Don’t get me wrong by the title: as a society we should definitely support our elderly. But what I want to consider here is: given a fixed amount of money to spend on a given citizen, when is the optimal time to spend it?
If you retired today, as a 65 year old man, the expected benefits you would receive from social security and medicare combined would be about $500,000. (This hypothetical average man would have also paid in $400,000 in combined social security and medicare taxes). What if we could move around this spending? That is, given this $500,000, if we were allowed to spend it at anytime in our lives, where would we put it? We could make college free (25k/year), and move back the social security age by 3 years. We could go further and give everyone a trust to help pay for schooling and to fall back on in their 20’s. Or we could leave things as is. How do we decide when the best time to spend it is?
To make this more concrete, let’s try to define the utility of a particular year of our life: how important is it that year to us? Our childhood is obviously very important for learning good habits and skills: there is a prominent income gain just for completing high school. If you make it through a bachelors degree, you’re looking at an extra $20k a year for the rest of your life.
(This graph brings up a side-point: paying for someone to go to college more than pays for itself. That is, if we put someone through college, at a 25% tax rate, we’d reap an extra $5000 a year in taxes vs a high school graduate. If we imagine a college costs $100k, and our average citizen has a 40-year career (25 to 65), we’d make $100k extra in taxes. Win-win! We can’t tell the effect of more graduates on the balance directly, but looking at a country like Canada with a higher percentage of college graduates, the difference in incomes seems to hold. )
Similarly, a few good productive years early in your career have powerful knock-on effects: both in terms of increased salary and the connections needed to find new work easily. As time goes on, this becomes less relevant. Getting a promotion 3 months before you retire is far less beneficlal than if you got it 30 years earlier.
With this in mind, we can define a measure of the utility of a year as a constant (the joy we get for living in the moment!) + some fraction of the utility of any future years:
JOY = 100
CARRY_OVER = 0.05
total = 0
for i in range(80, 0, -1):
utility = JOY + total * CARRY_OVER
total += utility
If we allow for even a 5% carryover between years, the effect is dramatic:
I’m arbitrarily choosing 80 years old here as an average lifespan.
The point of the graph should be apparent: we should be investing hugely more money and effort towards improving the outcome of our youths than we spend on making sure our old-age is comfortable. (Ideally we would do both, but here we’re limiting ourselves to existing spending). Even though we’re working with a very simplified model here, it’s capturing an obvious fact: something I learn at age 2 or 20 can help me for the remainder of my life. If I learn the same thing (say how to manage my savings) at age 80, there’s a lot less time for me to benefit from it.
A parallel of this exists in the business world. If my company makes widgets and is doing well, do I take out a loan and buy a manufacturing facility now (thereby making more money over the next 10 years), or wait until I can buy the facility outright? Assuming I can sell enough widgets (as a person, find a job), I obviously want to take out the loan: you’ll make more than enough money to offset the interest.
A naive interpretation of this model might imply that we should simply abandon our old and dump all of our money on our 10-year olds. A more sophisticated model could apportion money based on multiple factors, not just the utility value of a given year. For instance, it could incorporate the psychological benefits of knowing that you’ll be taken care of when you get older. The net effect would be to dampen the exponential here and push more benefits towards the right.
But this more complex model would still lean heavily to the left, with some strong implications. We should shift a large fraction of late life spending to earlier in life: in effect taking a loan from ourselves. By doing this, we can improve services for early childhood (good preschools and after-school care for all!), and pay for bachelors or masters degrees for anyone who is interested. The overall effect should be to increase our happiness and wealth across our entire life. And thanks to the increased savings, the overall effect on late-life should be positive. Our safety net in our later years would be lessened, but our increased earnings earlier in life would more than exceed the difference.