The marginal cost of procrastination at age 60

After this post, a fair and dispassionate reader might be forgiven for thinking that I spend WAY too much time looking at this stuff. ...and I would share that opinion. The proximal reason for the post was me thinking about the nexus between things like personal relationship games and the time left in one's life to play them (to which the other relationship game players would perhaps say "If you'd put as much energy into the real game as you do the fake-blog-math you wouldn't have a nexus-question in the first place").  But this way of thinking could be just as easily applied to other things like retirement-start, un-pursued hobbies, un-executed bucket lists, whatever.


Let's say that mean life expectancy can be extracted from a mortality table like this (keeping in mind I am always insecure about notation; I am an amateur):

where E[L(x)] is some kind of mean cohort longevity expectation at age x when d is set to 0, w is something like max age = 121 but could also kinda be infinity, x is one's age at examination of the idea of some longevity proposition, and tPx is a conditional survival probability at time t for someone age x.

Then further, let's say that the cost of procrastination can be defined in unit terms as 1 year of remaining L at any x.  I'll leave the continuous stuff to the wonks and eggheads.    That means that the cost of procrastination at age x might be defined as:

c(x) = 1/E[L(x)]

When we play this game using a mortality table like the SOA IAM table, it would look like this:

Which would make c(x) = 3.9% of remaining lifetime at 60. That's bad enough (and even worse if using a Soc Security life table and worse still if we used some subjective threshold for future cognitive/mobility declines), especially if I compared it to me at age 25, but the calculus is implacable because over the entire interval of interest, no matter how you slice it:

c' > 0, and, more importantly...

c'' > 0

Conclusion? 

The cost of procrastination is damn expensive and getting moreso by the day.

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post script

Here is a second curve in red for when a fixed age 85 is used as a subjective threshold in evaluating the cost of procrastination. But 85 is the new 82, right?