Finally, one appears. He’s headed north, on his way home after leaving the last of his clients downtown. But my waving hand and the fare it promises is too much to resist. He U-turns. I jump in. “Fitler Square,” I say. He speeds away.
At first blush, the business model for a cabbie is relatively simple: He – and they are almost all he – who spends more of his day with a passenger in tow will be the wealthier cabbie.
But cabbies are not paid linearly; while each 10th of a mile traveled or 38 seconds lingered earns a cabbie 10 cents, a passenger is charged $2.70 off-the-bat. Thus, a cabbie who spends his shift driving just one passenger will make less than another cabbie who solicits 10 clients for 10 one-tenth portions of his shift.
This model makes sense, of course. Cabs were born and now live in urban America, where traffic snarls. If cabbies were not compensated a minimum sum or for time spent lingering, a trip across town would be worth only the distance traveled, a paltry sum.
Nevertheless, the situation presents a quintessential economic optimization problem: How exactly should your cabbie drive?
My route home provides the setting for a perfect experiment. On Spruce and Pine streets, as you may know, the traffic lights are timed such that the driver who averages 20 mph will meet only greens. Stay disciplined and traveling across town becomes crossing the Red Sea.
I’ve driven this stretch before and can tell you that the synchronization is good government nudging: it promotes good public policy – slowing cars – while preserving freedom – go faster than 20 if you want to – and does nothing to diminish the utility of the activity in question: the cost of driving slower is the benefit of avoiding red lights.
But how would a cab navigate these streets? Assume my cabbie turns onto Spruce just as the first light is turning green. My destination is just before the Schuylkill River, about one mile.
One option would be to drive at 20 miles per hour and make all the lights. If he did so he would make 10 cents for each one-tenth of a mile, or $1, plus the $2.70 paid up front for a total fare – excluding taxes and surcharges and the like – of $3.70.
But that’s not the only way he could drive. In fact, the pricing structure encourages him not to. Think of it this way: if my cabbie, instead of driving 20 miles per hour, averaged 30, he would still travel the one mile from Broad Street to the river in the same amount of time and still make the $1.
But now that he is no longer complying with the government’s sensible nudge – driving 20 miles per hour to perfectly make each light – he will be stopped at each of the 10 lights, just about equally spaced at one-tenth of a mile intervals, and linger for at least some period of time greater than zero.
Imagine two cabs: the 30-mile-per-hour Speedster and the 20-mile-per-hour Optimizer. The Speedster, racing ahead, will be forced to wait at each light for the Optimizer to catch up. And, as the nudge has presupposed, once the Optimizer arrives, the light turns green. Doing a little math, the Speedster will have to wait six seconds at each red light, or about one minute across 10 lights.
Finishing the problem, the Speedster, because he raced ahead and lingered at each red light, will be compensated for his inefficiency: 20 additional cents for the 60 seconds lingered. Thus, his earnings will increase from $3.70 to $3.90, or about 5 percent. On a yearly salary of $50,000, the 5 percent margin represents a $2,500 bonus. You could have a few fun nights at the Draught Horse with that kind of inefficiency.
What does this say about taxi cabs? One possibility is nothing: I’ve simply discovered a strange quirk in an otherwise sensible system. But another possibility is something more.
The something more is that incentives and nudges are omnipresent and unavoidable, and amazingly interesting. Some are good, like those encouraging cars to slow. Some are bad, like those encouraging cars to speed. And some, oddly, are both.
Kevin Trainer can be reached at email@example.com