I often amuse myself by considering odd and interesting questions, and thinking to a reasonable estimate. This is an excellent way to pass the time while say, delayed by the MTA.
One morning in this past fall, the subway train I was on was opening and shutting it doors in a futile attempt to mimic a politician flip-flopping. Of course, this was due to various persons holding the doors open for stragglers.
Irritating as this is for all commuters (unless that commuter is oneself, of course) I found myself considering what cost - and benefit - is entailed by this action:
First, how many people are on this entire train? Hmmmm. The car I am in has about 25 people. We are split about 50-50 between college students and people who are (presumably) traveling to a workplace or to an errand-place. There are a few children, who I will discount for the purposes of this calculation.
There are 10 cars on this particular train (NYC MTA lines vary between 8 and 11 cars (according to Wikipedia)). Therefore, assume a total of say 120 students, 120 [working] adults, and 30 children. (For the purpose of this thought, a student is one (presumably) in college, an adult is one who is at least that old but not in a college, and a child is anyone else (there were no elderly or retired people in my car, so I assume that at this time of day on this line there is a negligible number)).
Now, I will estimate the smallest value of time (in dollars per second) of all students and adults on the train. [Value of time with respect to work is far easier to define and calculate. Simply, it is the amount of money that one could earn at one's regular job in that amount of time (in theory).]
Since I am looking for the least amount, I will assume the minimum wage. At the time of this occurrence, it is $7.25 per hour (smartphones are awesome!). It is scheduled to increase (in NYC) to $9 per hour in stages, completing on the last day of 2015. For the adults on the train, this comes to (I will write the computation as it was done initially):
($7.25 per adult per hour) * (120 adults) = $(72.5 * 12) per hour = $(725 + 145) per hour = $870 per hour.
The students are more difficult. Some are heading to CCNY, and some to Columbia. The split is about 75-25 (rough guess, and there are likely some who are heading to neither (the split is based on how many left at those respective stops)) in my car. Extending this, there are 90 CCNY students and 30 Columbia students.
Columbia estimates tuition at $48,846 per academic year (two semesters), excluding travel costs, food, etc. and $64,144 excluding only transportation. Assuming that time traveling has no college-value, and that everyone is spending 15 hours per week on campus utilizing the academic expenditure, and that one semester is 15 weeks:
$48,846 per academic year = $24,423 per semester = $1628.20 per week ≈ $108.55 per hour.
30 Columbia Students * $108.55 per hour per student = (3 * 1085.50) = $(3000 + 240 + 15 + 1.5) per hour = $3256.5 per hour
CCNY has a semesterly tuition of about $2300:
$2300 per semester ≈ $153 per week = $10.2 per hour.
90 CCNY Students * $10.2 per hour per student = $9*102 per hour = $918 per hour.
So the total time value per hour of this entire train is:
$(918 + 3256.5 + 870) = $5044.50 per hour
≈ $84.08 per minute
≈ $1.40 per second
The average delay I measured on this train ride from someone holding the door was about 10 seconds. This is counted from the time at which the door stops closing and begins to open again through the time at which it fully closes. The amount of time per delay, as well as the probability of a delay occurring, presumably varies greatly with respect to time of day, and location.
The average time cost to of all of the passengers per holding event is therefore $14 (for this exact train demographic, of course). This implies that in order to have some sort of moral or financial equilibrium between the one(s) who the door is being held for and all the current passengers, the time cost in waiting for the next train for the former party would have to be equal to this $14. As the average time between 1 trains is about 5 minutes or so, the hourly wage for this individual would be:
$14 per 5 minutes * 60 minutes per hour = $(14 * 12) per hour = $168 per hour (about 23 times the then-current minimum wage). That hourly wage yields:
$168 per hour * 8 hours per day = $1344 per day
* 5 days per week = $6720 per week
* 46 weeks per year = $309,120 (assuming 8 weeks of vacation per year)
Generally one living in NYC (at least in Manhattan) seems to be considered "Doing OK" at $200,000 (gross) per year. One making half that again might prefer not to utilize the subway at all...
Therefore, taking into consideration all of this, as well as that a train traveling uptown in late morning is hardly crowded, I conclude that with the exception of quite empty trains (i.e. end of line, very late or early, etc.) the time cost to everyone else far outweighs any individual's gain. However, bear in mind that there are many top-of-the-head scenarios where this calculation will not apply, such as where social costs and gains are involved (being late to an anniversary dinner can be hazardous ;)) or relatively rare financial events - such as a job interview.
...and I missed my stop.
Well, that's why I math.
-Aryeh
Edit: Thanks to my friend S. Klein for pointing out a computational error in the original version of this post.
