rational rich riders

From Matt Yglesias:

Ryan Avent excerpts a bit from an interesting paper by Edward Glaeser, Matthew Kahn, and Jordan Rappaport. Let W_Rich be a rich person's opportunity cost of time, F be the fixed time cost of public transportation, and C be the fixed time cost of driving you get:

Alternatively, if W_RichF < C then some rich people will take public transportation. In this case, a four ring city can be one outcome. In the inner ring, the rich take public transportation. In the next ring, the poor take public transportation. In the third ring, the rich drive and there may be a fourth ring where the poor drive.

What I like about this model is that it's easy to speculate about how changes to one variable can feed back into the others--and we can see who the changes would benefit. In the posited four-ring city, a fare decrease would benefit the current ridership, of course, but it won't convince the rich drivers of the third ring to ride, because the significant cost is time, not cash. Faster trains and buses would be more convincing to this population. An increase in C (in the form of tolls or parking fees) should effectively target the rich drivers of ring three, but might unfairly burden the poor long-distance commuters of ring four. Of course, as ridership increases, the time-cost of riding increases and the time-cost of driving decreases. Lowered highway speed limits could restore the balance.