A Short Sidenote On Transit Fares

So, for those of you who don't live in Vancouver transit fares are increasing. So I thought I would do a comparison, to show what we pay for transit versus what it costs to drive.

The fare hikes will result in the following prices:
1 Zone: $2.75
2 Zone: $4.00
3 Zone: $5.50

Now to be fair, you only have to pay the 1 zone on weekends and after 6, so thats not too bad depending on how far you're going. However, let's imagine we are deciding between paying this fare and driving to work. In the US (because its difficult to find these types of statistics for Canada, but we can assume they're reasonably similar) the average passenger car gets 30.1 miles to the gallon (http://www.bts.gov/publications/national_transportation_statistics/html/table_04_23.html). This is 12.7968 km / l, or for the sake of simplicity, 13 km / l. A liter of gas, as of this morning, was $1.27, which we will round to $1.30 to make the calculations a little nicer to start with.

The distance your fare would get you with an average efficiency car would then be:
(Money / Cost per Liter) * (Distance Travelled per Liter) = Distance Travelled
1 Zone: (2.75 / 1.30) * 13 = 27.5 km
2 Zone: (4.00 / 1.30) * 13 = 40 km
3 Zone: (5.50 / 1.30) * 13 = 55 km

So how far do these fares actually get you via translink? Well Translink Fare Zone Map indicates where the fare zones are, though not the distances. Google maps should help us here. We know that:
-Waterfront station is the far edge of the yellow zone
-Joyce station borders the red and yellow zones
-Lougheed mall is the edge of the yellow and green zones
-Maple Ridge station is the on the far side of the green zone

From Waterfront to Joyce Station: 9.5km
From Joyce Station to Lougheed Station: 13km
From Lougheed Station to Maple Ridge Station: 25.3km

Wait, what?

So for starters, all zones are certainly not made equal. 2.75 can get you 25 km (or more, I believe services extends past Maple Ridge but don't quote me on that) or a maximum of 10 km downtown. Now downtown service is probably more reliable and more frequent but I'm not sure how justifiable that is. Furthermore, we can see that driving from lougheed station to maple ridge station, a trip which has to be made by bus, is slightly cheaper then actually taking the bus. Two zones, giving you a maximum possible distance of 23 km, can get you almost twice that, 40 km by car.

So far, what we've seen is that it is much better to drive. So then why doesn't everyone do it? The numbers look much more efficient. But there is another catch. Speed. To perform another very rough estimate, lets look at the 143 bus (Bus Timetable). It takes the bus an average of 30 minutes to get from Coquitlam Station to SFU. I can drive this in 20. So we save ten minutes by not taking the bus. Plus, lets assume that on average you arrive 15 minutes before the bus arrives (exactly half the time between buses, so not a bad average guess, especially since when the bus is more frequent it takes longer due to traffic). So you lose 25 minutes by not driving.

Now assume you make minimum wage, $10.00 an hour. So that 25 minutes is worth $4.16 to you. This works out to an additional cost to taking the bus. If we assume you take the bus twice a day (once there, once back) then the real cost of the fares for each zone are:
Zone Cost + ((25/60)*wage)
1 Zone: 2.75 + ((0.416)*10.00) = 6.91
2 Zone: 8.16
3 Zone: 9.66

Now the distances are:
1 Zone: (6.91 / 1.30) * 13 = 69 km
2 Zone: 81 km
3 Zone: 96 km

Unsurprisingly, this makes it much better to drive. By saving ourselves time by driving, we are doing much better. Finally, we must ask ourselves what happens when a bus doesn't come. Say, approximately 2% of the time a bus doesn't show up (this estimate is based on the bus failing to show up ~1.5 days a month). Then in 2% of cases, our wait cost is increased by 30 minutes.

(Zone Cost + ((25/60)*wage)) + ((0.5 * wage * 0.02)) / 1.30) * 13
1 Zone: 70 km
2 Zone: 82 km
3 Zone: 97 km

So not much of a gain, but a little bit of one. But surely it isn't all peaches and roses for driving. Skytrains are much faster then cars, and are a considerably easier way to travel. In addition, we have to pay some cost to park. We can modify are equation to accommodate these two things, and end up with this final equation:

(Zone Cost + ((Time Cost in Minutes / 60) * wage) + (Time Cost if Missed * wage * 0.02) - Cost to Park) / Cost of Gas) * Distance car travels per liter = Distance travelled

It's unfair to include the parking cost without noting a couple things. Parking isn't a one way payment, so we change our equation to reflect going both there and back. We should also note that unless we live on a bus route, we have to drive to a transit hub and park, which incurs a cost as well.

((Zone Cost + ((Time Cost in Minutes / 60) * wage) + (Time Cost if Missed * wage * 0.02)) * 2) - (Cost to Park - Cost to Park Anyways)) / Cost of Gas) * Distance car travels per liter = distance travelled

What's interesting about this is that we now compute what the zone costs should actually be, by manipulating the equation

My car gets 375 km from 47 liters of gas, to 8 km per liter
SFU is 14 km away from my house
It costs me an additional 1.50 to park at SFU over parking at the transit hub
I make 12.90 an hour
The cost of gas this morning was 1.27

((zone cost + 5.375 + 0.1075 - 1.50) / 1.27) * 8 = 14
((zoneCost + 3.9825) / 1.27) = 1.75
zoneCost + 3.9825 = 1.75 * 1.27
zoneCost = -1.76

This means that translink should pay me $1.76 to take transit. Or more accurately, I would save $1.76 by driving based on my wage. This means that translink, which I will pay 4 dollars to use this system, is costing me $5.76 to use its transit system. Yikes!

Now the reason we get a result where transit pays me is because we factor in the lost time at my wage of $12.90 and hour. So lets ignore that part of the equation, since it may be a little unrealistic.

 ((Zone Cost - (Cost to Park - Cost to Park Anyways)) / Cost of Gas) * Distance car travels per liter = distance travelled

Now the equation doesn't reflect the time we lose by being on a bus. But this may be more correct. A sky train may be faster, or at least as fast as, a car. We'll give it the benefit of the doubt, ignore lost time and discover that:

((Zone cost - 1.50) / 1.27) * 8 = 14
zoneCost - 1.50 = 2.225
zoneCost = 3.75

The 2 zone bus ticket, ignoring time loss, should only cost $3.75. This means that translink is making off with 25c, which isn't such a huge deal I suppose, except that we know that driving is going to be at least as fast as taking transit.

Now what's disturbing about this equation is that my car is well below average with its 8 km per liter. Using the average 13 we find that the ticket should only cost about $2.87. So if you have a half decent car (or even a better car), you're getting robbed to the tune of $1.20 every day you take transit. Simplifying our equation a little bit:

((Distance to Travel / (km per liter of vehicle)) * Cost of Gas) + cost to park = zone cost

Is our final result. This equation doesn't show time lost due to transit, but if we assume there is no difference in time, then we can conclude that given a car with an average amount of fuel consumption, you would have to pay $2.70 more per day to park then at a transit hub then at work in order for it to ever be worth taking transit. We can conclude that, if there is not cost to park, it is never more efficient to take transit at these prices with a car with above average efficiency. Without a cost to park you will always save money if we assume that the two systems have equal speeds. The only way transit is viable is if it faster then driving, which in my experience is almost never the case.

So to conclude, if you wonder why people don't take transit, its because it doesn't make economic sense. And since it doesn't make sense, people don't take it, and less people taking it = less people paying the wages of the bus drivers = increased fares to pay wages = even less people taking it. Lower fares would make it economical. We end up with a situation of Sgt. Vimes Rule of Economics. That is, if you own a car you save money by using it, the lump sum you pay once for the car saves you money in the long run over those who can't afford the car. Over the long run, the people taking transit will lose out, losing more money then the car would have cost in the first place. So yeah, as much as it pains me to say this because I like to try and be Eco-concious, if you want to save money, don't take the bus to work.

I would like to note that a lot of this ignores the 2.75 evening and weekend fares, which are good deals given you travel more then one zone (the distance from Coquitlam to waterfront station, for example, costs more then 2.75 in fare). This focuses only on taking the bus during regular operating hours and to work or school.

***

Edit:

The reason the cost of buying, maintaining, and insuring the car are not included in the above cost analysis is because I personally would have to pay these costs anyways. Unfortunately, in order for me to participate in recreational sports, meet my grandparents for lunch, go to friends houses, and so forth I need a vehicle since public transit is either too difficult to use to get to these locations, does not go to these locations or is simply not fast enough to get me to these locations on time. Especially living in the suburbs, it is very difficult to function without a vehicle. In addition, while there will obviously be more wear on a vehicle which is driven everyday as opposed to one driven only for certain events, it is very difficult to estimate how much more wear this would result in since different vehicles will wear at different rates and rates of wear are largely dependent on the drive.