Saturday, January 14, 2006

Transportation Options

I was standing in the pouring rain in the Mission on Thursday, contemplating the value of my time. The walk home from that bart station takes roughly 30 minutes, which is normally how I get home. It's mostly uphill, so it's good exercise. But it's a lot less fun in the rain, which got me thinking about alternate forms of transportation. I can take the bart to Glen Park, then get on a bus, and walk 1-2 blocks to get home; this route has almost no rain exposure, but takes significantly longer than 30 minutes and is not free ($1.40 bart fare as of this week, $1.25 bus fare, 5 minutes wait/ride time for the bart, expected value of 25 minutes wait/ride for the bus, 5 minutes walk from the bus stop). Finally, there's the cab: expected value $9 fare/tip, 10 minutes ride plus 5 minutes finding the cab. (The final option, asking Andrew to come pick me up in a car, works only when the car is not in the shop and when he is physically capable of driving, but it's the cheapest: expected value 15 minutes, negligible cost.)

So, the question is, how many dollars must my time be worth before the cab option is the most optimal? Assume that there is some factor X which converts minutes to dollars. The public transit and cab options are "equal" in total cost to me when this equation is satisfied:

1.40 + 1.25 + (40 * X) = 9.00 + (15 * X)

which happens when X is 0.25 dollars-per-minute, or $15.24 per hour.

Similarly, comparing the cab vs. walking:

30 * X = 9.00 + (15 * X)

suggests that the cab is a better option if my time is worth at least $36 per hour.

The upshot is that I think I'll never take the bus again. :) The exercise (in non-rainy weather) has tangible benefits to me, but I'm pretty sure my time is worth more than $15/hour. Or would be, if I weren't salaried - this is sort of academic at this point.

Having figured this out while wandering down Valencia, I finally found a cab. He called in the pickup as Army Street - I wonder how long he's been driving a cab, if he still thinks of it as Army? - and in fact made better time than ten minutes. Sweet.

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