her plan to spend $550k/year over the next 5 years and then $50k/year subsequently (if she survives). Then her expected utility is log(5500)*5+.5*log(500)*45 = 79.4, which is worse. In fact her expected utility is maximized by spending $182k over the next five years and $91k after that, yielding an expected utility of about 82.9, only a tiny increase in EV. If she has to pay extra interest to time-shift consumption (either via borrowing or forgoing investment returns) she probably just won’t bother. So it seems like you need very high confidence of very short timelines before it’s worth giving up the benefits of consumption-smoothing.