Mr. Henao’s analysis suggests the optimal target, at least in Austin, occurs when drivers average 3.4 trip requests per hour. That translates to having about 30 drivers for every 100 trip requests there. Beyond that point, adding more trips per driver doesn’t save drivers — or the city — much in empty miles traveled with no passenger in the back. And beyond that point, the system would most likely have too many passengers and not enough drivers, and passenger wait times would increase.

These specific numbers would differ in other cities or circumstances (including if you looked at only, say, downtown Austin). But the principle is the same anywhere, Mr. Henao argues: Cities should neither cap these services nor welcome a free-for-all. They should try to optimize the number of drivers to the amount of demand — or nudge companies to do that more effectively, by requiring them to share their utilization rates. Cities could withhold licenses from companies with low utilization, for instance, and reward those with high rates.

In New York, politicians have been reacting to the suspicion that ride-hailing companies have goosed the number of cars on the road to minimize wait times for passengers, at the expense of driver wages and public streets. “The Uber business model,” Mayor Bill de Blasio said, is “flood the market with as many cars and drivers as possible.”

Uber and Lyft counter that they’re motivated to balance all of these interests, and certainly more so than the taxi industry has been. Both companies also support an alternative policy in congestion pricing, a strategy that would manage the supply of all vehicles in crowded parts of Manhattan, rather than targeting the ride-hailing industry.

“Picking a number of vehicles is not the best way to serve residents across entire cities — just look at yellow taxis in NYC who do 92 percent of their trips in Manhattan,” the Uber spokesman Josh Gold said in a statement. “Ultimately, we have a natural incentive to keep drivers busy; otherwise they won’t choose to continue driving with us.”