The cabdrivers have their own litany. They drive long hours for little money: the average cabdriver earns $27,060 a year, before expenses. They are at high risk for traffic accidents and, because they carry a lot of cash, for robbery. When drivers turn down fares to neighborhoods like mine, it’s not because they don’t want to miss a second of The Diane Rehm Show while they take my cash and make change. Those trips, where they probably won’t get a return fare, and must instead burn time and gas while the meter’s off, can mean the difference between profit and loss for the day; cabbies can’t afford too many of them.

What I’m describing is a classic market failure: people who are willing to do business together can’t make it happen. If taxis and passengers only knew how to find each other, and could strike deals that would appeal to both, everyone would be better off. Why can’t we fix this?

As it turns out, a small but rapidly growing business is trying. One Friday night in December, my husband and I drove over to Adams Morgan for some karaoke with friends. “You drove?” a friend who lives near us asked incredulously. “I just used Uber.”

Travis Kalanick, who co-founded Uber, told me that he and his partner “wanted to be able to push a button and get a ride.” That’s a fair enough description of the service that they launched in San Francisco in 2010, and that is now available in nine major cities—including New York, Boston, and Paris—with plans for expansion to at least 25 more. Set up an account, plug in your credit-card number, and in less than five minutes Uber’s smartphone app will be showing you a map of your location, the nearest available cars, and how soon one can get to you. Click the screen a couple of times, and a sleek black sedan is on its way.

Unlike traditional limo services, which rent you a car and driver by the hour, and usually on no less than an hour’s notice, Uber charges time-and-mileage fares, just like taxis, and the cars it finds for you typically show up within 15 minutes of your request. That convenience and style is costly; in D.C., the price is usually at least 50 percent more than that of an equivalent cab ride. Uber’s critics frequently imply—perhaps with a grain of truth—that it’s a service for the affluent that takes fares from hardworking taxi drivers who are struggling to make rent. “Uber’s real defenders,” a D.C. blogger has written acidly, “comprise a mix of socialites, transportation fanatics, and libertarians.”

And yet, this analysis misses something important. Yes, Uber has created a higher-priced, higher-class service for people who can afford it—but it has also broadened the market to people who formerly couldn’t get cabs at all. For my husband and me, the appeal of Uber is simple: it’s there. A car that will actually show up to take me to the airport, or to my home, is worth considerably more than a cheaper, but unreliable, alternative.