The Taxi and the Bus: Pricing Exclusive and Shared Transportation in ξ

How much does a ride in a taxi cost with fiat money versus the bus?  We already intuitively know that they are priced differently in fiat money already: taxis are more expensive.  Without considering the price of fuel, another factor in pricing that will need to be accounted for, let’s compare the values between walking, taking the taxi and taking the bus.

Walking — Let’s use the example of a “six mile trip” for a passenger in a town that averages about 35 mph travel speeds on local roads. Average walking speed for adults is about three miles per hour.  So, a six-mile walk is, on average, about 2 hours.  Now we have a baseline “price” of doing it yourself in actual time–for you to walk six miles takes you about 2 hours.

Taxi The taxi driver is an exclusive resource: the driver can only take passengers to one destination at a time.  Also, the taxi driver is a skilled resource: you’re not going to be very happy with a taxi driver who is totally dependent on a GPS to find the way.  On your six-mile trip, the taxi driver takes you six-miles distance in about 10.2 minutes (1.7 minutes/mile). The “value” of the trip to you versus walking is two hours – 10.2 minutes = 1.83 hours.  The taxi fare should be close to ξ1.83 and will be slightly more expensive with the cost of fuel.

Bus Taking the taxi for ξ1.83 is a lot of value-time, what if you need a more affordable method of transportation?  Now, we’re thinking about a shared resource: the bus.  The bus driver follows a fixed route and picks up and drops passengers at pre-arranged stops–this trip takes longer, so you save less time.  Maybe the six-mile trip now takes you 15 minutes instead of 10.2 minutes.  The savings is now 1.75 hours of time for the trip.  Now instead of one passenger, there are many passengers. Lets assume the average passenger capacity of the bus to be about 20 people. Simply dividing the expected “value” provided by the bus by the number of people utilizing it gives us ξ1.75 ⁄ 20 = ξ0.0875 per passenger over six-miles–or about 5 minutes of “value time.”  The trip saves you 1.83 actual hours (if you had merely walked six-miles), costs you about ξ0.0875, much less than the cost of “actual time” elapsed because you’re sharing with other passengers. In fact, given that it does cost you less than actual time elapsed, perhaps the bus line has set their prices too low–that’s a bargain!

The same kind of logic should be easily applied to trains and airplanes or even steamboat or rickshaw.  If you are getting a “benefit” from transportation, you can likely measure it in terms of time.  Next time around, I’ll see if we can find a way to divide this into freight, taking into account large amounts of mass and the energy required to move it.

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