The Wheels on the Bus
Temperament matters a lot. Case in point: a few weeks ago, while riding home from work, the traffic suddenly slowed down and from behind us I hear a loud "thwunk." My bus had just been rear ended. Everyone was fine, except for the tiny car whose front just crumpled. Even its driver seemed ok (or at least aware enough to discretely slide her phone away). It was a funny story (made much better in person because I could properly pronounce "thwunk" for you), but as I was sitting there on the bus for an hour I heard two distinct conversations. One type started, "Dude, this is crazy. Has this ever happened to you?", while the other type stared, "Dude, I'm never riding the bus again. It's not worth it." I know, only in Portland would everybody on the bus start their conversation with "Dude", but what it got me thinking about was how do we know if the bus is "worth it".When my wife and I moved to our current apartment, we didn't think about the fact that she would be driving to work and I would be taking the bus. It was just intuitive. That said, her work is closer. She's also more environmentally conscious than I am and the ticket price for her bus route is less than for my route. All of that seems like it would switch our roles. So that is today's goal. Lets add up real costs to see why it makes sense for me to ride the bus and not her.
A Non-Ideal Gas Law
On the surface, it seems like this should be simple. Does the gas to get there cost more than the cost of the ticket? For her a round trip looks like this:
And for me:
So as a first pass it looks like it wouldn't make sense for either of us. Of course, this is the simple case. Since we know gas isn't the only expense that goes into the car, lets overly complicate it.
Four Car-dinal Virtues
The way I see it there are fixed costs of owning a car, and there are per-mile costs. Fixed costs include the actual purchase, the license and registration, as well as the insurance. These don't scale with how much you drive. (Within reason, of course. The difference between 10k miles and 12k miles per year is zero. There is still a difference between 10k miles and 0 miles or 30k miles.) Instead, these costs scale with how pricey a car you have and how good of a driver you are. On average these costs end up being ~$16 a day (almost $6000 a year!). Maybe I'll tackle this another day, but for the current post lets say that we are keeping the car, just deciding if it makes sense to use it for a certain trip.
The flip side of this is the per-mile costs. By my count you could group these into four categories. Lets find the {inputs} we will need for each cost. The first one, gas, we already mentioned. It will only depend on {car's MPG}, {cost of gas}, and {miles traveled}. The second cost is what to do with your car once you reach your destination, as there is often an associated parking fee. This is pretty straightforward, so we'll just spread the {parking fee} over the whole round-trip. The third cost is wear and tear on the car. As a back of the envelope calculation I'm guessing for every 30k miles you need about $500 of tune up, $500 of brake pads and tires, and ten $50 oil changes. This works out to $0.05 a mile, which is a figure I've seen repeated on several auto maintenance sites (backing out gas prices). So again we just need {miles traveled}. Finally, the fourth cost I'll throw in is carbon offset credits. The market has determined a price of $0.011 per mile for offsetting the carbon emissions from your car. This isn't quite fair as they must be assuming you have an average car (23 mpg). Instead, you can convert that price (just multiplying it by 23 mpg) to get $0.25 per gallon of gas you consume. Again we need {miles} and {mpg}. All of these things could be split between multiple {passengers} if you carpool.
We can do the same cost analysis for the bus. They only have two costs, and the first one is easy: the {ticket cost}. Once again, we'll go for round trip. They also have a carbon offset, and this one is a bit more tricky. Buses get lousy gas milage (about 5.5 mpg once you convert from diesel to regular), but spread it out over many {passengers}. My commuter bus routinely fills up its 45 seats, but some routes are nearly empty. By using the {bus mpg} and {miles traveled} then dividing by {people riding} we get gallons of gas used per passenger, which can get us to our carbon offset credit price. What happens when we add these things up?
For My Wife's Commute:
And Mine:
So now the bus seems to make sense for both of us. Still not the intuitive result, though.
As an Aside: Taking a Test-Drive Around Portlandia
Before I go any further, one cool thing you can do with this model is look at when it makes sense to take the bus on smaller trips. Other than parking, the price to make a trip by car scales linearly with the number of miles you go. The Portland bus system is a fixed price of $2.50 for 2 hours or $5 all day. So if you know your cost of parking, you could choose your best method of transport based on the following cost curves (assuming one person in the car and average 23 mpg).
This chart also explores the idea of a free-ride zone and tiered pricing, in that it doesn't really make sense to pay for a bus ride less than 20 minutes unless there is a parking fee, while an hour and a half ride might be worth $10 to someone. Downtown parking is in the $5 range, so Portland's recent move to a single price structure has little impact on their overall downtown bus usage. Oh, and as an aside to this aside, look at how awesome the mpg can be when you get a full bus... it's in the 300 mpg range!
Time is Money
Getting back to my earlier question, why is it that my wife's commute makes no sense by bus. The answer really comes down to the fact that there is no direct route. While it certainly is annoying to spend 20 minutes and $6.30 in driving expenses to get to work, this is dwarfed by the 90 minutes it would take by bus. We need a way to put a value on this time.One way we can do this is to think about our "real" wage. This is the value that you put on your time. By implicit agreement, if you work for money you have agreed that a certain amount of money is worth at least a specific amount of your time (if not more). If you make $40k a year, your per hour wage is just under $20 an hour for a 40 h workweek. But if you commute to work, think about work off the clock, or spend any money on clothes/computers/vuvuzelas for work, you don't really make $20/h. Maybe it is more like $15/h. This is your value of time. Do you really love your job? Would you do it for less money? Maybe your time value is more like $5/h.
If your time value is $10/h and you spend time not being productive, it costs you $10/h. This may be fine if you are spending time playing with your kids, reading a book, or watching an episode of dancing with the stars. You agree that the lost time is worth $10, otherwise you would work and earn yourself $10. This is obviously simplified, and because your work/life balance is not a free market you could end up mowing the lawn for an hour (for no pay) when you would rather read a book. Ideally you'd pay someone less than $10 to mow the lawn for you.
So, why is this important again? Well, imagine your time value is still $10/h. If your choices are to drive 30 min (and lose $5 of productive time) or ride the bus for 90 min (and lose $15 of productive time), that money needs to go into the car/bus equation. This can be mediated somewhat by being productive on the bus (or in the car). If you do some work on the bus, you might be able to be at work for less time. If you read a book on the bus, that is "productive" time that you don't do at home and still doesn't count against you. The way you "lose" the money is to sit around doing nothing or doing something you don't want to do. You wouldn't pay $10 to do that. Lets apply this to our model. I haven't shown you how I defined everything, so lets do that now (typing the items [in brackets]).
Oh, and you can follow my work here.
You Details
Time value (per hour) = C5
Car Details
Car route (miles) = C8
Car trip time (min) = C9
Productivity in car (min) = C10
Price of gas ($) = C11 (Currently $3.77 near me)
Mpg = C12 (Average for cars is 23, but we'll allow any value)
Gas used = C13 [=C8/C12]
Parking = C14
Total people = C15 (1, unless you are carpooling)
Cost of gas per person = C16 [=C13*C12/C15]
Cost of parking per person = C17 [=C14/C15]
Cost of wear & tear = C18 [=0.05*C8/C15]
Cost of lost productivity = C19 [=(C9-C10)/(C5/60)]
Cost of carbon offset = C20 [=0.25*C13/C15]
Cost of driving = C21 [=SUM(C16:C20)]
Bus Details
Bus route (miles) = F11
Bus trip time (min) = F12
Productivity on bus (min) = F13
Mpg (equivalence of diesel) = F14 = 5.5
Gas used = F15 [=F11/F14]
Total people = F16 (10 = low use, 20 = moderate use, 45 = seat capacity, 60 can fit with standing)
Effective mpg = F17 [=F11/(F15/F16)]
Cost of (round-trip) ticket = F18
Cost of lost productivity = F19 [=(F12-F13)/(C5/60)]
Cost of carbon offset = F20 [=0.25*F15/F16]
Cost of bus = F21 [=SUM(F18-F20)]
And lets throw one more in:
Walking details
Time = F5
Productivity while walking = F6
Cost of walking = Cost of lost productivity = F8 = [(F5-F6)/(C5/60)]
Running the Model... Or Driving it... Or Taking It On The Bus, I Guess
Now, when you plug in my wife's commute, it seems much more obvious that driving is the economically favored option.
Which is different than for my commute:
Obviously productivity can change a lot with minor input changes. Does the bus evade traffic? Do I enjoy driving enough to count it as productive time worth $15/h? (In short, no.) Some of this productivity can be conceptualized if you look at walking to work (noted top right but not added to the graph). It would take me about 7 hours to walk the round-trip. With a bike I could do it in 3. I like walking and biking, but only for perhaps the first hour, so after that it is non-productive time. Am I willing to pay the extra money to get some of that time back? If you are using this model as a tool for your own circumstances, (and I recommend you try it), keep in mind that some things are flexible (like your love of walking... in the Portland rain) and some things are fixed (like a monthly or yearly bus pass that saves you money).
Interestingly, you can also go backwards in the analysis. If you know that you like your bus commute at least as much as the drive, you can back-calculate from your lost productivity calculation how much you value your time. Maybe you realize that you value time at less than $5/h. It might make you think twice about paying someone $10 to mow your lawn for an hour.
Taking The Long View (past Longview)
One final note. My wife and I love going to Seattle for the weekend to visit friends and family. In the past I often thought of it as a low cost outing. Yeah, the price of gas is a pain, but the total cost isn't much if you have low cost fun like board-games and "hanging out." When I first started building the model, though, I started having second thoughts. ("It really costs that much just for my commute?" etc.) Here is what the trip looks like when compared with a greyhound bus.
It's actually not that bad. Split between the two of us, the cost of the car is less than $33 round trip (compared to ~$41 for the bus) before lost productivity. And with two of us in the car, I'd say I get at least two hours of conversation, reading, and other fun activities that I'd count as productive time. That doesn't hold if it were just one of us going up though.
What can I say... at least I didn't have to walk!
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